This document discusses identifying independent and dependent variables from scientific and mathematical perspectives. It begins with an example from a middle school classroom where students struggled to identify the independent and dependent variables in equations. It then outlines four rationales for identifying these variables: two from science related to control and causation, and two from mathematics related to conventions and functions. Finally, it reports on an analysis of mathematics textbooks that examined how well problems supported understanding independent and dependent variables.
FINANCIAL T HEORY AND CORPORATE POLICY 4TH EDITIONCHAPTER 10.docxvoversbyobersby
FINANCIAL T HEORY AND CORPORATE POLICY 4TH EDITION
CHAPTER 10
Problem set
10.1 Suppose you know with certainty that the Clark Capital Corporation will pay a dividend of $10 per share on ever January 1 forever. The continuously compounded risk-free rate is 5% (also forever).
a. Graph the price path of Clark Corporation Capital common stock over time.
b. Is this (highly artificial) example a random walk? A matingale? A submartingale? Why?
10.5 The efficient market hypothesis implies that abnormal returns are expected to be zero. Yet in order for markets to be efficient , arbitrageurs must be able to force prices back into equilibrium. If they earn profits in doing so, is this fact inconsistent with market efficiency?
10.6 (a) In a poker a game with six players, you can expect to lose 83% of the time. How can this still be a martingale?
(b) In the options market, call options expire unexercised over 80% of the time. Thus the option holders frequently lose all their investment. Does this imply that the options market is not a fair game? Not a martingale? Not a submartingale?
10.8 From time to time the federal government considers passing into law an excess profits tax on U.S. corporations. Given what you know about efficient markets and the CAPM, how would you define excess profits? What would be the effect of an excess profits tax on the investor ?
Problems Identifying Independent and Dependent Variables
Keith R. Leatham
Brigham Young University
This paper discusses one step from the scientific method—that of identifying independent and dependent variables—
from both scientific and mathematical perspectives. It begins by analyzing an episode from a middle school mathematics
classroom that illustrates the need for students and teachers alike to develop a robust understanding of independent and
dependent variables. It then outlines four rationales (two from science and two from mathematics) for identifying
independent and dependent variables. Finally, it reports the results of a textbook analysis that used these rationales to
examine the extent to which typical mathematics textbook problems support or supplant a sensible view of independent
and dependent variables. The findings indicate that often, mathematics textbook problems misrepresent the sense-
making aspect of identifying independent and dependent variables, possibly setting students up to develop misconcep-
tions about this step from the scientific method.
Problems Identifying Independent and
Dependent Variables
The scientific method has had great influence over
science textbooks over the past century (Blachowicz,
2009). Although there is debate about the degree to which
this influence has been positive (Bauer, 1994; Nola &
Sankey, 2007), most scientists agree that viewing the sci-
entific method as a “recipe for doing science” is unhealthy
and counterproductive. Instead, the scientific community
desires that students, scientists, and the general populace
see the w ...
The importance of problem solving in the K - 12 mathematics curriculum is well documented. One of the most recent documentations is the Principles and Standards for School Mathematics (National Council of Teachers of Mathematics [NCTM] 2000). In this publication, problem solving is listed as one of the five Process Standards. “Problem solving is an integral part of all mathematics learning, and so it should not be an isolated part of the mathematics program” (NCTM, 2000, p. 52). Since problem solving has been accorded such prominence, it is necessary to have an understanding of what a mathematical problem is. After all, mathematical problems existed since the time of the ancient civilizations
Unit I of the syllabus covers propositional logic and counting theory. It introduces concepts such as propositions, logical connectives like conjunction, disjunction, negation, implication and biconditional. It discusses how to represent compound statements using these connectives and their truth tables. The unit also covers topics like predicate logic, methods of proof, mathematical induction and fundamental counting principles like permutations and combinations. It aims to provide the logical foundations for discrete mathematics concepts that will be useful in computer science and information technology.
Solving Exponential Equations: Learning from the Students We Teachinventionjournals
The purpose of this paper is to share with the mathematics community what I discovered from analyzingone of myGrade 11 students’ approach to solving exponential equations of the form a a k x p x q , where a and k are positive integers greater than 1, and p , q . The student got a correct answer using a procedure which does not conform with the known exponential laws, thereby making it difficult to evaluate the student’s work. I gave the student’s script to fellow mathematics educators and they marked the student wrong, arguing that laws of exponents cannot be extended to a sum or difference of exponentials with the same base. Ithen decided to present the student’s solution method to other mathematics experts (through the Math Forum)for further evaluation. The responses and comments I received were far from being conclusive. It was suggested that there was need to use mathematical proof to verify whether the student’s approach was valid or not. I then set out to investigate why what looked like invalid reasoning on the surface gave the right answer in the end.After a careful analysis of the student’s approach, coupled with some kind of empirical investigations and mathematical proof, I eventually discovered that there was some logic in the student’s approach, only that it was not supported by the known theory of exponents. I therefore recommend that mathematics educators should not take students’ solution methods for granted. We might be marking some of the students’ solution methods wrong when they are valid, and robbing them of their precious marks. It is possible for students to come up with new and valid methods of solving mathematics problems which are not known to the educators.Good mathematics educators should therefore be on the lookout for new unanticipated approaches to solving mathematical problems that students of exceptional abilities may use in class. The famous German mathematician and astronomer, Carl Friedrich Gauss (1777-1855)amazed his teachers when he discovered a quick way of summing the integers from 1 to 100, at the age of seven. Such exceptional intellectual abilities still existeven in school children of today.
The document discusses the distinction between theoretical and practical thinking in mathematics. It presents a model that defines theoretical thinking as focusing on conceptual connections, logical reasoning, and developing consistent theories, while practical thinking focuses on solving particular problems and understanding factual relationships. The author argues that successful mathematics students demonstrate a "practical understanding of theory" by applying theoretical knowledge flexibly to efficiently solve problems. Examples of student work show the importance of both theoretical and practical thinking skills for high achievement in university mathematics.
This document discusses the challenges of establishing cause and effect relationships in psychology research. It explains that correlational research can identify relationships between variables but cannot prove causation, as correlations may be due to other unmeasured variables or reverse causation. Experimental research allows stronger claims about causation by manipulating an independent variable and measuring its effect on a dependent variable while controlling for other influences. However, not all variables can be experimentally manipulated. Overall, determining causes requires considering alternative explanations for observed relationships.
This document describes Bloom's Taxonomy, an educational framework for classifying learning objectives into levels of complexity and cognitive process. The taxonomy includes knowledge, comprehension, application, analysis, synthesis, and evaluation. The author interprets how these levels can be applied to mathematics education, providing example questions for each level targeting introductory calculus students. Questions become more complex through the levels, moving from knowledge-based questions testing terms and methods to evaluation questions requiring judgment on what information to use in word problems.
This document describes Bloom's Taxonomy, an educational framework for classifying learning objectives into levels of complexity and cognitive process. The taxonomy includes knowledge, comprehension, application, analysis, synthesis, and evaluation. The author interprets how these levels can be applied to mathematics education, providing example questions for each level targeting introductory calculus students. Questions become more complex through the levels, moving from knowledge-based questions testing terms and methods to evaluation questions requiring judgment on what information to use in word problems.
FINANCIAL T HEORY AND CORPORATE POLICY 4TH EDITIONCHAPTER 10.docxvoversbyobersby
FINANCIAL T HEORY AND CORPORATE POLICY 4TH EDITION
CHAPTER 10
Problem set
10.1 Suppose you know with certainty that the Clark Capital Corporation will pay a dividend of $10 per share on ever January 1 forever. The continuously compounded risk-free rate is 5% (also forever).
a. Graph the price path of Clark Corporation Capital common stock over time.
b. Is this (highly artificial) example a random walk? A matingale? A submartingale? Why?
10.5 The efficient market hypothesis implies that abnormal returns are expected to be zero. Yet in order for markets to be efficient , arbitrageurs must be able to force prices back into equilibrium. If they earn profits in doing so, is this fact inconsistent with market efficiency?
10.6 (a) In a poker a game with six players, you can expect to lose 83% of the time. How can this still be a martingale?
(b) In the options market, call options expire unexercised over 80% of the time. Thus the option holders frequently lose all their investment. Does this imply that the options market is not a fair game? Not a martingale? Not a submartingale?
10.8 From time to time the federal government considers passing into law an excess profits tax on U.S. corporations. Given what you know about efficient markets and the CAPM, how would you define excess profits? What would be the effect of an excess profits tax on the investor ?
Problems Identifying Independent and Dependent Variables
Keith R. Leatham
Brigham Young University
This paper discusses one step from the scientific method—that of identifying independent and dependent variables—
from both scientific and mathematical perspectives. It begins by analyzing an episode from a middle school mathematics
classroom that illustrates the need for students and teachers alike to develop a robust understanding of independent and
dependent variables. It then outlines four rationales (two from science and two from mathematics) for identifying
independent and dependent variables. Finally, it reports the results of a textbook analysis that used these rationales to
examine the extent to which typical mathematics textbook problems support or supplant a sensible view of independent
and dependent variables. The findings indicate that often, mathematics textbook problems misrepresent the sense-
making aspect of identifying independent and dependent variables, possibly setting students up to develop misconcep-
tions about this step from the scientific method.
Problems Identifying Independent and
Dependent Variables
The scientific method has had great influence over
science textbooks over the past century (Blachowicz,
2009). Although there is debate about the degree to which
this influence has been positive (Bauer, 1994; Nola &
Sankey, 2007), most scientists agree that viewing the sci-
entific method as a “recipe for doing science” is unhealthy
and counterproductive. Instead, the scientific community
desires that students, scientists, and the general populace
see the w ...
The importance of problem solving in the K - 12 mathematics curriculum is well documented. One of the most recent documentations is the Principles and Standards for School Mathematics (National Council of Teachers of Mathematics [NCTM] 2000). In this publication, problem solving is listed as one of the five Process Standards. “Problem solving is an integral part of all mathematics learning, and so it should not be an isolated part of the mathematics program” (NCTM, 2000, p. 52). Since problem solving has been accorded such prominence, it is necessary to have an understanding of what a mathematical problem is. After all, mathematical problems existed since the time of the ancient civilizations
Unit I of the syllabus covers propositional logic and counting theory. It introduces concepts such as propositions, logical connectives like conjunction, disjunction, negation, implication and biconditional. It discusses how to represent compound statements using these connectives and their truth tables. The unit also covers topics like predicate logic, methods of proof, mathematical induction and fundamental counting principles like permutations and combinations. It aims to provide the logical foundations for discrete mathematics concepts that will be useful in computer science and information technology.
Solving Exponential Equations: Learning from the Students We Teachinventionjournals
The purpose of this paper is to share with the mathematics community what I discovered from analyzingone of myGrade 11 students’ approach to solving exponential equations of the form a a k x p x q , where a and k are positive integers greater than 1, and p , q . The student got a correct answer using a procedure which does not conform with the known exponential laws, thereby making it difficult to evaluate the student’s work. I gave the student’s script to fellow mathematics educators and they marked the student wrong, arguing that laws of exponents cannot be extended to a sum or difference of exponentials with the same base. Ithen decided to present the student’s solution method to other mathematics experts (through the Math Forum)for further evaluation. The responses and comments I received were far from being conclusive. It was suggested that there was need to use mathematical proof to verify whether the student’s approach was valid or not. I then set out to investigate why what looked like invalid reasoning on the surface gave the right answer in the end.After a careful analysis of the student’s approach, coupled with some kind of empirical investigations and mathematical proof, I eventually discovered that there was some logic in the student’s approach, only that it was not supported by the known theory of exponents. I therefore recommend that mathematics educators should not take students’ solution methods for granted. We might be marking some of the students’ solution methods wrong when they are valid, and robbing them of their precious marks. It is possible for students to come up with new and valid methods of solving mathematics problems which are not known to the educators.Good mathematics educators should therefore be on the lookout for new unanticipated approaches to solving mathematical problems that students of exceptional abilities may use in class. The famous German mathematician and astronomer, Carl Friedrich Gauss (1777-1855)amazed his teachers when he discovered a quick way of summing the integers from 1 to 100, at the age of seven. Such exceptional intellectual abilities still existeven in school children of today.
The document discusses the distinction between theoretical and practical thinking in mathematics. It presents a model that defines theoretical thinking as focusing on conceptual connections, logical reasoning, and developing consistent theories, while practical thinking focuses on solving particular problems and understanding factual relationships. The author argues that successful mathematics students demonstrate a "practical understanding of theory" by applying theoretical knowledge flexibly to efficiently solve problems. Examples of student work show the importance of both theoretical and practical thinking skills for high achievement in university mathematics.
This document discusses the challenges of establishing cause and effect relationships in psychology research. It explains that correlational research can identify relationships between variables but cannot prove causation, as correlations may be due to other unmeasured variables or reverse causation. Experimental research allows stronger claims about causation by manipulating an independent variable and measuring its effect on a dependent variable while controlling for other influences. However, not all variables can be experimentally manipulated. Overall, determining causes requires considering alternative explanations for observed relationships.
This document describes Bloom's Taxonomy, an educational framework for classifying learning objectives into levels of complexity and cognitive process. The taxonomy includes knowledge, comprehension, application, analysis, synthesis, and evaluation. The author interprets how these levels can be applied to mathematics education, providing example questions for each level targeting introductory calculus students. Questions become more complex through the levels, moving from knowledge-based questions testing terms and methods to evaluation questions requiring judgment on what information to use in word problems.
This document describes Bloom's Taxonomy, an educational framework for classifying learning objectives into levels of complexity and cognitive process. The taxonomy includes knowledge, comprehension, application, analysis, synthesis, and evaluation. The author interprets how these levels can be applied to mathematics education, providing example questions for each level targeting introductory calculus students. Questions become more complex through the levels, moving from knowledge-based questions testing terms and methods to evaluation questions requiring judgment on what information to use in word problems.
This document is the introduction chapter of a textbook on probability. It introduces fundamental probability concepts like outcome spaces, events, and probability as a function of events. Probability is first discussed in the context of equally likely outcomes, where each outcome has the same probability of occurring. Two common interpretations of probability - as the long-run frequency of an event occurring or as a subjective measure of uncertainty - are also introduced. The chapter then covers probability distributions, conditional probability, independence, Bayes' rule, and sequences of events.
Assessing Algebraic Solving Ability A Theoretical FrameworkAmy Cernava
This document presents a theoretical framework for assessing algebraic solving ability. It discusses three phases of algebraic processes: 1) investigating patterns in numerical data, 2) representing patterns in tables and equations, and 3) interpreting and applying equations to new situations. It also reviews different approaches for developing algebraic solving ability in students, such as game-based learning, building conceptual understanding of variables/functions, and representing problems in multiple ways. The theoretical framework is based on these algebraic processes and how they align with levels of the SOLO model for assessing student understanding.
[W]-REFERENCIA-Paul Waltman (Auth.) - A Second Course in Elementary Different...EdgarJalistoMedina1
Here are the key properties of matrix multiplication:
i. Associative: A(BC) = (AB)C
ii. Distributive over scalar multiplication: x(AB) = (xA)B = A(xB)
iii. Distributive over matrix addition: (A + B)C = AC + BC
iv. Distributive over matrix addition: C(A + B) = CA + CB
v. Transpose: (AB)T = BTAT
These properties allow matrix algebra to behave similarly to real or complex number algebra, which greatly simplifies working with matrices.
WRITTEN EXERCISE #2 COMPREHENSION DOES NOT MEAN DENYING THE.docxjeffevans62972
WRITTEN EXERCISE #2
“COMPREHENSION DOES NOT MEAN DENYING THE OUTRAGEOUS, DEDUCING THE
UNPRECED ENT ED FROM PRECED ENCE, OR EXPLAI NING PHENOMENA BY SUCH ANALOGIES AND
GENERALITIES THAT THE IMPACT OF REALITY AND THE SHOCK OF EXPERIENCE ARE NO
LONGER FELT. IT MEANS, RATHER, EX AMINING AND BEARING CONSCIOUSLY THE BURD EN
WHICH OUR CENT URY HAS PLACED ON US – NEITHER DENYING IT S EXISTENCE NOR
SUBMITTING MEEKLY TO ITS WEIGHT.”
~ HANNAH ARENDT
Who, exactly, were the Progressives? One historian writes that they “offered an
impressive array of reform proposals.” Why did they do so? What was our country like
during the Gilded Age? What, exactly, were these proposals and what benefit did they
bring to “life in these United States?” To what extent was the nation altered by their
proposals? Please explain why the U.S. did (or did not) become a “kinder, gentler
nation” as a result of the Progressive movement. Finally, how do some historians assess
the Progressives? What examples from the Progressive Era and from today can you
provide to support or refute their arguments?
“HISTORY IS FICTION, EXCEPT FOR THE PARTS THAT I LIKE, WHICH ARE, OF COURSE, TRUE.”
~ JIM CORDER
U N I T E D S T A T E S H I S T O R Y
A M Y B E L L
DIRECTIONS
1) Your response to the question must be typed—twelve point font, double-spaced.
In writing your answer, please do not exceed five pages.
2) In your response, try to mainly use only your assigned text(s), the instructor’s
handouts, or class notes taken from discussions. You may use additional
library or internet scholarly sources.
3) Your generalizations must be supported by direct citations from the text, class
notes, or instructor’s handouts.
4) Citations should be made in MLA format. For class notes or presentations, you
might use: (Discussion Board 1) or (class notes) or (Zinn 23).
Note: You must cite parenthetically throughout your narrative. Please follow this format. There
should be many citations throughout your response taken from the sources noted above because
assumptions and interpretations must be bolstered by citations.
The strength of your response is dependent largely upon your citation of the assigned sources.
5) Do not include a bibliography.
6) You may consult with your classmates in formulating an answer to this question.
However, you must write your own, unique, independent answer to this question.
7) Date Due: Please see date on eCampus Calendar.
“ONE IS ASTONISHED IN THE STUDY OF HISTORY AT THE RECURRENCE OF THE IDEA THAT
EVIL MUST BE FORGOTTEN, DISTORTED, SKIMMED OVER. WE MUST NOT REMEMBER THAT
DANIEL WEBSTER GOT DRUNK BUT ONLY REMEMBER T HAT HE WAS A SPLENDID
CONSTITUTIONAL LAWYER. WE MUST FORGET THAT GEORGE WAHINGTON WAS A SLAVE
OWNER…AND SIMPLY REMEMBER THE THINGS WE REGARD AS CREDITABLE AND INSPIRING.
THE DIFFICULTY, OF COURSE, WITH THIS PHILOSOPHY.
This article discusses research on students' understanding of trigonometric functions. It finds that traditional instruction emphasizes trigonometric ratios over understanding functions. As a result, students have difficulty understanding trigonometric functions as mathematical operations that can be applied to angles. Many students cannot approximate values or reason about properties of trigonometric functions without direct computation. The article recommends instruction help students conceive of trigonometric operations as processes that take angles as inputs and map them to real number outputs.
Assessment Knowledge, Process, Understanding, Process/ProductCarlo Magno
The document discusses assessment for learning. It begins by defining assessment competencies for teachers, including choosing appropriate assessment methods, administering and interpreting various assessment tools, using results to inform instructional decisions, developing valid grading procedures, and communicating results. It then discusses the need for academic standards to ensure quality. The document proposes assessing students based on their knowledge, processes, understanding, and products/performance (KPUP). It provides examples of assessing each dimension and determining which examples measure each.
This document presents a research project on second order linear ordinary differential equations and their applications to physics problems. It begins by introducing second order linear equations and establishes a theorem for the existence and uniqueness of solutions to the initial value problem. It then proves the theorem by converting the second order equation into a system of first order equations. Several physical problems are also described that can be modeled using second order linear differential equations, including mass-spring systems, resonant vibrations, electric circuits, and electric motors. It concludes with a stability analysis of the equilibrium solution for one of the physical problems.
This document summarizes the results of a longitudinal study on introducing algebraic concepts to elementary school students. The study involved over 70 students from grades 2-4 participating in weekly algebraic activities over 2.5 years. Key findings include:
1) Students were able to understand elementary algebraic ideas such as thinking of arithmetic operations as functions, using the number line to represent numbers and operations, and accepting negative numbers.
2) Students could work with algebraic notation like mappings and expressions, represent relationships involving unknown quantities, and solve problems using multiple representations like tables, graphs, and equations.
3) By the end of 4th grade, students in the study group significantly outperformed a control group on tasks involving equations, functions,
This document discusses key aspects of research including definitions, components, processes, and characteristics. It provides three definitions of research that emphasize it as a systematic approach to answering questions. The main components of research are identified as a systematic approach, answers, and questions. The key processes involved in research are defined as identifying a problem, formulating a hypothesis, and stating an objective. Characteristics of a good research problem and hypothesis are outlined. The importance of literature review in providing background and identifying what others have found is also highlighted.
This document outlines a teaching manual for a lesson on direct proportion using the concept attainment model. It details the steps the teacher and students will take to attain the concept of direct proportion. The teacher will present positive and negative examples without labeling the concept. Students will observe the examples to form a hypothesis about the concept. The teacher will then confirm if students correctly identified the concept of direct proportion as when two quantities change such that one is a constant multiple of the other.
This section introduces the real number system by stating its defining properties as an ordered field that satisfies the axioms of (A)–(H). Specifically, it is a set with operations of addition and multiplication that satisfy the commutative, associative, and distributive laws, contains elements 0 and 1, and has an order relation < that is transitive. The key property introduced is completeness. Common notation involving the order relation and absolute value are also defined. The triangle inequality, which plays an important role in analysis, is proven.
This document outlines a mathematics teaching plan for a group of 5 students. It includes:
1. Examples of declarative, procedural, and principles-based knowledge in mathematics.
2. Examples of creating a diversity-responsive curriculum, including teaching about diversity, using inclusive content, and connecting content to students' lives.
3. Examples of introductory and developed understanding in geometry and algebra lessons.
The document discusses properties of equalities that can be used to solve equations. It defines seven properties: reflexive, symmetric, transitive, addition, subtraction, multiplication, and division. Examples are provided to illustrate each property, such as how adding the same number to both sides of an equation maintains equality. Understanding these properties allows equations to be transformed into equivalent equations to solve for variables.
Nature and principles of teaching and learning mathJunarie Ramirez
This document discusses effective teaching of mathematics. It outlines three phases of mathematical inquiry: (1) abstraction and symbolic representation, (2) manipulating mathematical statements, and (3) application. It also discusses the nature and principles of teaching mathematics, including that mathematics relies on both logic and creativity. Effective teaching requires understanding what students know and challenging them, as well as using worthwhile tasks to engage them intellectually. Teachers must have mathematical knowledge and commit to students' understanding.
Visual Presentation in Algebra for First Year Studentsmyda rose penuliar
The document discusses properties of equalities that can be used to solve equations. It defines seven properties of equalities: reflexive, symmetric, transitive, addition, subtraction, multiplication, and division. Examples are provided to illustrate each property. The properties allow equations to be transformed into equivalent equations through operations like adding or multiplying the same term to both sides.
Visual Presentation in Algebra for First Year Studentsmyda rose penuliar
The document discusses properties of equalities that can be used to solve equations. It defines seven properties of equalities: reflexive, symmetric, transitive, addition, subtraction, multiplication, and division. Examples are provided to illustrate each property. The properties allow equations to be transformed into equivalent equations through operations like adding or multiplying the same quantity to both sides.
Melissa HinkhouseWeek 3-Original PostNURS 6050 Policy and A.docxwkyra78
Melissa Hinkhouse
Week 3-Original Post
NURS 6050: Policy and Advocacy for Improving Population Health
Walden University
In 2010 The Affordable Care Act (ACA) was enacted; the hope was to expand access to medical care, make coverage more affordable, and decrease the number of people without medical insurance. The Affordable Care Act (ACA) expanded and improved health insurance coverage in two primary ways. First, the number of individuals receiving insurance coverage grown by increasing access to coverage through Medicaid expansion and providing subsidies to purchase private insurance on the health care exchanges. Second, the ACA upgraded the quality and scope of coverage by improving benefit design, including implementing the essential health benefits (Willison & Singer, 2017). People who did not have coverage through their employer or Medicaid were required to purchase insurance through the Marketplace. The Marketplace was created as a one-stop-shop for people to view multiple plans and purchase insurance. Just because you have access to health care insurance does not mean you are going to receive quality health care (Teitelbaum, 2018).
Both parties have asked that the ACA be repealed or replaced for multiple reasons. Every Republican presidential candidate for 2016 has called for the repeal of the ACA. Some, but not all, Republican candidates have proposed health policies that they would like to put in place after repeal, but there is no broad agreement on a replacement for the ACA (Buettgens & Blumberg, 2016). The federal government would spend $90.9 billion less on health care for the nonelderly in 2021 if the ACA were repealed (Buettgens & Blumberg, 2016). State governments as a whole would spend $5.2 billion more on health care for the nonelderly in 2021 if the ACA were repealed (Buettgens & Blumberg, 2016). Healthcare is a priority to many Americans for obvious reasons; it was more costly for those with preexisting conditions before the ACA to obtain Medical Insurance. With the ACA the income guidelines for Medicaid where changed so additional people qualified that didn’t prior. As a Behavioral Health Nurse, I am a fan of anyone and everyone having access to Healthcare Services. I have seen to many times my patient not have the money for their medications because insurance was canceled so they go off their medications, they become unstable and ended up in the Emergency Department and admitted Inpatient, costing more money, hurting themselves and their loved ones.
Politicians are aware that election time is the best time to play the tug of war game with the heavy ticket items to capture someone votes. Republicans ran hard on promises to get rid of the law in every election since it passed in 2010. But when the GOP finally got control of the House, the Senate and the White House in 2017, Republicans found
they could not reach agreement
on how to "repeal and replace" the law (Kaiser Health News, 2018). And political strategists s.
Melissa Hinkhouse
Advanced Pharmacology NURS-6521N-43
Professor Dr. Vicki Gardin
Discussion Board Week 1-Original Post
11/30/2020
I have worked in an outpatient behavioral health clinic for the past seven years with many different providers. I live in a rural community, many patients wait six to twelve months to be seen. Patients being treated for Attention Deficit Disorder must be officially tested before being seen by a Psychologist. For this discussion board post, I have changed the name of my patient to Paul to ensure patient confidentially. The provider I worked with this particular patient will also be referred to as PMHNP to ensure provider confidentiality.
Paul was a ten-year-old Caucasian male referred to our clinic diagnosed per DSM criteria, confirmed via Psychologist testing with ADHD. When he saw the Psychologist, he was also diagnosed with mild depression and anxiety. He struggled with concentration, hyperactivity, impulse control, and disorganization. He presented to his appointment with his mother and father, clean, well-nourished, pleasant, interactive with staff, reported no medication allergies, current medication Zyrtec for seasonal allergies. Paul just had his well-child exam and is current on vaccinations and his primary care provider completed lab work to include CBC, CMP, TSH, Vit D, B12, and A1C, all have returned normal. Family history reported father has a history of ADHD (never medicated), brother has a history of depression and anxiety (never medicated treating with psychotherapy), no other significant family history to report. Paul’s current weight at his appointment was 30kg.
PMHNP spent one hour with Paul and his parents for the initial new patient appointment (Thursday). It was decided Paul would be prescribed Strattera (atomoxetine) 40mg once a day for one week then increase to 80mg once a day. I returned to work on Monday and received a call from Paul’s mom, she said he was acting strange. He was tearful, had been in his room with the door closed for most of the weekend, she stated on Sunday she went into his room and he was crying and said he was just thinking about dying and his parents dying. She stated he had already had his meds Sunday so she kept him with her that entire day and made Sunday night a campout night in the Livingroom so he would think it was fun and she could keep a close eye on him. I had a cancelation that morning for him to come to see PMHNP and he was in to see her within twenty minutes and removed from Strattera. His parents decided medications were no longer the route they wanted to try for treatment and a referral was made for psychotherapy.
The only medication Paul takes on occasion is Zyrtec which is in an antihistamine drug class, Strattera is a selective norepinephrine reuptake inhibitor; there is no known drug interaction between the two medications. Reflecting on his age and the medication, Strattera has a black box labeled for suicidal ideation with adolescents dia.
Meiner, S. E., & Yeager, J. J. (2019). Chapter 17Chap.docxwkyra78
Meiner, S. E., & Yeager, J. J. (2019).
Chapter 17
Chapter_017.pptx
Chapter 18
Chapter_018.pptx
Chapter 19
Chapter_019.pptx
Chapter 20
Chapter_020.pptx
Watch
None.
Supplemental Materials & Resources
Visit the
CINAHL Complete
under the
A-to-Z Databases
on the
University Library's
website and locate the article(s) below:
O’Keefe-McCarthy, S. (2009). Technologically-mediated nursing care: The impact on moral agency. Nursing Ethics, 16(6), 76-796.
Teutsch, S., & Rechel, B. (2012). Ethics of resource allocation and rationing medical care in a time of fiscal restraint: US and Europe. Public Health Reviews, 34(1), 1-10.
QUESTION
Define presbycusis, name signs and symptoms, etiology and differential diagnosis.
Create 3 interventions-education measures with a patient with Presbycusis.
List, define and elaborate on three different retinal and macular diseases age-related.
Submission Instructions:
Your initial post should be at least 500 words, formatted and cited in current APA style with support from at least 2 academic sources
Your assignment will be graded according to the grading rubric.
.
member is a security software architect in a cloud service provider .docxwkyra78
member is a security software architect in a cloud service provider company, assigned to a project to provide the client with data integrity and confidentiality protections for data in transit that will be using applications in the cloud. Your client is an HR company that is moving HR applications and HR data into a community cloud, sharing tenancy with other clients. Your company has set up a software as a service, SAS, offering for its client base.
The data that the HR company will be pushing to and from the cloud will contain sensitive employee information, such as personally identifiable information, PII. You will have to address sensitive data and transit issues of the client data using the HR applications stored in the cloud, and provide a life cycle management report that includes solutions to the cloud computing architect of your company.
Software Development Life Cycle
Technology development and implementation usually follow a software development life cycle (SDLC) methodology. This approach ensures accuracy of information for analysis and decision making, as well as appropriate resources for effective technology management.
You and your team members will use components of the SDLC methodology to develop a
life cycle management report
for the cloud computing architect of a company. This is a group exercise, representing the kind of collaboration often required in the cybersecurity technology community.
There are 11 steps to lead you through this project. Similar steps are typically used in organizational SDLC projects. Most steps should take no more than two hours to complete, and the entire project should take no more than three weeks to complete. Begin with the workplace scenario, and then continue with Step 1: “Initiating the Project.”
Life Cycle Management Report:
A 10- to 15-page double-spaced Word document on data protection techniques for a cloud-based service with citations in APA format. The page count does not include figures or tables. There is no penalty for using additional pages if you need them. Include a minimum of six references. Include a reference list with the report.
As the cloud security architect, you must understand the security development life cycle process. Review the following resources to learn about the security development life cycle process:
security development life cycle
software development methodologies
Click the following links to learn more about critical infrastructure sectors:
Critical Infrastructure Sectors
. Read their descriptions and consider which sector you support in your role.
Process Control Systems: Cybersecurity and Defense
To be completed by a designated team member:
You will begin your Life Cycle Management Report now.
Choose a fictional or actual organization. Describe the mission of the organization and the business need to move to a cloud environment.
Identify the scope of the security architecture and include a topology. To narrow your scope, focus on is.
Melissa ShortridgeWeek 6COLLAPSEMy own attitude has ch.docxwkyra78
Melissa Shortridge
Week 6
COLLAPSE
My own attitude has changed from lack of understanding to enlightenment over the years. In elementary school I never experienced students with disabilities in my classrooms, growing up. But as the years went on and legislation changed students with disabilities started trickling into general education classrooms. They were always ignored by other students and often times had an aide to assist them with assignments. As an adult my heart has opened up to accept all types of people. In the Pennhurst documentary, it was reiterated, they are just people (Baldini, 1968). Which is my outlook on how to treat everyone. Every single person is a human being, treat them the way you wish to be treated. Everyone no matter their race, disability or socio-economic status deserves to be treated humanely.
As an educator I have worked with several different types of students. Students from low socio-economic areas, behavioral issues, vision impairments, hearing impairments, with autism, hyper activity and down syndrome, and with all of these students I have given them my best effort to show them that they are students first. Slavin and Schunk (2017) said it best, “Each student has many characteristics, and the disability is only one of them. To define the child in terms of the disability does him or her an injustice” (p. 235). It is our role as an educator to incorporate different learning styles to give each student, regardless of disabilities, the education that they deserve.
Welcoming students with disabilities into my classroom will be an important aspect in my role as an educator. Allowing each student to feel love and acceptance by peers is important for any students success. Van Brummelen (2009) states, “ It is important to appreciate students with special needs for who they are. Always look beyond their disabilities and teach them as whole persons” (p. 208). Being an advocate for my students with learning disabilities will garner them respect and dignity that they need to be self sufficient. In the Pennhurst documentary, the children did not have complete proper advocacy from the people that worked with them. They were simply shuffled along and not given the proper education and care that they needed to be self-sufficient (Baldini, 1968). “Defend the weak and the fatherless; uphold the cause of the poor and oppressed. Rescue the weak and the needy; deliver them from the hand of the wicked” (Psalm 82:3-4, New International Version). It is our Godly duty to defend individuals who can not defend themselves. In His eyes we are all created equal and in that we all deserve equal treatment and opportunities.
References
Baldini, B. (1968). Suffer the Little Children: Pennhurst Pennsylvania State Home for Disabled Children [Video file]. Retrieved from
https://youtu.be/YG33HvIKOgQ
Slavin, R.E., & Schunk D.H. (2017). Learning Theories: EDUC 500 (1st ed.) Boston, MA: Pearson.
Van Brummelen, H. (2009). Walking wit.
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Melissa Hinkhouse
Week 3-Original Post
NURS 6050: Policy and Advocacy for Improving Population Health
Walden University
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Both parties have asked that the ACA be repealed or replaced for multiple reasons. Every Republican presidential candidate for 2016 has called for the repeal of the ACA. Some, but not all, Republican candidates have proposed health policies that they would like to put in place after repeal, but there is no broad agreement on a replacement for the ACA (Buettgens & Blumberg, 2016). The federal government would spend $90.9 billion less on health care for the nonelderly in 2021 if the ACA were repealed (Buettgens & Blumberg, 2016). State governments as a whole would spend $5.2 billion more on health care for the nonelderly in 2021 if the ACA were repealed (Buettgens & Blumberg, 2016). Healthcare is a priority to many Americans for obvious reasons; it was more costly for those with preexisting conditions before the ACA to obtain Medical Insurance. With the ACA the income guidelines for Medicaid where changed so additional people qualified that didn’t prior. As a Behavioral Health Nurse, I am a fan of anyone and everyone having access to Healthcare Services. I have seen to many times my patient not have the money for their medications because insurance was canceled so they go off their medications, they become unstable and ended up in the Emergency Department and admitted Inpatient, costing more money, hurting themselves and their loved ones.
Politicians are aware that election time is the best time to play the tug of war game with the heavy ticket items to capture someone votes. Republicans ran hard on promises to get rid of the law in every election since it passed in 2010. But when the GOP finally got control of the House, the Senate and the White House in 2017, Republicans found
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Melissa Hinkhouse
Advanced Pharmacology NURS-6521N-43
Professor Dr. Vicki Gardin
Discussion Board Week 1-Original Post
11/30/2020
I have worked in an outpatient behavioral health clinic for the past seven years with many different providers. I live in a rural community, many patients wait six to twelve months to be seen. Patients being treated for Attention Deficit Disorder must be officially tested before being seen by a Psychologist. For this discussion board post, I have changed the name of my patient to Paul to ensure patient confidentially. The provider I worked with this particular patient will also be referred to as PMHNP to ensure provider confidentiality.
Paul was a ten-year-old Caucasian male referred to our clinic diagnosed per DSM criteria, confirmed via Psychologist testing with ADHD. When he saw the Psychologist, he was also diagnosed with mild depression and anxiety. He struggled with concentration, hyperactivity, impulse control, and disorganization. He presented to his appointment with his mother and father, clean, well-nourished, pleasant, interactive with staff, reported no medication allergies, current medication Zyrtec for seasonal allergies. Paul just had his well-child exam and is current on vaccinations and his primary care provider completed lab work to include CBC, CMP, TSH, Vit D, B12, and A1C, all have returned normal. Family history reported father has a history of ADHD (never medicated), brother has a history of depression and anxiety (never medicated treating with psychotherapy), no other significant family history to report. Paul’s current weight at his appointment was 30kg.
PMHNP spent one hour with Paul and his parents for the initial new patient appointment (Thursday). It was decided Paul would be prescribed Strattera (atomoxetine) 40mg once a day for one week then increase to 80mg once a day. I returned to work on Monday and received a call from Paul’s mom, she said he was acting strange. He was tearful, had been in his room with the door closed for most of the weekend, she stated on Sunday she went into his room and he was crying and said he was just thinking about dying and his parents dying. She stated he had already had his meds Sunday so she kept him with her that entire day and made Sunday night a campout night in the Livingroom so he would think it was fun and she could keep a close eye on him. I had a cancelation that morning for him to come to see PMHNP and he was in to see her within twenty minutes and removed from Strattera. His parents decided medications were no longer the route they wanted to try for treatment and a referral was made for psychotherapy.
The only medication Paul takes on occasion is Zyrtec which is in an antihistamine drug class, Strattera is a selective norepinephrine reuptake inhibitor; there is no known drug interaction between the two medications. Reflecting on his age and the medication, Strattera has a black box labeled for suicidal ideation with adolescents dia.
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Meiner, S. E., & Yeager, J. J. (2019).
Chapter 17
Chapter_017.pptx
Chapter 18
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Chapter 19
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Chapter 20
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Watch
None.
Supplemental Materials & Resources
Visit the
CINAHL Complete
under the
A-to-Z Databases
on the
University Library's
website and locate the article(s) below:
O’Keefe-McCarthy, S. (2009). Technologically-mediated nursing care: The impact on moral agency. Nursing Ethics, 16(6), 76-796.
Teutsch, S., & Rechel, B. (2012). Ethics of resource allocation and rationing medical care in a time of fiscal restraint: US and Europe. Public Health Reviews, 34(1), 1-10.
QUESTION
Define presbycusis, name signs and symptoms, etiology and differential diagnosis.
Create 3 interventions-education measures with a patient with Presbycusis.
List, define and elaborate on three different retinal and macular diseases age-related.
Submission Instructions:
Your initial post should be at least 500 words, formatted and cited in current APA style with support from at least 2 academic sources
Your assignment will be graded according to the grading rubric.
.
member is a security software architect in a cloud service provider .docxwkyra78
member is a security software architect in a cloud service provider company, assigned to a project to provide the client with data integrity and confidentiality protections for data in transit that will be using applications in the cloud. Your client is an HR company that is moving HR applications and HR data into a community cloud, sharing tenancy with other clients. Your company has set up a software as a service, SAS, offering for its client base.
The data that the HR company will be pushing to and from the cloud will contain sensitive employee information, such as personally identifiable information, PII. You will have to address sensitive data and transit issues of the client data using the HR applications stored in the cloud, and provide a life cycle management report that includes solutions to the cloud computing architect of your company.
Software Development Life Cycle
Technology development and implementation usually follow a software development life cycle (SDLC) methodology. This approach ensures accuracy of information for analysis and decision making, as well as appropriate resources for effective technology management.
You and your team members will use components of the SDLC methodology to develop a
life cycle management report
for the cloud computing architect of a company. This is a group exercise, representing the kind of collaboration often required in the cybersecurity technology community.
There are 11 steps to lead you through this project. Similar steps are typically used in organizational SDLC projects. Most steps should take no more than two hours to complete, and the entire project should take no more than three weeks to complete. Begin with the workplace scenario, and then continue with Step 1: “Initiating the Project.”
Life Cycle Management Report:
A 10- to 15-page double-spaced Word document on data protection techniques for a cloud-based service with citations in APA format. The page count does not include figures or tables. There is no penalty for using additional pages if you need them. Include a minimum of six references. Include a reference list with the report.
As the cloud security architect, you must understand the security development life cycle process. Review the following resources to learn about the security development life cycle process:
security development life cycle
software development methodologies
Click the following links to learn more about critical infrastructure sectors:
Critical Infrastructure Sectors
. Read their descriptions and consider which sector you support in your role.
Process Control Systems: Cybersecurity and Defense
To be completed by a designated team member:
You will begin your Life Cycle Management Report now.
Choose a fictional or actual organization. Describe the mission of the organization and the business need to move to a cloud environment.
Identify the scope of the security architecture and include a topology. To narrow your scope, focus on is.
Melissa ShortridgeWeek 6COLLAPSEMy own attitude has ch.docxwkyra78
Melissa Shortridge
Week 6
COLLAPSE
My own attitude has changed from lack of understanding to enlightenment over the years. In elementary school I never experienced students with disabilities in my classrooms, growing up. But as the years went on and legislation changed students with disabilities started trickling into general education classrooms. They were always ignored by other students and often times had an aide to assist them with assignments. As an adult my heart has opened up to accept all types of people. In the Pennhurst documentary, it was reiterated, they are just people (Baldini, 1968). Which is my outlook on how to treat everyone. Every single person is a human being, treat them the way you wish to be treated. Everyone no matter their race, disability or socio-economic status deserves to be treated humanely.
As an educator I have worked with several different types of students. Students from low socio-economic areas, behavioral issues, vision impairments, hearing impairments, with autism, hyper activity and down syndrome, and with all of these students I have given them my best effort to show them that they are students first. Slavin and Schunk (2017) said it best, “Each student has many characteristics, and the disability is only one of them. To define the child in terms of the disability does him or her an injustice” (p. 235). It is our role as an educator to incorporate different learning styles to give each student, regardless of disabilities, the education that they deserve.
Welcoming students with disabilities into my classroom will be an important aspect in my role as an educator. Allowing each student to feel love and acceptance by peers is important for any students success. Van Brummelen (2009) states, “ It is important to appreciate students with special needs for who they are. Always look beyond their disabilities and teach them as whole persons” (p. 208). Being an advocate for my students with learning disabilities will garner them respect and dignity that they need to be self sufficient. In the Pennhurst documentary, the children did not have complete proper advocacy from the people that worked with them. They were simply shuffled along and not given the proper education and care that they needed to be self-sufficient (Baldini, 1968). “Defend the weak and the fatherless; uphold the cause of the poor and oppressed. Rescue the weak and the needy; deliver them from the hand of the wicked” (Psalm 82:3-4, New International Version). It is our Godly duty to defend individuals who can not defend themselves. In His eyes we are all created equal and in that we all deserve equal treatment and opportunities.
References
Baldini, B. (1968). Suffer the Little Children: Pennhurst Pennsylvania State Home for Disabled Children [Video file]. Retrieved from
https://youtu.be/YG33HvIKOgQ
Slavin, R.E., & Schunk D.H. (2017). Learning Theories: EDUC 500 (1st ed.) Boston, MA: Pearson.
Van Brummelen, H. (2009). Walking wit.
Melissa is a 15-year-old high school student. Over the last week.docxwkyra78
Melissa is a 15-year-old high school student. Over the last week, she had been feeling tired and found it difficult to stay awake in class. By the time the weekend had arrived, she developed a sore throat that made it difficult to eat and even drink. Melissa was too tired to get out of bed, and she said her head ached. On Monday morning, her mother took her to her doctor. Upon completing the physical exam, he told Melissa the lymph nodes were enlarged in her neck and she had a fever. He ordered blood tests and told Melissa he thought she had mononucleosis, a viral infection requiring much bed rest.
Innate and adaptive immune defenses work collectively in destroying invasive microorganisms. What is the interaction between macrophages and T lymphocytes during the presentation of antigen?
Melissa’s illness is caused by a virus. Where are type I interferons produced, and why are they important in combating viral infections?
Humoral immunity involves the activation of B lymphocytes and production of antibodies. What are the general mechanisms of action that make antibodies a key component of an immune response?
.
1. The document describes measuring the angle θ between momentum vectors of particles π- and Σ- produced in a particle interaction using a bubble chamber photograph. The angle can be determined by drawing tangents to the particle tracks and measuring the angle between them.
2. An alternative method to measure the angle not requiring a protractor is described using ratios of distances along the tangents.
3. Instructions are given to estimate uncertainties in measurements taken from repeated readings using calculations of average and standard deviation.
Measurement of the angle θ For better understanding .docxwkyra78
Measurement of the angle θ
For better understanding I am showing you a different particle track diagram bellow. Where at
point C particle 𝜋 − 𝑎𝑛𝑑 Σ− are created and the Σ− decays into 𝜋 ∓ 𝑎𝑛𝑑 K− particles
The angle θ between the π− and Σ− momentum vectors can be determined by drawing tangents
to the π− and Σ− tracks at the point of the Σ− decay. We can then measure the angle between
the tangents using a protractor. Alternative method which does not require a protractor is also
possible. Let AC and BC be the tangents to the π− and Σ− tracks respectively. Drop a
perpendicular (AB) and measure the distances AB and BC. The ratio AB/BC gives the tangent of
the angle180◦−θ. It should be noted that only some of the time will the angle θ exceed 90◦ as
shown here.
Determining the uncertainty of Measurements
In part B, It is asked to estimate the uncertainty of your measurements of 𝜃 and r.
Uncertainty of measurement is the doubt that exists about the result of any measurement. You
might think that well-made rulers, clocks and thermometers should be trustworthy, and give
the right answers. But for every measurement - even the most careful - there is always a margin
of doubt.
It is important not to confuse the terms ‘error’ and ‘uncertainty’.
Error is the difference between the measured value and the ‘true value’ of the thing being
measured.
Uncertainty is a quantification of the doubt about the measurement result
Since there is always a margin of doubt about any measurement, we need to ask ‘How big is the
margin?’ and ‘How bad is the doubt?’ Thus, two numbers are really needed in order to quantify
an uncertainty. One is the width of the margin, or interval. The other is a confidence level, and
states how sure we are that the ‘true value’ is within that margin.
You can increase the amount of information you get from your measurements by taking a
number of readings and carrying out some basic statistical calculations. The two most
important statistical calculations are to find the average or arithmetic mean, and the standard
deviation for a set of numbers.
The ‘true’ value for the standard deviation can only be found from a very large (infinite) set of
readings. From a moderate number of values, only an estimate of the standard deviation can be
found. The symbol s is usually used for the estimated standard deviation.
Suppose you have a set of n readings. Start by finding the average:
For the set of readings x={16, 19, 18, 16, 17, 19, 20, 15, 17 and 13}, the average is �̅� =
∑ 𝑥𝑖
𝑛
=
17.
Next find (𝑥𝑖 − �̅�)
2
Then 𝑠 = √
(𝑥𝑖−�̅�)
2
𝑛−1
= 2.21
Lifetime calculation
In part C you are asked to determine the life time of the neutral particles from their
momentums.
The Σ− lifetime can be approximately determined using the measured values of the Σ− track
lengths. The average momentum of the Σ− particle can be found from its initial and fin
Meaning-Making Forum 2 (Week 5)Meaning-Making Forums 1-4 are thi.docxwkyra78
Meaning-Making Forum 2 (Week 5)
Meaning-Making Forums 1-4 are this course's unique final project.
Be fully engaged in Phase Two!
After reviewing the readings, presentations, lecture notes, articles, and web-engagements, and previous assignments, artificially move your predetermined careseeker (i.e., Crossroads’ Careseekers: Bruce, Joshua, Brody, Justin, or Melissa) through Phase Two.
NOTE: These research-based forums require that you draw upon ALL
of the course readings and learning activities to date, in order to substantively develop each phase in our
Solution
-based, Short-term, Pastoral Counseling (SbStPC) process. Noticeably support each core assertion.
Rapport and Relational Alignment.
Briefly discuss how you will continue to build rapport and shift your relational style in order to best align with the careseeker’s style (i.e., use DISC language) and current behavioral position (i.e., attending, blaming, or willing).
Phase Two Distinctive Features.
Narrate movement of careseeker through Phase Two’s distinctive features (i.e., purpose, goal, chief aim, role/responsibility, use of guiding assumptions) and apply pertinent insights and techniques from ALL the readings, previous assignments, and the Bible.
Supportive Feedback Break.
What portrait, definition(s), key thought(s), and/or assessment insight from the
Quick Reference Guide
might be utilized in the supportive feedback technique?
Phase Two Marker.
Describe a marker that indicates you have collaboratively ‘imagineered” a picture of life without the problem. In what way does this marker indicate the careseeker is in a willing position and ready for Phase Three?
Food for Thought:
When learning a new people skill or counseling technique, is it normal to “feel” awkward and fake? Use at least 1 example and thoughtfully explain how this “feeling” might be normalized.
TIPS:
Carefully Follow Meaning-Making Forum Guidelines & Tips!
Make sure to use headings (5) so that the most inattentive reader may easily follow your thoughts.
Use the annotated outline approach. Bullets should have concise, complete, well-developed sentences or paragraphs.
Foster a “noble-minded” climate for investigating claims through well-supported core assertions (i.e., consider the validation pattern of the Bereans; Acts 17:11).
Noticeably support assertions to facilitate further investigation and to avoid the appearance of plagiarism.
Since you have the required materials (e.g.,
Masterpiece)
, abridge any related citations (Nichols, p. 12) and do not list the required source in a References’ section.
Secondary sources must follow current APA guidelines for citations and References.
Make every effort to prove that you care about the subject matter by proofreading to eliminate grammar and spelling distractions.
A substantive thread (at least 450 words)
.
MBA6231 - 1.1 - project charter.docxProject Charter Pr.docxwkyra78
MBA6231 - 1.1 - project charter.docx
Project Charter
Project Charter
Student Name
Institution
Course Code
Project Title: Michael Joseph Place, The place to be
Project Start Date: 25/7/2018
Projected Finish Date: 25/12/2018
Budget Information: $ 4,500.00
Project Manager: Student name,[email protected], 210- 105 - 6676
Business Need
The project manager will be hosting an evening lounge event that will be targeting the clientele to an upscale lounge to be built in downtown. Through such an event the city will have a positive exposure.
There will be need for effective marketing, music, modern décor and most likely investors. The menu for food and drinks will need to be within budget. The venue needs to have amiable space and adequate seats for all guests.
The first step to this project involves coming up with a plan on a piece of paper. Once this is done the next step will involve selection of vendors to various goods and services. Once everything has been put to perspective the next stage will be to involve investors who will include local business owners. These investors will be encouraged to do so with the exchange for them to market and advertise their products at the event. We will have three packages for investors including Silver, Gold and Platinum packages.
Project Objectives
The proposal is to have a social entertainment evening lounge in Chicago. The project managers will be showcasing the new concept of entertainment by holding a series of events known as “The Place to be!”
· The events will be used to showcase the atmosphere that the new lounge will be offering
· The events will offer the professional audiences an opportunity to network while at the same time being entertained.
· The events will be targeting an audience of 150 attendants
· To have an environment where attendants can dance, dine and drink socially while discussing business.
Approach
This project will be managed in accordance with the PMI approach as modified.
Assumptions/Constraints/Dependencies
The assumption is that with the provision of an exquisite and upscale venue that is mature in Chicago, IL, will be successful due to the fact that there is no such a venue within a 100 mile radius.
One of the likely constraint is finding a venue that grabs attention of the targeted crowd.
The success of these events depends on attracting two sets of individuals. One of them is investors and the other is private professionals who will attend a social event at night.
Initial Risk Factors
· Obtaining a liquor license on time for the event is the major risk factor.
· Failure of attendees despite investing money and time is another risk.
· Failing to complete the organizational plans within 30 days before the event series begin.
· Not attracting any viable investors
Regulatory cost/impact
One of the needed licensing is from the city council where I will be required to get a special event license. This will enable us to have alcohol i.
Medication Errors Led to Disastrous Outcomes1. Search th.docxwkyra78
Medication Errors Led to Disastrous Outcomes
1. Search the internet and learn about the cases of nurses Julie Thao and Kimberly Hiatt.
2. List and discuss lessons that you and all healthcare professionals can learn from these two cases.
3. Describe how the principle of beneficence and the virtue of benevolence could be applied to these cases. Do you think the hospital administrators handled the situations legally and ethically?
4. In addition to benevolence, which other virtues exhibited by their colleagues might have helped Thao and Hiatt?
5. Discuss personal virtues that might be helpful to second victims themselves to navigate the grieving process.
.
Meet, call, Skype or Zoom with a retired athlete and interview himh.docxwkyra78
Meet, call, Skype or Zoom with a retired athlete and interview him/her about his or her transition experiences.
Please use this
interview guide
Actions
when conducting your interview.
Submit a minimum 400 word written reflection with the following:
Brief summary of the athlete's sport career transition
Main takeaways from the conversation
Advice you received and what you learned
Connection to course material
.
Medication Administration Make a list of the most common med.docxwkyra78
Medication Administration
Make a list of the most common medication administration errors and suggest steps that can be taken to prevent these errors.
APA format is required for this written assignment. This is a safe assign homework, no more that 20% of similarities permitted.
.
media portfolio”about chapter 1 to 15 from the book Ci.docxwkyra78
“media portfolio”
about chapter 1 to 15
from the book
Ciccarelli, S., & White, J. (2017).
Psychology
(5th Edition), Pearson.
which can include
newspaper,
magazine clippings
, and other media
that illustrate
psychological concepts covered in this course.
o
It is encouraged to be creative as possible and consider a wide variety of
sources which include: newspapers, magazines, editorials, advice and
medical columns, cartoons, etc. The sky is the l
imit!
o
A minimum of 15 clippings
should be included and should cover each
chapter
in the text book
(Chapters 1 through 15).
o
Each clipping should be explained by providing the source and how it is
related to a particular psychological concept, theory, or research finding
from the text or class lectures.
o
Sources should be in APA format!
Each “media clipping” should be on letter sized (8 ½ x 11) sized paper,
Paper can colored, etc...be creative!
.
Mediation
Name
AMU
Date
Mediation
Recently, I had a dispute with a friend based on sharing of roles and duties at work. If I were to use a mediation to solve the conflict I would have used facilitative mediation instead of evaluative mediation. Facilitative mediation refers to the types of solving conflicts where the mediator creates a process to assist the parties in reaching into a mutual agreement. Evaluative mediation on the other hand refers to the type of mediation where the judge helps the parties in reaching into a resolution through using the weakness of the case (Shrout & Bolger, 2017). The nature of the dispute plays a very huge role when choosing the type of mediation style to use. Since some cases can not fit well or makes it hard to find a solution when using a certain mediation style. For instance work related disputes and family related disputes require mediation that won’t seem to favor one party.
I would use transformative mediation, since it is mostly bases on improving the personal power of each party (Folberg & Taylor, 2016). Also transformative mediation mainly helps in creating a sense of understanding between the two parties through communication so as to solve the dispute. And lastly the reason why I would use the mediation is because; the process that is used does not favor one party. During the process, the mediator listens to both parties and from this he or she is able to help in making the two understand each other and be able to come into a mutual agreement.
References
Folberg, J., & Taylor, A. (2016). Mediation: A comprehensive guide to resolving conflicts without litigation.
Preacher, K. J., & Hayes, A. F. (2014). SPSS and SAS procedures for estimating indirect effects in simple mediation models. Behavior research methods, instruments, & computers, 36(4), 717-731.
Shrout, P. E., & Bolger, N. (2017). Mediation in experimental and nonexperimental studies: new procedures and recommendations. Psychological methods, 7(4), 422.
.
Media coverage influences the publics perception of the crimina.docxwkyra78
Media coverage influences the public's perception of the criminal justice system and the policy agendas of those within the system. This often results in changes within the operational structure of the police, courts, and corrections centers. These changes include the firing of employees, the initiation of internal investigations, and the privatization of services. Respond to the following questions, and support your positions using credible research:
Assignment Guidelines
Address the following in 1,250–1,750 words:
How is the criminal justice system portrayed in the media? Explain.
What impact do the media have on a viewer's perception as to the system's efficacy in dealing with crime? Explain.
Does coverage of sensationalistic and violent crime create fear among the general public? Explain.
Does this fear influence criminal justice policy attitudes? Explain in detail.
Is there a correlation between gender, education, income, age, and perceived neighborhood problems and police effectiveness in dealing with crime? Explain in detail.
In this assignment, external research is essential to successful submission. You must utilize at least 5–7 academic or scholarly external resources to support your arguments.
Be sure to reference all of your sources using APA style.
.
Media Content AnalysisPurpose Evaluate the quality and value of.docxwkyra78
Media Content Analysis
Purpose: Evaluate the quality and value of claims made and information presented by various authors.
Task: Write an essay in which you critically analyze at least 3 published commentaries/presentations related to an issue connected to social media. For each commentary/presentation, your analysis must include an evaluation of the evidence and reasoning presented as well as an examination of the value the commentary/presentation has for its intended audience and others. Compare and contrast various authors’ claims and perspectives.
Points: 200 (160 points from rubric-based assessment; 40 points for submitting a Reviewed Draft*).
Requirements:
Review a minimum of three substantive articles, videos, or presentations that have been published in major print or multimedia sources (e.g., a magazine article; a blog; a YouTube video),
Provide a brief, meaningful summary of each of the published presentations.
Analyze the quality of the claim, evidence, and reasoning in each presentation, with a focus on the validity and value of the presentations.
Use APA format – including in-text parenthetical citations along with a reference list at the end of the assignment.
Answer the following questions in your analysis:
What are the purpose, claims, evidence, and reasoning of each presentation?
What are the qualifications and authority of each author?
In what ways do the authors reflect bias? How do the authors account for their bias?
Are there any significant statements or omissions that might affect the reliability of the information or arguments presented?
Presentation Format:
1000 - 2,000 words
12 point, Times New Roman or Arial Font
Double-Spaced
APA format for body and References page
Follow the paragraph format below to be sure that you have covered all the requirements for the topic you have chosen:
Paragraph #1 1st article title, author and their qualifications along with a summary of it. 20 points
Paragraph #2 2nd article title/presentation, author and their qualifications along with a summary of it 20 points
Paragraph #3 3rd article title/presentation, author and their qualifications and of course a summary of it. 20 points
Paragraph #4 compare and contrast the purpose and the claims of each of the three authors 20 points
Paragraph #5 compare and contrast the evidence shown and the reasoning of each author/presentation 30 points
Paragraph #6 in what ways do the author's reflect bias/fallacies and how do they account for them? 20 points
Paragraph #7 Are there any significant statements or omissions that might affect the reliability of the
information or arguments presented? Which one drew your attention and why? 20 points
APA References alphabetized, double spaced and indented on t.
Mayan gods and goddesses are very much a part of this text. Their i.docxwkyra78
Mayan gods and goddesses are very much a part of this text. Their interactions with one another and later with humans form a major part of our reading. How are the gods and goddesses portrayed in this text? How are those portrayals similar to or different from other representations of gods we have encountered?
.
Media and SocietyIn 1,100 words, complete the followingAn.docxwkyra78
Media and Society
In 1,100 words, complete the following:
Analyze two ways that media affect culture and society. Identify at least one positive and one negative implication arising from technology’s effect on society.
Media has changed exponentially over the past 25 years with the introduction of the Internet and social media. How can people enhance their media literacy? Identify one to two challenges that media will introduce for society in the next 20-30 years and how people can use their media literacy to meet these challenges.
Prepare this assignment according to the guidelines found in the APA Style Guide, located in the Student Success Center. An abstract is not required.
This assignment uses a rubric. Please review the rubric prior to beginning the assignment to become familiar with the expectations for successful completion.
You are required to submit this assignment to LopesWrite. Refer to the
LopesWrite Technical Support articles
for assistance.
FOLLOW THE RUBRIC- CHECK YOUR FINAL PAPER WITH THE ATTACHED RUBRIC!
.
MBA 5110 – Business Organization and ManagementMidterm ExamAns.docxwkyra78
MBA 5110 – Business Organization and Management
Midterm Exam
Answer each of the following questions in this document, inserting your answers between each question. You may use your textbook and notes, but you may not consult with another individual. You may not use the Internet for assistance in answering these questions. Each question should be answered with a minimum of one paragraph, properly formatted according to APA 6th edition guidelines and referencing your textbook. Please list your textbook in a reference section at the end of this document. Submit this Word document with your answers to Moodle.
1. How have organizational structures and management styles changed over the past century?
2. Explain the concept of open and closed systems and how this relates to organization theory.
3. Define each of Porter’s Competitive Strategies and give an example of a company using each of these strategies.
4. Compare vertical and horizontal organizational structures in terms of effectiveness and adaptability in the rapidly changing business environment.
5. Choose one of the following theories and explain the theory. Give an example of a company that demonstrates the chosen theory and how the company uses the theory.
Theories: Chaos Theory, Resource-Dependence Theory, Population-Ecology Perspective, Contingency Theory, or Organizational Learning Theory
Response 1 PD
Question 1
A set of beliefs, norms and values that is shared by a group, culture is a systemic sense that can create a common commitment to an organization’s mission. With identifying markers that extend beyond the individual, it can be represented in a fabric of shared themes and feelings. Whether displayed in forms of dress, symbols, verbal phrases or typical behaviors, its permeance can be silent in its mode of action, yet quite visible to internal and external stakeholders (Daft, 2018).
Serving two fundamental and critical functions, the culture of an organization can be a catalyst in uniting members in how they relate to one another within the organization and how the members follow the same process in relation to the outside environment (Daft, 2018). However, although it is often associated with ethical decision making (Kara, Rojas-Mendez & Turan), the element of inequality can create fear and discourse if an unrealistic and bias culture themes are dictated, thus resulting in disagreement or conflict with management. Therefore, the perception of stakeholders or groups of interest regarding the cultural practices of the organization may not be entirely correct (Gonzalez-Rodriguez, Diaz-Fernández & Biagio, 2019).
Directly related to the perception of the value system of the organization and its management, the acceptable cultural differences that shape the internal behavior of members can have an impact in external relationships (Gonzalez-Rodriguez, Diaz-Fernández & Biagio, 2019). However, as Daft (2018) noted, a mechanistic or controlling system may block any organic input,.
हिंदी वर्णमाला पीपीटी, hindi alphabet PPT presentation, hindi varnamala PPT, Hindi Varnamala pdf, हिंदी स्वर, हिंदी व्यंजन, sikhiye hindi varnmala, dr. mulla adam ali, hindi language and literature, hindi alphabet with drawing, hindi alphabet pdf, hindi varnamala for childrens, hindi language, hindi varnamala practice for kids, https://www.drmullaadamali.com
How to Fix the Import Error in the Odoo 17Celine George
An import error occurs when a program fails to import a module or library, disrupting its execution. In languages like Python, this issue arises when the specified module cannot be found or accessed, hindering the program's functionality. Resolving import errors is crucial for maintaining smooth software operation and uninterrupted development processes.
Leveraging Generative AI to Drive Nonprofit InnovationTechSoup
In this webinar, participants learned how to utilize Generative AI to streamline operations and elevate member engagement. Amazon Web Service experts provided a customer specific use cases and dived into low/no-code tools that are quick and easy to deploy through Amazon Web Service (AWS.)
Reimagining Your Library Space: How to Increase the Vibes in Your Library No ...Diana Rendina
Librarians are leading the way in creating future-ready citizens – now we need to update our spaces to match. In this session, attendees will get inspiration for transforming their library spaces. You’ll learn how to survey students and patrons, create a focus group, and use design thinking to brainstorm ideas for your space. We’ll discuss budget friendly ways to change your space as well as how to find funding. No matter where you’re at, you’ll find ideas for reimagining your space in this session.
This document provides an overview of wound healing, its functions, stages, mechanisms, factors affecting it, and complications.
A wound is a break in the integrity of the skin or tissues, which may be associated with disruption of the structure and function.
Healing is the body’s response to injury in an attempt to restore normal structure and functions.
Healing can occur in two ways: Regeneration and Repair
There are 4 phases of wound healing: hemostasis, inflammation, proliferation, and remodeling. This document also describes the mechanism of wound healing. Factors that affect healing include infection, uncontrolled diabetes, poor nutrition, age, anemia, the presence of foreign bodies, etc.
Complications of wound healing like infection, hyperpigmentation of scar, contractures, and keloid formation.
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...PECB
Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
Certified as an ISO/IEC 27001: Information Security Management Systems (ISMS) Lead Implementer, Data Protection Officer, and Cyber Risks Analyst, Denis brings a heightened focus on data security, privacy, and cyber resilience to every endeavor.
His expertise extends across a diverse spectrum of reporting, database, and web development applications, underpinned by an exceptional grasp of data storage and virtualization technologies. His proficiency in application testing, database administration, and data cleansing ensures seamless execution of complex projects.
What sets Denis apart is his comprehensive understanding of Business and Systems Analysis technologies, honed through involvement in all phases of the Software Development Lifecycle (SDLC). From meticulous requirements gathering to precise analysis, innovative design, rigorous development, thorough testing, and successful implementation, he has consistently delivered exceptional results.
Throughout his career, he has taken on multifaceted roles, from leading technical project management teams to owning solutions that drive operational excellence. His conscientious and proactive approach is unwavering, whether he is working independently or collaboratively within a team. His ability to connect with colleagues on a personal level underscores his commitment to fostering a harmonious and productive workplace environment.
Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
-------------------------------------------------------------------------------
Find out more about ISO training and certification services
Training: ISO/IEC 27001 Information Security Management System - EN | PECB
ISO/IEC 42001 Artificial Intelligence Management System - EN | PECB
General Data Protection Regulation (GDPR) - Training Courses - EN | PECB
Webinars: https://pecb.com/webinars
Article: https://pecb.com/article
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For more information about PECB:
Website: https://pecb.com/
LinkedIn: https://www.linkedin.com/company/pecb/
Facebook: https://www.facebook.com/PECBInternational/
Slideshare: http://www.slideshare.net/PECBCERTIFICATION
This presentation was provided by Steph Pollock of The American Psychological Association’s Journals Program, and Damita Snow, of The American Society of Civil Engineers (ASCE), for the initial session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session One: 'Setting Expectations: a DEIA Primer,' was held June 6, 2024.
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UPRAHUL
This Dissertation explores the particular circumstances of Mirzapur, a region located in the
core of India. Mirzapur, with its varied terrains and abundant biodiversity, offers an optimal
environment for investigating the changes in vegetation cover dynamics. Our study utilizes
advanced technologies such as GIS (Geographic Information Systems) and Remote sensing to
analyze the transformations that have taken place over the course of a decade.
The complex relationship between human activities and the environment has been the focus
of extensive research and worry. As the global community grapples with swift urbanization,
population expansion, and economic progress, the effects on natural ecosystems are becoming
more evident. A crucial element of this impact is the alteration of vegetation cover, which plays a
significant role in maintaining the ecological equilibrium of our planet.Land serves as the foundation for all human activities and provides the necessary materials for
these activities. As the most crucial natural resource, its utilization by humans results in different
'Land uses,' which are determined by both human activities and the physical characteristics of the
land.
The utilization of land is impacted by human needs and environmental factors. In countries
like India, rapid population growth and the emphasis on extensive resource exploitation can lead
to significant land degradation, adversely affecting the region's land cover.
Therefore, human intervention has significantly influenced land use patterns over many
centuries, evolving its structure over time and space. In the present era, these changes have
accelerated due to factors such as agriculture and urbanization. Information regarding land use and
cover is essential for various planning and management tasks related to the Earth's surface,
providing crucial environmental data for scientific, resource management, policy purposes, and
diverse human activities.
Accurate understanding of land use and cover is imperative for the development planning
of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
these patterns indicate shifts in economic and social conditions. Monitoring such changes with the
help of Advanced technologies like Remote Sensing and Geographic Information Systems is
crucial for coordinated efforts across different administrative levels. Advanced technologies like
Remote Sensing and Geographic Information Systems
9
Changes in vegetation cover refer to variations in the distribution, composition, and overall
structure of plant communities across different temporal and spatial scales. These changes can
occur natural.
Strategies for Effective Upskilling is a presentation by Chinwendu Peace in a Your Skill Boost Masterclass organisation by the Excellence Foundation for South Sudan on 08th and 09th June 2024 from 1 PM to 3 PM on each day.
How to Add Chatter in the odoo 17 ERP ModuleCeline George
In Odoo, the chatter is like a chat tool that helps you work together on records. You can leave notes and track things, making it easier to talk with your team and partners. Inside chatter, all communication history, activity, and changes will be displayed.
বাংলাদেশের অর্থনৈতিক সমীক্ষা ২০২৪ [Bangladesh Economic Review 2024 Bangla.pdf] কম্পিউটার , ট্যাব ও স্মার্ট ফোন ভার্সন সহ সম্পূর্ণ বাংলা ই-বুক বা pdf বই " সুচিপত্র ...বুকমার্ক মেনু 🔖 ও হাইপার লিংক মেনু 📝👆 যুক্ত ..
আমাদের সবার জন্য খুব খুব গুরুত্বপূর্ণ একটি বই ..বিসিএস, ব্যাংক, ইউনিভার্সিটি ভর্তি ও যে কোন প্রতিযোগিতা মূলক পরীক্ষার জন্য এর খুব ইম্পরট্যান্ট একটি বিষয় ...তাছাড়া বাংলাদেশের সাম্প্রতিক যে কোন ডাটা বা তথ্য এই বইতে পাবেন ...
তাই একজন নাগরিক হিসাবে এই তথ্য গুলো আপনার জানা প্রয়োজন ...।
বিসিএস ও ব্যাংক এর লিখিত পরীক্ষা ...+এছাড়া মাধ্যমিক ও উচ্চমাধ্যমিকের স্টুডেন্টদের জন্য অনেক কাজে আসবে ...
How to Manage Your Lost Opportunities in Odoo 17 CRMCeline George
Odoo 17 CRM allows us to track why we lose sales opportunities with "Lost Reasons." This helps analyze our sales process and identify areas for improvement. Here's how to configure lost reasons in Odoo 17 CRM
A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.
South African Journal of Science: Writing with integrity workshop (2024)
Problems Identifying Independent and Dependent VariablesKe.docx
1. Problems Identifying Independent and Dependent Variables
Keith R. Leatham
Brigham Young University
This paper discusses one step from the scientific method—that
of identifying independent and dependent variables—
from both scientific and mathematical perspectives. It begins by
analyzing an episode from a middle school mathematics
classroom that illustrates the need for students and teachers
alike to develop a robust understanding of independent and
dependent variables. It then outlines four rationales (two from
science and two from mathematics) for identifying
independent and dependent variables. Finally, it reports the
results of a textbook analysis that used these rationales to
examine the extent to which typical mathematics textbook
problems support or supplant a sensible view of independent
and dependent variables. The findings indicate that often,
mathematics textbook problems misrepresent the sense-
making aspect of identifying independent and dependent
variables, possibly setting students up to develop misconcep-
tions about this step from the scientific method.
Problems Identifying Independent and
Dependent Variables
The scientific method has had great influence over
science textbooks over the past century (Blachowicz,
2009). Although there is debate about the degree to which
this influence has been positive (Bauer, 1994; Nola &
Sankey, 2007), most scientists agree that viewing the sci-
entific method as a “recipe for doing science” is unhealthy
2. and counterproductive. Instead, the scientific community
desires that students, scientists, and the general populace
see the work of a scientist as that of exploring and trying
to understand the world around us. Their basic argument is
that “doing science” is exploratory, nonlinear, and cre-
ative. The scientific method should help one to make sense
of scientific work, not remove the need to make sense of
things (Bauer, 1994; Kuhn, 1970; McComas, 1996).
Trying to distill this work into a linear, decontextualized
set of steps trivializes and misrepresents the actual work.
Similar arguments have been made with regard to other
subjects such as mathematics (Hiebert et al., 1997), statis-
tics (Tukey, 1977), and music (Elliott, 1994). In each case,
the argument is that disciplines are made of more than
mere procedures; there are important underlying concepts
and ideas that give meaning to procedures and their
application.
In this paper, I discuss one step from the scientific
method—that of identifying independent and dependent
variables—from both scientific and mathematical perspec-
tives, scientific rationales because of the grounding of the
topic to the scientific method, and mathematical rationales
because of the preponderance of such problems in math-
ematics textbooks. In doing so, I highlight ways procedur-
alized application of these rationales can easily supplant
the underlying conceptual ideas to which they are related.
I also discuss the danger in removing the disciplinary
focus (in this case, mathematical or scientific) when learn-
ing to identify and classify variables. I begin by discussing
an episode from a middle school mathematics classroom
that illustrates the need for teachers and students alike to
develop a robust understanding of independent and depen-
dent variables. I then share four rationales (two from
science and two from mathematics) for identifying inde-
3. pendent and dependent variables. Finally, I report the
results of a mathematics textbook analysis that used these
rationales to examine the extent to which typical math-
ematics textbook problems support or supplant a sensible
view of independent and dependent variables.
A Classroom Example
Before we discuss in some detail various scientific and
mathematical issues related to determining independent
and dependent variables, consider an episode from a
middle school pre-algebra classroom that illustrates how
these issues can collide.1 The teacher, Ms. Christina2 (a
student teacher in this classroom), was launching a lesson
wherein students were going to input equations into a
calculator and look at the tabular outputs to make deci-
sions about the situations modeled by those equations. In
anticipation of this approach, Ms. Christina asked the stu-
dents to identify the independent and dependent variables
in the equations A = pr2 and C = 2pr.
Now, before proceeding with the episode, consider the
nature of these algebraic “situations.” These equations rep-
resent generalized mathematical relationships, although
not completely generalized, as it is clear in these equations
that the variables stand for particular, contextualized quan-
tities (as opposed to mere abstract quantities). Ms. Chris-
tina’s question indicates that students should be able to
School Science and Mathematics 349
determine the independent and dependent variables here,
possibly by looking at the form of the equations or maybe
by considering the contexts the equations represent.
4. As the lesson proceeded, it quickly became clear that
Ms. Christina wanted to hear that r was the independent
variable and that A and C were the dependent variables in
their respective equations. After a student had shared his
response that r was the independent variable and A was the
dependent variable in the former equation, Morgan said
that she thought C was the independent variable and r was
the dependent variable in the latter equation. Because this
response was not what Ms. Christina expected, she asked
Morgan to explain her reasoning, in hopes that in so doing,
the “correct” answer would be revealed. We join the lesson
at this point:
Morgan: I did the circumference because the
radius depends on how big or small
the circle is. So I said the circumfer-
ence is independent and the radius is
dependent on the circumference.
Ms. Christina: Okay. Thanks Morgan. Who has the
same thing as Morgan? Who has
something different? Who doesn’t
know? [pause] Who said they have
something different? . . . Kathryn, do
you? Do you want to explain?
Kathryn: I just said the independent would be
the radius and the dependent would be
the circumference.
Ms. Christina: Okay, why?
Kathryn: Because . . . the circumference is
the—. Wait, no, I agree with her
[Morgan].
5. Ms. Christina: Are you sure? You were going good
there. Do you want to keep explaining
what you were saying?
Kathryn: I was going to say that the circumfer-
ence would change if the circle gets
smaller. But um, you can find the
circumference without the radius, I
think.
Ms. Christina: You can find the circumference
without the radius? How would you
do that?
Kathryn: Um. I don’t know.
.
.
.
Ms. Christina: Brian, what do you think?
Brian: Couldn’t kind of both of them go both
ways? Because like in area, like as the
area gets smaller so does the—. Oh,
never mind.
At this point in the episode, there is a fairly long pause as
Ms. Christina considers where to go next. She asks Abe,
who has not participated thus far, what he thinks and he
indicates that he does not really know what is going
on. Ms. Christina takes this opportunity to explain,
with input from the class, the definitions of circumfer-
ence and radius. Ms. Christina then continues her line of
reasoning:
Ms. Christina: So we’ve got this radius and we are
6. saying, “What happens as we change
this radius? What does it do to our
circumference?”
Abe: It gets smaller?
Ms. Christina: It gets smaller. So do you see how that,
how it depends on it? And so do you
see why we would switch those?
[Meaning switch Morgan’s responses
around, so r is independent rather than
C] Morgan, does that kind of make
sense?
Morgan: Yeah.
Ms. Christina: Okay, how does that look? [r is now
labeled as the independent variable in
both situations.] Are we okay? Who
agrees with me? I’m getting two
thumbs up from Madison. Who dis-
agrees? Kathryn, do you? Okay. It’s
okay if you do. It’s okay to disagree
with the teacher.
With no further disagreements from the class, Ms. Chris-
tina attempts to move ahead with the lesson. She notices,
however, that Kathryn is still puzzled and is wrestling with
whether she should raise her hand.
Ms. Christina: Kathryn, do you have—?
Kathryn: I have a question about that. In
elementary school we measured a
circle with some string. And so, if you
didn’t have the radius, couldn’t you
7. also measure the circumference
without the radius?
Ms. Christina: With using that string?
Kathryn: Yes.
Identifying Independent and Dependent Variables
350 Volume 112 (6)
Ms. Christina: Good job. Yeah, you can. We can do it
different ways. Maybe we will do that
sometime. We will be able to figure
that out. But yeah, you are right. There
are different ways that, maybe if you
don’t have the—
Kathryn: Why is the radius the independent?
In this classroom excerpt, Ms. Christina and her stu-
dents seem to be engaged in different, although related,
activities. Ms. Christina is operating under the assumption
that the form of an equation reveals the independent and
dependent variables. The students, on the other hand, seem
to be operating under a different assumption. Their focus
is on whether it is possible to find or control one variable
without needing to know the other. If they can control one
variable without knowing the other, then that variable is
independent. This assumption becomes problematic in this
situation, however, when reasonable arguments are put
forth for being able to determine either variable without
first knowing the other.3
Identifying Independent and Dependent Variables
8. In this section, I discuss various rationales (such as
those used in the preceding classroom episode) one might
use in identifying independent and dependent variables. I
describe and contrast scientific and mathematical ration-
ales. A review of the literature revealed no treatises to date
on such rationales, nor on students’ understanding of inde-
pendent and dependent variables. Thus, these rationales
are derived from a conceptual analysis of independent and
dependent variables and the ways they are commonly used
in science and mathematics. Therefore, I present a frame-
work of rationales that proved useful in the textbook
problem analysis that follows and that can be tested, devel-
oped, and refined through applying it in future research.
Scientific Rationales
When conducting formal experiments, scientists often
seek to identify the variables involved in a phenomenon.
They also seek to identify the effect of these variables on
each other. Such work entails isolating, controlling for,
and measuring varying quantities in order to posit relation-
ships among them. For example, a study of crickets might
lead one to wonder at the variation in their chirp frequen-
cies. The wondering might lead to initial data collection
and exploration in various contexts. Eventually, one might
hypothesize that chirp frequencies are related to the time
of day, the time of year, the ambient temperature, or maybe
the size or age of the cricket. Eventually, the following
conjecture might be made: Cricket chirp frequency is
related to ambient temperature. An experiment could then
be designed wherein one places crickets in environments
of varying temperature and records their chirp frequency.
Other variables such as age, sex, or time of day or of year
could also be held constant or controlled in order to ascer-
tain their possible relation to chirp frequency. In this
9. example, there are three types of variables—independent,
dependent, and constant. The constant variables are the
ones we hold constant (e.g., age, sex, time of day); the
independent variable is the one over which we have control
and which we choose to vary (in this case, ambient tem-
perature); the dependent variable (in this case, chirp fre-
quency) is the one over which we do not have direct
control and whose variance we seek to measure as we
change the independent variable.
When viewed in the context of an experiment, the
process of identifying the independent and dependent vari-
ables in a situation involves considering the context and
the purpose of the experiment. It also involves considering
what you can or do control. Identifying independent and
dependent variables in a situation void of experimental
context or causation means very little. A robust under-
standing of independent and dependent variables from the
scientific standpoint recognizes it is up to the individual
who is exploring a relationship between variables to
choose (not so much determine) the independent and
dependent variables. Although context (including issues of
causality and control) certainly helps one to make this
decision and also helps one to determine just how reason-
able that decision is, in many situations, context is insuf-
ficient; purpose is preeminent.4 The upshot of this
requirement for understanding and decision making is that
it makes little sense and is actually misleading from a
scientific standpoint to ask someone to identify the inde-
pendent and dependent variable in a decontextualized situ-
ation, as the answer is almost always, “It depends on what
your are doing and the questions you are asking.”
Mathematical Rationales
One significant purpose of mathematics is to describe,
generalize, and abstract relationships between varying
10. quantities. At its most fundamental level, mathematics
seeks to describe relationships. Theorems, formulas, and
algorithms all have at their core the desire to describe what
always happens under given circumstances. The more this
description can be abstracted from the context and
described in terms of the underlying mathematical struc-
tures and relationships, the better.
In mathematics, we have many different ways of repre-
senting relationships between variables. For example (the
rule of four): verbal, symbolic, graphic, numeric. There
Identifying Independent and Dependent Variables
School Science and Mathematics 351
are certain meanings or conventions associated with each
of these representations. In the symbolic representation, y
= 2x + 1 can be read as the equation of a line where x is the
independent variable and y is the dependent variable. We
do this by convention, however, as the equation y = 2x + 1
actually only defines a relationship between x and y. There
are at least two conventions at play when we assume that x
is the independent variable here: (1) In general, we use the
variable x to be the independent and y to be the dependent.
The choice of letter actually carries meaning; and (2) the
equation is “solved for y,” meaning, y is isolated from the
x and constant terms. A (somewhat implicit) convention is
that when we have equations solved in this manner, we
intend people to read the equation like this: Given an x
value, what is y? In other words, the form of the equation
somehow tells us which variable is independent and which
is dependent.
11. However, mathematics generally eschews these conven-
tions. There is nothing sacred about x—any placeholder
will do. And one reason for introducing function and func-
tion notation is because y = 2x + 1 does not provide
sufficient information to determine the independent and
dependent variables. One could as easily write this rela-
tionship as p = 2k + 1 or x y= −( )
1
2
1 (okay, perhaps not as
easily in the latter case, but certainly as valid). When we
write the equation as f (x) = 2x + 1, however, the notation
itself defines the independent and dependent variables.
Our decision to write the relationship as a function has
indicated our choice of independent and dependent
variables.
A robust understanding of independent and dependent
variables in mathematics includes an understanding of the
difference between a relation and a function. A relation
carries no meaning when it comes to identifying indepen-
dent and dependent variables; it simply communicates a
relationship between variables. A function, on the other
hand, carries all the meaning when it comes to identifying
independent and dependent variables; by definition, in y =
f (x), y is the dependent variable and x is independent. In
addition, certain mathematical conventions for given rep-
resentations (whether advocated or not by the mathemati-
cal community) often complicate matters. Thus, a robust
understanding of independent and dependent variables in
mathematics includes an understanding of the affor-
dances and constraints of such conventions for various
representations.5
12. Comparing Scientific and Mathematical Rationales
Thus far, I have argued that the primary rationales for
identifying independent and dependent variables in science
and in mathematics differ. In science, the main rationales
are control and causation; in mathematics, the main ration-
ales are convention and function (Table 1). In mathematical
and scientific contexts, both logic and choice play a role in
applying these rationales. For example, consider again our
previous example of the experiment involving number of
cricket6 chirps per minute (N) and temperature in degree
Fahrenheit (T). According to Dolbear (1897), there is
indeed a relationship between these two variables, which
can be written as follows: N = 4 (T - 50) + 40. And this
relationship is a causal one—the temperature influences or
causes the change in number of cricket chirps per minute.
So changes in T cause changes in N.
So how does one determine the independent and depen-
dent variables in this situation? From a “control” stand-
point, the only thing you have control over is the
temperature—you can alter the temperature and measure
the number of chirps per minute. The alternative experi-
ment is ludicrous. In addition, although one could cer-
tainly attempt to change (i.e., control) the number of
chirps per minute by some means other than temperature
(biologically, socially, medicinally), we certainly do not
expect such changes to influence the ambient temperature,
or even the temperature of the cricket. There is no reason
to believe that N causes T, regardless of whether one could
control N. Thus, when considering the scientific rationales
of control and causation, it is reasonable and defendable
to define T as the independent variable and N as the
dependent.
13. This situation looks somewhat different, however, when
viewed with the mathematical rationales, for there is
clearly a relationship between T and N. It is certainly a
meaningful question to ask, “Given this number of chirps
per minute, what is the approximate temperature?”
In actuality, that was Dolbear’s (1897) point in presenting
his findings: “The rate of chirp seems to be entirely
Table 1
Descriptions of Scientific and Mathematical Rationales for
Determining Inde-
pendent and Dependent Variables
Rationale Description
Scientific
control
Whether one has the ability to directly control
the values of a given variable.
Causation Whether variation in the values of a given
variable cause changes in another variable.
Mathematical
convention
Whether there are conventional notations or
practices that communicate which variable
should be thought of as independent.
Function Whether the mathematical relation at hand is
defined more specifically as a function.
Identifying Independent and Dependent Variables
14. 352 Volume 112 (6)
determined by the temperature and this to such a degree
that one may easily compute the temperature when the
number of chirps per minute is known” (p. 971). In fact,
Dolbear’s original formula is not solved for N as earlier,
but rather for T: T N= + −( )50 1
4
40 . One particularly
valuable result of this experiment is that one can think of
the dependent variable from the experiment (N) as the
independent variable. (In other words, Dolbear found a
relationship between variables.) Once that relationship is
represented in symbolic form, either variable can be
chosen as the dependent variable, so appealing to the func-
tion rationale does not determine dependence. By contrast,
by convention (solving for T), which Dolbear used more
than 100 years ago, the intention of the formula is for N to
be independent and T to be dependent. This example thus
illustrates how the scientific and mathematical rationales
can lead to quite different determinations.7
Textbook Analysis
Analysis of the classroom episode presented earlier left
me wondering how one “should” identify the independent
and dependent variables in a given situation. My answer to
that question is the conceptual descriptions for scientific
and mathematical rationales just outlined (and summa-
rized in Table 1). It might be tempting for the reader to
15. assume that the primary cause of the independent/
dependent variable dilemma discussed in the episode was
the inexperience and somewhat misguided mathematical
conception of the student teacher (i.e., unquestioned reli-
ance on mathematical convention). I had similar thoughts
as I analyzed the situation. But the student teacher’s under-
standing of independent and dependent variables origi-
nated somewhere, likely in her own middle school
mathematics experiences, and mathematics textbooks both
reflect and influence the nature of classroom mathematics.
Because of this important relationship, many researchers
have used textbook analyses as one lens to explore the
mathematics students are learning (e.g., da Ponte &
Marques, 2007; Son, 2005; Vincent & Stacey, 2008; Zhu
& Fan, 2006). How do mathematics textbooks address the
identification of independent and dependent variables? In
particular, what is the nature of textbook problems asso-
ciated with this identification? I conclude this paper with
the results of a small textbook analysis study designed to
begin to answer this latter question.
Analysis began with an ad hoc review of textbooks from
publishers with multiple mathematics textbook series
(Glencoe McGraw-Hill and McDougal Littell) in order to
get a sense of where in curricula series the concept of
independent and dependent variables seemed to be placed.8
We discovered it tended to be discussed in Algebra I texts,
but was sometimes located in pre-algebra texts, and some-
times in Algebra II and precalculus texts. With this infor-
mation in mind, we then scoured our curriculum library for
the latest edition of every Algebra I (or roughly equivalent)
textbook we could find, as well as a sampling of the other
textbooks just mentioned. Our intent was to locate a sub-
stantial number of problems associated with independent
16. and dependent variables so as to analyze their nature, not to
analyze the textbooks per se. As such, the textbooks were
purposefully selected in an attempt to create a collection of
typical problems. In the end, our sample consisted of a
collection of 23 textbooks (Table 2). We then reviewed each
text looking for any discussion of variables and, in particu-
lar, independent and dependent variables. We scanned each
chapter and analyzed the table of contents and index. We
sought to identify every instance where the textbook asked
students to identify independent and dependent variable.
Our search of 23 textbooks yielded a total of 73 problems
from 10 of these texts (Table 2). Thus, a number of these
textbooks contained no problems related to identifying
independent and dependent variables.9
We then analyzed each of these 73 problems according
to the scientific and mathematical rationales described pre-
viously (Table 1). For each rationale, we answered yes or
no to the question of whether one could reasonably deter-
mine the independent and dependent variables by appeal-
ing to that rationale. As an example of how this analysis
played out, consider the problem from the classroom
episode previously discussed. In a textbook, the problem
would be stated as follows:
Identify the independent and dependent variables: C =
2pr
We now consider each rationale:
1. Control: No—One can control either r or C (as so
eloquently argued by Kathryn in the classroom episode).
2. Causation: No—Varying either variable causes the
other to change.
3. Convention: Yes—The representation is symbolic
17. and solved for C, so one could appeal to convention to
argue that C is the dependent variable.
4. Function: No—The equation is presented as a rela-
tion, but not as a function.
Each problem can thus receive yes or no for each of the
four rationales, yielding a total of 16 permutations or
“types” of problems, as determined by they type of ratio-
nale one might use in order to solve the problem (Table 3).
The sections that follow consider several of the most inter-
esting subsets of these permutations.
Identifying Independent and Dependent Variables
School Science and Mathematics 353
No Reasonable Rationales
As can be seen in Table 3, almost half of the problems
received “No” in all four categories. This means that for
these 32 problems, the problem statements and situations
were insufficient to determine the independent and depen-
dent variables based on any of the four rationales. Let us
take a closer look at several NNNN problems. For
example, consider the following problem:
(A) Name the two variables involved. Explain which
you would list first and represent on the x-axis. Which
would you list second and represent on the y-axis?
Height and weight of players on a soccer team.
(Answer: [height, weight])
18. According to the textbook, there is a correct answer to
problem A. So, how could students determine that answer?
Table 2
Collection of Textbooks and the Number of “Identify the
Independent and Dependent Variables” Problems in Each
Title Series Textbook Publisher Number of “Identify”
Problems (n = 73)
Algebra I Glencoe/McGraw-Hill 12
Algebra: Concepts and
Applications
Glencoe/McGraw-Hill 2
MathMatters 3 MathMatters: An Integrated Program
Glencoe/McGraw-Hill 0
Contemporary Mathematics
in Context: Course 1
Core-Plus Mathematics Project (CPMP) Glencoe/McGraw-Hill 8
Grade 8 Core-Plus Mathematics Project (CPMP)
Glencoe/McGraw-Hill 0
Algebra I Holt 25
Algebra II Holt 3
Algebra I McDougal Littell 3
Algebra II McDougal Littell 1
Integrated Mathematics 1:
Algebra
McDougal Littell 0
Book 1 Mathematics Thematics McDougal Littell 0
19. Book 2 Mathematics Thematics McDougal Littell 0
Book 3 Mathematics Thematics McDougal Littell 0
Algebra University of Chicago School
Mathematics Project (UCSMP)
McGraw-Hill/Wright Group 0
Pre-Transition Mathematics University of Chicago School
Mathematics Project (UCSMP)
McGraw-Hill/Wright Group 0
Pre-Transition Mathematics University of Chicago School
Mathematics Project (UCSMP)
McGraw-Hill/Wright Group 0
Precalculus: Enhanced with
Graphing Unilities
Pearson 0
Algebra I Center for Mathematics Education
(CME)
Pearson 0
Grade 7 Connected Mathematics Project (CMP) Pearson 8
Grade 8 Connected Mathematics Project (CMP) Pearson 0
Algebra I Prentice Hall 6
Grade 8/7 Saxon Math Saxon Publishers 0
Functions Modeling Change: A
Preparation for Calculus
Wiley 5
20. Table 3
Summary of Categorization of the 73 Problems According to the
16 Possible
Permutations
Control Causation Convention Function Total
(n = 73)
N N N N 32
N N N Y 4
N N Y N 7
N N Y Y 2
N Y N N 11
N Y N Y 0
N Y Y N 5
N Y Y Y 0
Y N N N 3
Y N N Y 1
Y N Y N 0
Y N Y Y 0
Y Y N N 7
Y Y N Y 0
Y Y Y N 0
Y Y Y Y 1
Identifying Independent and Dependent Variables
354 Volume 112 (6)
Again, let us consider the four rationales. First, consider
causation. Although height and weight are likely corre-
lated (remember, these are middle school students answer-
ing this question, and no other data are provided), changes
in an individual’s height do not necessarily cause changes
21. in their weight, nor do changes in their weight cause
changes in their height. It could be argued here, however,
that the one is much more likely than the other. That is, it
makes sense that if you get taller, your weight will
increase; whereas if you gain weight, you may not grow
taller at all. Thus, it is likely that the textbook problem
expected students to use “causation” in order to determine
the solution, although changes in neither variable actually
cause changes in the other.
Considering the control rationale illustrates how confus-
ing such scenarios might be for students. We have no direct
control over our weight or our height. But of these variables,
the only one that is even reasonable to try to control is
weight. Managing to change our weight, however, does not
cause changes in our height. Thus, the one variable we
might try to control does not cause change in the other. The
other variable, height, we have no control over, yet changes
in height are likely to accompany changes in weight.
There are no verbal conventions to appeal to in this
situation, but notice the use of conventions in the state-
ment of the problem. Students are not actually asked to
identify the independent and dependent variables, but
instead are asked to identify which variable they would list
first (in an ordered pair) and place on the x-axis. Thus,
although convention does not help in determining whether
height or weight is the independent variable, an under-
standing of convention is necessary in order to answer the
question as intended. Finally, the situation implies a rela-
tionship between height and weight but not necessarily a
function. None of the four rationales considered here
would be adequate for merely determining the indepen-
dent and dependent variables in this problem (as
requested), but one could certainly justify a sensible
choice were one asked to do so.
22. Next, consider this pair of problems from two different
textbooks:
(B) Identify the independent and dependent variables:
The faster Ron walks, the quicker he gets home.
(C) Name the two variables involved. Explain which
you would list first and represent on the x-axis. Which
would you list second and represent on the y-axis?
Driving speed and time required for a trip.
Both problems B and C are situated in the context of the
relationship between distance, rate, and time, with the
main variables in question being speed and time. Now,
does one of these variables either control or cause the
other? For either rationale, one can reasonably argue either
direction. I can certainly determine my rate based on how
much time I have (I’ve got to get home by my curfew, so
I’ll pick up my pace) or I can determine my time based on
my rate (I’m driving 60 mph, so it will take me a certain
amount of time to get to my destination), and such changes
in one variable do cause a change in the other. So, on what
basis can one possibly determine the independent and
dependent variables in these situations? By the way, the
textbook for problem B gives the answer of (speed, time).
The textbook for problem C says that either (speed, time)
or (time, speed) are acceptable answers.
Causation and Control
Another interesting subset of the 73 problems are the
seven problems that were coded as YYNN (Table 3)—that
is, problems that could reasonably be determined by con-
sidering either control or causation. Here is an example:
23. (D) Identify the independent and dependent variables.
In warm climates, the average amount of electricity
used rises as the daily average temperature increases
and falls as the daily average temperature decreases.
(Answer: [temperature, amount of electricity used])
In this problem, it is fairly straightforward that the daily
temperature is heating homes, which causes the use of
air-conditioning to cool off the homes, which in turn causes
increased electricity use. So it is reasonable to determine
the solution given by the textbook based on causality (as
electricity use clearly does not cause changes in daily
temperature). Neither convention nor function comes into
play here, but it is interesting to consider the issue of
control. One cannot control daily average temperature, but
one can control electricity use. The latter, however, cer-
tainly does not cause a change in the former. Thus, in this
problem, the variable one does not have control over is the
one that causes the change in the variable one does have
control over. Appealing to either control or causation as a
rationale results in different responses to the question.
Contrast problem D with problem E, also from the set of
problems coded as YYNN—that is, problems that could be
determined by either causality or control:
(E) Identify the independent and dependent variables.
An employee receives two vacation days for every
month worked.
Identifying Independent and Dependent Variables
School Science and Mathematics 355
24. In this instance (and all YYNN instances), cause and
control issues coincide. One can only control the number
of months worked and changes in that variable also cause
the variable of vacation days to change. Thus, for problems
like problem E, consideration of either the control or the
causation rationales results in the same determination of
independent and dependent variables; whereas for prob-
lems like problem D, consideration of either of these
rationales results in different determinations.
Convention and Function
Finally, consider the set of problems for which either
convention or function are reasonable rationales, but
neither causation nor control are (NNNY, NNYY, NNYN).
There are 13 problems in this subset. Here are three
examples of NNYN problems:
(F) Copy and complete: In the equation y = x + 5, x is
the ___ variable and y is the ___ variable.
(G) Identify the independent and dependent variables
(Figure 1):
(H) A convenience store has been keeping track of its
popcorn sales (Figure 2). Make a coordinate graph of
the data in the table. Which variable did you put on the
x-axis? Why?
In each of these problems, convention (symbolic,
graphic, then numeric) is really the only way one could
determine the answer to the given problem. Imagine how
confusing such problems might be to students who are
unaware of the conventions, or who are trying to
make sense of these situations by appealing to other
rationales.
25. Conclusion
The quality of the contexts of these “Identify the inde-
pendent and dependent variable” problems varies signifi-
cantly. Such variation potentially sets students up to
develop misconceptions about independent and dependent
variables. On the one hand, students are given contexts
from which one might reasonably conclude that one vari-
able clearly must depend on the other, and that the alter-
native is unrealistic (e.g., problem D). On the other hand,
students are asked to determine the independent and
dependent variables in mere mathematical relationships
(e.g., problem F). Given this range of contexts for these
problems and the fact that almost all problems had a “right
answer” in the text, one could infer the intended learning
outcome of these textbooks with regard to independent
and dependent variables: Given any situation, one can
objectively determine the independent and dependent vari-
ables. When students are asked to make sense of such
situations, however, as illustrated in the classroom
example, they are able to see through this fallacy.
The terms “independent” and “dependent” are relatively
straightforward for students to understand; they easily
grasp the idea that the dependent variable “depends” on
the other. What is not so clear to students—and I posit
because this idea is unclear in some textbooks, textbook
problems, and for many teachers—is just what it means for
a variable to “depend” on another. Is the issue “cause and
effect”? Is the issue “control”? Or is the issue merely “can
be determined by”? These variations are complicated, and
in fact, are quite useful dilemmas in building a rationale
Figure 1. The graph provided for problem G.
26. Time Total Bags Sold
6:00 A.M. 0
7:00 A.M. 3
8:00 A.M. 15
9:00 A.M. 20
10:00 A.M. 26
11:00 A.M. 30
noon 45
1:00 P.M. 58
2:00 P.M. 58
3:00 P.M. 62
4:00 P.M. 74
5:00 P.M. 83
6:00 P.M. 88
7:00 P.M. 92
Figure 2. The table provided for problem H.
Identifying Independent and Dependent Variables
356 Volume 112 (6)
for the development of a function; for once one has a
function y = f (x), one knows by definition that y depends
on x. However, if one is merely looking at a relationship
between y and x, one is left with insufficient information to
determine which is the independent and which is the
dependent variable. The correct response really is, “It
depends on what you want.”
Most textbook problems asking for the identification of
independent and dependent variables seem to be sending
27. mixed messages and implicitly impeding students from
developing a robust understanding of independent and
dependent variables. These messages include: (1) one can
determine the independent and dependent variables not
just from functions, but from any relation, often, it seems,
by using implicit conventions; (2) given a context, one
can determine the independent and dependent variables;
and (3) if one determines what causes or controls, one
can determine the independent and dependent variables.
Messages such as these not only confound students’
understanding, they serve to perpetuate the belief that
mathematics is mysterious and nonsensical.
What message should we send? The scientific and
mathematical rationales discussed in this paper might
provide a good starting point. In particular, mathematics
textbooks should make it clear how they use independent
and dependent variables, and should discuss the differ-
ence between mathematical and scientific uses of the
terms. Students need explicit opportunities to make sense
of the meaning of “dependence” and that the variation in
situations, all the way from real-world cause-and-effect
situations to mathematical functions, need to be com-
pared and contrasted. I fear we are mistaken if we think
conceptually problematic problems like the ones dis-
cussed in this paper will simply take care of themselves.
Further research could help to support this conceptual
analysis by analyzing the same kinds of problems in text-
books from disciplines such as science, statistics, and
economics; by expanding the analysis to study how the
entire curriculum (the problems and the text) addresses
the topic; by documenting students’ current understand-
ings of identifying independent and dependent variables;
and by developing and testing curricular materials that
are designed to help students make these important
connections. I was unable to locate any extant research
28. literature on students’ or teachers’ understanding of
independent and dependent variables.
This paper illustrates one small corner of the curriculum
where typical textbook problems may be thwarting rather
than supporting students’ attempts to make sense of the
content. Conceptual analysis of curricular holes such as this
one have the potential to contribute to our ever-increasing
commitment to viewing science and mathematics as a
sense-making activity and to deepen our understanding of
how to enact such a view in classroom teaching and learn-
ing. Our students’ understanding depends on it.
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Identifying Independent and Dependent Variables
School Science and Mathematics 357
Author’s Notes
1 An earlier analysis of this episode initially motivated
this paper (see Peterson & Leatham, 2009 for a related
discussion of the episode).
2 All names are pseudonyms.
3 Certainly, there are aspects of this episode that can be
attributed to the inexperience of the student teacher. The
phenomenon of significant differences between teachers’
and students’ mathematics, however, is common to all
teaching situations and is, in fact, a hallmark of what
makes teaching “problematic” (Simon, 1995; Steffe &
D’Ambrosio, 1995).
32. 4 Hill’s (1965) classic causality criteria illustrate the
problematic nature of determining causation and the pre-
eminence of purpose in the process.
5 In the numeric representation, numbers are often orga-
nized into tables, and by convention, the independent vari-
able is often listed first, the dependent variable second.
This convention is in line with the conventional ordered
pair (independent, dependent). In the graphic representa-
tion, the independent variable is often placed on the hori-
zontal axis, the dependent variable on the vertical axis.
6 Snowy tree crickets, to be exact.
7 The rationales are likely not exhaustive. Further analy-
sis (in science and mathematics, as well as of other disci-
plines such as statistics) may reveal yet further refinement
to the framework of rationales. For example, in science,
one ideally looks for cause and effect. In statistics, on the
other hand, one is more concerned with an exploration of
correlation than necessarily determining cause and effect.
Because of this focus on correlation, statisticians often
give preference to terms like “explanatory” and
“response” variables (Yates, Moore, & Starnes, 2008).
8 Many thanks to Jillian Busath for her help in data
collection and to Annalisse Daly for her help in refining
the problem analysis.
9 We make no judgment as to whether such textbooks
should or should not have problems asking students to
identify independent and dependent variables. Our con-
ceptual analysis focused on the nature of the problems that
do exist, wherever they were.
Identifying Independent and Dependent Variables
33. 358 Volume 112 (6)
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