Use of technology in the field of education has been a blessing. Faster grading, quicker notes / media availability for students, interactive communication outside of classrooms with students and faculty, online courses etc. have added to the enhancement of our education system. But when technology is pushed in teaching without proper thought, it becomes a black box approach at the cost of intuition, commonsense, and overall understanding of the concepts. Instead of supplementing technology in the process of learning, it has been used in making the black box approach more common. When we can shift the question from “How to educate with technology?” to “How to teach people best, and how should we design learning experiences in light of existing technology?”, then learning becomes a way to quench curiosity, and passion for learning will become a never ending pursuit for students. Models and textbook theories can help build the knowledge base, but they miss the context [5,7]. Students take them at face value without thinking through the real world implications. This is a recipe for failure since the industry expects business school students to tell the story with a strong reference to the context. A simplistic understanding of the formulas is what students’ need instead of a plug and solve formula based teaching method.
A pupil actively constructs their own mathematical knowledge by interacting new ideas with existing ideas, which can lead to misconceptions. Diagnostic teaching is important as it involves identifying misconceptions, challenging them through discussion to resolve conflicts, and replacing misconceptions with correct understanding. The teacher must understand the source of the misconception to effectively challenge it, and research shows this diagnostic approach promotes better learning compared to simply explaining again.
The document is a 12-page extended essay on Vedic mathematics and its methods for multiplication. It explores several Vedic multiplication techniques including vertically and crosswise, multiplying numbers above 10, multiplying by one more than the number before for squaring numbers ending in 5. The essay finds that Vedic multiplication can shorten and ease both basic and complex multiplication problems by using numerical patterns, though some problems require adapting the methods.
The document discusses common student misconceptions about fractions, specifically the misconception that larger denominators correspond to larger fractions. It proposes several hands-on activities and visual aids to help students understand the concept, including using real-world objects like pizza, playing with play-dough or blocks, and technology-based tools. The effectiveness of these interventions could be evaluated by informal assessments of students' understanding before and after the activities.
An Intelligent Microworld as an Alternative Way to Learn Algebraic ThinkingCITE
This document summarizes a research project that designed and tested an online environment called eXpresser to help students learn algebraic thinking and mathematical generalization. The project involved:
1) Developing eXpresser as an interactive microworld for building patterns and expressing rules that govern the patterns.
2) Conducting design experiments with 11-12 year old students to test eXpresser and gather feedback.
3) Interviewing students and finding that eXpresser helped them articulate relationships between quantities in patterns and validate rules through animation.
4) Designing group tasks for students to share and compare patterns/rules, finding most could determine if rules were equivalent.
1. The document discusses numerical methods which are computational techniques that use iterative methods to approximate solutions that are difficult to obtain analytically.
2. Numerical methods are important because most physical problems do not have exact solutions and numerical techniques provide insights into engineering problems.
3. Errors are introduced in numerical methods from various sources and can be classified as numerical or non-numerical. Accuracy and precision are important concepts when analyzing errors.
4. Historical numerical methods date back thousands of years and involved iterative approximations of solutions. Modern numerical methods are now widely used due to availability of computers.
This document provides guidance on best practices for math instruction using the Common Core Mathematical Practices and district curriculum. It emphasizes integrating the Habits of Mind and Interaction into daily math lessons through strategies like using a high-level problem of the day, facilitating student math talks, and creating public records of strategies and representations. Teachers are advised to plan lessons that encourage productive struggle and facilitate students discovering mathematical ideas on their own.
A pupil actively constructs their own mathematical knowledge by interacting new ideas with existing ideas, which can lead to misconceptions. Diagnostic teaching is important as it involves identifying misconceptions, challenging them through discussion to resolve conflicts, and replacing misconceptions with correct understanding. The teacher must understand the source of the misconception to effectively challenge it, and research shows this diagnostic approach promotes better learning compared to simply explaining again.
The document is a 12-page extended essay on Vedic mathematics and its methods for multiplication. It explores several Vedic multiplication techniques including vertically and crosswise, multiplying numbers above 10, multiplying by one more than the number before for squaring numbers ending in 5. The essay finds that Vedic multiplication can shorten and ease both basic and complex multiplication problems by using numerical patterns, though some problems require adapting the methods.
The document discusses common student misconceptions about fractions, specifically the misconception that larger denominators correspond to larger fractions. It proposes several hands-on activities and visual aids to help students understand the concept, including using real-world objects like pizza, playing with play-dough or blocks, and technology-based tools. The effectiveness of these interventions could be evaluated by informal assessments of students' understanding before and after the activities.
An Intelligent Microworld as an Alternative Way to Learn Algebraic ThinkingCITE
This document summarizes a research project that designed and tested an online environment called eXpresser to help students learn algebraic thinking and mathematical generalization. The project involved:
1) Developing eXpresser as an interactive microworld for building patterns and expressing rules that govern the patterns.
2) Conducting design experiments with 11-12 year old students to test eXpresser and gather feedback.
3) Interviewing students and finding that eXpresser helped them articulate relationships between quantities in patterns and validate rules through animation.
4) Designing group tasks for students to share and compare patterns/rules, finding most could determine if rules were equivalent.
1. The document discusses numerical methods which are computational techniques that use iterative methods to approximate solutions that are difficult to obtain analytically.
2. Numerical methods are important because most physical problems do not have exact solutions and numerical techniques provide insights into engineering problems.
3. Errors are introduced in numerical methods from various sources and can be classified as numerical or non-numerical. Accuracy and precision are important concepts when analyzing errors.
4. Historical numerical methods date back thousands of years and involved iterative approximations of solutions. Modern numerical methods are now widely used due to availability of computers.
This document provides guidance on best practices for math instruction using the Common Core Mathematical Practices and district curriculum. It emphasizes integrating the Habits of Mind and Interaction into daily math lessons through strategies like using a high-level problem of the day, facilitating student math talks, and creating public records of strategies and representations. Teachers are advised to plan lessons that encourage productive struggle and facilitate students discovering mathematical ideas on their own.
The document discusses issues with how fractions are currently taught in US schools and recommends improvements. It notes that students struggle with fractions and this hinders later success in algebra. A presidential panel recommends schools focus more on mastering the basics like fractions, in addition to geometry. It emphasizes fractions are a major obstacle and schools should teach them in a more in-depth way.
Basic Business Statistics Chapter 3Numerical Descriptive Measures
Chapters Objectives:
Learn about Measures of Center.
How to calculate mean, median and midrange
Learn about Measures of Spread
Learn how to calculate Standard Deviation, IQR and Range
Learn about 5 number summaries
Coefficient of Correlation
This document discusses calculating the arithmetic mean of a data set. It provides examples of finding the mean goals scored by a hockey team and the mean number of times students bought lunch. The mean is calculated by summing all values and dividing by the total number of values. For data with frequencies, each value is multiplied by its frequency before summing. The document also reviews calculating the mean from frequency tables and lists of raw data values.
This document provides teaching ideas and resources for problem solving in the GCSE mathematics classroom. It discusses developing a problem solving environment, asking open-ended questions, modeling problem solving techniques, using diagrams, and the importance of regular mini-tests and recalling basics to help students learn. A variety of problem solving resources and example problems are also presented.
The document discusses developing primary teachers' math skills through professional development programs. It addresses the concept of number sense, which refers to a well-organized conceptual understanding of numbers that allows one to solve problems beyond basic algorithms. Examples are provided for dot arrangements and personal numbers to illustrate number sense strategies. Arithmetic proficiency is defined as achieving fluency through calculation with understanding. The benefits of improved teacher math skills are outlined as developing students' number sense, fluency, conceptual understanding, problem solving and engagement. Examples are given for teaching subtraction and extending students. The importance of understanding over procedural fluency alone is emphasized.
The document provides guidance on solving physics problems using a general 5-step strategy and the KUDOS method for word problems. It begins with an overview of the learning objectives which are to learn a general problem-solving technique, how to solve word problems, how to prepare for exams, and tips for taking exams. Examples then demonstrate applying the 5-step general strategy and the KUDOS (Known, Unknown, Definitions, Output, Substantiate) method to solve sample physics problems step-by-step. The strategies provide a systematic approach to breaking down problems and connecting known information to unknowns through definitions and equations.
This document provides guidance for teaching basic math operations like addition, subtraction, multiplication and division to students. It emphasizes applying concepts to real-life situations to motivate students. Teachers should focus on conceptual understanding rather than rote memorization and provide examples for students to apply the operations. Using manipulatives, word problems, number lines and flashcards can help reinforce skills in an engaging way. Specific suggestions are also given for teaching addition and subtraction concepts.
This document discusses a science assessment question that tested students' ability to apply observations and identify the appropriate context for a "no honking" sign. Less than 50% of students chose the correct answer of a hospital. The document analyzes possible reasons for incorrect answers and emphasizes the importance of developing students' observation and critical thinking skills from an early age. It provides suggestions for classroom activities to help students better understand signs and symbols and improve their observation abilities.
An Investigation of Errors Related to Solving Problems on Percentagestheijes
In primary schools of Viet Nam, solving problems on percentages is a very important bit of knowledge because it not only provides a full range of knowledge of percentages but also a lot of practical applications and has a great effect in the development of thinking for students. However, it is a kind of new and difficult problem, so students often commit errors to solve problems on percentages. A survey of 149 primary school students was done. The students had to answer 7 questions about the problems on percentages. Results show that they suffer some errors such as: misunderstanding kinds of problems, doing wrong calculation, confusing the units of measurements. At the end of the paper, some suggestions in mathematics education are made to teachers to support students avoiding errors in solving problems on percentages
The document discusses a high school calculus lesson on anti-differentiation. The teacher used various instructional methods including flipped classroom techniques by screencasting lessons, whiteboarding in small groups, and emphasizing a "rule of four" approach using graphical, numerical, analytical and verbal methods. To assess student understanding, the teacher observed whiteboarding groups and could provide individual help as needed. The teacher also used online tools like Edmodo for assignments, feedback and discussions to guide learning.
This document provides a summary and collection of online resources for teaching fractions. It begins by noting the importance of visual representations for understanding fractions. The remainder of the document provides brief descriptions and hyperlinks to fraction resources available on various websites, including visual diagrams, practice problems, lesson plans, and interactive activities. The resources are organized for teaching fractions at various levels, from key stage 3 through key stage 4.
Learning & Teaching GCSE MathematicsColleen Young
This document provides teaching resources and ideas for GCSE Mathematics. It includes information on specification changes, assessment objectives, teaching guidance from exam boards, and problem solving strategies. Sample exam questions, topic tests, and diagnostic questions are provided. Additional resources on areas like extension materials, revision activities, and developing recall are also referenced.
The document announces the 26th annual Long Island Mathematics Conference to be held on March 16, 2012 at SUNY College at Old Westbury. The keynote speaker will be Dr. John Ewing, President of Math for America, who will speak on "Who Owns the Common Core Standards?". The day-long conference will include sessions and workshops on mathematics education, pedagogy, and problem solving focused on the theme "Math: Getting to the Core".
This lesson teaches students about the relationship between visual fraction models and equations when dividing fractions. Students will formally connect fraction models to multiplication through the use of multiplicative inverses. They will use fraction strips and tape diagrams to model division problems involving fractions. Students will learn that dividing a fraction by another fraction is the same as multiplying by the inverse or reciprocal of the divisor fraction. The lesson provides examples showing how to set up and solve word problems involving division of fractions using visual models and equations.
The document discusses various strategies for teaching early number concepts and operations such as counting, addition, subtraction and basic facts to young children. It describes strategies like subtizing small quantities, sequencing events, matching quantities, one-to-one correspondence and using models and word problems to develop understanding of addition and subtraction concepts. It also outlines approaches for helping children master basic addition and subtraction facts through understanding relationships between numbers and using strategies like thinking addition for subtraction, doubles facts and making ten.
Use of Excel in Statistics: Problem Solving Vs Problem UnderstandingIJITE
This document discusses using Microsoft Excel to help students better understand statistical concepts rather than just solve problems. It presents exercises using Excel functions to visualize probability distributions, sampling distributions, confidence intervals, and hypothesis testing. For example, the normal distribution can be demystified by using Excel to generate normal distribution tables from the NORM.S.DIST function. Sampling and the central limit theorem are illustrated by generating random samples from a population and calculating sample means and standard deviations. Confidence intervals and hypothesis testing are demonstrated on sample data where the population is known. The goal is for students to intuitively understand the statistical concepts behind techniques rather than just using tools to solve pre-made problems.
USE OF TECHNOLOGY IN EDUCATION, BUT AT WHAT COST?IJITE
Use of technology in the field of education has been a blessing. Faster grading, quicker notes /
media availability for students, interactive communication outside of classrooms with students
and faculty, online courses etc. have added to the enhancement of our education system. But
when technology is pushed in teaching without proper thought, it becomes a black box approach
at the cost of intuition, commonsense, and overall understanding of the concepts. Instead of
supplementing technology in the process of learning, it has been used in making the black box
approach more common. When we can shift the question from “How to educate with
technology?” to “How to teach people best, and how should we design learning experiences in
light of existing technology?”, then learning becomes a way to quench curiosity, and passion for
learning will become a never ending pursuit for students. Models and textbook theories can help
build the knowledge base, but they miss the context [5,7]. Students take them at face value
without thinking through the real world implications. This is a recipe for failure since the
industry expects business school students to tell the story with a strong reference to the context. A
simplistic understanding of the formulas is what students’ need instead of a plug and solve
formula based teaching method.
Use of Excel in Statistics: Problem Solving Vs Problem Understanding IJITE
MS-Excel’s statistical features and functions are traditionally used in solving problems in a statistics class.
Carefully designed problems around these can help a student visualize the working of statistical concepts
such as Hypothesis testing or Confidence Interval.
USE OF EXCEL IN STATISTICS: PROBLEM SOLVING VS PROBLEM UNDERSTANDINGIJITE
ABSTRACT
MS-Excel’s statistical features and functions are traditionally used in solving problems in a statistics class. Carefully designed problems around these can help a student visualize the working of statistical concepts such as Hypothesis testing or Confidence Interval
KEYWORDS
MS Excel, Data Analysis,Hypothesis Testing, Confidence Interval
Presentation on Teaching Quantitative Methods using Excel workbook courseware. -- at the 25th International Conference on Technology in Collegiate Mathematics, Boston, March 21 - 24, 2013. A Pearson Education event.
This document contains information about various math teaching strategies and techniques for helping students transfer math concept knowledge and link concepts. It discusses five techniques that aid in transferring knowledge: problem-based learning, interactive math tools, using manipulatives, explaining problems in writing, and making connections. It also provides examples of effective math teaching strategies like questioning, encouragement, modelling, clarity and expectations. Finally, it addresses topics like basic math operations, fractions, word problems and telling time.
A Case Study of Teaching the Concept of Differential in Mathematics Teacher T...theijes
In high schools of Viet Nam, teaching calculus includes the knowledge of the real function with a real variable. A mathematics educator in France, Artigue (1996) has shown that the methods and approximate techniques are the centers of the major problems (including number approximation and function approximation...) in calculus. However, in teaching mathematics in Vietnam, the problems of approximation almost do not appear. With the task of training mathematics teachers in high schools under the new orientations, we present a part of our research with the goal of improving the contents and methods of teacher training
The document discusses issues with how fractions are currently taught in US schools and recommends improvements. It notes that students struggle with fractions and this hinders later success in algebra. A presidential panel recommends schools focus more on mastering the basics like fractions, in addition to geometry. It emphasizes fractions are a major obstacle and schools should teach them in a more in-depth way.
Basic Business Statistics Chapter 3Numerical Descriptive Measures
Chapters Objectives:
Learn about Measures of Center.
How to calculate mean, median and midrange
Learn about Measures of Spread
Learn how to calculate Standard Deviation, IQR and Range
Learn about 5 number summaries
Coefficient of Correlation
This document discusses calculating the arithmetic mean of a data set. It provides examples of finding the mean goals scored by a hockey team and the mean number of times students bought lunch. The mean is calculated by summing all values and dividing by the total number of values. For data with frequencies, each value is multiplied by its frequency before summing. The document also reviews calculating the mean from frequency tables and lists of raw data values.
This document provides teaching ideas and resources for problem solving in the GCSE mathematics classroom. It discusses developing a problem solving environment, asking open-ended questions, modeling problem solving techniques, using diagrams, and the importance of regular mini-tests and recalling basics to help students learn. A variety of problem solving resources and example problems are also presented.
The document discusses developing primary teachers' math skills through professional development programs. It addresses the concept of number sense, which refers to a well-organized conceptual understanding of numbers that allows one to solve problems beyond basic algorithms. Examples are provided for dot arrangements and personal numbers to illustrate number sense strategies. Arithmetic proficiency is defined as achieving fluency through calculation with understanding. The benefits of improved teacher math skills are outlined as developing students' number sense, fluency, conceptual understanding, problem solving and engagement. Examples are given for teaching subtraction and extending students. The importance of understanding over procedural fluency alone is emphasized.
The document provides guidance on solving physics problems using a general 5-step strategy and the KUDOS method for word problems. It begins with an overview of the learning objectives which are to learn a general problem-solving technique, how to solve word problems, how to prepare for exams, and tips for taking exams. Examples then demonstrate applying the 5-step general strategy and the KUDOS (Known, Unknown, Definitions, Output, Substantiate) method to solve sample physics problems step-by-step. The strategies provide a systematic approach to breaking down problems and connecting known information to unknowns through definitions and equations.
This document provides guidance for teaching basic math operations like addition, subtraction, multiplication and division to students. It emphasizes applying concepts to real-life situations to motivate students. Teachers should focus on conceptual understanding rather than rote memorization and provide examples for students to apply the operations. Using manipulatives, word problems, number lines and flashcards can help reinforce skills in an engaging way. Specific suggestions are also given for teaching addition and subtraction concepts.
This document discusses a science assessment question that tested students' ability to apply observations and identify the appropriate context for a "no honking" sign. Less than 50% of students chose the correct answer of a hospital. The document analyzes possible reasons for incorrect answers and emphasizes the importance of developing students' observation and critical thinking skills from an early age. It provides suggestions for classroom activities to help students better understand signs and symbols and improve their observation abilities.
An Investigation of Errors Related to Solving Problems on Percentagestheijes
In primary schools of Viet Nam, solving problems on percentages is a very important bit of knowledge because it not only provides a full range of knowledge of percentages but also a lot of practical applications and has a great effect in the development of thinking for students. However, it is a kind of new and difficult problem, so students often commit errors to solve problems on percentages. A survey of 149 primary school students was done. The students had to answer 7 questions about the problems on percentages. Results show that they suffer some errors such as: misunderstanding kinds of problems, doing wrong calculation, confusing the units of measurements. At the end of the paper, some suggestions in mathematics education are made to teachers to support students avoiding errors in solving problems on percentages
The document discusses a high school calculus lesson on anti-differentiation. The teacher used various instructional methods including flipped classroom techniques by screencasting lessons, whiteboarding in small groups, and emphasizing a "rule of four" approach using graphical, numerical, analytical and verbal methods. To assess student understanding, the teacher observed whiteboarding groups and could provide individual help as needed. The teacher also used online tools like Edmodo for assignments, feedback and discussions to guide learning.
This document provides a summary and collection of online resources for teaching fractions. It begins by noting the importance of visual representations for understanding fractions. The remainder of the document provides brief descriptions and hyperlinks to fraction resources available on various websites, including visual diagrams, practice problems, lesson plans, and interactive activities. The resources are organized for teaching fractions at various levels, from key stage 3 through key stage 4.
Learning & Teaching GCSE MathematicsColleen Young
This document provides teaching resources and ideas for GCSE Mathematics. It includes information on specification changes, assessment objectives, teaching guidance from exam boards, and problem solving strategies. Sample exam questions, topic tests, and diagnostic questions are provided. Additional resources on areas like extension materials, revision activities, and developing recall are also referenced.
The document announces the 26th annual Long Island Mathematics Conference to be held on March 16, 2012 at SUNY College at Old Westbury. The keynote speaker will be Dr. John Ewing, President of Math for America, who will speak on "Who Owns the Common Core Standards?". The day-long conference will include sessions and workshops on mathematics education, pedagogy, and problem solving focused on the theme "Math: Getting to the Core".
This lesson teaches students about the relationship between visual fraction models and equations when dividing fractions. Students will formally connect fraction models to multiplication through the use of multiplicative inverses. They will use fraction strips and tape diagrams to model division problems involving fractions. Students will learn that dividing a fraction by another fraction is the same as multiplying by the inverse or reciprocal of the divisor fraction. The lesson provides examples showing how to set up and solve word problems involving division of fractions using visual models and equations.
The document discusses various strategies for teaching early number concepts and operations such as counting, addition, subtraction and basic facts to young children. It describes strategies like subtizing small quantities, sequencing events, matching quantities, one-to-one correspondence and using models and word problems to develop understanding of addition and subtraction concepts. It also outlines approaches for helping children master basic addition and subtraction facts through understanding relationships between numbers and using strategies like thinking addition for subtraction, doubles facts and making ten.
Use of Excel in Statistics: Problem Solving Vs Problem UnderstandingIJITE
This document discusses using Microsoft Excel to help students better understand statistical concepts rather than just solve problems. It presents exercises using Excel functions to visualize probability distributions, sampling distributions, confidence intervals, and hypothesis testing. For example, the normal distribution can be demystified by using Excel to generate normal distribution tables from the NORM.S.DIST function. Sampling and the central limit theorem are illustrated by generating random samples from a population and calculating sample means and standard deviations. Confidence intervals and hypothesis testing are demonstrated on sample data where the population is known. The goal is for students to intuitively understand the statistical concepts behind techniques rather than just using tools to solve pre-made problems.
USE OF TECHNOLOGY IN EDUCATION, BUT AT WHAT COST?IJITE
Use of technology in the field of education has been a blessing. Faster grading, quicker notes /
media availability for students, interactive communication outside of classrooms with students
and faculty, online courses etc. have added to the enhancement of our education system. But
when technology is pushed in teaching without proper thought, it becomes a black box approach
at the cost of intuition, commonsense, and overall understanding of the concepts. Instead of
supplementing technology in the process of learning, it has been used in making the black box
approach more common. When we can shift the question from “How to educate with
technology?” to “How to teach people best, and how should we design learning experiences in
light of existing technology?”, then learning becomes a way to quench curiosity, and passion for
learning will become a never ending pursuit for students. Models and textbook theories can help
build the knowledge base, but they miss the context [5,7]. Students take them at face value
without thinking through the real world implications. This is a recipe for failure since the
industry expects business school students to tell the story with a strong reference to the context. A
simplistic understanding of the formulas is what students’ need instead of a plug and solve
formula based teaching method.
Use of Excel in Statistics: Problem Solving Vs Problem Understanding IJITE
MS-Excel’s statistical features and functions are traditionally used in solving problems in a statistics class.
Carefully designed problems around these can help a student visualize the working of statistical concepts
such as Hypothesis testing or Confidence Interval.
USE OF EXCEL IN STATISTICS: PROBLEM SOLVING VS PROBLEM UNDERSTANDINGIJITE
ABSTRACT
MS-Excel’s statistical features and functions are traditionally used in solving problems in a statistics class. Carefully designed problems around these can help a student visualize the working of statistical concepts such as Hypothesis testing or Confidence Interval
KEYWORDS
MS Excel, Data Analysis,Hypothesis Testing, Confidence Interval
Presentation on Teaching Quantitative Methods using Excel workbook courseware. -- at the 25th International Conference on Technology in Collegiate Mathematics, Boston, March 21 - 24, 2013. A Pearson Education event.
This document contains information about various math teaching strategies and techniques for helping students transfer math concept knowledge and link concepts. It discusses five techniques that aid in transferring knowledge: problem-based learning, interactive math tools, using manipulatives, explaining problems in writing, and making connections. It also provides examples of effective math teaching strategies like questioning, encouragement, modelling, clarity and expectations. Finally, it addresses topics like basic math operations, fractions, word problems and telling time.
A Case Study of Teaching the Concept of Differential in Mathematics Teacher T...theijes
In high schools of Viet Nam, teaching calculus includes the knowledge of the real function with a real variable. A mathematics educator in France, Artigue (1996) has shown that the methods and approximate techniques are the centers of the major problems (including number approximation and function approximation...) in calculus. However, in teaching mathematics in Vietnam, the problems of approximation almost do not appear. With the task of training mathematics teachers in high schools under the new orientations, we present a part of our research with the goal of improving the contents and methods of teacher training
This document summarizes key learning principles for teaching statistics and describes an example lesson plan that incorporates these principles. The principles discussed are: (1) prior knowledge influences new learning, (2) how knowledge is organized impacts its use, (3) timely feedback and practice are needed, and (4) engagement promotes deeper learning. The example lesson uses simulations to help students explore sampling and variability. It provides opportunities for conjecture, discussion, and feedback to actively engage students in learning.
This document discusses using mathematical modelling in early grades to develop 21st century skills. It suggests providing students opportunities to solve authentic real-world problems from their own experiences. Examples of student work include generating problems and data, quantifying information, representing solutions, and communicating results. The document provides examples of turning word problems into mathematical equations and using real-world contexts to bring meaning to operations and concepts. It advocates for using a mathematics laboratory for students to explore ideas through games and puzzles in a low-stakes environment. Critical thinking, communication, collaboration, and creative problem solving are skills that can be developed through posing problems based on real phenomena and evaluating models and solutions. An example problem and approach is provided for planning a family vacation trip
R is a free and open-source statistical software that provides more advanced analytical abilities than Excel. It requires writing code, giving students insight into statistical procedures. Simple code from teachers allows students to analyze their own data and choose appropriate graphs. Examples include creating pie charts of daily activities or histograms of homework times. Students can collect and analyze class data like heights or sports results to explore trends.
This document is a newsletter from the Council for Learning Disabilities that provides information on upcoming events and initiatives. It includes the following:
- A message from the CLD President thanking members and recognizing leadership.
- An article on using interactive whiteboards to teach math concepts to students with learning disabilities, combining concrete, representational, and abstract instruction.
- Details about nominating people for awards, calls for committee members, and information on the upcoming annual conference in Las Vegas.
2021 eLearning Success Summit Engagement Manual from LMS Pulse.pdfOblivionY
This document provides an introduction to an engagement field diary tool for tracking experiments and improvements made to an elearning system to maximize student engagement. It outlines 10 key areas to focus on, including accessibility, delivery methods, formats, gamification, and help/support. Instructions are provided on how to set up and update the field diary by documenting hypotheses, experiments, and results for each area. Background on each area is also given, highlighting organizations doing good work related to that principle. The goal is to help users of the tool engage in a process of continuous learning and improvement to enhance the student experience.
This document outlines a lesson on measuring central tendency. The lesson is one hour and involves reviewing measures of central tendency like mean, median, and mode. Students will work through three case studies calculating these measures and discussing their strengths and limitations. Assessments will evaluate students' ability to calculate the measures and understand how they are affected by changes in data. The lesson aims to help students calculate common measures of central tendency, interpret them, and discuss their limitations.
Universal Design for Learning (UDL) began as an effort to help learners with disabilities succeed in general education by adapting existing curriculum. Educators realized it was better to design curriculum from the start using UDL principles of multiple means of representation, engagement, and expression. UDL is informed by three brain networks - recognition, strategic, and affective - and provides multiple options to appeal to these networks through representation, expression and engagement. Technology supports effective implementation of UDL by providing flexible tools that appeal to the brain networks.
Math 012Midterm ExamPage 3Please remember to show all w.docxandreecapon
Math 012
Midterm Exam Page 3
Please remember to show all work on every problem.
1) Solve the equation using the methods discussed in Chapter 2 of our text. If the equation has a unique solution, please show the complete check of your answer.
2) Solve the equation using the methods discussed in Chapter 2 of our text. If the equation has a unique solution, please show the complete check of your answer.
3) Solve the equation using the methods discussed in Chapter 2 of our text. If the equation has a unique solution, please show the complete check of your answer.
4) Solve the inequality using the methods discussed in Chapter 2 of our text. Write your answer in interval notation and graph the solution set on a number line.
5) Solve the inequality using the methods discussed in Chapter 2 of our text. Write your answer in interval notation and graph the solution set on a number line.
6) Solve the inequality using the methods discussed in Chapter 2 of our text. Write your answer in interval notation and graph the solution set on a number line.
7) Solve the inequality using the methods discussed in Chapter 2 of our text. Write your answer in interval notation and graph the solution set on a number line.
8) After Amanda received a 4.5% raise, her new annual salary was $75,240. What was her annual salary before the raise?
9) Patrick wins $900,000 (after taxes) in the lottery and decides to invest half of it in a 5-year CD that pays 6.72% interest compounded quarterly. He invests the other half in a money market fund that unfortunately turns out to average only 2.4% interest compounded annually over the 5-year period. How much money will he have altogether in the two accounts at the end of the 5-year period?
10) The average annual tuition and fees at public 4-year institutions in the US in 2005 was $13,847 and in 2010 was $16,384. Let y be the average tuition and fees in the year x, where x = 0 represents the year 2005.
a) Write a linear equation that models the growth in average tuition and fees at public 4-year institutions in the US in terms of the year x.
b) Use this equation to predict the average tuition and fees at public 4-year institutions in the US in the year 2020.
c) Explain what the slope of this line means in the context of the problem.
11) Given the linear equation :
a) Find both intercepts of the equation. Show all work and state intercepts as ordered pairs.
x-intercept =
y-intercept =
b) Use the intercepts to find the slope of the line. Show all work.
12) Given the following two linear equations, determine whether the lines are parallel, perpendicular, or neither. Show the work that leads to your conclusion.
13) Write an equation of a line through the point (5, -2) that is perpendicular to the y-ax ...
- Marriott Corporation is an international company that operates in three divisions: lodging, contract services, and restaurants. It aims to grow each of these divisions.
- To determine its cost of capital, Marriott needs to calculate the weighted average cost of capital (WACC) for the corporation overall and for each division.
- Calculating the WACC requires determining the costs of debt and equity, using tools like the capital asset pricing model to estimate the cost of equity based on risk-free rates and beta values. Estimating these components will allow Marriott to evaluate investment opportunities and ensure its financial strategy supports its growth objectives.
Effect of technology use on teaching and learning of mathematicsguest9a2d39a
Technology can positively impact the teaching and learning of mathematics when used appropriately. Research shows that students who use computers for specific applications and real problem solving score better than those using computers only for drills. While frequent computer use does not necessarily translate to higher test scores, technology can help develop skills, support learning, and transform understanding when teachers guide students in applying it for higher-order thinking. Younger students with access to calculators perform better in interpreting answers and demonstrate deeper understanding, while maintaining computational skills. Classroom interactions also change as teachers take on more of a consulting role, and students show increased interest and confidence in mathematics.
Similar to Use of Technology in Education, But at What Cost? (16)
Level 3 NCEA - NZ: A Nation In the Making 1872 - 1900 SML.pptHenry Hollis
The History of NZ 1870-1900.
Making of a Nation.
From the NZ Wars to Liberals,
Richard Seddon, George Grey,
Social Laboratory, New Zealand,
Confiscations, Kotahitanga, Kingitanga, Parliament, Suffrage, Repudiation, Economic Change, Agriculture, Gold Mining, Timber, Flax, Sheep, Dairying,
Chapter wise All Notes of First year Basic Civil Engineering.pptxDenish Jangid
Chapter wise All Notes of First year Basic Civil Engineering
Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
Buildings: Selection of site for Buildings, Layout of Building Plan, Types of buildings, Plinth area, carpet area, floor space index, Introduction to building byelaws, concept of sun light & ventilation. Components of Buildings & their functions, Basic concept of R.C.C., Introduction to types of foundation
Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
4. BCP, Surveying volume 1
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.)
This presentation was provided by Racquel Jemison, Ph.D., Christina MacLaughlin, Ph.D., and Paulomi Majumder. Ph.D., all of the American Chemical Society, for the second session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session Two: 'Expanding Pathways to Publishing Careers,' was held June 13, 2024.
1. International Journal on Integrating Technology in Education (IJITE) Vol.8, No.1, March 2019
DOI :10.5121/ijite.2019.8102 13
USE OF TECHNOLOGY IN EDUCATION, BUT AT
WHAT COST?
Avanti P. Sethi & Ramesh Subramoniam
Jindal School of Management, University of Texas at Dallas, Texas, USA
ABSTRACT
Use of technology in the field of education has been a blessing. Faster grading, quicker notes /
media availability for students, interactive communication outside of classrooms with students
and faculty, online courses etc. have added to the enhancement of our education system. But
when technology is pushed in teaching without proper thought, it becomes a black box approach
at the cost of intuition, commonsense, and overall understanding of the concepts. Instead of
supplementing technology in the process of learning, it has been used in making the black box
approach more common. When we can shift the question from “How to educate with
technology?” to “How to teach people best, and how should we design learning experiences in
light of existing technology?”, then learning becomes a way to quench curiosity, and passion for
learning will become a never ending pursuit for students. Models and textbook theories can help
build the knowledge base, but they miss the context [5,7]. Students take them at face value
without thinking through the real world implications. This is a recipe for failure since the
industry expects business school students to tell the story with a strong reference to the context. A
simplistic understanding of the formulas is what students’ need instead of a plug and solve
formula based teaching method.
KEYWORDS
MS Excel,Break-even Analysis,Probability Distribution, Lines and circles
1. INTRODUCTION
There was a time, not long ago, when we travelled all over the world by following “paper” maps.
We learned how to brake cars during icy conditions to avoid skids. We scratched our heads or
call 5 friends if we forgot who won Superbowl XIII.
There was a time teaching meant making and saving the precious order of transparencies.
Multimedia presentation meant lots of video and audio tapes. We communicated with the
students only during the class time or office hours.
We can go on and on, but the point is, our lives are no longer the same. Internet, cell phones,
computers, artificial intelligence, medical science, etc. have changed us so much that we would
feel utterly helpless if we went back just a few years. Researchers [6] found increased student
independence using technology and found it easier to differentiate and provide corrective
feedback, while helping students build fluency. Researchers [8] believed that the integration of
technology into the learning environment of schools creates a student-centered, technology-based
learning environment that allows the student to have greater control and responsibility of the
learning process. As students take control of the learning process, the role of the teacher changes
from knowledge provider to facilitator of learning.
The facilitation of the learning process is what we believe has become critically important more
than ever for teachers as technology grips the business schools. This insight is a result of 57 years
2. International Journal on Integrating Technology in Education (IJITE) Vol.8, No.1, March 2019
14
of combined experience of the authors of this article from industry, consulting and academic
teaching in business schools. At the same time, the fundamentals haven’t changed. We still need
to eat healthy food as we did 50 years ago to keep healthy. We can use whichever exercise
machine we want, but still have to huff and puff to remain fit. A similar logic can be applied to
learning. After all, learning is a form of exercise and regardless of the tool, until we “sweat”, we
can’t really process knowledge. There is no one-a-day pill that will make us a scientist or a
doctor or a financial analyst. But, unfortunately, the trend in education has been in this.
As discussed in this article, there is a predominance of this one-a-day pill approach which is
commonly known as a black-box approach. The availability of technology – in terms of modern
calculators (read smart phones) and Excel – has made it so painless that the students don’t even
complain. A typical test scenario could be that the professor provides the formulas, the student
uses a calculator, plugs-in the numbers, and writes the answer.
Here by giving very simple examples, some from popular textbooks, we show how learning, with
the aid of constantly changing technology, has become a mechanical process.
2. COST-VOLUME ANALYSIS
Stevenson [1] in one of the widely used textbook in Operations Management provides and applies
a set of 5 formulas for a simple break-even problem:
TC = FC + WC
VC = Q x V
TR = R x Q
P = R x Q – (FC = V x Q)
Q = (P + FC)/(R – V);
A student can plug-in the values of the Q’s and V’s etc. and get the solution. And a collection of
such solution awards the student an A grade.
Now, if Fixed cost = $4,000, Variable cost = $7 and Selling price = $9, then wouldn’t the break-
even point simply be 2000 because we make a profit of $2 / unit and we need to cover $4,000 of
Fixed cost? And if we want to make a profit of $5,000, we have to make an additional 2,500
units which makes it a total of 4,500 units.
A student who understands the logic can solve any problem in any format, but taught with the
blackbox approach as suggested by the above textbook will make him always uneasy and unsure.
In fact, there is a better chance of a student solving this problem on his own if he is not actually
taught because then he will use commonsense and reasoning to figure it out.
3. PROBABILITY AND STATISTICS
A very important parameter in statistics is the variance σ2
the formula for which is
=
( − )
The students are typically asked to memorize this formula because it is “so important. In Excel,
there are functions to compute variances straight from the dataset. Most advanced calculators
have built-in such functions. These are a perfect aid to analyze data, especially when the sets are
large.
3. International Journal on Integrating Technology in Education (IJITE) Vol.8, No.1, March 2019
15
But, in this paper, we are discussing the learning side of it. What exactly the variance is? What
makes it large or small? How do outliers influence the variance of a dataset? Unfortunately,
many the technology has made us and the students so lazy that we tend skip most of the
underlying intuition.
We can start out by explaining that variance represents the variability of the data with respect to
the center, that is mean. If the data is too scattered around the mean, the variance will be high. If
all the numbers are close to the mean, the variance will be low. So, conceptually, we can add the
distance of each point (x) from the mean (µ) and divide this total by N to get the average distance.
If it is high, the variability will be high, and vice-versa. But since the mean is the “center of
gravity” – that is both halves of the mean are being equal weight, this total, and hence the
average, will always be 0. Our next option could be to use absolute values and we could call the
resulting average as Mean Absolute Deviation.
However, we prefer to use the squared distance as this also exemplifies the “problematic” larger
distances. So, we can measure the distance of each point (x) from the mean µ, square it, and add
them up. This will be give us the sum of the squared distances or deviations. The average of it
can be called Mean Squared Deviation, popularly known as Variance. To emphasize one more
time (to the student) – what is variance? It is the mean squared deviation (from the mean). A
student who understands the variance this way will never forget the formula as he never has to
memorize it. Now, while using a computer or a calculator to get variance, he will have a feel for
what he is trying to accomplish. A larger than expected variance will create a red flag in his mind
and prompt him to analyze data. All this because he understand what variance exactly represent.
Another widely used book in Probability and Statistics by Keller [2] explains the use of Normal
Distribution table in the following way:
“We standardize a random variable by subtracting its mean and dividing by its standard deviation.
When the variable is normal, the transformed variable is called a standard normal random
variable and denoted by Z; that is,
=
−
Those of us who know statistics well can understand the above statement which seems quite
“obvious”. But how will a student who is already struggling see it?
Instead, we can start by explaining that we measure the distance of a point from the mean in
terms of standard deviations because the standard deviation (variability) impacts the distribution.
This distance is called z-score. So, if the mean is 60 and standard deviation is 20, a point 90 will
be (90-60)/20 = 1.5 standard deviations away from the mean. This is what z-score is. And, if the
number is 30, then the z-score will be -1.5 indicating that we are at the same distance, but on the
left side of the mean.
This explanation will also make the student understand, for example, t-score or F-score. He can
also see why a high z-score will have a lower tail-area as high z-score implies a larger distance
from the mean.
Because of the ease of availability of statistical functions on the computer, such as Norm. Dist in
Excel, many of us completely skip the whole process of explaining the central idea behind such
distribution because all we have to do is enter the relevant numbers such as x, µ, and σ and we get
the probability. The problem is, as we have seen in our classes, students trained this way can’t
explain what they get because they have no sense of what exactly they have done.
4. International Journal on Integrating Technology in Education (IJITE) Vol.8, No.1, March 2019
16
4. LINES AND CIRCLES
What is the slope of a line that passes through (3,5) and (7,7)? The formula for this will be
=
( − )
( − )
=
7 − 5
7 − 3
= .5
If the student has memorized the formula, calculating the slope is a very easy process. But how
many will remember this formula once the semester is over?
However, taught properly, calculating slope (or other related functions) can be a breeze that the
student will never forget. Just one look at the image below will make the student never need the
formula again.
And, while we are at it, we can also talk about the distance between two points using Pythagoras
theorem which says c2
= a2
+ b2
. So the distance between (3,5) and (7,7) will be √2 + 4 =
√20. The interesting point is, the distance formula itself can be derived now as shown below:
(7 − 5) + (7 − 3)
( − ) + ( − )
The same concept can be used to derive the equation of a circle. After all, a circle is nothing but
a collection of points which are equidistant from a certain point – called the center. This distance
is called the radius. So, if we have a point (a,b), then a point (x, y) which has a distance of r from
this point can be represented as
( − ) + ( − ) =
Which is the equation of a circle.
7
5
Slope = Rise / Run = 2/4
= 0.5
3 5
(3,5) 4
(7,7)
(3,7)
2
7
5
Distance between (3,5) and (7,7) =
3 5
(3,5) 4
(7,7)
(3,7)
2
5. International Journal on Integrating Technology in Education (IJITE) Vol.8, No.1, March 2019
17
5. CONCLUSION
By showing some very simple examples, we have tried to show that teaching and problem solving
shouldn’t be mixed. The process of teaching must involve understanding and common sense.
Technology can be used in making the process easier as discussed in Sethi [3]. But using
technology in bypassing the conceptual aspect of learning can be detrimental to the process.
Once the students get the basic idea, then available tools can be used in solving the problems.
The new generation of students will swing more towards use of electronic devices such as
calculators and computers, and concepts if not well explained in class as discussed in this paper
will lead to overkill of computers and a plugin society. The lack of a clear understanding of the
concepts will affect the student’s ability to come up with a high level quick solution without a
plug in formula. This type of ability is very much in demand in industries and consulting
projects, where the participant in front of senior management has to quickly come up with the
potential impact of say a change in forecast in a exponential smoothing model and how it will
affect the outcome if we were to change the alpha value. The alpha value is only a percentage of
the difference between actual and forecast and the participant can make the call quickly that
considering a higher percentage of the variance can be a positive or negative impact based on
historical data. This type of a holistic understanding is what we need to teach in classes as we
explain the importance of “Why” we are learning a concept to how we can derive high level
solutions with a simplistic understanding of the formulas. A deeper analysis can always follow to
confirm the results and computers of course are very powerful to handle these tasks.
Modern electronic tools such as Excel, Tableau etc. are great ways for educators to create
meaningful simulations to deep dive in classes [4]. The students, in turn can discover meaningful
relationships, and develop new knowledge that was difficult to do in the past. The educators has
to become the gate keepers in the education process to make sure that the technology becomes a
aid in the learning process and not a plug in solution.
REFERENCES
[1] Stevenson, Operations Management, McGraw Hill Education, 2018, 13th edition, ISBN 978-1-259-
66747-3
[2] Keller, Gerald, Statistics for Management and Economics, Cengage Publishing, 10th Edition, ISBN-
10: 1285425456
[3] Sethi, Avanti, “Use of Excel in Statistics: Problem Solving vs Problem Understanding” International
Journal on Integrating Technology in Education, Vol. 4, No. 4, December 2015
[4] Peck, Kyle L. and Dorricott, Denise, “Why Use Technology?”, 11-14, Vol. 51, April 1994.
[5] Carlson, Ben, “9 Things they don’t teach you in business school”, Business Insider, October 2015.
[6] Rachael Law Schuetz, Gina Biancarosa & Joanna Goode (2018) Is Technology the Answer?
Investigating Students’ Engagement in Math, Journal of Research on Technology in Education, 50:4,
318-332, DOI: 10.1080/15391523.2018.1490937
[7] Subhash C. Mehta PhD, Sanjay S. Mehta PhD & Beh Lip Aun MBA (1999) The Evaluation of
Business Text Books: An International Perspective, Journal of Professional Services Marketing, 19:2,
141-149, DOI: 10.1300/J090v19n02_09
[8] Jorge A. Gaytan & John R. Slate (2002) Multimedia and the College of Business, Journal of Research
on Technology in Education, 35:2, 186-205, DOI: 10.1080/15391523.2002.10782379
6. International Journal on Integrating Technology in Education (IJITE) Vol.8, No.1, March 2019
18
AUTHORS
Dr. Avanti Sethi, a faculty member at Jindal School of Management at UT Dallas,
received his MS and Ph. D. in Operations Research from Carnegie-Mellon University
in Pittsburgh, USA.
Dr. Ramesh Subramoniam, a faculty member at the Jindal School of Management at
UT Dallas, received his PhD from Erasmus University, Rotterdam, NL and joined UT
Dallas with 27 years of experience in industry and consulting.