The document discusses mathematical investigation and provides guidance on conducting investigations. It defines mathematical investigation as a problem solving strategy that assesses students' ability to solve real-life tasks through long-term exploration. Students develop alternative solutions and cooperate with others on projects. The stages of an investigation are outlined as statement of the problem, exploring systematically, making conjectures, testing conjectures, explaining/justifying, reorganizing, and summarizing. Sample investigation topics and types are provided. Guidance is given on writing an investigation report by outlining its typical parts.
Your Math Students: Engaging and Understanding Every DayDreamBox Learning
The most important and challenging aspect of daily planning is to regularly—and yes, that means every day—create, adapt, locate, and consider mathematical tasks that are appropriate to the developmental learning needs of each student. A concern Francis (Skip) Fennell often shares with teachers is that many of us can find or create a lot of “fun” tasks that are, for the most part, worthless in regards to learning mathematics. Mathematical
tasks should provide a level of demand on the part of the student that ensures a focus on understanding and involves them in actually doing mathematics.
Problem-based learning promotes guidance for teachers and education on how to apply effectively in their field of teaching problem based teaching and learning
Your Math Students: Engaging and Understanding Every DayDreamBox Learning
The most important and challenging aspect of daily planning is to regularly—and yes, that means every day—create, adapt, locate, and consider mathematical tasks that are appropriate to the developmental learning needs of each student. A concern Francis (Skip) Fennell often shares with teachers is that many of us can find or create a lot of “fun” tasks that are, for the most part, worthless in regards to learning mathematics. Mathematical
tasks should provide a level of demand on the part of the student that ensures a focus on understanding and involves them in actually doing mathematics.
Problem-based learning promotes guidance for teachers and education on how to apply effectively in their field of teaching problem based teaching and learning
Designing and Planning a Research.pptxDrHafizKosar
Research:
Research is a process of steps used to collect and analyze information to increase our understanding of a topic or issue. At a general level, research consists of three steps:
1. Pose a question.
2. Collect data to answer the question.
3. Present an answer to the question.
Salient Feature of Quantitative Research
Quantitative research is a methodological approach used in the social sciences and other fields to collect, analyze, and interpret numerical data. Here are some salient features of quantitative research:
1. Objective and Empirical: Quantitative research is focused on gathering objective, measurable data that can be analyzed statistically. It relies on empirical evidence rather than subjective opinions or interpretations.
2. Numerical Data: This research method involves the collection of numerical data, often in the form of statistics, percentages, or numerical measurements. The data can be subjected to statistical analysis for patterns and trends.
3. Structured Research Design: Quantitative studies typically have a structured and predetermined research design. The research process is planned in advance, and the data collection instruments, such as surveys or experiments, are carefully designed.
4. Large Sample Size: Quantitative research often requires a large sample size to ensure statistical reliability and generalizability of findings to a broader population. The goal is to make inferences about the population based on the data collected from the sample.
5. Statistical Analysis: Statistical methods and techniques, such as descriptive statistics, inferential statistics, and correlation analysis, are commonly used in quantitative research. These analyses help researchers draw conclusions and make predictions about the population under study.
6. Replicable and Generalizable Results: The aim of quantitative research is to produce results that are replicable and can be generalized to a larger population. This contributes to the scientific rigor and validity of the findings.
7. Closed-Ended Questions: Data collection instruments, such as surveys or questionnaires, often use closed-ended questions with predefined response options. This facilitates the quantification of responses and simplifies the analysis process.
8. Controlled Environment: In experimental quantitative research, efforts are made to control and manipulate variables to isolate cause-and-effect relationships. This allows researchers to make more precise statements about the impact of independent variables on dependent variables.
9. Objective Measurement: Quantitative research relies on objective measurements and standardized data collection methods to ensure consistency and reduce bias in the data.
10. Cross-Sectional or Longitudinal Design: Quantitative studies can be cross-sectional, examining data at a single point in time, or longitudinal, collecting data over an extended period to observe changes and trends over time.
Lots covered developing from the exercise in Part One: leading to designs and pathways to consider, how methodology plays a part and what makes a review outstanding or disappointing.
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
Designing and Planning a Research.pptxDrHafizKosar
Research:
Research is a process of steps used to collect and analyze information to increase our understanding of a topic or issue. At a general level, research consists of three steps:
1. Pose a question.
2. Collect data to answer the question.
3. Present an answer to the question.
Salient Feature of Quantitative Research
Quantitative research is a methodological approach used in the social sciences and other fields to collect, analyze, and interpret numerical data. Here are some salient features of quantitative research:
1. Objective and Empirical: Quantitative research is focused on gathering objective, measurable data that can be analyzed statistically. It relies on empirical evidence rather than subjective opinions or interpretations.
2. Numerical Data: This research method involves the collection of numerical data, often in the form of statistics, percentages, or numerical measurements. The data can be subjected to statistical analysis for patterns and trends.
3. Structured Research Design: Quantitative studies typically have a structured and predetermined research design. The research process is planned in advance, and the data collection instruments, such as surveys or experiments, are carefully designed.
4. Large Sample Size: Quantitative research often requires a large sample size to ensure statistical reliability and generalizability of findings to a broader population. The goal is to make inferences about the population based on the data collected from the sample.
5. Statistical Analysis: Statistical methods and techniques, such as descriptive statistics, inferential statistics, and correlation analysis, are commonly used in quantitative research. These analyses help researchers draw conclusions and make predictions about the population under study.
6. Replicable and Generalizable Results: The aim of quantitative research is to produce results that are replicable and can be generalized to a larger population. This contributes to the scientific rigor and validity of the findings.
7. Closed-Ended Questions: Data collection instruments, such as surveys or questionnaires, often use closed-ended questions with predefined response options. This facilitates the quantification of responses and simplifies the analysis process.
8. Controlled Environment: In experimental quantitative research, efforts are made to control and manipulate variables to isolate cause-and-effect relationships. This allows researchers to make more precise statements about the impact of independent variables on dependent variables.
9. Objective Measurement: Quantitative research relies on objective measurements and standardized data collection methods to ensure consistency and reduce bias in the data.
10. Cross-Sectional or Longitudinal Design: Quantitative studies can be cross-sectional, examining data at a single point in time, or longitudinal, collecting data over an extended period to observe changes and trends over time.
Lots covered developing from the exercise in Part One: leading to designs and pathways to consider, how methodology plays a part and what makes a review outstanding or disappointing.
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
A Strategic Approach: GenAI in EducationPeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
7. Mathematics Curriculum
Current mathematics curricula ask students, from time to time,
to “investigate.” But how does one do that?
Another question: Why all the fuss about investigation?
Investigation is not the only way to learn mathematics, nor even
the best way in every situation.
DEPARTMENT OF EDUCATION - ROXI
8. DEPARTMENT OF EDUCATION -ROXI
• The ability to investigate a situation is, in itself, an important
skill for students to acquire.
• In mathematics—as in science, or
diagnosing the ills of an automobile, a computer, or a person—
proper investigation is often the first step in successful problem
solving.
• Furthermore, investigation helps to bring to the fore an
essential feature of the subject itself
10. • MI - is a problem solving strategy that assess the
students’ ability to real-life tasks. It is usually long
term. It gives the students’ opportunity to
develop alternative solutions and to actively
participate in and cooperate with others in
working on projects
DEPARTMENT OF EDUCATION-RO XI
11. •Students’ creativity; planning and
investigative research skills and the extent of
integration of knowledge can be assessed
through MI.
DEPARTMENT OF EDUCATION –RO XI
12. Mathematical habits of mind has to be observed
a . Respect for mathematical data
b. Recognition of reasoning and proofs as essential and powerful
parts of mathematics
c . Develop a disposition to formulate, represent, abstract and
generalize in situations within outside mathematics.
DEPARTMENT OF EDUCATION –RO XI
13. • Ability to “look at” a problem in different ways
• Ability to describe clearly, make precise definitions
• Ability to write
• Broad mathematics background both teachers and learners
• Open-minded, curious , persevering…
Some conducive conditions for investigations
DEPARTMENT OF EDUCATION –RO XI
15. Math Investigation
DEPARTMENT OF EDUCATION- RO XI
• Is a sustained exploration of an open-ended math situation
where students:
Experience methods of planning, organizing, analyzing
and evaluating data.
Choose what aspects of the problem, situation they would
like to pursue and what strategies they would use.
Apply appropriate mathematics or discover math
relationship
16. Mathematical Research
• Is a mathematical investigation which aims to produce new
mathematical results, knowledge or interpretations.
DEPARTMENT OF EDUCATION-ROXI
17. • “Why bring problem-solving and investigatory activities into the
classroom”- Why not?
• Teachers who are unfamiliar with these will easily bring up
reasons on “why not”.
• Teachers who experience the excitement and vitality of
investigations e.g false starts and better restarts, bad and good
guesses, frustrations and hopes) and the sweet smell of
success are probably better able to tell “why”.
DEPARTMENT OF EDUCATION –RO XI
19. • Attaining familiarity with situation to be investigated
• Producing instances, maybe starting from the simplest or
whatever is interesting
• Deciding on what is worth-pursuing
1. Statement of the Problem
DEPARTMENT OF EDUCATION –RO XI
20. 2. Exploring Systematically(Organize and Record Data)
- Systematic listing/drawing
- -organizing relationships in tables or graphs
DEPARTMENT OF EDUCATION-ROXI
21. • HOTS: Organizing
• Comparing-Identifying similarities/differences
• Classifying – grouping into categories
• Ordering- sequencing according to criterion.
DEPARTMENT OF EDUCATION –RO XI
22. Take time to think
3. Taking a Break (Gestating) Optional
DEPARTMENT OF EDUCATION –RO XI
23. • Making a general statements about patterns or relationships
observed in the cases considered
- A conjecture is a generalization obtained inductively, which has
not been validated or proven true
4. Making Conjectures (like a hypothesis)
24. 5. Testing/Verifying Conjectures
• -checking consistency of conjectures using existing cases
• -predicting results for untried cases for which data is available
DEPARTMENT OF EDUCATION-ROXI
25. • - explaining why the conjectures made will work for new or all
cases
Proving the conjectures (by math induction, direct/indirect proof,
visual proof)
HOTS- Evaluating – involves assessing the reasonableness of
ideas.
6. Explaining/Justifying Conjectures
DEPARTMENT OF EDUCATION –RO XI
26. • -simplifying /generalizing the approach
• -seeing the connection among the conjectures
• This stages may emerge earlier and several times during the
course of the investigation
HOTS. Generating – involves using prior knowledge to add
information beyond what is given.
Inferring, predicting, elaborating
7. Reorganizing
DEPARTMENT OF EDUCATION –RO XI
27. • Extending the investigation by considering other aspects of the
situation
• HOTS : Analyzing
7. Elaborating
DEPARTMENT OF EDUCATION –RO XI
28. • Involves an account or summary written or oral, of what has
been obtained in stages 2-7, with some reference on the
experience in stage 1
• HOTS: Synthesizing , Evaluating
8. Summarizing
29. Let us try!
Mark a number of points on
a circle and join them by
chords.
Investigate.
36. Types of Mathematical Investigation
a. Nature
b. Exploratory
c. Mathematical modeling(instrumentation)
d. Theory Building
e. Others if there are more
DEPARTMENT OF EDUCATION-RO XI
37. Writing an M.I.(Parts)
I. Overview (abstract)
II. Introduction
III. Mathematical Ideas Related
to the Study
IV. Materials (Tool Box)
39. Title- it gives a very specific and accurate
index in the main theme of the study
- It is explicit on the variables to be
investigated and the subjects involved in the
study
-Should be in Capital letters.
40. ABSTRACT (capitalized) – One page
with a maximum of 250 words.
-Contain: purpose,
procedure used, results, conclusions
41. Introduction: The present
problem of the study should be
described (What observations led to the
selection of the present problem?) The
need to solve the problem must be
stated. The solutions to the problem
should be stated. The focus of the
study should be stated.
The background
stated(Theoretical/historical )based on
review of literature is/are relevant to the
problem
42. Review of Related Literature-
The RRL should be relevant and
adequate to the problem under
investigation.
The review should provide with what is
already KNOWN AND NOT YET
KNOWN about the subject under
investigation.
46. Bibliography- APA style
American Psychological Association
American Psychology, Finney, J.
(1970). Time and again. New York,
NY: Simon and. Schuster
Psychological Association
47. Distance Determination in Refraction with Respect to the Incident
and Refracted Segments Angles
Sample
48. • The study, Distance Determination in Refraction with Respect to
Incident and Refracted Segments and Angles, gives way to a
new derived mathematical formula in obtaining the distance in
different phenomena of refraction. Since Mathematics is the
language of Physics, this investigation shows the application of
distance formula, law of cosines and reflexive Property of
equality in Physics, specifically in refraction.
52. • Lines are drawn on a plane .
• Investigate what occurs.
Lines
53. • The primes less than 4000.
• Find patterns.
• Investigate
Number Theory
54. • How many rectangles are there in this diagram?
Rectangles
55. • Take any whole number between 1 and 999, add the squares of
the digits to get a new number. Make some conjectures about
what happens in general.
Happy Numbers
56. Determine Your Birthday - Math Number
Trick
Just follow the steps with a calculator or by hand for building math
skills! Go ahead and try the trick without cheating!
• Add 18 to your birth month
• Multiply by 25
• Subtract 333
• Multiply by 8
• Subtract 554
• Divide by 2
• Add your birth date
• Multiply by 5
• Add 692
• Multiply by 20
• Add only the last two digits of your birth year
• Subtract 32940 to get your birthday!
57. The answer’s format is:
month/day/year. For example, an answer
of 123199 means that you were born on
December 31, 1999. If the answer is not
right, you followed the directions incorrectly
or lied about your birthday.
58. • How did young Karl discovered the
Sn = n (
𝑎𝑛+𝑎1
2
)
How did Rene Descartes discovered the Cartesian Plane?
How many bulbs did Thomas Edison break before he
succeeded?
Points to Ponder
59. “Do not worry about your difficulties in Math , mine
is much greater?
Famous Quote:
