This document summarizes a presentation on supporting reasoning and proof in K-12 mathematics classrooms. It discusses how focusing on reasoning and proof can help develop students' mathematical understanding. The presentation will explore tools and strategies for teacher collaboration to plan lessons and examine student thinking with the goal of supporting students in developing convincing arguments. It provides context from mathematics standards and research on the importance of reasoning and proof across grade levels and the challenges of implementing these practices in classrooms.
while practicing for ctet I came across some word which i didn't find in syllabus. so in this PPT I am discussing all those key words. wish it will help you in your studies. if you find any other words which I this PPt doesn't contain then plz let me know I will definitely try to find out.
while practicing for ctet I came across some word which i didn't find in syllabus. so in this PPT I am discussing all those key words. wish it will help you in your studies. if you find any other words which I this PPt doesn't contain then plz let me know I will definitely try to find out.
DETECTING AND IMPROVING STUDENT EMOTIONS USING ACTIONABLE PATTERN DISCOVERY I...adeij1
Each year number of students enrolling in higher education is increasing significantly. Students from diverse backgrounds can be found in a class. These changing circumstances are making it necessary to develop Innovative teaching and Learning methodologies. Active Learning methodology is an innovative strategy and Lightweight Team comes under this Active Learning methodology. Lightweight Team approach is one such low-stake activity and it has very little or no direct impact on a student's grade whereas it makes the learning process fun and interesting. A student’s Emotion towards a class plays a major role in their class performance. In this work we use the feedback from the Student Survey Data which aims to evaluate student emotions and overall satisfaction with Course Teaching methods and Group Work experience. We use Actionable Pattern Discovery methodology to provide suggestions in the form of Action Rules to enhance student Emotions thereby achieving a Positive Learning and Teaching experience.
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Learn how Rocky Ridge Elementary Principal, Michelle Fox, was able to help Rocky Ridge students make significant gains in math by working with teachers to implement a system of standards-based math assessments and interventions.
The path of learning requires that students demonstrate the mastery of both skills and concepts in any class. In the traditional model of mastery in higher education, both formative and summative assessments are conducted via a rigid set of assignments, activities, and tests that require all students to perform the same set of skills for each concept mastery demonstration. The idea of choice in the classroom is a concept of Universal Design for Learning (UDL), and while choice can be easily produced for content delivery (text, audio, video, interactive materials), assessment of both skills and concept mastery is not addressed in most classrooms. This leads to the development of homogenous courses and assignments where many students show objective mastery via exams and subjective mastery via writing. Students can be given choice on their demonstration of mastery without undue burden on the faculty member while also creating increased mastery of skills important to their respective fields. In business, a fungible asset is one that is mutually interchangeable. In this case, I am applying the concept of fungibility to learning assessment. Faculty can give students choice; but, in order to create fungible assignments that do not, faculty must ensure that proper design of instruction and assessment is used. In order to facilitate the assessment of fungible assignments, faculty must be able to create clear and concise criteria for assessment that tie directly to objectives for learning. Allowing students to choose how they show their knowledge of concepts and mastery of skills gives them control over their learning and ultimately improving educational outcomes.
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In the edWeb.net Blended Learning community’s latest webinar, Elliot Sanchez joined Dr. Tim Hudson, Senior Director of Curriculum Design for DreamBox Learning, Inc., and discussed the future of math education. Elliot, Founder & CEO of mSchool, and one of the 2014 Forbes 30 Under 30, is a leading education innovator with 14 state-funded classrooms that successfully leverage blended learning. Elliot and Tim discussed mSchool’s approach and successes, blended learning, formative assessment, meeting the diverse needs of all students, Common Core State Standards, and digital learning technologies. They provided a recap of insights from the January 22, 2014 The Future of Math Education: A Panel Discussion of Promising Practices webinar, with a focus on blended learning. That panel included NCSM President Valerie Mills, renowned math educator; author Dr. Cathy Fosnot, and past NCTM and AMTE President Dr. Francis (Skip) Fennell. Everyone interested in the success of all students in learning mathematics—educators, parents, and community members— can appreciate the valuable insights and approach to innovation from these education thought leaders.
Ijaems apr-2016-25 BS Mathematics Student’s Personal Beliefs in Engaging in a...INFOGAIN PUBLICATION
Belief-change among students in mathematics learning is an elemental source of concern in the field of mathematics education. In the Philippines, BS Mathematics is one of the programs less chosen by many students. In spite of the efforts of the schools to market the program, it remains in the last options for those who are planning to take mathematics in the tertiary level. This study, through a qualitative research, explores the beliefs and feelings of BS Mathematics students of De La Salle Lipa about engaging in and learning Mathematics. It presents the change in beliefs of the students particularly those who did not intend to enroll in the said program. The views and feelings expressed by the subjects during a face-to-face interview reflect the kind of experience they have in school. The findings of the study indicate that (negative) beliefs of the students about pursuing mathematics as a program and learning the subject can change with the sound support of the school to provide an encouraging and learning environment. Such can eventually promote positive reception and achievement in the subject among the students.
Effect of Utilizing Geometer’s Sketchpad Software on Students’ Academic Achie...theijes
The study is carried out in order to measure the effectiveness of “Geometer’s Sketchpad software” inside the classroom environment and analyzed how this training is helping high school students while solving mathematics problems. In order to measure the effectiveness, regression and co-relation analysis has been done and finally the mean responses have been analyzed to evaluate the method effectiveness correctly on SPSS computer statistic program.
International Journal of Humanities and Social Science Invention (IJHSSI)inventionjournals
International Journal of Humanities and Social Science Invention (IJHSSI) is an international journal intended for professionals and researchers in all fields of Humanities and Social Science. IJHSSI publishes research articles and reviews within the whole field Humanities and Social Science, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online
DETECTING AND IMPROVING STUDENT EMOTIONS USING ACTIONABLE PATTERN DISCOVERY I...adeij1
Each year number of students enrolling in higher education is increasing significantly. Students from diverse backgrounds can be found in a class. These changing circumstances are making it necessary to develop Innovative teaching and Learning methodologies. Active Learning methodology is an innovative strategy and Lightweight Team comes under this Active Learning methodology. Lightweight Team approach is one such low-stake activity and it has very little or no direct impact on a student's grade whereas it makes the learning process fun and interesting. A student’s Emotion towards a class plays a major role in their class performance. In this work we use the feedback from the Student Survey Data which aims to evaluate student emotions and overall satisfaction with Course Teaching methods and Group Work experience. We use Actionable Pattern Discovery methodology to provide suggestions in the form of Action Rules to enhance student Emotions thereby achieving a Positive Learning and Teaching experience.
Strategic Math Warfare - Fighting to Help our Students Understand the Math th...Michelle Fox
Learn how Rocky Ridge Elementary Principal, Michelle Fox, was able to help Rocky Ridge students make significant gains in math by working with teachers to implement a system of standards-based math assessments and interventions.
The path of learning requires that students demonstrate the mastery of both skills and concepts in any class. In the traditional model of mastery in higher education, both formative and summative assessments are conducted via a rigid set of assignments, activities, and tests that require all students to perform the same set of skills for each concept mastery demonstration. The idea of choice in the classroom is a concept of Universal Design for Learning (UDL), and while choice can be easily produced for content delivery (text, audio, video, interactive materials), assessment of both skills and concept mastery is not addressed in most classrooms. This leads to the development of homogenous courses and assignments where many students show objective mastery via exams and subjective mastery via writing. Students can be given choice on their demonstration of mastery without undue burden on the faculty member while also creating increased mastery of skills important to their respective fields. In business, a fungible asset is one that is mutually interchangeable. In this case, I am applying the concept of fungibility to learning assessment. Faculty can give students choice; but, in order to create fungible assignments that do not, faculty must ensure that proper design of instruction and assessment is used. In order to facilitate the assessment of fungible assignments, faculty must be able to create clear and concise criteria for assessment that tie directly to objectives for learning. Allowing students to choose how they show their knowledge of concepts and mastery of skills gives them control over their learning and ultimately improving educational outcomes.
Highlights From Future of Education - mSchool + DreamBox LearningDreamBox Learning
In the edWeb.net Blended Learning community’s latest webinar, Elliot Sanchez joined Dr. Tim Hudson, Senior Director of Curriculum Design for DreamBox Learning, Inc., and discussed the future of math education. Elliot, Founder & CEO of mSchool, and one of the 2014 Forbes 30 Under 30, is a leading education innovator with 14 state-funded classrooms that successfully leverage blended learning. Elliot and Tim discussed mSchool’s approach and successes, blended learning, formative assessment, meeting the diverse needs of all students, Common Core State Standards, and digital learning technologies. They provided a recap of insights from the January 22, 2014 The Future of Math Education: A Panel Discussion of Promising Practices webinar, with a focus on blended learning. That panel included NCSM President Valerie Mills, renowned math educator; author Dr. Cathy Fosnot, and past NCTM and AMTE President Dr. Francis (Skip) Fennell. Everyone interested in the success of all students in learning mathematics—educators, parents, and community members— can appreciate the valuable insights and approach to innovation from these education thought leaders.
Ijaems apr-2016-25 BS Mathematics Student’s Personal Beliefs in Engaging in a...INFOGAIN PUBLICATION
Belief-change among students in mathematics learning is an elemental source of concern in the field of mathematics education. In the Philippines, BS Mathematics is one of the programs less chosen by many students. In spite of the efforts of the schools to market the program, it remains in the last options for those who are planning to take mathematics in the tertiary level. This study, through a qualitative research, explores the beliefs and feelings of BS Mathematics students of De La Salle Lipa about engaging in and learning Mathematics. It presents the change in beliefs of the students particularly those who did not intend to enroll in the said program. The views and feelings expressed by the subjects during a face-to-face interview reflect the kind of experience they have in school. The findings of the study indicate that (negative) beliefs of the students about pursuing mathematics as a program and learning the subject can change with the sound support of the school to provide an encouraging and learning environment. Such can eventually promote positive reception and achievement in the subject among the students.
Effect of Utilizing Geometer’s Sketchpad Software on Students’ Academic Achie...theijes
The study is carried out in order to measure the effectiveness of “Geometer’s Sketchpad software” inside the classroom environment and analyzed how this training is helping high school students while solving mathematics problems. In order to measure the effectiveness, regression and co-relation analysis has been done and finally the mean responses have been analyzed to evaluate the method effectiveness correctly on SPSS computer statistic program.
International Journal of Humanities and Social Science Invention (IJHSSI)inventionjournals
International Journal of Humanities and Social Science Invention (IJHSSI) is an international journal intended for professionals and researchers in all fields of Humanities and Social Science. IJHSSI publishes research articles and reviews within the whole field Humanities and Social Science, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online
This PowerPoint is one small part of the Astronomy Topics unit from www.sciencepowerpoint.com. This unit consists of a five part 3000+ slide PowerPoint roadmap, 12 page bundled homework package, modified homework, detailed answer keys, 8 pages of unit notes for students who may require assistance, follow along worksheets, and many review games. The homework and lesson notes chronologically follow the PowerPoint slideshow. The answer keys and unit notes are great for support professionals. The activities and discussion questions in the slideshow and meaningful. The PowerPoint includes built-in instructions, visuals, and follow up questions. Also included are critical class notes (color coded red), project ideas, video links, and review games. This unit also includes four PowerPoint review games (110+ slides each with Answers), 38+ video links, lab handouts, activity sheets, rubrics, materials list, templates, guides, and much more. Also included is a 190 slide first day of school PowerPoint presentation. Teaching Duration = 5+ weeks. Areas of Focus in the Astronomy Topics Unit: The Solar System and the Sun, Order of the Planets, Our Sun, Life Cycle of a Star, Size of Stars, Solar Eclipse, Lunar Eclipse, The Inner Planets, Mercury, Venus, Earth, Moon, Craters, Tides, Phases of the Moon, Mars and Moons, Rocketry, Asteroid Belt, NEOs, The Torino Scale, The Outer Planets and Gas Giants, Jupiter / Moons, Saturn / Moons, Uranus / Moons, Neptune / Moons, Pluto's Demotion, The Kuiper Belt, Oort Cloud, Comets / Other, Beyond the Solar System, Types of Galaxies, Blackholes, Extrasolar Planets, The Big Bang, Dark Matter, Dark Energy, The Special Theory of Relativity, Hubble Space Telescope, Constellations, Spacetime and much more. If you have any questions please feel free to contact me. Thanks again and best wishes. Sincerely, Ryan Murphy M.Ed www.sciencepowerpoint@gmail.com
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Vídeo de la presentación: https://www.youtube.com/watch?v=HPfNDL-jIGM
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Este material, se ha preparado como una hoja de ruta que le servirá de guía en el proceso de digitalización de su empresa.
Applying language learning theories to the use of virtual classroom in teaching literature –a pilot study
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Gagnon and Collay (1999) state that in constructivist paradigm, knowledge is constructed by learners during (1) active learning, (2) making their own representation of action, (3) conveying meaning to others, and (4) explaining things they don‘t understand completely. At the minimum, a learning environment contains: the student and a setting or space wherein the student acts, uses tools and devices, collects and interprets information, interacts with others, etc. (Wilson, 1996)
According to constructivists, knowledge is not received from the outside or from someone else; it is the individual student’s interpretation and processing of what is received through the senses that creates knowledge. Students should be allowed to construct knowledge rather than being given knowledge through instruction (Duffy & Cunningham, 1996).
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
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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
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By Dr. Vinod Kumar Kanvaria
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Unit 8 - Information and Communication Technology (Paper I).pdf
Is it True? Always? Supporting Reasoning and Proof Focused Collaboration among Teachers
1. Is it true? Always? Supporting
Reasoning-and-Proof Focused
Collaboration among Teachers
2013 NCTM Annual Conference
Denver, Colorado
Nicole Miller Rigelman * Portland State University
rigelman@pdx.edu
http://goo.gl/ys4Qd
2. Rate this presentation on the
conference app.
www.nctm.org/confapp
Download available presentation
handouts from the Online Planner!
www.nctm.org/planner
Join the conversation! Tweet us
using the hashtag #NCTMDenver
3. Session Overview
In this session we will:
Unpack what it is meant by reasoning-and-proving
and consider what it looks like to prompt such
thinking.
Explore tools to support teacher collaboration with
selecting tasks, planning, and observing/examining
classroom practice and student thinking with an eye
on supporting students with developing convincing
arguments.
4. Why focus on reasoning and proof in
your PLC?
Growing consensus in the community that it should
be “a natural, ongoing part of classroom discussions,
no matter what topic is being studied,” (NCTM, 2000,
p. 342).
What gets in the way?
It is difficult for teachers and student.
We have a limited vision of what counts as reasoningand-proving, particularly at the elementary grades.
5. Reasoning and Proof
Instructional programs [preK-12] should enable students to
develop and evaluate mathematical arguments and proofs.
- NCTM, 2000, p. 56
[In grades 3-5] mathematical reasoning develops in
classrooms where students are encouraged to put forth
their own ideas for examination. Teachers and students
should be open to questions, reactions, and elaborations
from others in the classroom. Students need to explain and
justify their thinking and learn how to detect fallacies and
critique others thinking.
- NCTM, 2000, p. 188
6. Reasoning and Proof
…both plausible and flawed arguments that are offered by
students create an opportunity for discussion. As students
move through the grades, they should compare their ideas
with others’ ideas, which may cause them to modify,
consolidate, or strengthen their arguments or reasoning.
Classrooms in which students are encouraged to present
their thinking, and in which everyone contributes by
evaluating one another’s thinking, provide rich environments
for learning mathematical reasoning.
- NCTM, 2000, p. 58
7. Reasoning and Proof
In the domain of Number and Operation…
Computation strategy. Purposeful manipulations that
may be chosen for specific problems, may not have a
fixed order, and may be aimed at converting one
problem into another.
Computation algorithm. A set of predefined steps
applicable to a class of problems that gives the
correct result in every case when the steps are carried
out correctly.
- K-5 Progressions, Number and Operations in Base Ten, 2011, p. 3
8. Standards for Mathematical Practice
1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of
others
4. Model with mathematics
5. Use appropriate tools strategically
6. Attend to precision
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning
- Common Core State Standards for Mathematics, 2010, pp. 6-7
9. Standards for Mathematical Practice
1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of
others
4. Model with mathematics
5. Use appropriate tools strategically
6. Attend to precision
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning
- Common Core State Standards for Mathematics, 2010, pp. 6-7
11. Mathematics Task Framework
Mathematical task
as represented in
curricular/
instructional
materials
Mathematical task
as set up by the
teacher in the
classroom
*Task features
*Cognitive
demands
Factors
influencing setup
*Teachers’ goals
*Teachers’ knowledge
of subject matter
*Teachers’ knowledge
of students
Mathematical task as
implemented by
students in the
classroom
*Enactment of task
features
*Cognitive processing
Factors
influencing students’
implementation
*Classroom norms
*Teachers’ instructional
dispositions
*Students’ learning
dispositions
Students’
Learning
outcomes
Relationships among
various task-related
variables and students’
learning outcomes.
Henningsen and Stein,
1997, p. 528; Stein and
Smith, 1998, p. 270
12. Visiting Grandma
Jamie’s family visited their grandmother
who lives 634 miles from their house. On
the first day they drove 319 miles. How
many miles did they have left to drive the
second day?
From Investigations in Number, Data, and Space,
Russell & Economopoulos, 2008
13. Task Analysis Guide
Henningsen and Stein, 1997, p. 528; Stein and
Smith, 1998, p. 270
Memorization
•
•
•
involve either reproducing previously learned facts, rules,
formulas, or definitions or committing facts, rules,
formulas or definitions to memory.
cannot be solved using procedures because a procedure
does not exist or because a time frame in which the task is
being completed is too short to use a procedure.
are not ambiguous. Such tasks involve exact reproduction
of previously seen material, and what is to be reproduced
is clearly and directly stated.
Procedures with Connections
•
•
•
•
Procedures without Connections
•
•
•
•
•
are algorithmic. Use of the procedure either is specifically
called for or is evident from prior instruction, experience, or
placement of the task.
require limited cognitive demand for successful completion.
Little ambiguity exists about what needs to be done and
how to do it.
have no connection to the concepts or meaning that
underlie the procedure being used.
are focused on producing correct answers instead of on
developing mathematical understanding.
require no explanations or explanations that focus sole on
describing the procedure that was used.
focus students’ attention on the use of procedures for the purpose of
developing deeper levels of understanding of mathematical concepts
and ideas.
suggest explicitly or implicitly pathways to follow that are broad
general procedures that have close connections to underlying
concepts.
usually are represented in multiple ways, such as visual diagrams,
manipulatives, symbols, and problem situations. Making connections
among multiple representations helps develop meaning.
require some degree of cognitive effort. Although general procedures
may be followed, they cannot be followed mindlessly. Students need
to engage with conceptual ideas that underlie the procedures to
complete the task successfully and that develop understanding.
Doing Mathematics
•
•
•
•
•
require complex and non-algorithmic thinking -- a predictable, wellrehearsed approach or pathway is not explicitly suggested by the
task, task instructions, or a worked-out example.
require students to explore and understand the nature of
mathematical concepts, processes, or relationships.
demand self-monitoring or self-regulation of one’s own cognitive
processes.
require students to access relevant knowledge and experiences and
make appropriate use them in working through the task.
require students to analyze the task and actively examine task
constraints that may limit possible solution strategies and solutions.
14. Task Analysis Guide
Henningsen and Stein, 1997, p. 528; Stein and
Smith, 1998, p. 270
Procedures with Connections
• focus students’ attention on the use of procedures for the purpose
of developing deeper levels of understanding of mathematical
concepts and ideas.
• suggest explicitly or implicitly pathways to follow that are broad
general procedures that have close connections to underlying
concepts.
• usually are represented in multiple ways, such as visual diagrams,
manipulatives, symbols, and problem situations. Making
connections among multiple representations helps develop
meaning.
• require some degree of cognitive effort. Although general
procedures may be followed, they cannot be followed mindlessly.
Students need to engage with conceptual ideas that underlie the
procedures to complete the task successfully and that develop
understanding.
21. Orchestrating Productive Mathematical Discourse
Chart for Monitoring, Selecting, Sequencing, and Connecting Student Thinking
Strategy
A.
B.
C.
D.
Work of Specific Students
Sequence
Compare
22. Student Justifications
Students’ justifications can be separated into three
broad classes:
appeal to authority;
justification by example;
generalizable arguments.
Carpenter, Franke, Levi, 2003, p. 87
23. Discourse Types
Type 1 – Answering, Stating, or Sharing
Type 2 – Explaining
Type 3 – Questioning or Challenging
Type 4 – Relating, Predicting, or Conjecturing
Type 5 – Justifying or Generalizing
- Weaver, Dick, & Rigelman, 2005
24. Discourse Types
Type 1 – Answering, Stating, or Sharing A student
gives a short right or wrong answer to a direct
question or makes a simple statement or shares work
that does not involve an explanation of how or why.
Type 2 – Explaining
Type 3 – Questioning or Challenging
Type 4 – Relating, Predicting, or Conjecturing
Type 5 – Justifying or Generalizing
- Weaver, Dick, & Rigelman, 2005
25. Discourse Types
Type 1 – Answering, Stating, or Sharing
Type 2 – Explaining A student explains a
mathematical idea or procedure by describing how or
what he or she did but does not explain why.
Type 3 – Questioning or Challenging
Type 4 – Relating, Predicting, or Conjecturing
Type 5 – Justifying or Generalizing
- Weaver, Dick, & Rigelman, 2005
26. Discourse Types
Type 1 – Answering, Stating, or Sharing
Type 2 – Explaining
Type 3 – Questioning or Challenging A student asks a
question to clarify his or her understanding of a
mathematical idea or procedure or makes a
statement or asks a question in a way that challenges
the validity of an idea or procedure.
Type 4 – Relating, Predicting, or Conjecturing
Type 5 – Justifying or Generalizing
- Weaver, Dick, & Rigelman, 2005
27. Discourse Types
Type 1 – Answering, Stating, or Sharing
Type 2 – Explaining
Type 3 – Questioning or Challenging
Type 4 – Relating, Predicting, or Conjecturing A
student makes a statement indicating that he or she
has made a connection or sees a relationship to some
prior knowledge or experience or makes a prediction
or a conjecture based on an understanding of the
mathematics behind the problem.
Type 5 – Justifying or Generalizing
- Weaver, Dick, & Rigelman, 2005
28. Discourse Types
Type 1 – Answering, Stating, or Sharing
Type 2 – Explaining
Type 3 – Questioning or Challenging
Type 4 – Relating, Predicting, or Conjecturing
Type 5 – Justifying or Generalizing A student
provides a justification for the validity of a
mathematical idea or procedure or makes a
statement that is evidence of a shift from a specific
example to the general case.
- Weaver, Dick, & Rigelman, 2005
29. Discourse Analysis Tool
Discourse Types
Type 1 – Answering, Stating, or
Sharing A student gives a short right
or wrong answer to a direct question or
makes a simple statement or shares
work that does not involve an
explanation of how or why.
Predicted
Actual
Type 2 – Explaining A student
explains a mathematical idea or
procedure by describing how or what
he or she did but does not explain why.
Type 3 – Questioning or Challenging
A student asks a question to clarify his
or her understanding of a mathematical
idea or procedure or makes a statement
or asks a question in a way that
challenges the validity of an idea or
procedure.
Type 4 – Relating, Predicting, or
Conjecturing A student makes a
statement indicating that he or she has
made a connection or sees a
relationship to some prior knowledge
or experience or makes a prediction or
a conjecture based on an understanding
of the mathematics behind the
problem.
Type 5 – Justifying or Generalizing
A student provides a justification for
the validity of a mathematical idea or
procedure or makes a statement that is
evidence of a shift from a specific
example to the general case.
For more information about the Student Discourse Observation Protocol see, Weaver, D. & Dick, T. (September 2006). Assessing the Quantity and Quality of Student Discourse in Mathematics
Classrooms, Year 1 Results. Paper presented at Math Science Partnership Evaluation Summit II, Minneapolis, MN. Available at: http://ormath.mspnet.org/index.cfm/14122.
31. Criteria for Representation-Based Proof
The meaning of the operation(s) involved is
represented in diagrams, manipulatives, or story
contexts.
The representation can accommodate a class of
instances (for example, all whole numbers).
The conclusion of the claim follows from the
structure of the representation.
- Schifter, Bastable, & Russell, 2008
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Editor's Notes
Strategy - Purposeful manipulations… that are mathematically justifiable.Algorithm - Steps that are generalizable to other problems of this type.