Process dimensions of mathematics
Overview
Includes information to help learn and facilitate the learning and use of the process dimensions of mathematics.
Problem solving Tools to facilitate mathematical problem solving
- Problem solving Concepts, misconceptions, & outcomes by levels in the mathematical knowledge base
Information to facilitate literacy in problem solving & tools to achieve it
- Development of problem solving - page contents includes:
- Heuristic:
- Strategies for solving problems with sample problems
- Planning & teaching tools pedagogical and curriculum
- Teacher's role in problem solving
- Suggestions to help learners solve problems
- Assessment sample questions to assess learners' mathematical problem solving
- Characteristics of a good problem ideas to consider when writing or selecting problems
- Planning questions to prepare to facilitate problem solving & investigating suggestions to consider when writing or planning to use problems
- Problem Solving Goals and Outcomes to review for the inclusion in appropriate curricular documents and plans
- Problem solving vocabulary to introduce to learners
- Dispositions to review & select to focus on
- Learner's materials
- Learners problem solving guide or checklist to use to as a guide with suggestions to solve problems
- Learners solving checklist - with before, during, and after suggestions
- Learners Solving Attitude Inventory with yes - no questions
- See also communication dimension -
Activities to facilitate problem solving
Reasoning and proof
- Reasoning & proof Concepts, misconceptions, & outcomes by levels in the mathematical knowledge base
Information to facilitate literacy in reasoning & proof & tools to achieve it
- Reasoning and Proof Explanations and development of reasoning, proof, & logic - information on reasoning and proof with examples of different types of proof, teaching suggestions, & an extensive scoring guide
- Reasoning and proof big idea, concept, or generalization instructional planning map
- Development of reasoning from birth to maturity
- Reasoning, conservation, and cognitive development tasks & activities
- Application of proof by elimination & verification with a card trick
- Bucket problems reasoning, proof, conjecture, combinations
- Decision making, critical thinging, and change processes
- Structure for Analyzing and Presenting Arguments
- Logical Reasoning and Reasoning Errors
- Position analysis
- Issue analysis & sample issues analysed for democratic education for all
- Reasoning solutions for SUDOKU
- Imagining
- An Outline of Goals for a Critical Thinking Curriculum and Its Assessment
Activities to facilitate reasoning & proof
Representation
Representation Concepts, misconceptions, & outcomes by levels in the mathematical knowledge base
Information to facilitate representation & tools to achieve it
- Examples of mathematical representations with language as nouns and verbs.
- Function exploration - includes definitions with examples, diagrams, & representations including a function machine. Also activity with work sheet and charts to explore a function with a variable factor (3) & constant factor (27) & discover casting out nines
Area representations
Lynne Outhred and Michael Mitchelmore asked learners to illustrate the area of a rectangular shape. They found learners demonstrated four different strategies: incomplete covering, visual covering, concrete covering, and measurement. The drawings below show samples from each.
![area image](represntatns/areaRepresentations.jpg)
Representation of relative position of objects
![image](represntatns/indoorTrackDrawing505Wide.jpg)
Illustration of Internal Representation
![image](represntatns/indoortrackPicture.jpg)
Actual object, real world, or external representation
Representation of external objects with points on an other external object
![image](represntatns/handPinPrint504.jpg)
What does this have to do with mathematical representations?
Activities to facilitate representation
Communication
Communication Concepts, misconceptions, & outcomes by levels in the mathematical knowledge base
Information to facilitate literacy in communitation & tools to achieve it
- Different ways to communicate problems with sample problems
- Ways to communicate mathematical representations as objects, properties, actions, & operations
- Graphing with line graphs as communication
Activities to facilitate reasoning & proof
Connections & perspective
Connections & perspective Concepts, misconceptions, & outcomes by levels in the mathematical knowledge base
Information to facilitate literacy in connections & perspective & tools to achieve it
- Mathematical ideas build upon each other.
- Mathematical ideas are connected to other mathematical ideas.
- Mathematical ideas are connected to the world.
Activities to facilitate reasoning & proof
Contents:
Other math knowlege base &
activity pages
Content dimensions
Common sense & knowledge
Counting in Winnebago
- WIn
- NOnBA
- THABTHIn
- DUBA
- SATOn
- SHAPE
- PETHOnBA
- PETHABTHIn
- SHOnKA
- GTHEBOn
Interesting book
The Power of Logical Thinking: Easy Lessons in the Art of Reasoning... and Hard Facts About Its Absence in Our Lives, Marilyn Vos Savant (1996) ISBN 0-312-13985-3 Saint Martin's Press: New York.