Processes for the practice of mathematics
- Problem solving concepts & list of problem solving strategies
- Problems by categories (number value, algebra, geometry, measurement, probability, reasoning & problem solving)
- Goals and Outcomes for Problem Solving
- Year plan or curriculum starter for problem solving
- Heuristics - 4 step - 5 step - 8 step
- Vocabulary for Problem Solving
- Vocabulary for Calculators
- See also communication dimension - particularly Six ways to communicate problems
- Examples of Problems for different problem solving strategies
- Teacher's Role during problem solving sessions
- Steps to Help Students Solve Problems
- Features of a Good Problem
- Guiding Questions to Help Select Good Problems and Investigations
- Questions to use to assess students problem solving attitudes and skill
- Student Problem Solving Guide
- Problem Solving Checklist for students
- Student Attitudes Inventory for Mathematical Problem Solving
Scoring guides and rubrics
- Problem solving scoring guide or rubric in three formats | See assessment for discussion on its creation |
- Problem solving check sheet with 8 categories and levels for doing with a prompt, without prompt, and unable to do without significant help
- Problem solving - with six categories: problem solving, reasoning, communication, representation, habits of mind or attitudes, and math understanding with four levels
- Problem solving - with three categories (understand problem, strategy slection, and accuracy) and three levels
- Reasoning and Proof Explanations: Mini article on reasoning and proof with examples to use with students and an extensive scoring guide
- Reasoning and proof big idea, concept, or generalization instructional planning map
- Development of reasoning from birth to maturity
- 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
- Reasoning solutions for SUDOKU
- An Outline of Goals for a Critical Thinking Curriculum and Its Assessment
Sample Problems for Reasoning and Proof
Representation of relative position of objects
Illustration of Internal Representation
Actual object, real world, or external representation
Representation of external objects with points on an other external object
What does this have to do with mathematical representations?
Six Ways to communicate mathematically: with sample of each
- Pictures - Four ways to make 25 cents
- Manipulatives - use of - cubes Writing after Average student height
- Writing - Percentage - Sale problem
- Acting it out - The Door Bell Rang - from the book, The Door Bell Rang by Pat Hutchins
- Symbols - Pigs Go to Dinner - from the book, Pigs Will Be Pigs: Fun with Math and Money. by Amy Axelrod, 1994
- Orally - talk it out.
Graphing notes for line graphs.
Connections and perspective
- Mathematical ideas build upon each other.
- Mathematical ideas are connected to other mathematical ideas.
- Mathematical ideas are connected to the world.
Common sense & knowledge
Counting in Winnebago
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.