What are the foundational principles in mathematics teaching and learning?

Considerations:

  • the First Peoples Principles of Learning and other ways of knowing contribute to a more holistic and experiential experience of mathematics and benefits all learners
  • students learn to think like mathematicians by being immersed in the "mathematical habits of mind" (from BC Mathematics Curriculum):
    • persevering and using mathematics to solve problems in everyday life
    • recognizing there are multiple ways to solve a problem
    • demonstrating respect for diversity in approaches to solving problems
    • choosing and using appropriate strategies and tools
    • pursuing accuracy in problem solving
  • students learn to be mathematicians by embodying dispositions such as:
    • curiosity and a sense of wonder
    • playfulness
    • flexibility
    • sense making
    • resilience
  • problem-solving is foundational to the study of mathematics
  • an inquiry-based approach includes rich tasks and student problem posing, which nurtures engagement, curiosity and deep understanding
  • the language of mathematics supports learning and thinking like a mathematician
  • the foundational mathematical big ideas include:
    • number represents and describes quantity
    • development of computational fluency requires a strong sense of number
    • we use patterns to represent identified regularities and to form generalizations
    • we can describe, measure, and compare spatial relationships
    • analyzing data and chance enable to compare and interpret information
  • there is a progression of learning in mathematics
  • mathematics has underlying structures such as the associative property, the commutative property, and the distributive property

Resources:

Assessment through curricular competencies Grades 6-9 and K-5 developed by Island Numeracy:

Assessment through curricular competencies poster k-5 draft.pdf
Assessment through curricular competencies poster 6-9 draft.pdf
Assessing Early Numeracy.pdf

Habits of Mind

Extensive research indicates that for students to develop mathematical habits of mind they must encounter and interact in intentional learning settings. Classroom design combined with active participation strategies will enhance student learning, increase achievement, and factor in the development of the well-educated citizen.

Students who have developed mathematics habits of mind exhibit expertise in:

  • persevering and using mathematics to solve problems in everyday life
  • recognizing there are multiple ways to solve a problem
  • demonstrating respect for diversity in approaches to solving problems
  • choosing and using appropriate strategies and tools
  • pursuing accuracy in problem solving

From: BC's New Curriculum Introduction to Mathematics

George Polya, an influential mathematicican from the 1940s, described four steps in problem-solving in his book How to Solve It:

  • understand the problem
  • develop a plan and consider possible strategies
  • carry out the plan and use the strategies
  • look back and reflect
NCTMResearch_brief_14_-_Problem_Solving.pdf

Problem Solving

For more information see chapter: "Teaching Through Problem Solving," from Van de Walle's Elementary and Middle School Mathematics: Teaching Developmentally.

Developmental Continuum Grade k-9.docx