What are the foundational principles in mathematics teaching and learning?
Math is about sense-making. "This the most fundamental idea that a teacher of mathematics needs to believe and act on. It is through the teacher's actions that every [learner] in his or her own way can come to believe this simple truth and, more importantly, believe that he or she is capable of making sense of mathematics. Helping students come to this belief should be the goal of every teacher. "
(Van de Walle, Teaching Student-Centred Mathematics, 2006, p. ix)
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":
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 Mathematics Curriculum
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:
The First Peoples Principles of Learning contribute to a more holistic and experiential experience of mathematics.
There are a number of resources to support the First Peoples Principles of Learning and other ways of knowing in the context of learning mathematics. Below is a list of online resources from a variety of organizations including the First Nations Education Steering Committee.
Principles-of-Learning-First-Peoples-poster-11x17.pdfFirst Peoples Principles of Learning Online Resources:
First Peoples Principles of Learning
First Nations Education Steering Committee (FNESC) Homepage
Math Catchers: Mathematics Through Storytelling
Students learn to think like mathematicians by being immersed in the mathematical habits of mind.
Assessing Early Numeracy.pdfObservation checklist for teachers drawn from the BC Early Numeracy Project
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
Problem-solving is foundational to the study of 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.pdfOther resources on problem solving include this Research Brief put together by The National Council of Teachers of Mathematics on why it is important to student learning to teach with problem solving.
An inquiry-based approach includes rich tasks and student problem posing, which nurtures engagement, curiosity and deep understanding
Canadian resource for supporting inquiry in mathematics and science.
Jo Boaler - Enquiry Based Learning for Mathematics
Professor Jo Boaler works with secondary school students in the inQbate at the University of Sussex using Inquiry Based Learning methods for mathematics.
Creativity in Mathematics: Inquiry - Based Learning and the Moore Method
Explores the world of Inquiry-Based Learning and seeks to identify the reasons behind its celebrated success.
Inquiry-Based Learning in the Primary Classroom
Webinar
The language of mathematics is critical for engagement, understanding and communication.
"90% of math language happens only within the math classroom." - Krpan, 2018
Author Cathy Marks Krpan believes that through competency-based learning, students and teachers alike can deepen their mathematical understanding and share and impart that knowledge in and out of the math classroom. Teaching Math With Meaning takes a practical approach to embedding this deep learning in K to Grade 8 mathematics classrooms.
The Digest edition 2010-2 - Language in the mathematics classroom.pdfThe article Language in the Mathematics Classroom describes the role of language in Numeracy learning and the complexity of math language which often leads to ambiguity in conceptual understanding.
There is a progression of learning in mathematics.
The following resources include professional resources, programs that provide a framework for teaching with progressions, learning continuums for mathematics and online resources. These resources draw upon the research from cognitive science, educational psychology and mathematics education research.
First Steps Mathematics is a series of resource books that will help teachers increase their capacity as mathematics educators. The program includes strategies to diagnose, plan, implement and judge the effectiveness of the learning experiences they provide for students. The link will take you to a site where you can access these resources for free.
PRIME stands for Professional Resources and Instruction for Mathematics Educators.
This resource provides courses and resources for teachers.
Learning Trajectories: A web-based tool for early childhood educators to learn about Learning Trajectories for math, review video clips of children’s thinking around the progression and activities to support development along the math trajectories. Educators must create an account in order to access this free resource.
ClementsSaramaLearning_trajectories_math.pdfNumber Worlds Learning Trajectories
New South Wales, Australia
en_math_k-9_content.pdfBC Math K-9 Content
Continuous view
en_math_k-9_curricular_competencies.pdfBC Math K-9 Curricular Competencies
Continuous view
Pearson Mathematics Learning Progression available in English & French
Math specialist Graham Fletcher has created a number of videos that demonstrate the progression of learning math on the following topics:
Early number and counting
Addition and subtraction
Progression of division
Progression of multiplication
Fractions: the meaning, equivalence, and comparison
NOTE: Graham is an American educator, so he is referencing the Common Core curriculum (ie. don't pay attention to the grades!)
The Coast Metro Consortium invited educators from the Lower Mainland Math Contacts (LMMC) group to develop an elementary math framework to support teachers in the Coast Metro region in the teaching and assessment of elementary mathematics. A team of teachers from the LMMC collaborated over the summer of 2022 using suggested elements from the Coast Metro Consortium to develop a shared vision for elementary mathematics education, grounded in the BC K-7 mathematics curriculum. The website contains K-7 resources focused on Number and Number Operations and the corresponding curricular competencies.