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Critical Thinking in Math: A Focus on Mathematical Reasoning Competencies
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Critical Thinking in Math: A Focus on Mathematical Reasoning Competencies
Critical Thinking in Math: A Focus on Mathematical Reasoning Competencies
TC²’s approach to math embraces the idea that sustained quality mathematical thinking, or reasoning, is the key to the success of current and future generations of math students.
What Is Mathematical Reasoning?
A mathematical reasoning approach optimizes the learning opportunities for every student in the classroom. It empowers students with the capacity to independently detect the need for, and to use, a wide range of math reasoning abilities.
This approach ensures that students develop both
a strong understanding of foundational math concepts and content, and
the capacity to reason soundly about and with these concepts and content.
When we focus on reasoning competencies, students continue to learn important math concepts while also learning how to
deeply understand
appropriately act on, and
effectively communicate using those concepts.
What Are Mathematical Reasoning Competencies?
Eight key mathematical reasoning competencies underpin all math learning and are needed for student success in math. These are presented in A Math Pedagogy Designed to Empower Learners [PDF].
Competency
Definition
Core competencies
Sound thinking or reasoning
Reasoning about the quality of one’s thinking
Reflective reasoning
Reasoning about the quality of one’s understanding, actions, and communication
Understanding
Conceptual reasoning
Reasoning about what makes a concept what it is and how to recognize that concept
Detail-minded reasoning
Reasoning about which mathematical details to use and how to use them effectively
Acting
Connective reasoning
Reasoning about how to effectively connect ideas
Problem-managing reasoning
Reasoning about how to effectively identify and solve math problems (including how to effectively select, organize, and use mathematical strategies, tools, and resources)
Communicating
Representational reasoning
Reasoning about how to effectively represent ideas
Language reasoning
Reasoning about how to effectively use the language of mathematics including its structure and symbols
"To provide each and every student equitable opportunities to improve their learning success in math, students need to learn how to reason soundly in a variety of ways through the application of critical thinking.
—Laura Gini Newman (2020)
A Math Pedagogy Designed to Empower Learners
Math Resources Survey
Let us know how we can best support the implementation of a mathematical reasoning approach in your classroom(s) or school(s). Complete our short survey and receive 10% off our publications!
NEW! Assessing Mathematical Thinking: A Focus on Reasoning Competencies
This new title in our Quick Guides to Thinking Classrooms series presents a framework for effectively assessing and evaluating thinking in math. It shows how building math assessment practices on a foundation of essential mathematical reasoning competencies provides a clearly defined, manageable, and consistent way to focus assessments.
A Math Pedagogy Designed to Empower Learners [PDF]
Laura Gini-Newman outlines a new pedagogical approach to the teaching and learning of mathematics that is focused on building student capacity to reason mathematically through critical inquiry.
Critical Inquiry in Math Class
During TC²’s 25th Anniversary celebration, each month explored a different focus. April focussed on how we can bring critical thinking into math. This webpage introduces the focus and explores ways to enrich your classroom with critical inquiry in math.
OAME Talks
Listen to TC² math consultant Laura Gini-Newman as she shares her thoughts on Assessing Mathematical Thinking: Who, What, When, and How on the OAME Talks podcast (Season 5, Talk 41)
How Thinking Mathematically Changed My Teaching
Jocelynn Foxon talks about her experience completing the Math Lead Teacher Certification Program (MLTCP) offered by TC², and the work she did with teachers and students in supporting the implementation of this approach in the math classroom.
Generating Enthusiasm in the Math Classroom
Nina Perreault-Primeau talks about the transformation in her math classroom when she planned lessons focussing on student interest, creating authentic learning opportunities accompanied by sound critical inquiry questions.
But will it also work in math? [PDF]
Sarah Sommers describes what happened when she and her teaching partner took a critical inquiry approach with their Grade 5 students during a math patterning unit.
Basics vs Inquiry in Math? A critical inquiry approach can achieve both
Chris Achong talks about his experience with his Grade 9 math team implementing this approach to math learning—a comprehensive and balanced approach that improves the quality of every student’s capacity to think mathematically.
Math Lead Teacher Certification
This program supports teacher development of a rich understanding of the diverse role of critical thinking in math classrooms through 18 hours of personalized coaching and 10 hours of implementation support. Available as face-to-face and online sessions or a combination of both.
Book Professional Learning in Math
Learn how we can help you plan affordable professional learning in math facilitated by our experienced team. We consult and collaborate with you to develop custom, focused, and engaging face-to-face and online sessions to meet your math specific needs and grade level requirements.
