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  • ISBN: 978-1-9991413-9-4
  • Pages: 62
  • Publication year: 2022
  • Online supplement
  • Type of resource

    Professional resources

  • Audience

    Educational leaders/instructors

  • Format


  • Subject area


  • Targeted grade range

    Primary (K-3)
    Intermediate (4-6)
    Middle (7-9)
    Senior (10-12)

  • Series

    Quick Guides to Thinking Classrooms

  • Language


Assessing Mathematical Thinking: A Focus on Reasoning Competencies

Author(s): Laura Gini-Newman
Publisher(s): The Critical Thinking Consortium


Assessing Mathematical Thinking presents a framework for effectively assessing and evaluating thinking in math. It shows how building assessment practices on a foundation of essential mathematical reasoning competencies provides a clearly defined, manageable, and consistent way to target assessments. The guide introduces assessment practices and tools that focus on what matters most to supporting student success in math—developing a strong ability to reason mathematically.

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  • Frameworks and templates to help educators design empowering math assessments
  • Strategies to best support thinking and learning opportunities
  • Thinking routines to assess, support, and evaluate student thinking
  • Classroom examples from across the grades
  • Online Supplement with modifiable templates and additional resources, including
    -Fully developed teacher slides for student inquiry challenge
    -Using a Guide to Success to Assign Marks (narrated PPT presentation)

It is perfect for:

  • Math teachers, coaches, leads and others who support math learning at any grade level and are interested in learning how to use assessment as a way to build student capacity to reason mathematically as part of their day-to-day learning.

Author Laura Gini-Newman began consulting with TC² after a diverse career as a classroom and university educator, consultant, coach, and textbook and curriculum writer. She has worked with teachers around the world highlighting the significant role of sustained critical inquiry in mathematics in empowering all students to become independent, self‑regulated learners who understand the societal value of mathematics.

Why assess mathematical reasoning competencies?

Focussing on reasoning competencies rather than content might seem like a significant shift in math assessment. But in reality, it’s not. When we focus on reasoning competencies, students continue to learn foundational math concepts while also learning how to deeply understand, appropriately act on, and effectively communicate using those concepts.

By teaching students to reason mathematically, we are empowering them to independently make mathematical decisions that they feel confident about and that they can see support their learning.

Building the capacity to reason mathematically helps students learn how to

  • effectively learn math no matter the grade level or content
  • reflect productively on the quality of their thinking and understanding
  • take ownership of their learning journey and personalize it in meaningful, productive, and accessible ways that serves each student well

What are mathematical reasoning competencies?

Eight key mathematical reasoning competencies underpin all math learning and should frame our assessment practices. These are presented in “A Math Pedagogy Designed to Empower Learners” (Laura Gini-Newman, 2020).

In this guide, we will focus on the two competencies that are foundational for creating great mathematical thinkers: sound reasoning and reflective reasoning.

Assessing Mathematical Thinking Quick Guide Sound Reasoning

“When students are able to inquire about math and think about their thinking during the learning process the results are unbelievable. Assessment occurs on a daily basis because students are not only explaining what they know, they are also justifying how they know it. Students who once struggled in math before are now given the opportunities to share their thinking in new and different ways and they are shocked to see they CAN do math!”

— Jocelynn Foxon, K-12 Numeracy Coach

Quick Guides to Thinking Classrooms

Quick Guides to Thinking Classrooms series emerged from the success of Creating Thinking Classrooms, a TC2 resource that explores the key pedagogical principles and ideas that will best shape learning in the 21st century. Each title in the series focuses on practical strategies for developing deep understanding, real-life competencies, and thoughtful commitment by students. Useful for beginning and experienced teachers, the Quick Guides are designed to inspire and reinforce creative, critical, and collaborative thinking in students at every grade level.

ASupporting All Learners: Creating the Conditions for Inclusive Classrooms Quick Guide

Supporting All Learners: Creating the Conditions for Inclusive Classrooms

Designed to guide educators in taking an inclusive approach in all subjects and grades, Supporting All Learners provides simple but powerful starting points for creating inclusive classrooms.

Teaching Students to Use Criteria Quick Guide

Teaching Students to Use Criteria

This new title in our Quick Guides to Thinking Classrooms explores criteria for judgment: what they are, how to support student use of criteria, when and where to best make use of criteria, and how to assess for effective student use of criteria.

Building a Community of Thinkers Quick Guide

Building a Community of Thinkers

Use the practical ideas, examples and templates in this resource to build a learning community in which high-quality thinking is modeled, supported and explicitly encouraged.

View the Quick Guides to Thinking Classrooms series

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