Summary of "An Introduction to the Why, What, How, When, and Who of Assessing Mathematical Thinking"

Summary of An Introduction to the Why, What, How, When, and Who of Assessing Mathematical Thinking

This video, presented by Laura Jeannie Newman, a math consultant for the Critical Thinking Consortium, introduces a new resource—a quick guide focused on assessing mathematical thinking with an emphasis on reasoning competencies. The guide aims to help educators understand why assessing mathematical reasoning is essential and provides practical advice on what, how, when, and who should be involved in this process.

Main Ideas and Concepts

Importance of Assessing Mathematical Reasoning

Mathematical reasoning is central to mathematical competence.
It involves reasoning abilities to understand, act, and communicate effectively in solving complex and unfamiliar problems.
International assessments (e.g., PISA, TIMSS) emphasize reasoning at the core of math competency.
Reasoning-focused assessment benefits both teachers and students by:
- Providing clear, quality-focused assessment targets.
- Balancing content knowledge with process skills.
- Reducing math anxiety by making assessment less judgmental.
- Supporting transfer, creativity, collaboration, independence, and inclusivity.
- Aligning with international education goals supporting learner agency, well-being, and co-agency (integration of diverse perspectives).

What to Assess

Both content knowledge and reasoning processes are important.
Reasoning competencies underpin understanding, acting (doing), and communicating mathematically.
Reasoning competencies are consistent across grade levels and content strands, serving as a unifying focus for assessment.

How to Assess

Frame assessment questions and tasks that invite high-quality mathematical thinking.
Use open, closed, or bounded questions designed to:
- Make thinking processes explicit.
- Encourage metacognition (thinking about thinking).
- Require students to use mathematical knowledge as evidence.
General thinking process involves:
- Making decisions/judgments based on plausible options.
- Explicitly considering criteria relevant to the task.
- Using metacognition and mathematical tools.
Specific reasoning competencies (e.g., conceptual reasoning) relate to particular types of questions/tasks.
Use shared criteria for assessing reasoning quality, adaptable by grade and content.
Employ templates and examples to align reasoning competencies with assessment tasks.

When to Assess

Use an iterative learning process starting with a rich, complex reasoning-focused assessment.
Follow with smaller, sequenced assessments to scaffold learning and reasoning development.
This differs from spiraling; it revisits and integrates prior learning to support reasoning growth.
The iterative process helps students build capacity gradually and personalize learning.

Who Should Assess

Students should be primary assessors of their own thinking to develop reflective reasoning skills.
Tools such as “learning launches” and “thought books” help students document, track, and reflect on their reasoning over time.
A “guide to success” supports ongoing reflection with:
- Clear task requirements.
- Criteria for quality.
- Space for student self-assessment.
- Teacher guidance with reasoning-focused questions.
This approach empowers students and supports continuous improvement in reasoning quality.

Additional Notes

The guide provides planning templates, examples, and supplementary materials to support implementation.
Emphasizes that reasoning-focused assessment acknowledges teaching complexity but is worth the effort.
Encourages educators to find personal entry points into this professional learning and to let reflective thinking guide their practice.

Detailed Methodology / Instructions for Assessing Mathematical Thinking

Reflect on Your Current Assessment Practices
- Consider your responses to why, what, how, when, and who regarding math assessment.
- Compare your views with perspectives from practicing teachers.
Understand the Central Role of Reasoning
- Recognize reasoning as the core competency in math learning.
- Focus assessments on reasoning competencies alongside content knowledge.
Frame Assessment Questions and Tasks
- Design questions that:
  - Invite explicit mathematical reasoning.
  - Encourage metacognition.
  - Use mathematical knowledge as evidence.
- Use a mix of open, closed, and bounded questions to balance depth and manageability.
- Ensure tasks are meaningful and motivate student engagement.
Align Reasoning Competencies with Tasks
- Identify which reasoning competency (e.g., conceptual reasoning) each task targets.
- Use provided templates to map competencies to tasks.
- Incorporate sound and reflective reasoning as foundational for all tasks.
Use Shared Criteria for Assessment
- Adapt general criteria to specific content and grade-level vocabulary.
- Maintain consistency in learning targets across time and content.
Implement Iterative Learning and Assessment
- Begin with a complex, rich reasoning-focused assessment.
- Follow with smaller, sequenced assessments to scaffold learning.
- Use a three-part reasoning lesson design:
  1. Independent initial thinking.
  2. Collaborative growth of ideas.
  3. Independent synthesis and extension of thinking.
Empower Students as Assessors
- Introduce learning launches and thought books for students to track thinking.
- Provide a guide to success with:
  - Clear task requirements.
  - Quality criteria.
  - Self-assessment prompts.
  - Teacher guidance questions.
- Encourage ongoing reflection and revision of thinking.
Move from Assessment to Evaluation
- Use the reasoning-focused approach to guide professional learning and improve assessment practices.

Speakers / Sources Featured

Laura Jeannie Newman – Math consultant for the Critical Thinking Consortium and presenter of the video.
Chris – Secondary school math department head from York Region, providing perspective on the importance of metacognition.
Bill – Grade 3-5 math teacher from Manitoba, emphasizing student understanding and independent thinking.

This video serves as an introduction and invitation to explore the quick guide and associated resources for effectively assessing mathematical thinking through a reasoning-focused approach.