Author(s): Laura Gini-Newman
ISBN: 978-1-9991413-9-4
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.
See all of the titles in the Quick Guides to Thinking Classrooms series
-Fully developed teacher slides for student inquiry challenge -Using a Guide to Success to Assign Marks (narrated PPT presentation)
Why assess reasoning competencies? The benefits of assessing reasoning competencies Assessing for thinking in action: The big picture
What mathematical reasoning competencies should we assess? Assessing for thinking in action: Making math fun! Two core reasoning competencies Sound reasoning Reflective reasoning The important role of quality
How can we design empowering math assessments? Assessing for thinking in action: Making math meaningful Making assessments curriculum and concept focussed Making assessments context focussed Making assessments reasoning focussed Framing reasoning-focussed questions and tasks Imposing constraints to narrow open-ended assessments Inviting students to make productive mathematical decisions
How can we best sequence thinking and learning opportunities? Starting with the assessment Scaffolding reasoning opportunities
What routines can we use to assess, support, and evaluate student thinking? Assessing for thinking in action: Using thinking routines Learning launches Thoughtbooks Guides to Success Using Guides to Success to move seamlessly from assessment to evaluation
Conclusion References and Notes Appendix
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
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.
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
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