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Be sure to check out Part 1 and Part 2 of our “Coaching for a Mathematical Mindset” blog series.
Below are two conversations between a teacher and a coach. How are they different? What might the teachers’ observations and explanations reveal about their mathematical mindsets?
Conversation 1
Coach: You’ve been trying some new instructional practices to support your students’ math learning. How’s it going?
Teacher 1: One thing I’ve noticed is that my students are using more math vocabulary in explanations of their strategies.
Coach: What factors do you think may have contributed to this improvement?
Teacher 2: We’ve been doing Number Talks on a daily basis so my students have had lots of practice talking about their math thinking. I believe this daily opportunity to explain their strategies and listen to others’ explanations has made them more aware of the importance of using precise language. I’ve also been using more word banks and sentence frames in my lessons, and even in small group instruction.
Conversation 2
Coach: You’ve been trying some new instructional practices to support your students’ math learning. How’s it going?
Teacher 2: I noticed that my students’ benchmark scores are better this time than last.
Coach: What factors do you think may have contributed to this improvement?
Teacher 2: I’m not sure. This unit seemed easier for the students than our last unit. It may just be the time of the year.
A teacher’s identity as a math learner and her relationship to mathematics shape what she sees in her students’ math learning. This in turn impacts how she facilitates student thinking through scaffolding and questioning. Whether a teacher defines mathematics in terms of thinking and reasoning or as memorization of facts and procedures will determine how she designs learning tasks as well as how she measures her students’ progress. A teacher’s mathematical mindset impacts her students’ learning and the development of her students’ mindsets.
A teacher’s mathematical mindset impacts her students’ learning and the development of her students’ mindsets.
In her book Math: Facing an American Phobia, Marilyn Burns talks about the widespread feelings of inadequacy and anxiety related to mathematics that exist in our country, and how these are a direct result of ineffective and outdated instructional practices: “The way we’ve traditionally been taught mathematics has created a recurring cycle of math phobia, generation to generation, that has been difficult to break” (p. x). Marilyn has spent more than 30 years defining best practice in the mathematics classroom and helping teachers learn how to create classrooms where students are continually asked to think, reason, and make sense of mathematics. Based on Marilyn’s extensive work, the Math Solutions Instructional Practices Inventory is now available as a guide to recognizing and growing model mathematics classrooms.
The Instructional Practices Inventory makes explicit the connection between teacher instructional practices and student outcomes in four categories representing important aspects of mathematics teaching and learning: Learning Environment, Reasoning and Sense-Making, Focus and Coherence, Formative Assessment. The teacher and student indicators within each of these categories also operationalize a mathematical mindset. Perhaps you could use the Instructional Practices Inventory to launch a discussion of mathematical mindset. You might ask teachers to study the indicators and then talk about how they represent the mindsets we want to see in our students as well as the mindsets we need to operate from and model as teachers. Afterward, you might have teachers work in groups to create a poster depicting a mathematical mindset. Teachers could adapt this experience for use in their classes to build their students’ awareness of the importance of mindset to mathematics learning.
What are your ideas about how the Instructional Practices Inventory might be used to help teachers and students strengthen their mathematical mindsets?
Please share your thoughts in the comments.
Sue Chapman is a professional educator, presenter, and author who has devoted over 30 years to instructional improvement and mathematics education. Throughout her career, Sue has served and taught in several different areas of professional education, including instructional and leadership positions. Sue’s passion for professional learning and her ability to inspire teachers to come together around a shared vision of success have been instrumental in helping schools and districts develop systems and internal capacity to achieve continuous improvement of mathematics instruction.
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