In Part 1 of this mini-series, we looked at how we can promote diverse identities in mathematics from the first artifacts students see: you, your syllabus, and your classroom. Here in Part 2, we’ll examine the mathematical habits, behaviors, and skills that ensure students will be able to participate fully.
Like with identity, students and adults can have a very rigid, narrow understanding of what mathematicians do and what skills are valuable to the discipline. Often people equate speedy calculation as “good at math.” There is a persistent belief that arriving at the correct number is the thing that makes you good at math. On the contrary, Andrew Wiles took years to find a proof to Fermat’s Last Theorem. And when he did, it had an error! It took two additional years for he and colleagues to come up with a correct proof!
Mathematics is a foray into folly. Every now and then you get a right answer. Most of the time is spent figuring out where you went wrong. In fact, I’d argue that’s one of the benefits of math: it can teach you how to analyze and scrutinize your own actions and thought processes. How do these habits of revision, error-making, and metacognition in your syllabus (and in turn, your class throughout a school year)?
One of the most rudimentary things you can do to promote varying ways of mathematical thinking is by explicitly naming them. I really like this poster from Erika. Make sure to name these specifically in your syllabus: these are the habits and skills that you are going to value in this classroom. I appreciate and welcome students who ask questions,
Now, there are lots of “Mathematicians do ‘X’” posters floating around. It’s another thing to truly promote these habits and ways of thinking. So how will you do that in your class (and therefore communicate as such in your syllabus)? Here are some possibilities to consider.
- Provide a few of your non-traditional mathematical strengths (and perhaps a few weaknesses) and ask students to do the same.
- Explicitly name that you’re reducing the emphasis on correctness, instead focusing on effort and revision.
- Invite weekly or monthly reflection journals.
- Make connections between mathematical profiles (see Part 1) and mathematical habits and skills. For example, in the first paragraph of this blog post, I cited Wiles’ published error and the length of time to come up with the correct answer.
- Provide grading structures that promote the mathematical habits you wish to promote. For example, state up front how you’re grading and why.
- “Because mathematicians constantly revise work, you are allowed to revise your work for full credit.”
- “You will be graded on your ability to collaborate, be creative, and communicate via a rubric. All such grades will be accompanied by a conversation so we can come to a consensus on where you can grow as a mathematician.”
- “Your grade will partially be determined by your mathematical portfolio.”
- “Your grade is always up for discussion. I’m happy to meet at any time to discuss your grade and how to improve it.”
Ideally, some of these structures will be agreed upon by an entire grade level, math department, or even school. It’s one thing for a lone educator to honor revised work, it’s more powerful when students experience that at multiple successive grade levels.
We want all students to feel like they have strengths to bring to the math classroom. We also want to identify areas for potential growth in students in a way that is academically safe. Show students what you value from the outset and reinforce it with structures and norms throughout the year.
Be sure to check out other posts from this Emergent Math Mini-Series:
- Part 1: Identity. Who is a mathematician?
- Part 2: Smartness. What does it mean to be a mathematician?
- Part 3. Norms. What are the expectations for quality collaborative work?
- Part 4: Anchor Problems. A Hilbertian Approach to Curriculum Mapping.
- Part 5: Putting it all together. Additional nuts & bolts and an example syllabus.