In early October, I presented at NCTM Hartford with the incomparable Heidi Fessenden (@heidifessenden / blog). Our session was called “Strategies for Cultivating Mathematical Thinking for All Learners.”

**Slides available here.**

The first blog post, contextualizing these strategies and providing some research that inspired us, was published on Monday.

The second blog post, published on Tuesday, detailed the first of three strategies from our presentation: rewording the standards for mathematical practice (SMPs) in kid-friendly language, or “mathematician statements.”

After crafting mathematician statements, it’s important to:

2. **Assign competence**

*the practice of publicly identifying and praising times when students — especially low status students — are engaged in mathematical thinking*

Assigning competence is a practice that should be:

- Public
- Focused on low-status students
- Specific
**Intellectually meaningful**

(Horn, Ilana Seidel. Strength in Numbers: Collaborative Learning in Secondary Mathematics. Reston, VA: National Council of Teachers of Mathematics, 2012.)

You can read more about it on Ilana’s blog.

It is not about *feeling* competent, but *recognizing* competence*, *and continuing to build these competencies. Assigning competence must focus on mathematical thinking.

It’s much easier to assign competence in a live classroom, where you can witness students engaging in the mathematical practices. I say things like:

We then practiced assigning competence to students.

This first work sample came from an enactment of one of Graham Fletcher’s 3-Act Task, the Whopper Jar. A jar fit involved 4 bags of 19 whoppers, and 3 extras from the 5th bag.

This high status student in the classroom recorded this equation. There’s plenty to praise there — how he anchored on a fact he knew to figure out 19 x 4 (using compensation), or how he clearly and accurately recorded true equations.

It takes a minute to process the work in the next sample. To assign competence, we need to praise the *work* — the *ideas!* It’s not enough to say “Student 1, you used an awesome strategy! Student 2, you tried hard!” What genuine strengths can we determine from looking at this work?

This rehearsal was tricky for participants. Looking at student work requires you to wrap your mind around the problem, enveloping it, so that you can understand new strategies.

I think that this student demonstrated a strong understanding of 19 as tens and ones, and that we can use this decomposition to add more quickly. Mathematicians break down numbers and recombine them in efficient ways. I often praise the thinking over the product.

Strategy 3, using high-leverage instructional routines, will be published tomorrow.

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