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The Two Essential Ingredients

Writer's picture: Peter CoePeter Coe

When I'm talking to people that want to change the way math instruction happens in schools, the questions they ask often center on the technical side of things:

  • What curriculum should we use?

  • How should we spend our professional learning hours at the beginning of the school year?

  • What kind of a coaching program will help us achieve our goals?

  • How can we create an effective math tutoring program?

Of course I'm happy to talk about these things, but it's important also to steer the conversation over to what I have come to appreciate as the two most essential ingredients for bringing about change in mathematics instruction: trust and a common vision.

  1. Trust. Without an atmosphere of trust, technical changes made via curriculum, new structures in the school day, or professional learning won't matter. In particular, I'm talking about trust between teachers and leaders. When new initiatives emerge, will anyone pay attention? Or will they think, "this too, shall pass?" When staff are asked for their input, will they weigh in? Or will they assume they won't be heard? Leaders can lead only when staff trust them; conversely, leaders must be able to trust their staff if they are to take on ambitious goals. Three ways to start building trust immediately as a math leader are:

    1. Hold yourself accountable for meaning what you say. People will trust you when they see you keeping your word and as a leader it's easy to make promises, especially small ones. Track them! Make notes immediately when you commit to doing something and build a daily or weekly routine to check in on your own progress. If you aren't able to come through with what you've promised on time, let stakeholders know.

    2. Ask for feedback and act on it. It can be hard to hear feedback, but listening to staff and other stakeholders is a great way to earn trust. It shows that you trust your staff, care about what they think, and want to do better. Be mindful that acting is just as important as listening, if not more so; engaging in a "listening tour" without addressing the feedback you hear will further erode trust.

    3. Acknowledge mistakes you've made. Everyone makes mistakes! And everyone notices when a leader makes one. Acknowledging your own missteps helps staff to see you as a human being worthy of trust. It will also make staff more willing to bring you issues they are struggling with, because they have seen you be vulnerable.

  2. A Common Vision of Math Instruction. There's probably an alternate universe somewhere in which everyone shows up at school with a shared sense of what it looks like to teach math well. Alas, in the United States, that's not the case. We all carry culturally ingrained beliefs that may date back to when we were in school. Stigler and Hiebert's work synthesizing takeaways from the TIMSS Video Study (the accompanying book, The Teaching Gap is excellent and I strongly recommend it!) offers some great insight. This article from American Educator does a nice job of summarizing some key points, for example the idea of "cultural scripts" in math instruction:

Teaching, like other cultural activities, is learned through informal participation over long periods of time. It is something one learns to do by growing up in a culture rather than by formal study. Although most people have not studied to be teachers, most people have been students. People within a culture share a mental picture of what teaching is like. We call this mental picture a script.


We all enter into the teaching profession with a cultural "script" of what it means to teach math. If we want something different for our students, we have to explicitly name it. Here are a few things you can do to start building a common vision of math instruction:

a. Give time for reflection. Offer time for staff to reflect on what they remember about how they learned math in school. Are they confident problem solvers? If so, see if they can reflect on what experiences caused them to develop confidence. Also offer time for staff to reflect on what they want for their students. Do they want students to be mostly compliant and successful only with routine problems? Or do they want students that are also confident solvers, capable of reasoning and taking on non-routine problems?

b. Share alternative models. Using resources from the TIMSS Video Study or TNTP's Opportunity Gap can help staff imagine other models of instruction. Because we are so caught up in one cultural "script" it can be difficult to consider alternatives.

c. Collaborate on a shared vision document. Invest time across the school year allowing staff to play a role in defining a vision for math instruction. What do we do here, and why? This document could be a paragraph, a sample lesson template, or other succinct way of defining "who we are." Once a shared vision is in place, it will be clearer how other technical tools (curricula, observation tools, etc.) fit in.





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