Adam Holman asks **a really important question**:

What have you found to be the catalyst that helped either change your mindset/practice or helped change a ‘traditional’ teacher into one that cultivates relationships and student choice?

When I first started teaching, I talked too much. I really did. I spent too much time trying to clarify every permutation that could possibly come up, and not enough time letting students think about those permutations themselves.

However, over time, I experimented with different approaches. I wanted to find out what would work best for my students. I would try out a new project or a new instructional activity, and I would look at those activities critically to see what about the project or activity worked, and what didn’t work. If possible, I would try and fix what wasn’t working while keeping what was.

During the time I have been a teacher, I have noticed these (and other) things:

- The less I talk, the more time students have to grapple with mathematical ideas. Some talk is okay, but the balance should always be in favour of the students.

- Motivation and engagement are important. A student who believes that their ideas matter, and who is genuinely interested in what they are doing, learns far more effectively than otherwise.

- Students build persistence in mathematical problem solving most easily by working on problems and projects that are easily chunked and somewhat open-ended in terms of method, but have a clear goal that they can work toward.

- Discovery of mathematical ideas helps promote student ownership over their learning. A well-structured task through which students are likely to make mathematical discoveries for themselves leads to students who have a different mindset on mathematics. Does every topic lend itself well to discovery? No, but a great deal more do than most people might think. After all, every mathematical idea that we teach was discovered by someone, sometime.

- Peer collaboration is a chance for students to make connections and get feedback on their ideas and it takes time to develop effective math talk between students. There is only one of me, and there are so many students, so the potential for feedback is greater when students discuss mathematics with each other.

- An important objective of mathematics class is to develop mathematical reasoning in students. Most of them will forget whatever mathematics they learn eventually, but we hope that their core mathematical reasoning stays with them forever.

However, I would not have noticed these things if I did not take the time to reflect on my practice and look for evidence of what worked for my students, and what did not.

My advice therefore to Adam is that he try and have teachers start on **a road of reflection and inquiry into their own practices**. He may have to tackle some of their misconceptions about student learning directly, which is where **5 minutes talks like the one by Steve Leinwand** are useful but the teachers with whom he works will learn most effectively from each other, from reflection on their own practice, and from seeing other possible ways to teach.