The following is a Q&A with Dr. Juli K. Dixon, an author of HMH's Into Math and an expert in mathematics teaching and learning.
How can mathematics teachers benefit from professional learning?
It’s helpful for teachers to develop a shared image of what instruction looks like in mathematics. Classroom videos are really helpful, so that when teachers are preparing to teach a module, they are making sense of the standards for that module, they’re looking at the learning arc for that module, they’re seeing how concepts are linked to procedures within that module. So when we plan for instruction, we should plan collaboratively if we can; we should plan by making sense of the mathematics for teaching first, using tasks that support that mathematics with students, and then the structure of questioning to engage students.
What does a learning mindset look like in a mathematics classroom?
Mindset for students, learning mindset is “I can learn.” If we give students the opportunity to learn, they’re more likely to do so. So, we give them opportunities by providing really good tasks. We provide students tasks without giving them the direction to solve those tasks, but we provide them at the appropriate time. We don’t tell them how to think about the task, so they have the opportunity to experience what it feels like to learn. When students experience learning, they have pride in that, and that helps them with their mindset. “I can learn. I know I haven’t learned everything, but I know I’m capable.” To me, that’s a learning mindset.
Why and how should mathematics educators encourage student discourse?
Students are more likely to do the sense-making when they get to talk about the mathematics. And so we support teachers to help students facilitate this discourse. We support teachers to help students with questions for the students to use with students, with teacher conversation strategies, and with meaningful routines to develop language. This way, each and every learner, including our English Language Learners, have the opportunity to engage in the mathematical discussion.
How can I increase access and provide equity in mathematics classrooms?
When we think of equity and access, we can’t only think about our learners who struggle. We also have to think of our learners who need more of a challenge. So we’ve addressed each and every learner in the tasks that we use, the grouping we suggest, the supports and questions and scaffolding that we provide for the teacher and the Teacher’s Edition. We have supports for the learner who struggles, so the learner who struggles can still engage in meaningful mathematics.
What is productive perseverance, and why does it matter in mathematics classrooms?
Productive perseverance is all about the student, but the teacher facilitates students to engage in productive perseverance. It looks like a teacher using important tasks with students and students having the opportunity to do the sense-making of those tasks before the teacher tells the students how to think. It sounds like students talking, because students are developing this feeling in themselves that they can do math because they're engaging in mathematics. They're reasoning about mathematics. They're talking about mathematics. What it feels like for that teacher is wonderful; it's a win, my students are reasoning, they're doing the sense-making they're pushing through. What it feels like for the students is accessible, meaningful. The students develop this “Yes I can” attitude because they've worked through a difficult task and come out the other side, with the scaffolding provided by the teacher just-in-time. And that's an important part of scaffolding.
What role should scaffolding play in promoting productive perseverance?
Engaging students in productive perseverance, developing students as problem solvers, involves being very intentional about the support we provide them when they work on tasks. If we provide great tasks, but then we over-scaffold those tasks, we help students with too many clues too early, then we're not setting the stage to engage students and develop students who have productive perseverance. In contrast, if we provide these great tasks but we help the teachers to know when to provide the scaffolding, just-in-time, we're developing a situation where students can learn deeply at the same time, developing this learning mindset that's crucial. The difference between providing scaffolding just-in-case and just-in-time is the difference between students who follow procedures and then forget them and students who become problem solvers who can reason about mathematics.
Why is it important to engage students in inquiry, and what does that mean?
Inquiry is really described on a continuum. We have pure inquiry where we provide a task and students are just let to go, to explore, to discover. Then we have more guided or facilitated inquiry, where we begin with a task, but the teacher is more intentional about how students will come to understand the mathematics that's both implicitly and explicitly connected with that task. We want students to have the opportunity to discover, but we acknowledge the tension of the amount of time it takes to discover, so we guide students to make those discoveries. We spark their learning you could say. We use these tasks that we even named Spark Your Learning, to begin our lessons that focus on both concepts and connecting concepts to procedures. With those tasks, we provide opportunities for students to do the sense-making before we've told the students how to think -- that's allowing students to engage in inquiry.
Dr. Juli K. Dixon is an author of Into Math. Learn more about the HMH program for K-8 students here.
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