Category Archives: Numeracy

Open Questions in Math

With a background in high school Music and French, I was definitely terrified of teaching Math when I started teaching five years ago. I “succeeded” in Math in school, but I never enjoyed it or fully understood why I was doing what I was doing. However, as part of the Numeracy Project in our district, my school participated in a lot of professional development surrounding Numeracy and over the course of my first two years of teaching, I began to love the subject that I had hated growing up. By year three, I thought I had it figured out. I spent my time filling in students’ gaps, working with small groups, and offering choice in the problems students tackled. I was differentiating, for sure, and students were experiencing success in learning, but I don’t think I helped ignite a passion for Math in many students that year. The following year, I explored project-based learning in Math with some success although I didn’t feel I was addressing those knowledge gaps quite as effectively. I had completely shifted my teaching style, yet somehow, I lost my passion for teaching Math along the way. What was missing?

The problem isn’t that my students weren’t learning; it’s that I forgot about the big ideas. With so many learning outcomes in Math, it’s easy to become focussed on the minutiae of what students are supposed to learn and to forget about the big picture. However, it is the big ideas that should guide our instruction from K-12; by focussing on the big picture, we can encourage critical thinking and creativity in a domain traditionally seen as rigid and procedural.

I read Marian Small’s book “Good Questions: Great Ways to Differentiate Mathematics Instruction” about 3 years ago, but I don’t think I effectively put it into practice at that time. Now that my enthusiasm has been revived, I’ve been begun re-exploring how open questions impact student learning and student engagement.

Here are some examples of open questions we’ve tackled in our Math class over the past couple of weeks…

Using 12 base ten blocks, which decimal numbers can you represent?


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While some students came up with three possible answers for these questions, others came up with fifty. The point is that everyone could enter into the problem. Some students are just beginning to understand tents and hundredths, so they worked on using all of the same type of block. Others could easily see patterns in numbers and were challenged to find as many answers as possible and to represent them in different ways.

___ + ___ = 4.32 OR ___ – ___ = 4.32

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Again, this open question offered choice. Students could choose addition or subtraction. They could show their understanding with whatever tool they wanted. Some chose to work symbolically while others made visual patterns concretely with the base ten blocks. They were all on task, collaborating, and learning.

Sometimes teachers get bogged down with the PLOs and forget about the big ideas. Here, we are focused on representing numbers in different ways. Without explicitly talking about it yet, students are beginning to see how decimal numbers and fractions are connected through questions like “Represent one fraction and one decimal number in as many ways as you can. Which is bigger and how do you know?” They are already discovering that fractions and decimal numbers are closely connected, that there are ways we can represent both such as fraction circles and number lines, and that finding equivalent fractions is helpful when comparing and ordering. But most of all, I’m just excited to see kids engaged in Math, especially those who struggle. One simple change can sometimes make a bigger impact than trying to completely redesign the way we teach and learn.

How do you differentiate Math instruction for your students? What has worked well for you?

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