The Reflective Educator

Education ∪ Math ∪ Technology

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Month: September 2015

Why is it important for students to talk to each other in math class?

Why should students talk to each other in math class anyway? I was asked this question recently and I’m trying to avoid a tautological answer (eg. it’s important because it’s important).

In a classroom where students speak to each other about mathematics, the ideas of those students are valued instead of ignored or potentially marginalized. This gives students agency in their learning. It also allows new ideas the students learn to extend from the existing ways they understand the world.

Supporting students speaking to each other means that mathematics is much more likely to become a way of knowing and being rather than just a body of existing knowledge (although the value of mathematics as a set of tools that have been developed over time should not be marginalized). As students develop their understanding of what mathematics is and what it is useful for, they are more likely to insert themselves in the role of the mathematician rather than imagining this to be someone else, potentially from another culture. They can see themselves being part of a mathematical community.

In order to completely understand the language we know, we have to use it, either in writing or ideally in conversation, and hear other people using the same language. So from a practical perspective, students need to talk in order to develop their use of language (mathematical or otherwise), and rather than students talking in serial, one at a time mediated through a teacher, it is far more efficient for them to talk in parallel, to each other.

We remember what we think about. When students construct ideas and communicate them to each other, they necessarily have to think about these ideas, which means that they are building memories. While this occurs no matter what students do, the focus is more likely to be on the thinking with student discourse rather than the activity (eg. completing a task).

Finally, students talking and writing to each other also provides their teachers with more information about the ways they are thinking which makes it easier for the teacher to orchestrate productive whole group discussions and to plan activities that respond to the ways students are actually thinking. It is difficult to plan lessons that build off of student knowing if you don’t know how and why students think the way that they do. When students talk to each other, their teacher can gather formative assessment information about not only what they understand but ideally how they understand it.

This should not diminish the importance of students having independent time to work quietly on mathematical problems by themselves. Students are better positioned to work together when they have had time to think about ideas themselves first. Also, some students find working with other students really difficult for a variety of reasons, so in some cases the benefits of students working together may be outweighed by the challenges some students face with this activity.

What would you add as reasons students should talk to each other in a mathematics classroom?

 

 

Coherent conversations about teaching

Imagine four teachers each of whom teaches in different schools in a different context. Even if they all teach the same course, their individual teaching looks different.

Typical teaching #1 Typical teaching #2
Typical teaching #3 Typical teaching #4

If these four people come to talk together, they will find it challenging to have a conversation since the way they are teaching is so different from each other. Each person potentially has a valuable perspective but they may have so little in common that it is difficult for them to talk to each other.

Typical conversation about teaching

Now imagine instead these four teachers are all focused on working on the same instructional activity, perhaps even with the same mathematical tasks within the activity. Their teaching is still different as they still teach in different schools in different contexts but their conversation about teaching becomes much more coherent as they have far more in common to talk about. Instead of talking about their individual teaching they can talk about teaching practice.

With instructional activities

Over the last two weeks we launched the instructional activity, Contemplate then Calculate with 100 or so teachers for this exact purpose; to make our shared conversations about teaching focused and coherent. After two days of professional development, which included rehearsing the instructional activity together, virtually all of the teachers indicated that they were excited to try out this activity and then come back together in October to talk about its impact on students.

At one point during the two weeks, some participants and I ended up in a whole-group discussion about when exactly we should annotate our students’ strategy sharing. It was the most specific conversation I’ve ever had with a group of teachers and I feel fairly certain everyone understood the point that was being debated and why it might matter one way or another.

All of these teachers are going to go back to their individual schools and teach according to what they know with their individual contexts and their individual students but now, hopefully, at least one aspect of their teaching will be similar enough that they can come back and talk about the differences.

 

 

Apps for the math classroom

Here is an incomplete list of companies making apps for the math classroom. As far as I know, every application made by these people is fantastic.

  • The NY Hall of Science has recently published a series of science and math apps for the iPad.
  • Motion Math has some great low-cost math apps.
  • DragonBox has 4 really high quality math applications, all of which I have personally played and tested with my son. These are the most expensive apps on this list but also some of the best apps available for learning math.
  • BrainQuake’s math puzzles will present a challenge for people of all ages while being accessible to young children.
  • Geogebra is cross-platform and a must-have for people interested in constructing and exploring their own interactive math activities.
  • Desmos is a fantastic online graphing calculator which can be installed and used on many different types of devices.

As I learn about more companies publishing apps for the iPad (and as I have time!), I’ll update this list. I know there are lots of apps that I’m missing but this is what I had time to put together this morning.