So we all know it’s importance. We all understand that students learn more when they do it. The problem is how to facilitate it.

“It” is getting students to talk mathematically. As a teacher, you can’t really say “ok kiddos, work on this thing together and I WANT TO HEAR THAT MATH TALK.” Well, maybe you can, but I’m not able to. I have to be more insidious, more conniving, more sneaky to get my students using mathematical vocabulary and verbalizing mathematical arguments.

Over the past couple years I’ve tried to aggregate some of the more successful teaching activities into my toolbox. This post will introduce seven of these sneaky, math-talk-producing activities. Not only that, but they are a) **easily translatable** to many content areas and b) **quickly producible**. In many cases you could create these activities with a word document and maybe 30 minutes time. You could be doing this tomorrow.

I’ll credit each activity individually, but a bunch are cribbed straight from Malcolm Swan’s work here and (related) the Shell Centre here. Go to those places and learn stuff.

**Matching**

Students match cards to various similar or equivalent things. I have a sneaking suspicion that it’s simple the tactile nature of using cards (or shoot, just paper cuttouts), that makes it feel like a game.

What I also like about it is that as students are matching, they naturally go back and revise their work. It’s a wonderful thing when students come to the last grouping and they realize it’s incorrect, then they go back through and find where they erred.

This is perfect for almost anything that utilizes multiple representations, which is pretty much all of Algebra. In fact, I’d be willing to bet that there isn’t a mathematical concept where you could use some sort of Matching activity.

(From Shell Centre MAP Project: Interpreting Distance-Time Graphs)

**(Informally) Evaluating Student Work Samples**

Being doubly sneaky, I love having students analyzing and evaluating samples of mathematical work because it has a nice side-effect. Not only are the students deciphering mathematical information, but they’re also inadvertently figuring out for what makes good math work. (Sneaky, right??)

As students are asked to follow some protocol (see below), they’ll no doubt verbalize things like “I like this work because it’s clear” or “I don’t understand this work because it’s so messy.” And I’m all BOOM GOES THE DYNAMITE, I KNOW!

I like the protocol shown below. I would NOT have students give it a grade or evaluate it against a rubric or something like that. That tends to make the goal of the assignment to check things off from a grocery list (on the other hand, I DO like having students evaluate themselves against a scoring guide).

(from Shell Centre MAP Lesson Units: Geometry Problems)

**Determining “Truthiness”**

With a nod to Stephen Colbert, “truthiness” in this case refers to students deciding whether a statement is always, sometimes, or never true. This always seemed natural for Geometry because of activities like this:

(from Shell Centre MAP Lesson Units: Evaluating Statements about Length and Area)

However, recently I came across things like this from the Shell Centre, using the Truthiness activity for Algebra and equations:

(from Shell Centre MAP Project: Sorting Equations and Identities)

You could certainly also utilize the Truthiness activity for when you have a variable in the denominator. Truthiness (I’d imagine) works great with things like asymptotes and discontinuities.

**Ordering mathematical artifacts**

Basically, here’s some stuff, put it in order from “least [something]” to “most [something].” In this case, [something] = “Square-ness”.

Fun story: I was in the middle of some PD and I showed a teacher this activity and he said he hated it because it was “watering down” math language. And that this was just one in the long line of “new math” instruction that was more about creating “warm and fuzzy feelings” than delivering concrete rules to follow. He also said that we were doing a disservice to the creators of mathematical definitions by doing activities like this and it was pretty much the problem with society.

That was a fun conversation!

Anyway, I love stuff like this. It, again, “forces” the mathematical dialogue and arguments. I stole this from Jason (@jybuell) at alwaysformative.blogspot.com (even though the source materials specifically state that these are not intended to be classroom instructional materials – OOPS!).

Similar: EmergentMath Problem of the Year 2011 Winner, Mr. Honner’s Equilateral Triangle poser.

**“Odd one Out”**

Simple instructions: pick the one thing that doesn’t below.

Once again, you don’t even need to prompt students to explain their reasoning, because they’ll explain it to each other. Especially if there’s a disagreement about which one doesn’t belong

More complex perhaps: finding three mathematical things that all could potentially be the “odd one out.” Or, “find a reason that any of these three don’t belong.”

(from Swan, Malcom, 2005. Improving learning in mathematics: challenges and strategies. Link)

**Classifying Mathematical Artifacts**

Much like the Matching activities, I think it’s just the tactile nature and the natural work-revision that comes along with an activity such as this that makes it really valuable and conversation-producing.

(from Swan, Malcom, 2005. Improving learning in mathematics: challenges and strategies. Link)

**Any Questions?**

Act 1 – Pop Box Design from Timon Piccini on Vimeo.

Of course, we all know Dan Meyer as the Moses of “Any Questions”, but if Meyer is Moses, then Timon Piccini (@MrPicc112) is Joshua, because he’s been crushing it lately.

The “Any Questions?” activity is a sort of stripped down (and cleaner) version of the “Need-to-Know” process (read more about that here). The twitter hashtag #anyqs is a great place to find stuff. However, on twitter everything is assumed to be in rough draft form. A great *Any Questions?* will launch students directly into the content you are intending them to learn about. That differs a bit from stuff like this, that may solicit five different content-related questions. Those have a place too, but probably belong in a different category.

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What are some of the activities you conduct to promote mathematical discussion in your classrooms? Please share links and ideas in the comments!

Any time anybody wants to put me on the same page as the Shell Centre crowd, I’ll take it.

I love the informal evaluation idea. Reading through some student’s incoherent work is a nightmare; having them try and interpret their friends work will hopefully help them see that. Thanks for all the great ideas.

I love many of the activities you have showcased in this article.

So many of them are the “math without numbers” type that are more about getting students to “think” mathematically rather than calculate mathematically.

Problems like these are so good for getting at the conceptual root of the material and help to bring to the surface what students are thinking (making meaning).

I’ll bet most students would like math far more if they could spend more time doing work like this or doing problem-based math that you have spoken about.

I look forward to spending some time looking at more of the materials found in the Shell Centre MAP Project resouces.

I, too, like the parts where students need to think and manipulate to become one with the problem rather than reaching for pencil and paper looking for a quick answer. I believe they would love math if they could really experience it and take responsibility for it.

I like the “Odd one Out” activity because I teach middle school and this is so on their thought level. Each day they chose one student to be the odd one out, why not adjust the focus to mathematical topics. I also like the Classifying Mathematical Artifacts since it is tactile. I know from experience that the students thrive when math becomes multi-modal and kinesthetic. It is fun for them and I enjoy watching them enjoy the activity.

So helpful! Thank you for collecting and organizing and provoking!

The last question in #2 of the truthiness exercise has two answers depending on the students. Presumably, you’re working with students who don’t know anything about complex numbers, in which case the answer is “Never True”, but there’s the potential that a student will be correct in answering “Sometimes True” (x = 2i). Depending on where you want to go, you could either dodge that entirely or use that to open a conversation.