Alan November, in a workshop with teachers in Hong Kong where I found myself kind of randomly today:

- Give your students two sites that offer two competing versions of the truth. Have them determine which one is true.
- Assign one student each day the role of official researcher. Henceforth, whenever a question arises, the researcher answers it, not the teacher. Students eventually start asking more researchable questions more often.
- Come into class with your own research question. Tell the class you need someone on the planet who knows more than you do about it. Have them find that person.

I like the list. How adaptable are these items to a mathematics classroom?

## 7 Comments

## David Wees

January 28, 2013 - 5:01 pmHow about for #1, replace ‘site’ with solution or proof?

#2 is a role I assign to all of my students, at least part of the time. Research in this case is done with the tools of mathematics that they know, or whatever technology happens to be useful (Excel, Geogebra, Wolfram Alpha etc…). I hate answering the “am I right?” question, so I just don’t anymore. That’s their job to figure out.

#3 is not one I’ve used before, but I suppose we could use it when ALL of us get stuck. I’m less inclined to use the ‘ask an expert’ technique because I feel like this is too similar to the ‘ask Google’ solution that too many of my students rely on.

## Matt McCrea

January 29, 2013 - 6:35 amFor #1, I’d instead replace “application” with site, so that students are distinguishing between a pseudocontext application and a realistic application of the math.

Largely with David on #2. Another context might be in finding other solutions to problems.

As for #3, the difference here between ask an expert and ask Google is that you might realistically expect the expert to give you a reasonable, directed answer, instead of Google, in which you’d get a mess of results instead of a targeted solution. This one isn’t too terribly hard for the kids either given the plethora of math teacher bloggers out there (Dan, of course, included) that could be used as the class expert for the day.

## Chuck

January 29, 2013 - 8:21 amHow adaptable is mathematics to these three principles? Maybe that is the question to answer.

I like the idea of going back to ancient forms of numerology as a common curriculum and using abstraction as a tool to learn binary and hexidecimal code better than imposing artificial situations over a standard we have always taught because we have been teaching it for a while.

## William

January 29, 2013 - 4:39 pmMath is both a body of knowledge and a tradition of cultural practice.

The cultural practice that a modern curriculum teaches is that mathematicians pursue truth by doing lots of problems from a book, and decide whether they’ve arrived at the truth by looking in the back of the book or asking a teacher who knows the answers. The relationship the students have with mathematical truth is mediated through the infamous “they” (“what do they want me to do here?”) or their teacher.

What’s so compelling about the three-act math project isn’t that it does a better job of teaching the body of knowledge of mathematics (though it probably does?); it’s that it reshapes the cultural practice of mathematics in a way that more closely reflects how grown-ups engage in mathematical inquiry. The arbiter of truth isn’t the back of the book, the method of inquiry isn’t defined by the teacher, the bounds of the problem aren’t as artificially constrained.

What would it teach students about the cultural practice of mathematic if we gave them a couple of entirely worked questions that include material they’re not familiar with and asked them to research the techniques used, evaluate the correctness and style of the various arguments, and explain which argument they find the most compelling and why?

## shelpike

January 31, 2013 - 7:05 amFor number one it would be fun to try things like giving students links to one site that supports a square being a rectangle, and another site that supports a square not being a rectangle, and have them discuss and think about those ideas.

## Isaac

February 6, 2013 - 10:41 amOr better yet, the competing definitions of “trapezoid” (inclusive and exclusive) with the tangential complication of American vs. British usage of “trapezoid” vs. “trapezium.”

It brings up the arbitrary (but still important) nature of terminology as well as cultural/historical influences.

## Sarah Miller

February 11, 2013 - 4:29 pmWow! I like those. A lot. I’m not sure that I need to do too much adapting to make them valuable in my math classroom. I want my students to be able to do those things, whether it is about math or not. That is one of the goals my small charter school is all about.

For #1, I might ask my students to compare two sites who offer some math teaching. Which one is better? Which one is more useful?

I especially like #2….my students are decently good at asking researchable questions, and it would be great to encourage more of that.

I would do #3 just for fun, and to see what they could come up with.

On a side note…you found yourself randomly in Hong Kong today?