In my previous post, I discussed one way to provide tasks that help students reimagine the discipline of mathematics: doing creative math. This post discusses the second of three strategies: doing useful math.

To me, the interesting thing about math is that it is at once a plaything with seemingly no utility and an immensely crucial component to living. It is both of these things. Maybe that’s why it’s so difficult to teach: because each individual places their thumb along the scale of the utility-playful spectrum and our thumbs are in different places. This post discusses task types that can help students conceive of math’s usefulness.

What does it mean for math to be “useful?” In the most basic terms it means that the math that students are using helps solve a real or potentially real problem. Or it helps explain a natural phenomenon. Of course, just because something is real doesn’t mean it’s interesting. Also, it’s easy for allegedly “real-world” problems to succumb to the Skynet Line, a silly concept I introduced a decade ago. 

Problems that allege to be “real-word” sometimes don’t reflect the actual math involved.

That’s why I prefer the term “useful math” over “real world math.” Because something uses stuff that exists in the real world (watermelons, trains, cows, cell phone plans), doesn’t by definition make it a “real world problem.” If it did then you could say that most standardized tests incorporate “real world math.”

From Sample Items from the SBAC assessment. Is this problem “real world”? I’d suggest it is indeed “real world”, but not particularly useful (or interesting) (and sometimes that’s ok!).

Often math helps solve problems or explain natural phenomena that students, teachers, or community members experience. They can be big problems or small problems. An example of a big problem might be examining food deserts. A small problem might be planning a school field trip. It could be something that’s community-based, informed by the neighborhood around the school. It could also be something that’s just … useful. 

An example of a community-based experience could be something like the following. (Note: the following task will appear in an upcoming open-source book of mathematical tasks for 5th graders. I’ll include a link and citation when it’s up).

Students create a walking tour of the neighborhood to encourage parents to contribute to the local business economy. Students apply mathematics by using the appropriate units illustrating the path that visitors might take.

You can even make it an authentic solicitation from your principal.

Dear Students of __________ Elementary School,
Hello students! I’m excited to tell you about an opportunity for your class! I constantly have parents asking me what they can do to support the local businesses in the area. Sometimes parents drop off their kids and want to see what’s around. Other times they like to show up to the neighborhood early and do some shopping. I’d like you to help them out!

I would like you to create a brochure for parents that might like to hang out near our school. Your brochure should feature the following:
— A map of the school and surrounding area, highlighting at least four local businesses or attractions.
— A 2-3 sentence description of each local business.
— A chart showing the distances between each of the attractions as well as our school. The chart will be provided for you.
For each distance, please tell me the distance in miles, feet, kilometers, and meters and decide which might be the best to use for our brochure.
I am excited about the wonderful products you will bring to our community!
Sincerely, 
Your Principal

Example of a mapped out walking tour. This task will be published in an upcoming open source book, which I’ll link.

Of course, creating a community tour may not be interesting or useful for your students. While our goal ought to be to provide math that is both interesting and useful, that’s a difficult bar to clear every class. It is an important slice of knowledge for students to learn. Nurses need strong computational skills to pass the NCLEX exam. It’s important that we equip students with those skills, even if they’re not particularly fun. So long as we are complimenting useful math with creative math, we are hueing to our goal of helping students think more highly of the discipline of math. 

If you’re unsure where to start, consider these sample tasks.

3 Acts – TV Space – Embrace the Drawing Board
Area Contractor – National Council of Teachers of Mathematics (need to be an NCTM member)
Geometric Constructions Task: Pizza Delivery Regions – emergent math
Can You Earn $10/Hour Selling Lemonade? – Robert Kaplinsky
Electoral College
California wildfire – Yummy Math
Everybody is a Genius: Remodel
Questions?: Farming Project        

How do you employ useful mathematics for students? Add a link or a description in the comments and I’ll add ‘em to the blog post! 

Next time, I’ll discuss the third method of helping students broaden their conception of math: doing math with students (not at students).

One thought on “Three Strategies to Help Improve Students’ Conception of Math – Part 2: Do Useful Math

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