Getting Lean in Mathematics Education Technology

By: Dr. Theodore Chao

Why is it that when you pull up a math game, website, or app, it almost always pushes old and tired ways of teaching math? Flash cards emphasizing memorization over understanding? Quizzes pushing speed rather than thinking? Or worse yet, games using colorful graphics and adventures to hide operation result-unknown number sentences rather than exploring number relationships (e.g., 4+12=? rather than [6+?] = [-3+3]). These games assume you have to fool kids into learning math, rather than connecting to the inherent fun that comes from doing math.

Part of this disconnect comes from who actually gets to create math games. Education is one of unique fields which everyone has some expertise because, hey, we all went to school. I mean, I took at least one math class for 15 years of my life. And when I became a software developer, I believed part of the reason I was good at computer programming was because I was “good” at math. It wasn’t until after I became a middle-school teacher that I realized I didn’t have the first clue about how to teach math. I had good grades because I was good at memorizing, regurgitating, and choosing the answer that was the least wrong. And so, it was people like me who were “good” at math or tracked into upper-level math courses, that helped build math games.

And that won’t fly in today’s world. The field of mathematics education research has helped us understand so much more about how children learn mathematics. Memorization, speed, finding the “correct” answer? These are only a small part of developing deep, overall mathematical thinking. Creating your own strategies, engaging in mathematical discussion, and open-ended mathematical tasks are much better ways to engage students and build mathematical confidence.

So how do we do build math games that connect to this research? Well, to start, we can use the development process as a sort of research in of itself, to help unpack how children actually think mathematically. Let’s start by thinking lean, a business term introduced by Womack and Jones’ (1996) in describing how Toyota constantly switched up their car production techniques to be super-efficient and responsive to customers. Lean thinking embodies a philosophy of keeping things small and focused so that you always learn how people will use your product.

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At the heart of Lean Thinking is the Build-Measure-Learn (BML) feedback loop, an ongoing exercise of checking in with the user. In a BML loop, developers’ start with an idea about how a feature might work, then quickly test it to see what happens. Because developers only focus on one feature, they do not have to actually build out the product, which makes the BML loop super fast. Often, a BML loop involves no more than screenshots, with users mimicking the pushing of buttons and telling an interviewer what they would be doing. No time is wasted in developing or building superfluous features. Through this mindset, developers are able to stay lean by focusing their energy on listening and responding to users as opposed to building what they predict a user will want to use.

We’ve used this model here at Sokikom to continually develop our games. Let’s look at two examples of how Lean thinking has helped us create games that connect to how children think mathematically.

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One of our first BML loops investigated why our students would suddenly stop playing a game. Students usually started a game with excitement, but when they got stuck on a problem for more than 2 minutes, they’d start visiting other websites. So through a series of BML loop, we experimented with embedding hints into the games, providing help videos, and even providing real on-call mathematics tutors. We found that students remained engaged in a game when they knew instructional support was available from the beginning, and that the system would predict when they needed help. So through these BML loops, the development team designed a system of help videos that were always present, but only popped up after the student submitted two incorrect solutions. Immediately, we noticed much more perseverance in students playing our games. The screenshot above shows how a help video that pops up when a child submits two incorrect answer choices about simplifying 2/8 to ¼.

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Another BML loop involved a research project focused on developing Frachine, our fraction machine game. Teachers shared with us their struggles in teaching fractions in a visual way. Through focus groups, we learned that teachers wanted a game targeting fractional thinking to help students develop visual models of numbers smaller than 1. But, they did not want students to rely on number lines or confusing pie charts. So the development team used research on how children’s fractional models often involve breaking objects into two pieces to go through some BML loops with teachers and students. Through this process, the team built a fraction game revolving around repeated halving of blocks. The screenshot shows the final Frachine game, in which students use the machine on the left to partition each whole block into halves, quarters, or eighths. Being able to work with whole blocks and repeatedly halve them into smaller fractional units has helped our students situate fractions as real units that they can create themselves.

Sokikom is not the only mathematics learning platform utilizing lean thinking. We have found it a powerful way to think about our games as responsive to our children’s and our teacher’s needs. And lean thinking reminds us of that good mathematics teaching, essentially, is good listening.