Mathematics Learning Games that Break the Symbol Barrier
This post was written by Keith Devlin, Chief Scientist at BrainQuake Inc., and Bryan Matlen, Senior Research Associate in the Science, Technology, Engineering, & Mathematics (STEM) program at WestEd, and describes BrainQuake and WestEd’s collaborative work involving the design and testing of educational games that support student success in mathematics.
A Math Problem
Many K–12 students struggle in mathematics. This struggle serves as a major obstacle for pursuing some college majors and careers, and occurs on a large scale, contributing to our national skills shortage. Additionally, many people approach mathematics with a substantially negative attitude — in some cases even developing a phobia (Tobias, 1995) or fixed mindset (Dweck, 2007) that prevents students from moving forward.
The Root of the Problem
Symbolic representations are essential for solving advanced problems in mathematics, but often serve as major barriers for learners (Nunes et al., 1993). Consider the equation below.
24 – 6y = 12
Solving this equation involves not only an understanding of the symbolic “semantics” (e.g., y stands for an unknown number), but also the symbolic “grammar” (e.g., 24 can be subtracted from each side, but 6 cannot).
Devlin (2011) calls this a “symbol barrier,” a difficulty that is more one of language, rather than math.
A Potential Solution
Concrete representations that avoid the need to work with foreign symbols offer a possible solution. BrainQuake is a San Francisco-based company that creates learning apps with this guiding principle as a central focus. The company says its “proven mobile and web games significantly improve number sense, disposition to math, readiness to learn math, and formative proficiency assessment by radically overhauling math’s 10,000-year-old interface, revealing hidden learning and career potential.”
Figure 1. Wuzzit Trouble (left) and the symbolic representation of the same problem (right).
The left portion of Figure 1 above, for example, shows one of BrainQuake’s apps, Wuzzit™ Trouble. In the game, mathematics representations manifest as mechanical devices that a player can manipulate. The player solves the puzzle by rotating small gears to turn a large wheel in order to collect items hanging on the wheel. For a maximum score, all the items must be collected in the fewest number of possible rotations, following a similar sequence of logical steps required to solve more advanced algebraic problems (shown on the right of the figure). Using more intuitive representations allows students to engage in advanced mathematical problem solving.
WestEd Measurement Expertise and BrainQuake’s Impact
WestEd and BrainQuake are partnering to understand how these games impact student outcomes. The research — funded by the Institute of Education Sciences — provides support for this possibility.
During a three-week study in six middle-school mathematics classes with about 200 total students, WestEd evaluated the feasibility of Wuzzit Trouble for today’s classrooms and the ability of the games to support learning and motivation related to mathematics. A variety of information was collected from both students and teachers on their perceptions and use of the games (see Figure 2).
Figure 2. Student ratings of Wuzzit Trouble relative to usability/feasibility, ability to motivate, ability to support learning, and engagement.
The findings suggest that the Wuzzit Trouble app has the potential to support learning and help improve negative attitudes towards mathematics; thereby removing a key barrier to future success in mathematics.
Based on these early results, BrainQuake is developing even more games with direct mathematical representations. To test efficacy of these new games, WestEd conducted a randomized trial with 34 middle school teachers and more than 700 students — a rigorous evaluation of BrainQuake with a study designed to minimize outside influences affecting findings. Teachers were randomly assigned to either use the BrainQuake games or not use them during mathematics instruction.
The results: Students who used the BrainQuake games were approximately 1.5 to 2 times more likely than their control group peers to report improvement relative to the following:
- Searching for information when needing help on mathematics problems
- Having more confidence on some mathematics problems
- Believing that mathematics is one of their best subjects
Research thus far suggests that BrainQuake can support motivation and learning in mathematics. Eventually, students do need to know, interpret, and use formal symbolic representations. Students need a bridge, however, between the kinds of intuitive representations of mathematics featured in BrainQuake and more abstract symbolic, or algebraic, representations.
BrainQuake is currently developing what it calls a “Digital Manipulative (DM)” solution that supports this connection making. The DM aims to gradually fade the concrete, game-like representations of BrainQuake’s app into the abstract, symbolic ones used in formal mathematics.
As we continue our research and development efforts related to digital solutions that enhance learning, we look forward to an expanded suite of options and tools that enhance student outcomes in mathematics.
Devlin. (2011). Mathematics education for a new era: Video games as a medium for learning. AK Peters/CRC Press.
Kiili, Devlin, Perttula, & Tuomi. (2015, October). Using video games to combine learning and assessment in mathematics education, International Journal of Serious Games, 37–55.
Pope & Mangram. (2015, October). Wuzzit Trouble: The influence of a digital math game on student number sense. International Journal of Serious Games, 5–22.
Posted on August 18, 2018