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Stanford study shows how digital math games can teach more than rote skills

GSE scholars Charmaine Mangram and Holly Pope found evidence that a math game could improve students' proficiency. (Photo: Marc Franklin)
GSE scholars Charmaine Mangram and Holly Pope found evidence that a math game could improve students' proficiency. (Photo: Marc Franklin)

Stanford study shows how digital math games can teach more than rote skills

Education researchers find improvement in students' math proficiency after using app.

Third-graders who played a novel video math game for 30 minutes a week measurably improved their ability to reason through open-ended math problems, finds a recent study by researchers at Stanford Graduate School of Education.

The study by Holly Pope and Charmaine Mangram, both doctoral candidates in Curriculum Studies and Teacher Education, suggests that math-oriented computer games can help students improve their underlying math proficiency – their ability to think through problems, rather than simply speed up their performance of rote arithmetic.

Educators have long argued that math curricula need to put a higher emphasis on math proficiency and “numbers sense,” which becomes crucial when students begin learning algebra and other areas of higher mathematics.

But while digital math games are common, most games focus on speeding up standard mathematical operations rather than on the ability to conceptualize problems, use logic and test alternative solutions.

The study, published in the International Journal of Serious Games, was based on a controlled trial of third-graders and a math-learning game called Wuzzit Trouble. 

The game was created by Brainquake, a company co-founded by Keith Devlin, director of Stanford’s H-Star Institute as well as the “Math Guy” on National Public Radio’s Weekend Edition.  Pope and Mangram conducted their study independently of the game’s creator.  Because the game could be downloaded for free at the time of the study, neither they nor Devlin had a financial interest in the study’s results. 

The goal of the study was to find out if a math-oriented mobile app could improve a student’s proficiency with problems that have multiple constraints and that may have more than one solution path.

In the game, “Wuzzits” are colorful creatures that have been trapped in cages inside a castle.  The goal is to free the Wuzzits by aligning the keys with the pointer.  To get a key, a player has to turn a combination of small gears the right number of times to reach a particular number.  For example, if a player needs to reach a key at 20, and has two smaller gears with four and eight, the player can get to 20 by turning the four gear five times.  The player can also get to 20 by turning the eight gear twice and the four gear once.

The Stanford researchers tested the game on 59 third-graders at the Big Dipper Academy in the Big Tree School District of Sequoia, Calif. These students were in two separate classes, taught by the same teacher and placed in each class at the teacher’s discretion.    

One class, the comparison group, did not play the game as part of their math instruction, and the other class, the treatment group, did play Wuzzit Trouble.  The comparison group was taught in exactly the same way as before.  The treatment group  was also taught the same way as before, but their instruction included playing Wuzzit Trouble for 10 minutes in three classes per week over a four-week period.

In a pre-assessment test aimed at measuring numbers sense, the comparison group generally scored better on the test.  

In a follow-up test at the end of the four weeks, the gap narrowed significantly.  Both groups improved, but the students who played Wuzzit improved far more.  

Most of that improvement was tied to a particular problem that required students to answer a more unconventional and open-ended challenge.  Students were given a set of digits and a series of challenges and multiple constraints. 

In the pre-assessment, about 47 percent of the high performers and only 43 percent of the lower performers came up with the largest number. In the post-assessment, by contrast, 63 percent of the Wuzzit players but only 57 percent of the high-performers came up with the highest number.  

Both the game and pen-and-paper assessments required students to try, check and revise potential solutions, a structure that the researchers say supports adaptive reasoning and strategic competence. 

The researchers argue that the game promotes “productive practice” that goes beyond rote learning and strengthens a person’s ability to “make sense of the problem.”

The broader point, write Pope and Mangram, is that both traditional math classes and many digital math games focus on getting the right answer rather than on the process for getting to the right answer. 

“Students who are great memorizers and quick to answer tend to excel in traditional math environments,” they note.  But “this creates an atmosphere where very few students feel comfortable in taking risks for fear of getting the wrong answer…We argue that this fixed mindset is [also] evident in many mobile math games available to students.”  

Wuzzit Trouble, on the other hand, is one game that allows room for making mistakes and valuing the problem solving process in a low-threat context.

The Wuzzit experiment, they conclude, shows that a math game can strengthen a deeper understanding of mathematics as well as the kind of creative and flexible thinking that is essential to true math proficiency.


Edmund L. Andrews is a freelance journalist who wrote this story for Stanford Graduate School of Education.

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