Comparing mathematical games

Comparing mathematical games
By Justin Hill, Johns Hopkins University
In a recent meta-analysis, Gulsah Kacmaz and Adam K. Dubé analyzed the findings from 26 studies on mathematical games to better understand the types of pedagogical approaches supported in mathematical games, the types of mathematical knowledge emphasized in these games, and the overall effectiveness of different varieties of games. The authors suggest the improvement of mathematical games may bolster performance in math while appealing to the interests of students. However, the abundance of choices and inability to separate effective and ineffective mathematical games has limited their utility.
 
The most common pedagogical approach in the studies reviewed was direct instruction (n = 10), followed by experiential learning (n = 7), discovery learning (n = 3), and constructivist learning (n = 3), leaving 3 studies unclassified. The strongest effects were noted for direct instruction (g = 0.51), followed by experiential learning (g = 0.46), discovery learning (g = 0.24), and constructivist learning (g = 0.21). All effects were significant (p < .001).
 
Many of the studies focused on more than one type of mathematical knowledge, with conceptual knowledge being the most popular (n = 19), followed by factual knowledge (n = 12), and procedural knowledge (n = 6). Of the studies focused on direction instruction, 5 focused on factual knowledge and showed a significant effect (g = 0.58, p < .001). The other studies focused on a combination of knowledge types but did not demonstrate significant effects. Of the studies focused on experiential learning, 4 focused on conceptual knowledge and showed a significant effect (g = 0.47, p = .011). Of the studies focused on discovery learning, 2 focused on a combination of procedural and conceptual knowledge and showed a significant effect (g = 0.36, p < .001). Finally, of the studies focused on constructivist learning, all 3 focused on conceptual knowledge and showed a significant effect (g = 0.21, p < .001).
 
Thus, games based upon a direct instructional approach demonstrate the strongest effects, but also are generally limited to a focus on factual knowledge. Games focused on other instructional approaches show smaller effects but may also be better suited for procedural and conceptual knowledge acquisition. More studies on the combination of different pedagogical approaches and mathematical knowledge types may be needed to further elucidate these effects.

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