###### When Do Math Manipulatives Work Best?

When Do Math Maniputlatives Work Best?

If we look at the latest meta-analysis data by John Hattie, it shows a fairly low efficacy for math manipulatives of, with a mean effect size (ES) of .38. However, as I reflected on this, I could not help but think manipulatives seem like a context dependent intervention. Personally I typically teach intermediate and with intermediate students I rarely find manipulatives helpful. However, when I taught grade 2 math, I found manipulatives absolutely essential. Indeed this idea that manipulatives are context dependent in their usefulness is reflected within the scientific literature.

Ultimately, the only objective way we can determine pedagogical efficacy is through meta analysis data. Fortunately, Carbonneau, Et al, conducted a thorough meta-analysis of the topic in 2013, which synthesized the results of 55 studies, including 7237 students. Their meta-analysis examined all studies at the time that measured the impact of manipulatives, included a control group, and included direct instructional time with manipulatives.

Discussion:

This study suggests that manipulatives are most valuable, when teaching, fractions, place value, and in one on one settings. The data also suggests that manipulatives are more effective for students in junior grades (2-6), and paired with more explicit instruction. The data suggests that manipulatives are generally speaking not effective for teaching students in grade 7 or higher, for teaching Algebra, or for teaching with less explicit instruction. One important caveat to make, however, is that the study design was not by age, but by math developmental stage. Meaning that a low grade 7 student would likely still benefit from manipulatives; whereas, a high grade 5 student might not.

References:

Carbonneau, K. J., Marley, S. C., & Selig, J. P. (2013). A meta-analysis of the efficacy of teaching mathematics with concrete manipulatives. Journal of Educational Psychology, 105(2), 380-400. doi:http://dx.doi.org/10.1037/a0031084

J, Hattie. (2022). Meta-X. Visible Learning. Retrieved from <https://www.visiblelearningmetax.com/influences>.