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Subskill mastery per week impacts students’ math gains

Subskills graphic
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While quality student math practice is important, quantity of practice is just as crucial. Academic learning time (ALT)—the time students spend on actual learning activities—has long been identified as critical to academic growth (Batsche, 2007; Gettinger & Stoiber, 1999). An important, but often underemphasized aspect of ALT is time for practice of learned skills, which is as important as explicit instruction (Szadokierski & Burns, 2008). For example, Bahrick and Hall (1991) found that a student who achieved a C in his first algebra course and went on to take several more math courses remembered his algebra, whereas a student who got an A in algebra but took no further math courses forgot what he learned. The additional math courses ensured that the student continued to think about and practice what was learned.

Likewise an analysis of student math-practice data found that students who spent more time working on their math skills had higher growth overall (see figure). The quadrant graph illustrates how mastering more math subskills per week affects end-of-year performance (spring percentile rank, PR) and annual growth (fall-to-spring student growth percentile, SGP),1  with groups in the upper-right quadrant obtaining the best outcomes. Students are grouped according to math subskill mastery per week, with bubble color indicating grouping and bubble size indicating number of students per group.

Of course, frequent feedback on the results of student practice is essential, so teachers can intervene as necessary to assure each student is successful at a high level (above 85–90%) (Ericsson, Krampe, & Tesch-Römer, 1993; Topping & Sanders, 2000) and remains engaged and motivated.


Bahrick, H. P., & Hall, L. K. (1991). Lifetime maintenance of high school mathematics content. Journal of Experimental Psychology: General, 120(1), 20–33.

Batsche, G. M. (2007, Summer). Response to intervention: Overview and research-based impact on over-representation. Florida RtI Update, 1(1), 1–2, 5. Retrieved from http://www.floridarti.usf.edu/resources/newsletters/2007/summer2007.pdf

Ericsson, K. A., Krampe, R. T., & Tesch-Römer, C. (1993). The role of deliberate practice in the acquisition of expert performance. Psychological Review, 100(3), 363–406.

Gettinger, M., & Stoiber, K. C. (1999). Excellence in teaching: Review of instructional and environmental variables. In C. R. Reynolds & T. B. Gutlein (Eds.), The handbooks of school psychology (3rd ed., pp. 933–958). New York, NY: John Wiley.

Szadokierski, I., & Burns, M. K. (2008). Analogue evaluation of the effects of opportunities to respond and ratios of known items within drill rehearsal of Esperanto words. Journal of School Psychology, 46, 593–609.

Topping, K. J., & Sanders, W. L. (2000). Teacher effectiveness and computer assessment of reading: Relating value-added and learning information systems data. School Effectiveness and School Improvement, 11(3), 305–337.

Willingham, D. T. (2009). Why don’t students like school? A cognitive scientist answers questions about how the mind works and what it means for the classroom. San Francisco, CA: John Wiley & Sons.

1 Student growth percentile (SGP) compares a student’s growth to that of his or her academic peers nationwide.