How many times must students do it before they get it right?: New insights on math practice
By Jim Ysseldyke, PhD
As school begins this fall, one of the concerns on the minds of many educators and parents is the fact that far too many of our students continue to struggle to learn basic math skills. Recent data from the National Assessment of Educational Progress (NAEP) indicate that in the US only 39 percent of 4th graders and 34 percent of 8th graders are proficient in math, and that 19 percent and 29 percent of students are below basic levels in the 4th and 8th grades.
The Role of Computational Fluency
Although there are many factors that contribute to deficiencies in mathematics, the National Math Panel (2008) has noted that poor computational fluency plays a fundamental role. Children who lack fluency in basic computations are at risk for math difficulties that may arise in elementary school and persist into young adulthood. Moreover, students who successfully store basic math fact information in memory and retrieve it easily are more likely to develop the skills necessary for solving a wide variety of complex problems and interpreting abstract mathematical principles (Patton, Cronin, Bassett, & Koppel, 1997; Shapiro, 2010).
In a recent blog post, “Math Is Ruthlessly Cumulative,” Gene Kerns, Ph.D., makes a strong case for educators to devote more time to skills practice for automaticity. He expands the conversation to note the importance of fluency beyond the basics, but he also reminds us that the rung at each level must be strong before moving up the ladder.
Many elementary schools place less emphasis on instruction and practice of basic math facts as students progress through the curriculum because they assume that students have acquired a sufficient level of computational fluency from previous instruction to proceed with related or more complex tasks (Isaacs & Carroll, 1999). Teachers of upper elementary and higher grades should ask: Are my students masking an underlying lack of fluency with basic math facts—even if they appear to grasp some concepts of math at higher levels?
Recent Insights on Practice
My colleagues and I at the University of Minnesota recently conducted a series of investigations into important factors related to students learning math facts. In a study to be published in School Psychology Quarterly but available in an early online format (Burns, Ysseldyke, Nelson & Kanive, in press), we looked at the relative difficulty of learning specific multiplication facts (2s, 5s, 8s, etc.). We used a database of 15,402 elementary students in grades 3–5 from Renaissance’s database in Renaissance MathFacts in a Flash®. We grouped students based on their math proficiency as assessed by Renaissance Star Math® into three groups: at risk (< 25th percentile), average (25th thru 75th percentile), and above average (>75th percentile).
The study provided an unprecedented view into single-digit math fact difficulty for elementary-age students across multiple skill levels. Here’s what we learned:
Students with lower math skills require significantly more repetitions to learn multiplication facts.
Some math facts (4s, 5s, 6s, and 7s) require significantly more repetition to learn than do others.
The number of repetitions required decreased with rising grade level, indicating that younger students require more repetitions.
Our findings are comparable to arguments that other researchers are making in the professional literature. Together, these findings provide powerful implications for math instruction and math practice. For example:
It is increasingly important to match math instruction to specific student needs. Evaluating the specific skills that students possess and lack can inform the development of interventions that are appropriate for individual students (Poncy & Skinner, 2006).
Mastering basic math fluency is an important goal for individual students with learning difficulties in math (Geery et al, 2007), because fluency in math facts within an information processing model is fundamental for progression to more complex and abstract math skills (Woodward, 2006).
Moreover, early competence in basic skills predicts later success with more advanced skills (Geary, 2011). This is perhaps because as children develop math skills they tend to replace computation with memory retrieval by activating different areas of the brain (Price, Mazzocco & Ansari, 2013).
But what next? Which approaches work best for developing computational fluency, and do they work best for all students—regardless of grade and proficiency level? In a follow-up blog post coming soon, I’ll share what we’re learning about this and more.
Interested in learning more about MathFacts in a Flash? Click the button below to learn more.
Burns, M. K., Ysseldyke, J., Nelson, P. M., & Kanive, R. (2015). Number of repetitions required to retain single-digit multiplication math facts for elementary students. School Psychology Quarterly, 30(3), 398–405.
Geary, D.C. (2011). Cognitive predictors of achievement growth in mathematics: A 5-year longitudinal study. Developmental Psychology, 47, 1539–1552.
Geary, D.C., Hoard, M.K., Byrd-Cravens, J., Nugent, L, & Numtree, C. (2007). Cognitive mechanisms underlying achievement deficits in children with mathematical learning disability. Child Development, 78, 1343–1359. http://dx.doi.org/10.1037/a0025510.
Isaacs, A.C. & Carroll, W.M. (1999). Strategies for basic-facts instruction. Teaching Children Mathematics, 5, 502–515.
Patton, J.R., Cronin, M.E., Bassett, D.S. & Koppel, A.E. (1997). A life skills approach to mathematics instruction. Preparing students with learning disabilities for the real-life math demands of adulthood. Journal of Learning Disabilities, 30, 178–187. http://dx.doi.org/10.1177/002221949703000205.
Poncy, B. C., & Skinner, C. H. (2006). Detect, practice, and repair: The effects of a classwide intervention on elementary students’ math-fact fluency. Journal of Evidence-Based Practices for Schools, 7, 69–72.
Price, G.R., Mazzocco, M.M.M. & Ansari, D. (2013). Why mental arithmetic counts: Brain.tivation during single digit arithmetic predicts high school math scores. The Journal of Neuroscience, 33, 156–163. http://www.jneurosci.org/content/33/1/156.full
Woodward, J. (2006). Developing automaticity in basic multiplication facts: Integrating strategy instruction with time practice drills. Learning Disability Quarterly, 29, 269–289. http://ldq.sagepub.com/content/29/4/269.abstract