Much of learning mathematics involves memory–whether it is committing things to long term memory for later recall, like addition or multiplication facts, or short term memory when recalling steps to follow when carrying out multidigit calculations or solving a multi-step problem. There is also working memory, which involves the ability to hold information in mind while simultaneously working with that information or doing other calculations. (Geary, Hoard, Nugent, & Byrd-Craven, 2007) For example, a common way to add multi-digit numbers like 125 + 97 involves the ability to calculate that 7 + 5 is 12, write down the 2 in the ones column, then carry the 1 to the tens column, then add the numbers in the tens columns and so on, relies on working memory. More complex examples of processes that utilize working memory can be found in subtraction, multiplication, and division. For students who have working memory difficulties we often look for alternative algorithms, short cuts, or calculators to help support students’ memory needs. All too often working memory, short term memory, or long term memory deficits are common for students who experience difficulty learning mathematics.
Geary and colleagues (2007) report that students’ overall capacity for working memory increases from preschool through elementary school. For example, Kail (1990 as reported in Geary et al., 2007) found that when asked to repeat back a collection of numbers typical preschoolers could repeat back 3 to 4 number words correctly, and typical fourth graders could repeat back 5 to 6 number words correctly. Yet students with math learning disabilities lag about 1 year behind their typically achieving peers in working memory tasks. The growth in students ability to repeat back more numbers in fourth grade than preschool is due to their improved ability to use strategies (e. g., rehearsal), improved ability to focus attention, increased processing speed, or the slower decay of information (i.e., they don’t forget things as quickly). Each of these components improves as part of normal development in childhood, and each contributes to the observed improvement in overall working memory capacity (Cowan, Saults, & Elliott, 2002 as reported in Geary et al., 2007).
When students have difficulty with working memory, research indicates that they tend to use finger counting more frequently and for a longer period of time than their typically performing peers, and they also tend to have more computational and procedural errors than their peers especially during initial periods of learning (Geary, 1990, 1993). Researchers have also found that students with math learning disabilities have shorter working memory spans, of about 1 year of typical growth, than their same-grade peers, and do show age-related and school-based improvements in working memory (Geary, Hoard, Byrd-Craven, & DeSoto, 2004; McLean & Hitch, 1999; Swanson, 1993).
Students with math learning disabilities also tend to demonstrate a two-year delay in their ability to make adaptive shifts or changes in problem solving strategies when switching from solving simple to more complex problems. Research proposes that this difficulty is related to poor working memory (Geary, Hoard, Nugent, & Byrd-Craven, 2007). Although working memory difficulties can be corrected or improved upon, they continue to negatively influence students’ learning of mathematics throughout their education.
So, we know that students who experience difficulty in learning math often demonstrate deficits or weaknesses in working memory. We also know that they tend to lag behind their peers in improving their working memory skills and they also tend to lag behind in skill acquisition and advancement.
Strategies that can be utilized to help students support their working memory needs can include teaching them alternative algorithms that minimize a reliance on holding pieces of information in memory (see Agaliotis, 2008, February—for suggestions on using alternative algorithms), writing down instructions and steps to follow in a problem solving procedure for referral as needed (Zentall, 2007), and utilizing real-life and interesting content to facilitate recall (McLoughlin & Lewis, 2001). Allowing students to use calculators to support the problem solving process as long as calculation itself is not the focus of instruction can also support the learning process. Having students support memory needs by thinking aloud as they work a problem can also aid memory recall and development (Zentall, 2007). For example, have students think aloud as they solve problems or do calculations. They can also explain their thought processes to peers or answer process oriented questions posed by the teacher as they work to solve problems. By orally and actively engaging students in the learning process, students are working to support demands placed on their memory capacity. Overall, a good rule to keep in mind is that the more active the learning process the more likely learning will occur.
Agaliotis, I. (2008, February). Alternative algorithms or struggling learners. Strategies for Successful Learning, 1(3). Retrieved January 9, 2009, http://www.ldworldwide.org/ldinformation/educators/ssl/SSL02-08_agaliotis.html.
Cowan, H., Saults, J. S., & Elliott, E. M., (2002). The search for what is fundamental in the development of working memory. Advances in Child Development and Behavior, 29, 1-49.
Geary, D. C. (1990). A componential analysis of an early learning deficit in mathematics. Journal of Experimental Child Psychology, 49, 363-383.
Geary, D. C. (1993). Mathematical disabilities: Cognitive, neurophsychological, and genetic components. Psychological Bulletin, 114, 345-362.
Geary, D. C., Hoard, M. K., Byrd-Craven, J., & DeSoto, C. M. (2004). Strategy choices in simple and complex addition: Contributions of working memory and counting knowledge for children with mathematical disability. Journal of Experimental Child Psychology, 88, 121-151..
Geary, D. C., Hoard, M. K., Nugent, L., & Byrd-Craven, J. (2007). Strategy use, long-term memory, and working memory capacity. (pp. 83-106). In D. B. Berch, M. M. M. Mazzocco. Why is Math so Hard for Some Children? The Nature and Origins of Mathematical Learning Difficulties and Disabilities. Baltimore, MD: Brooks Cole Publishing Co.
Kail, R. (1990). The development of memory in children (3rd ed.). New York: W. H. Freeman.
McLean, J. F. & Hitch, G. J. (1999). Working memory impairments in children with specific arithmetic learning disabilities. Journal of Experimental Child Psychology, 74, 240-260.
J. A. & Lewis, R. B. (2001). Assessing Students with Special Needs, 5th ed. Upper Saddle River, NJ: Prentice Hall. (pp. 264-265).
Swanson, H. L. (1993). Working memory in learning disability subgroups. Journal of Experimental Child Psychology, 56, 87-114.
Zentall, S. S. (2007). Math performance of students with ADHD: Cognitive and behavioral contributors and interventions. (pp. 219-243). In D. B. Berch, M. M. M. Mazzocco. Why is Math so Hard for Some Children? The Nature and Origins of Mathematical Learning Difficulties and Disabilities. Baltimore, MD: Brooks Cole Publishing Co.
Teresa Foley is an Instructor of Mathematics at Asnuntuck Community College in Enfield, Connecticut.