Lack of Automaticity in the Basic Addition Facts as a Characteristic of Arithmetic Learning Problems and Instructional Needs

Abstract

Computational facility and the relationship between automaticity or efficient processing of addition facts and success in more complex tasks were examined in a cross-sectional study of 109 children from Grades 3 through 6. Latency data and interview protocols enabled identification of speed and strategy use on the addition facts, grouped into eight fact bundles (e.g. zeroes, small doubles), as a parsimonious procedure for exploring processing efficiency. Profiles of children based on latency performance on the fact bundles were clustered. The slowest cluster reported use of counting strategies on many bundles; the fastest cluster reported use of retrieval or efficient-thinking strategies. Cluster group was the best predictor of performance on multidigit tasks. Addition fact accuracy contributed only for tasks without carrying, and grade level was not significant. Analysis by error type showed most errors on the multidigit sums were due to fact inaccuracy, not algorithmic errors. The implication is that the cognitive demands caused by inefficient solutions of basic facts made the multidigit sums inaccessible. Suggestions for instruction of students who have problems learning basic arithmetic are made.Mathematics education has changed dramatically during the twentieth century from a focus on rote acquisition of arithmetic and geometric facts and algorithms, to a constructivist emphasis on meaning-making, conceptual understanding, and problem-solving. Activities that promote rote learning in mathematics have lost favour as being anti-learning (if not anti-mathematical), time-consuming, and Requests for reprints should be sent to J. Joy Cumming,

How teachers teach and students learn

“…For instance, knowing the multiplication table by heart can help in solving more advanced mathematics problems by reducing the cognitive load, or mental effort, in learners. In short, by helping students to retain and retrieve basic mathematics facts, rules and procedures, repetitive learning and memorisation can help students to solve mathematics problemseven the most complex -more efficiently (Cumming and Elkins, 1999). These benefits might explain why, in some education systems, particularly those in East Asia, many people believe that memorisation is compatible with creativity, understanding and a deep approach to mathematics learning, and why it has been described as the "springboard of learning" (Biggs, 1998;Hess and Azuma, 1991;Jin and Cortazzi, 1998;Kember, 1996;Orlin, 2014;Sadler-Smith and Tsang, 1998).…”

The Importance of Automaticity Development in Mathematics

“…Those standards are supposed to be "mastered" by the end of that school year. This research, along with others (Cumming & Elkins, 1999;Lin & Kubina, 2005;Stickney et al, 2012;Woodward, 2006), shows a different situation. Our math students are struggling when they are in elementary school, they are struggling when they are in middle school, and by the time they are in high school, they are years behind.…”

Improving multiplication fact fluency by choosing between competing answers

“…As previously noted, fact fluency is of high importance for problem-solving and conceptual understanding (Cumming & Elkins, 1999;Kilpatrick et al, 2001;NMAP, 2008;Woodward, 2006). Difficulties in achieving fluency in multiplication facts are often reported by students and teachers, however, and findings that may aid this process would be welcome in many classrooms (Kilpatrick et al, 2001;Wallace & Gurganus, 2005).…”

“…As well as affecting problem-solving, research has shown that inefficient solving of basic facts depletes resources that are needed for acquiring more advanced computational skills, such as those required for multi-digit sums (Cumming & Elkins, 1999). Weak ability to retrieve arithmetic facts can also impede children's ability to follow mathematical discourse and consequently to understand concepts that are introduced in class, such as equivalence, the commutative property and other concepts that form the basis of more advanced mathematics, such as algebra (Gersten, Jordan, & Flojo, 2005;NMAP, 2008;Woodward, 2006).…”

“…Achieving fluency in arithmetic facts is an important prerequisite for more complex mathematics, such as problem-solving and understanding higher-order concepts and procedures (Cumming & Elkins, 1999;Kilpatrick et al, 2001). Complex tasks place considerable demands on information processing capacity, including working memory (LeFevre, DeStefano, Coleman, & Shanahan, 2005).…”