Students with Learning Disabilities (LD) often encounter considerable difficulties in their effort to learn the multiplication facts (or arithmetic combinations of multiplication). Researchers and practitioners have devised and implemented several methods for teaching these facts to students with LD. In the remainder of this column I will describe briefly three such methods, and their instructional implications.
The first method is the MASTER (MAthematics Strategy Training for Educational Remediation) program for teaching multiplication and division (Van Luit & Naglieri, 1999). The program starts with the students trying to find results of multiplication (and division) facts by using concrete materials. Then a connection is made with a mental solution, and the child learns to check the solution. Students have the opportunity to use their own strategy to find the results of multiplications. The teacher discusses with the students their choices and tries to help them understand which is the most efficient strategy. A main goal of the program is to help students understand that both between multiplications (e.g. 5x7=35, 5x8=40) and between multiplications and divisions (e.g. 12÷3=4, 3x4=12) there are connections and relationships, which can be used for finding results. Another main goal is to help students use simple multiplications in more complex problems [e.g. 5x14=(5x10)+(5x4)]. The different phases of the program include modeling and self-instruction. According to Van Luit and Naglieri (1999), the MASTER arithmetic training program can effectively help students with LD learn the multiplication facts.
Another method for teaching multiplication facts to students with LD is mnemonic instruction (Greene, 1999). A core procedure of the method is the specification of the multiplications that will be targeted and the device or the selection of rhyming words (pegwords) or rhyming phrases with which all the numbers involved in the multiplication facts are corresponded (e.g. 4=door, 6=sticks, 24=twin doors). Flashcards, each containing one multiplication fact and one picture that depicts the content of a sentence with rhyming words, are presented to the students. The teacher orally presents both the math fact and the rhyming words (phrase) and the student looks at the multiplication fact and the picture on the flashcard, and repeats (approximately five times) what the teacher has said (e.g. "6x7=42; sticks in heaven with a warty shoe"). According to Greene (1999), mnemonic training contributes to the retention of multiplication facts more than the traditional instructional methods.
A final method that seems to be promising in supporting students with LD acquiring the multiplication facts is by combining strategy instruction and timed practice drills (Woodward, 2006). In this method multiplication facts are divided into easy and more difficult ones, with rule-based facts (like 0s, doubles, and times 5s) considered as the easy facts, and facts like 6x7 or 7x8 regarded as difficult. Easy facts are taught through rules and patterns. For the teaching of the difficult facts a derived strategy is implemented (e.g. 6x7= 6x6 + 6). The use of the derived strategy is supported through visual representations, in which number relationships and derivations of results are depicted through number lines or cubes. In order for automaticity in the use of acquired facts to take place, the method foresees the use of timed practice drills. The drill scheme includes the use of worksheets, each containing 40 facts. Half of these facts are review facts and half new facts, in random presentation. Automaticity is considered to be 36 correct answers within a 2-minute time period. The combination of strategy instruction and timed practice drills has also been used for teaching extended facts (e.g. teaching 50x4 after the acquirement of 5x4). According to Woodward, this combined method proved to be effective in raising the mean performance of students with LD to mastery and near mastery levels.
All three methods have proven to be valuable tools in helping students with LD acquire multiplication facts, despite (a) the diversity of the participants of the respective researches and the procedures through which they had been identified as presenting LD, and (b) the differences among the methods in terms of structure, means, and emphasis. Some of the conclusions that can be drawn from this fact, and the respective instructional implications, are:
Difficulty in acquiring the multiplication facts probably results from an array of causal factors. Hence, instruction should be flexible and should employ differentiated techniques for helping students with LD overcome their problem.
Understanding of the connections and relationships among numbers, and the use of already acquired facts for learning new ones, seems to substantially contribute to the success of the programs.
Instruction that allows students to effectively memorize strings of multiplied numbers and their results may enhance the effect of the intervention.
A combination of any specific method with basic principles of instructional methodology seems to produce superior results compared to the use of either the method or the principles in isolation.
Greene, G. (1999). Mnemonic multiplication fact instruction for students with learning disabilities. Learning Disabilities Research & Practice, 14(3), 141-148.
Van Luit, J. & Naglieri, J. (1999). Effectiveness of the MASTER program for teaching special children multiplication and division. Journal of Learning Disabilities, 32(2), 98-107.
Woodward, J. (2006). Developing automaticity in multiplication facts: Integrating strategy instruction with timed practice drills. Learning Disability Quarterly, 29(Fall), 269-289.
Ioannis Agaliotis, Ph.D. is Assistant Professor of Instructional Methodology for Students with Special Educational Needs in the Department of Educational and Social Policy of the University of Macedonia of Thessaloniki, Greece. Dr. Agaliotis is co-editor of the journal Insights on Learning Disabilities: From Prevailing Theories to Validated Practices, published by LDW®. He has presented at national and international conferences and has published articles and books on inclusive education, assessment and instruction for students with mild disabilities, mathematics for students with special needs, and academic and social support for students with learning disabilities.