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# V.2 #2 Mathematics - Teaching Division to Students with Learning Disabilities

Division is a complex operation, the efficient execution and use of which presupposes a considerable amount of prior knowledge and skills, such as:

• understanding the process of distributing the items of a large set into smaller equal sets.

• knowledge of number combinations in number families (e.g. 6x7=42, 7x6=42, 42÷6=7, 42÷7=6).

• understanding the correspondence between algorithmic steps and actual activities with real objects.

• knowledge of number combinations and algorithms of addition, subtraction, and multiplication.

We know that students, especially young students with learning disabilities (LD) face several challenges in their effort to learn how to execute division and use it in problem-solving equations. Most common among these difficulties are:

• immature, time-consuming or totally incorrect strategy use in division situations. For example, in their effort to divide 12 candies among 3 kids, they may be putting random quantities of candies in bags, until they achieve the formation of sets of 4.

• confusion with notation and respective verbal statements.

• incorrect algorithmic steps either regarding division itself or one of the included operations (e.g. subtraction).

• incorrect transfer of principles from other operations (e.g. use of commutativity).

• execution of a different operation than the one required due to misreading the operation sign.

• incorrect retrieval of number combinations (e.g. retrieving 5 instead of 6, as the result of the combination 42÷7).

• difficulty with the principles of division by “0” and “1”.

• difficulty with remainders.

Although these problems seem overwhelming, there are specific guidelines and techniques that are effective for students with LD who struggle with division. Keep in mind that before you begin any intervention you should conduct a through pre-assessment of your students’ pertinent knowledge and skills specifically noting any difficulties through a systematic error analysis.

• Use problems depicting everyday situations to familiarize the students with the concept of division.

• Present the problems and generally deliver instruction through a teaching sequence of Concrete—Semiconcrete—Abstract (CSA), using representational modes of increasing difficulty.

• Use a well-elaborated teaching procedure, including an advanced organizer, sufficient guided and independent practice, and appropriate feedback.

• Take into consideration the stages of learning (acquisition, proficiency, maintenance, generalization, adaptation) when organizing instruction.

• Use systematic drill for division arithmetic combinations.

• Use systematic drill for division arithmetic combinations.

• Teach systematically through the CSA sequence the standard algorithm of division, but be mindful that there are alternative algorithms (see column on alternative algorithms).

• Teach the students to use strategies for effectively processing the information included in the problem, such as the strategies DRAW or SOLVE we spoke about in previous columns.

• Keep in mind that, often, the most difficult skill within a group can be taught first, because students tend to generalize the process to easier problems. So, teaching the algorithm for dividing a 3-digit number (divident) by a 2-digit number (divisor) may generalize to dividing a 2-digit number by a 1-digit number, thus saving considerable time and providing the student with the satisfaction of achieving a superior goal.

References

Bryant Pedrotty, D., Hartman, P, & Kim, S. (2003). Using explicit and strategic instruction to teach division to students with learning disabilities. Exceptionality, 11(3), 151-164.

Montague, M. (2003). Teaching division to students with learning disabilities: A constructivist approach. Exceptionality, 11(3), 165-175.

Parmar, R. (2003). Understanding the concept of “division”: Assessment considerations. Exceptionality, 11(3), 177-189.

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.