alternative education

Teaching Techniques for 5th to 9th Grade Students with Learning
Disabilities in Algebra and Geometry

Massed Practice and Distributed Practice Strategies

F. D. Rivera, Ph.D.
Assistant Professor
Department of Mathematics
San Jose State University

~ Module 15, Session 7~
Lecture Notes

Students with learning disabilities in math are able to strengthen their mathematical knowledge when they are provided with ample examples and practice.

Examples and problems taken up in class for students with learning disabilities in math should contain enough variety so that students do not end up with misconceptions resulting from a limited understanding of the concept or process being discussed.

The type of examples and problems should also range from routine to nonroutine and from simple to complex.

Presentation and sequencing of examples and problems also count. students with learning disabilities in math should be exposed to them gradually. For example, if problem types range from less involved, involved, to more involved, students with learning disabilities in math should achieve success one type at a time. Integration between two types is possible only when students with learning disabilities in math have mastered each type.

Providing students with learning disabilities in math with massed practice involves giving them exercises and items that target the same concept, skill, or process. This is always the first stage in assisting students with learning disabilities in math obtain success and achieve mastery and control over the target knowledge.

Providing students with learning disabilities in math with opportunities for distributed practice should also be done. Distributed practice involves giving students with learning disabilities in math problems of a particular type that have just been discussed, including problems of another type that have been learned in a previous lesson. Another term for distributed practice is integrated practice.

In the following examples, the number of exercises should vary depending on the kind of students and their levels of competence.

Algebra Example: Solving linear equations:

Day 1:
Massed Practice: Ask students with learning disabilities in math to solve equations of type 1: x + a = b.

Example: 1. x + 3 = 5 2. x + 7 = 9 3. x – 4 = 7 4. x – 1 = 3
5. x + 5 = -7


Day 2:
Massed Practice: Ask students with learning disabilities in math to solve equations of type 2: ax = c.

Example: 1. 3x = 9 2. 4x = 8 3. 4x = 7 4. 2x = 3
5. –3x = 8


Day 3:
Distributed Practice: Ask students with learning disabilities in math to solve equations of types 1 and 2.

Example: 1. 2x + 3 = 7 2. 3x + 5 = 8 3. 2x – 3 = 7
4. 3x – 1 = 8 5. –2x + 1 = 5

Geometry Example: Calculating Areas

Day 1:
Massed Practice: Items involving asking students with learning disabilities in math to find areas of triangles of different types (right, isosceles, scalene, equilateral, obtuse)

Day 2:
Distributed Practice: Items involving asking students with learning disabilities in math to find an unknown side given the area of a triangle of any type.

Note: For Day 2, the items require an additional knowledge of solving linear equations of the type ax = c.

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