Key Instructional Principles for Teaching students with learning disabilities in math

1
Key Instructional Principles for Teaching
students with learning disabilities in math

• F. D. Rivera, Ph.D.
• Department of Mathematics
• San Jose State University, CA
• Module 15, Session 2

2
Olson and Platt (2004) Instructional Model

• Modeling

Guided Practice
Evaluation
Independent Practice
Feedback
3
FOCUS ON BIG IDEAS

• Prior to any actual teaching, teachers of
  students with learning disabilities in math
  should identify what big ideas will need to be
  studied in a given grading period, semester, and
  school year.
• Big ideas in school mathematics are the unifying,
  central concepts and processes that define the
  mathematics being explored.

4
Example Linear Functions
Sequences of Numbers
Tables of Numbers
Applications
Slopes
Equations
5
Example Geometry

• Big Ideas
• Polygons (including circles)
• Congruence of Polygons By Transformations
• Measurements Relevant to Polygons (Perimeters,
  Areas, and Volumes)

6
Geometry

• For students with learning disabilities in math,
  one possible strand Use one entire semester
  exploring triangles built around the following
  sets of activities
• Classifying triangles according to number of
  sides and type of angles
• Using reflection, rotation, and translation to
  show congruence between two triangles
• Determining the perimeters and areas of triangles

7
ORGANIZE CONCEPT- OR PROCESS-LEARNING BY STRAND
(TASK ANALYSIS)

• Break down the teaching of concepts into several
  components or parts.
• Activities should be developmental in sequence.

8
Task Analysis

• Example Teaching addition of polynomials
  involves the following strand
• students with learning disabilities in math
  should first know what a term is.
• students with learning disabilities in math
  should classify terms according to number and
  their meanings (monomials, binomials, trinomials,
  multinomials).
• students with learning disabilities in math
  should know what polynomials are.
• students with learning disabilities in math
  should know when two polynomials are similar and
  whe they are different.
• students with learning disabilities in math
  should perform addition of polynomials.

9
Task Analysis

• Example Teaching basic transformations
• students with learning disabilities in math
  should know translations.
• students with learning disabilities in math
  should know rotations.
• students with learning disabilities in math
  should know reflections.
• students with learning disabilities in math
  should know what congruent triangles are.
• students with learning disabilities in math
  should be able to prove simple cases of congruent
  triangles by 1, 2, and/or 3.

10
USE COGNITIVE TOOLS APPROPRIATELY

• Manipulatives and technology can assist students
  with learning disabilities in math deal with
  concept or process.
• Sequence the use of tools so that students with
  learning disabilities in math do not end up
  merely acquiring how to use them instead of
  learning the mathematics that they are supposed
  to know.

11
Cognitive Tools

• Examples
• Algebra use of algebra tiles, graphing
  calculators
• Geometry use of power polygons, geoblocks,
  dotpaper, patty paper,

12
USE STRATEGIES WISELY

• Parsimonious Efficacy Use the simplest model or
  strategy that could explain the most number of
  cases.
• Example
• Algebra FOIL versus ALGEBRA TILES
• Geometry Using cones and cylinders of the same
  height and base diameter in order to show how
  volume of 3 cones equals the volume of one
  cylinder

13
MAKE PROBLEM SOLVING IN REAL LIFE A SOURCE OF
MOTIVE FOR LEARNING MATHEMATICS

• The need to solve problems in life should drive
  the study of algebra and geometry.
• Example Teaching linear functions may use
  problems in business, in production, cost, rates
  of change
• Example Teaching measurement in geometry
  involves assigning an accurate numerical value
  that involves length, areas, and volumes.