# Differentiating Math Instruction

## Common Skill Deficits

• Remembering math facts, steps in problem solving, complex rules, and formulas.
• Understanding the meaning of math facts, operations, and formulas.
• Understanding why problem solving steps are needed and how rules and formulas affect numbers and the problems solving process.
• Solving problems quickly and efficiently.
• Focusing attention on details and accuracy.
• Becoming lost in the problem solving process.
• Making errors because of handwriting problems.
• Applying math skills in new problem-solving situations.
• Remembering and following multi-step instructions.
• Making logical leaps in problem solving based on previous learning.
• Inability to find the important information and/or choose the right problem solving strategy to correctly solve word problems.
• Inability to find errors in their own work or to identify mistakes they made in solving the problem.
• Understanding math terms.

## Recommended Instructional Methods for K~12 General Education Teachers

1. Teach students using explicit instruction on a regular basis.
2. Teach students using multiple instructional examples.

3. Have students verbalize decisions and solutions to a math problem.

4. Teach students to visually represent the information in the math problem.

5. Teach students to solve problems using multiple/heuristic strategies.

6. Provide ongoing formative assessment data and feedback to teachers.

7. Provide peer-assisted instruction to students.

## Strategies for K~12 General Education Teachers

Beginning Math

• Teach early number concepts and strategies for counting.
• Reinforce one-to-one correspondence.
• Introduce geometry concepts in the early years.

• Provide direct teaching for basic number and operation concepts (count-bys).
• Provide manipulatives (beads, buttons, dried beans, number lines, calculators, base-10 blocks, stencils, copying over dashed-line numbers).
• Teach vocabulary concepts through direct teaching, verbal elaboration and mnemonic strategies.
• Promote memory of basic facts through direct teaching, increased learning time, peer tutoring, specialized software (Math Blaster) and independent study strategies (Touch Math, flashcards).

Problem Solving

• Promote use of word meanings.
• Sequence instruction that progresses from concrete to semi-concrete to abstract.
• Provide specific cognitive problem-solving strategies such as seven-step self-monitoring (Read, Paraphrase, Visualize, Hypothesize, Estimate, Compute, Check or Read, Think, Decide, Write, Do, Label, Check) , clue words, highlighting, imagery and pictures.

Money & Time

• Can be enforced by direct teaching, increased practice of coin recognition, use of manipulatives, use of models and by providing careful sequence of skills.

Fractions & Decimals

• Initial teaching should involve students' own experiences (cookies, pizzas, pies)
• Provide appropriate manipulative materials (fraction flip charts, decimal squares) and self-monitoring strategies.

Area & Volume Concepts

• Provide visual and three-dimensional representations.
• Teach the "big ideas".

Algebra

• Provide early concept development.
• Teach algebraic representations early.
• Teach strategies for computation, solving quadratic equations and problem-solving.
• Provide manipulatives such as algebra tiles.
• Teach using mnemonics.

Time

• Provide manipulatives such as clocks.
• Teach vocabulary through direct teaching.

Functional Math (Daily Living)

• Use appropriate methods and materials.
• Reference to "Real Life" skills such as calendar, writing checks, keeping checking and savings account, paying bills, etc.
• May need to provide small group instruction.

## Kristyn Hall

SPED 6002~Summer 2015

East Carolina University