Evidence-Based Math Intervention Strategies

Evidence-Based Math Intervention Strategies

Core Principles of Math Intervention

1. Explicit instruction: Model thinking aloud, guided practice, independent practice
2. Concrete-Representational-Abstract (CRA): Always start with manipulatives
3. Focus on conceptual understanding: Don't just teach procedures
4. Systematic: Follow developmental sequence
5. Intensive practice: More repetition than core instruction
6. Error analysis: Use mistakes to diagnose misconceptions

Number Sense Intervention

For students who don't understand quantity and number relationships

Subitizing (Instant Recognition)

• Practice instantly recognizing small quantities (1-5)
• Use dot patterns, dice, dominoes
• Flash briefly (1-2 seconds), student says quantity
• Build to 6-10 using five-frames and ten-frames

Counting Intervention

One-to-One Correspondence: - Touch and count objects - Move objects as counting - Emphasize last number = total (cardinality)

Counting On: - Don't start from 1 every time - "Start at 7, count 3 more" - Use number line for support

Skip Counting: - Count by 2s, 5s, 10s - Use hundreds chart patterns - Connect to multiplication later

Number Relationships

Part-Part-Whole: - Use part-part-whole mats - "5 is made of 2 and 3" - Build flexibility: 5 = 1+4 = 2+3 = 0+5

Comparing Numbers: - Use comparison mats (more/less) - Build both quantities, compare - Introduce <, >, = symbols after concept is solid

Place Value Intervention

Critical foundation for all multi-digit operations

Concrete Phase

• Bundling: Group 10 ones into 1 ten (physically rubber band)
• Base-ten blocks: Trade 10 units for 1 rod
• Place value mat: Organized columns for ones, tens, hundreds

Key Activities

Build-Say-Write: 1. Build number with blocks (2 tens, 4 ones) 2. Say the number ("twenty-four") 3. Write the numeral (24)

Equivalence: - Show 24 as 2 tens + 4 ones - Also show as 1 ten + 14 ones - Critical for regrouping understanding

Expanded Form: - 347 = 300 + 40 + 7 - Connect to blocks: 3 flats + 4 rods + 7 units

Addition/Subtraction Intervention

Strategies Sequence (teach in order)

Level 1: Counting All - Count first set, count second set, count total - Most basic; identify students still here

Level 2: Counting On - Start with larger number, count on smaller - "8... 9, 10, 11" for 8+3 - Use number line or fingers

Level 3: Derived Facts - Use known facts to find unknown - Doubles: 6+6=12, so 6+7=13 - Making 10: 8+5 = 8+2+3 = 10+3 = 13

Level 4: Automatic Recall - Instant retrieval - Build through practice AFTER understanding

Multi-Digit Addition/Subtraction

Always use CRA sequence:

Concrete: - Use base-ten blocks - Physically trade 10 ones for 1 ten (regrouping)

Representational: - Draw base-ten pictures - Use place value charts

Abstract: - Standard algorithm - Explain steps using place value language

Multiplication/Division Intervention

Building Conceptual Understanding

Equal Groups Model: - 3 × 4 = 3 groups of 4 - Use counters in groups - Count total

Array Model: - 3 × 4 = 3 rows of 4 - Build with tiles or draw - Connect to area later

Repeated Addition: - 3 × 4 = 4 + 4 + 4 - Bridge from addition knowledge - Use number line jumps

Fact Fluency Intervention

Strategy-Based Approach (not just drill):

1. ×2 facts: Doubles from addition
2. ×10 facts: Place value pattern
3. ×5 facts: Skip counting, clock connection
4. ×1 facts: Identity property
5. ×0 facts: Zero property
6. ×3 facts: Double plus one more group
7. ×4 facts: Double the double
8. ×6 facts: ×3 doubled
9. ×9 facts: ×10 minus one group, finger trick
10. ×7, ×8 facts: Use commutative property; most already covered

Practice Methods: - Flashcards (known/unknown piles) - Games (multiplication war, around the world) - Timed practice AFTER strategies are learned - Cover-Copy-Compare

Word Problem Intervention

For students who struggle with problem-solving

Schema-Based Instruction

Identify Problem Types:

Change Problems: - Start + Change = End - "Sara had 5 apples. She got 3 more. How many now?"

Group Problems: - Part + Part = Whole - "There are 4 red balls and 5 blue balls. How many balls?"

Compare Problems: - Bigger - Smaller = Difference - "Tom has 8. Sue has 5. How many more does Tom have?"

CUBES Strategy (with caution)

• C: Circle the numbers
• U: Underline the question
• B: Box key words
• E: Evaluate (draw/write equation)
• S: Solve and check

Caution: Don't over-rely on "key words" - they can mislead. Focus on understanding the SITUATION.

Intervention Routine

1. Read problem aloud together
2. Retell in own words (no numbers)
3. Identify problem type (schema)
4. Draw or act out the situation
5. Write equation
6. Solve
7. Check: Does answer make sense?

Intervention for Specific Disabilities

Dyscalculia

• Extended time with concrete materials
• Reduce quantity of problems (quality over quantity)
• Graph paper for alignment
• Multiplication chart as tool (after understanding)
• Color-coding for place value
• Consistent visual models

ADHD

• Break tasks into small chunks
• Frequent movement breaks
• Reduce visual clutter on page
• One problem at a time
• Immediate feedback
• Games and competition elements

Working Memory Deficits

• Provide reference sheets
• Reduce steps held in memory
• Write down intermediate steps
• Use manipulatives as "external memory"
• Graphic organizers for word problems

Progress Monitoring for Math

Curriculum-Based Measurement (CBM): - Computation probes: Timed fact/computation tests - Concepts/Applications probes: Word problems, place value - Administer weekly for Tier 3, bi-weekly for Tier 2

What to Track: - Digits correct per minute (computation) - Problems correct (concepts) - Growth rate compared to goal

Intervention Intensity

Common Math Intervention Programs

• Number Worlds
• Do The Math (Marilyn Burns)
• TransMath
• MIND Research (ST Math)
• Dreambox (technology)
• Moby Max (technology)