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Which practices have evidence of effectiveness in the mathematics classroom? Where do I go to find more?
WHAT IS HIGH QUALITY MATHEMATICS INSTRUCTION, AND WHY IS IT IMPORTANT?
WHAT IS HIGH QUALITY MATHEMATICS INSTRUCTION, AND WHY IS IT IMPORTANT?
Which components of instruction time and time again have been shown to yield the best results for learning in math? The IRIS Center (Vanderbilt University) has created modules to highlight practices that have demonstrated moderate to strong evidence for boosting student outcomes in math. These practices include: explicit, systematic instruction, visual representations, schema instruction for word problems, and metacognitive strategies.
IRIS Center Modules: What is High Quality Mathematics, and Why Is It Important?
ESSENTIAL EVIDENCE-BASED INSTRUCTIONAL PRACTICES
EXPLICIT INSTRUCTION
Why Explicit Instruction? (Dr. Anita Archer)
Why Explicit Instruction? (Dr. Anita Archer)
High-Leverage Practices: Explicit Instruction (CEEDR Center)
High-Leverage Practices: Explicit Instruction (CEEDR Center)
Explicit, Systematic Instruction: Elementary (Iris Center)
Explicit, Systematic Instruction: Elementary (Iris Center)
Explicit, Systematic Instruction: High School (Iris Center)
Explicit, Systematic Instruction: High School (Iris Center)
ACTIVE PARTICIPATION
Active Participation in the Classroom, Pt. 1
Active Participation in the Classroom, Pt. 1
Dr. Anita Archer | PaTTAN
Active Participation in the Classroom, Pt. 2
Active Participation in the Classroom, Pt. 2
Dr. Anita Archer | PaTTAN
RETRIEVAL PRACTICE
Retrieval Practice
Retrieval Practice
Dr. Paul Ricommini, PaTTANpod
Making the Most of Retrieval Practice: Spaced Practice
Making the Most of Retrieval Practice: Spaced Practice
Pooja K. Agarwal, Ph.D. Cognitive Scientist
Benefits of Interleaved Practice
Benefits of Interleaved Practice
Robert Bjork, Ph.D. Distinguished Professor of Psychology at the University of California, Los Angeles
RESOURCES FOR RETRIEVAL PRACTICE
RESOURCES FOR RETRIEVAL PRACTICE
How to Use Retrieval Practice to Improve Student Learning | RetrievalPractice.org
How to Use Spaced Retrieval Practice to Boost Learning | RetrievalPractice.org
Interleaved Mathematics Practice: Giving Students a Chance to Learn What They Need to Know | Retrieval Practice.org
ADDITIONAL RESOURCES
ALGEBRA
ALGEBRA
IES Practice Guide: Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students | What Works Clearinghouse
EXPLICIT INSTRUCTION
EXPLICIT INSTRUCTION
2009 IES Practice Guide Recommendations for Explicit Instruction
2021 IES Practice Guide Recommendations for Systematic Instruction
Explicit Instruction Modules on NCII
Explicit Instruction Modules on Iris Center
Explicit Instruction Resources from Anita Archer
Explicit Instruction Videos by Sarah Powell
Explicit Instruction Video by VanDerHeyden & Codding (Part 5)
FLUENCY BUILDING
FLUENCY BUILDING
Kansas MTSS recommends ten minutes of computational fluency practice daily for all students. The recommendation is a direct relay of a What Works Clearinghouse publication under the direction of Dr. Russell Gersten and a panel of experts in Math interventions (Gersten, 2009). The recommendation as published is directly correlated to intervention time; however, research around basic arithmetic facts and automatic retrieval has shown such a strong correlation to future mathematical success that we recommend strengthening all students’ computational fluency for ten minutes each day. Thus it is recommended that the practice period be integrated into the core instruction as opposed to only during interventions.
This ten minute period is not meant to be rote memory practice; rather, automaticity must be built on the conceptual understanding underlying the computation at hand. This is done by addressing facts first through sufficient conceptual understanding instruction, mastery practice (goal of about 90% accuracy at a rate of about a fact per 2-3 seconds), and finally ensuring adequate spaced review to continue efficiency with each fact. For more specifics on this ten-minute period, please refer to the Kansas MTSS 10 Minutes of Computational Fluency Brief in the resources below.
General Guidance
Early Mathematics Fluency with CCSM (Matney)
Facts on Fire Fluency Probes | Measures and Interventions for Numeracy Development (M.I.N.D.)
Fluency Practice ‖ Best Practice ‖ K-12 Math Instruction | Project STAIR
Fluency Resources for Grade Level Routines (K-5)) | Achieve the Core
Instructional Strategies: Intensive Intervention with Mathematics Module #5 | National Center on Intensive Intervention
Kansas MTSS Computational Fluency Brief
Kansas MTSS Computational Fluency Webinar
Mathematical Fluency & Number Sense: Techniques, Access & Sustainability for All Students | CORE
Mathematics Fluency Support Grades 6-8 | EngageNY
Resources for Early Numeracy & Computation Skills | Measures & Interventions for Numeracy Development
What is Procedural Fluency? | Bay-Williams
MULTIPLE REPRESENTATIONS
MULTIPLE REPRESENTATIONS
IES Practice Guide: Use of a Well-Chosen Set of Concrete and Semi-Concrete Representations | What Works Clearinghouse
Intensive Intervention in Mathematics: Module 4 | National Center on Intensive Intervention
Video Example: A Tutor and Student Use Algebra Tiles to Solve an Equation | National Center on Intensive Intervention
Video Example: A Tutor Models How to Solve a Word Problem About Change | National Center on Intensive Intervention
What Should We Consider When Teaching Students with Math Difficulties | National Center on Intensive Intervention
Concrete, representational & abstract (CRA) manipulative virtual resources:
Math Playground Virtual Manipulatives
Mathigon Polypad Virtual Manipulatives
NUMBER SENSE
NUMBER SENSE
John SanGiovanni, mathematics supervisor for Maryland's Howard County Public School System, underscores the elusiveness of number sense when he says, "It's not measured. It's not a specific standard. It's not a lesson." Number sense is a student's "intuitive understanding of numbers, their magnitude, relationships, and how they are affected by operations," (Learn NC, University of North Carolina). When we find students who "don't have good number sense," what can we do about it? Below are links that demonstrate how educators have gone about building number sense in their learners.
CORE Fluency & Number Sense Webinars
Daily Routines to Jump Start Math Class - Quick Overview Video | John SanGiovanni, Corwin
Daily Routines to Jump Start Math Class, Grades 3-8 | John SanGiovanni, Corwin
Daily Routines to Jump Start Math Class - Elementary
Daily Routines to Jump Start Math Class - Middle School
Daily Routines to Jump Start Math Class - High School
Estimation 180: Start Here Introduction Video
Estimation180.com | Andrew Stadel
Esti-Mysteries | Steve Wyborney
IES Practice Guide: Recommendation #4: Number Lines
Number Sense through Puzzle and Play Webinar | John SanGiovanni
Number Talks: Building Numerical Reasoning | Sherri Parrish
PRECISE LANGUAGE / MATHEMATICAL VOCABULARY
PRECISE LANGUAGE / MATHEMATICAL VOCABULARY
12 Math Rules That Expire in the Middle Grades (Karp, Bush & Dougherty)
13 Rules That Expire (Karp, Bush & Dougherty)
How Do You Attend to Language Within Intensive Intervention? | National Center on Intensive Intervention
Why Kids Should Learn the Language of Mathematics (Harbin-Miles)
PROBLEM SOLVING
PROBLEM SOLVING
Effective Word-Problem Solving Instruction: Using Schemas to Facilitate Mathematical Reasoning (Powell & Fuchs)
How Do You Incorporate Effective Problem-Solving Strategies Within Intensive Intervention? | National Center on Intensive Intervention
IES Practice Guide: Improving Mathematical Problem Solving in Grades 4 through 8 | What Works Clearinghouse
IES Practice Guide Recommendation for Deliberate Instruction on Word Problems | What Works Clearinghouse
Video Example: A Tutor Models How to Solve a Word Problem About Change | National Center on Intensive Intervention
Video Example: A Tutor and Student Work on Word Problems | National Center on Intensive Intervention
John Hattie, Corwin
University of Texas, at Austin
Institute of Education Sciences
Teacher Talk vs. Student Talk!
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