INSTRUCTIONAL PRACTICES

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?

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)

High-Leverage Practices: Explicit Instruction (CEEDR Center)

Explicit, Systematic Instruction: Elementary (Iris Center)

Explicit, Systematic Instruction: High School (Iris Center)

ACTIVE PARTICIPATION

Active Participation in the Classroom, Pt. 1 

Dr. Anita Archer | PaTTAN

Active Participation in the Classroom, Pt. 2

Dr. Anita Archer | PaTTAN

RETRIEVAL PRACTICE

Retrieval Practice

Dr. Paul Ricommini, PaTTANpod

Making the Most of Retrieval Practice: Spaced Practice

Pooja K. Agarwal, Ph.D. Cognitive Scientist

Benefits of Interleaved Practice

Robert Bjork, Ph.D. Distinguished Professor of Psychology at the University of California, Los Angeles

RESOURCES FOR RETRIEVAL PRACTICE

ADDITIONAL RESOURCES

ALGEBRA

EXPLICIT INSTRUCTION

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

Instructional Hierarchy: Linking Stages of Learning to Effective Instructional Techniques | Intervention Central

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 

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

PROBLEM SOLVING

Visible Learning Meta X

John Hattie, Corwin

Sarah Powell, Ph.D., 

University of Texas, at Austin

What Works Clearinghouse

Institute of Education Sciences

Peter DeWitt, Ph.D.

Teacher Talk vs. Student Talk!