Provide explicit instruction and incorporate visual representations and motivational strategies.

Intervention instruction should be explicit and systematic, incorporating models of proficient problem solving, verbalization of thought processes, guided practice, corrective feedback, and frequent cumulative review. Instructional materials should include examples of easy and difficult problems. Students need guided practice with scaffolding, including opportunities to communicate their problem-solving strategies. Motivation is key for students struggling with math, so it is important to praise effort and engagement to encourage persistence.

Intervention materials should provide students opportunities to work with visual representations of math concepts, and interventionists should be proficient in their use. Tools such as number lines and strip diagrams have many different uses in explanation of mathematical concepts and problem solving. When introducing new concepts to students, it is helpful to begin with concrete experiences, follow up with visual representation, and then move to abstract concepts.

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Planning for Visual Representations

Interventionists can use this planner to develop lessons for Tier 2 and Tier 3 interventions that include visual representations as well as other features of explicit instruction. Related Media...

Tool
Document
06/04/2014
954 views

Intentional Teaching Observation and Feedback

Coaches and professional developers can use this observation tool to focus observations of interventionists and structure discussions during feedback conferences. Related Media: Explicit...

Tool
Document
06/04/2014
939 views

Learning Together About Visual Representations

Math coaches and specialists can use this tool to help elementary and middle school interventionists and tutors learn about the use of visual representations in mathematics. The tool details how to...

Tool
Document
06/04/2014
1388 views

Teaching Students Math Problem-Solving Through Graphic Representations

In this article, the author provides many examples of the use of different types of visualizations to teach mathematics concepts. Examples of visual representations are linked to solving word...

Sample Material
Document
06/04/2014
2685 views

Solving Algebra and Other Story Problems With Simple Diagrams

The article illustrates examples of word problems of increasing difficulty accompanied by the types of visualizations that help students analyze the problem statements and find solutions. The...

Sample Material
Document
06/04/2014
1043 views

Concrete-Representational-Abstract (CRA) Instructional Approach Summary Report

This document describes the CRA instructional strategy with examples of its use in teaching fractions. CRA is a framework for creating connections about levels of under

Sample Material
Document
06/04/2014
1262 views
Explicit Teaching in the Fifth-Grade Math Core

Explicit Teaching in the Fifth-Grade Math Core

A fifth-grade teacher describes explicit step-by-step approaches to teaching division of fractions. She emphasizes vocabulary teaching, demonstration, scaffolding, partner sharing, and checking for...

School Example
Video
06/04/2014
675 views
Pacing Instruction in Tier 3

Pacing Instruction in Tier 3

In this Tier 3 intervention lesson, the instructor reteaches a lesson on place value after it is clear that students have not grasped the concept of bundling ones to form a ten. Students create...

School Example
Video
06/04/2014
483 views
Organizing for Differentiation in the Core Classroom

Organizing for Differentiation in the Core Classroom

A second-grade teacher demonstrates a lesson on subtraction with regrouping. Through small group instruction she differentiates for struggling students and provides immediate reteaching after...

School Example
Video
06/04/2014
456 views
Concrete to Abstract Sequence

Concrete to Abstract Sequence

A middle-school special education teacher demonstrates a lesson on solving two-step equations. She shows how to begin with concrete materials and then represents the same concepts on the SMART...

School Example
Video
06/04/2014
684 views
Visual Representations

Visual Representations

Dr. Witzel provides examples of each stage of the concrete-representational-abstract teaching sequence, with special attention to visual representation. He shows several types of representation,...

Expert Interview
Video
06/02/2014
1057 views
Explicit Instruction

Explicit Instruction

Dr. Witzel describes the components of explicit instruction, including modeling and demonstration, guiding and scaffolding practice, providing independent practice, and providing meaningful...

Expert Interview
Video
06/02/2014
529 views
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