When teaching students who have difficulties in mathematics, it is important to incorporate instructional practices that have been shown, through evidence, to improve outcomes. Three evidence-based strategies for mathematics instruction are ** visual representations**,

**, and**

*metacognitive strategies**.*

**schema instruction**## Visual Representations

In order to develop every student’s mathematical proficiency, leaders and teachers must systematically integrate the use of concrete and virtual manipulatives into classroom instruction at all grade levels (NCSM, 2013). Virtual manipulatives can be used as a part of the Concrete-Representational-Abstract (C-R-A) learning cycle. These manipulatives are important tools for teacher modeling and demonstration, and provide students access to manipulatives both inside and outside of the school day via computers and other mobile devices (NCSM, 2013).

**Here’s a sample of virtual manipulatives that are available for teachers and students:**

Math Learning Center apps are free virtual manipulative apps that are available in two or more versions: a web app for all modern browsers, and downloadable versions for specific operating systems and devices (such as Apple iOS for iPad).

Didax Virtual Manipulatives offers free browser-based manipulatives that can also be embedded in online learning platforms. Elementary and secondary virtual manipulatives are available.

Houghton Mifflin Harcourt iTools contain virtual manipulatives with activities for the following: counters, base-ten blocks, number lines, number charts, graphs, fractions, geometry, measurement, algebra, and probability.

Glencoe/McGraw-Hill virtual manipulatives include a series of commonly used manipulatives. It also includes game boards, story boards, various grids, graph formats and number lines. Tools include a ruler, protractor, timer, stopwatch, straight line tool, pen, color options, text boxes, and more.

## Metacognitive Strategies

Metacognitive strategies enable students to become aware of how they think when solving problems in mathematics (Iris Center, 2019). One metacognitive strategy that can be used for problem-solving is **UPS-Check**. **UPS-Check** is a four-step process to assist students with understanding and solving problems in context. Utilizing UPS-Check helps students learn to plan how to solve problems, monitor to see if their approach is working, and modify if their strategy is not working (Iris Center, 2019).

#### The UPS-Check Process

UNDERSTAND | Read the problem. What is the problem asking? Identify key information. |

PLAN | Choose a strategy to solve the problem. |

SOLVE | Solve the problem. Work carefully. |

CHECK | Check my work. Does the answer make sense? |

## Schema Instruction

Schema-based instruction (SBI), a cognitive strategy, teaches students how to identify word problem types based on a given problem’s underlying structure, or schema (Iris Center, 2019). When working on problems in context, students are taught to identify the problem schema and to represent the features of the story problem using schematic diagrams (Jitendra, 2007). The details of the story problem are mapped out in the diagram to ensure that irrelevant information is not included (Jitendra, 2007).

**Schema-Based Instruction Problem Types**

## Resources for Evidence-Based Math Strategies

**Online Resources:**

- T-TAC ODU Downloadable Resource: Problem Solved! Building Understanding of Word Problems Using UPS-Check
- Iris Center Module: High-Quality Mathematics Instruction: What Teachers Should Know
- VDOE: Evidence-Based Specially Designed Instruction in Mathematics Resource Guide

**Materials Available in the T-TAC ODU Lending Library:**

*Solving Math Word Problems: Teaching Students with Disabilities Using Schema-Based Instruction**Word Problems for Model Drawing Practice*(Levels 1-6 and solution keys are available)*Problem Solved! Bar Model Math*(Books for Grades 1-6 are available)*Step-By-Step Model Drawing*

**References**

Iris Center. (2019). *High-quality mathematics instruction: What teachers should know*. Retrieved from https://iris.peabody.vanderbilt.edu/module/math/#content

Jitendra, A. K. (2007). *Solving math word problems: Teaching stuudents with learning disabilities using schema-based instruction.* Austin: PRO-ED.

McLeskey, J., Maheady, L., Brownwell, M. T., & Lewis, T. J. (2019). *High leverage practices for inclusive classrooms.* New York: Routledge.

National Council of Supervisors of Mathematics. (2013). *Improving student achievement in mathematics by using manipulatives with classroom instruction*. Retrieved from mathedleadership.org