# Research-Based Mathematics Instruction

## Are these math lesson workbooks research-based?

Yes!  Five recommendations taken from research are put into practice:

1. Explicit Instruction
2. Explicit Instruction on Word Problems
3. Visual Representations
4. Example Selection and Sequence
5. Student Verbalizations

“Research has indicated that teaching mathematics in this manner is highly effective and can significantly improve a student’s ability to perform mathematical operations (e.g., adding, multiplying) as well as to solve word problems. This strategy [explicit instruction] has been shown to be effective across all grade levels and for diverse groups of students, including students with disabilities and ELLs.”

“Although all students benefit from explicit, systematic instruction, students with mathematical disabilities and difficulties often require it if they are to learn foundational grade-level skills and concepts.”

## What does “explicit instruction” mean?

Explicit instruction involves teaching a specific concept or procedure in a highly structured manner.

The teacher will:

• Clearly identify the skill or concept to be learned
• Connect the new content to previous learning
• Give precise instructions
• Model concepts or procedures in a step-by-step manner and include “think alouds”— the teacher verbalizing his or her thought process while demonstrating the concept or procedure
• Lead students in guided practice – Students and the teacher work problems together, with the students gradually solving more of the problem.
• Provide independent practice – Students work independently to solve problems.
• Encourage the student to verbalize the strategy he is using to solve the problem
• Offer specific feedback about correct and incorrect actions, followed by time to correct errors
• Check for and promote maintenance of skills

## What does “systematic instruction” mean?

Systematic instruction is carefully planned and sequenced.

The teacher will:

• Present lessons that build on one another, moving from simple skills and concepts to more complex ones or from high-frequency skills to low-frequency skills
• Break complex skills into smaller, more manageable chunks, a method also known as task analysis.
• Prioritize and sequence tasks from easy to more difficult
• Scaffold instruction by providing temporary supports (e.g., manipulatives, written prompts or cues)

## What should I look for when evaluating math programs for special education?

A useful “Mathematics Program Evaluation Guide” was published in April 2018  Intervention in School and Clinic journal. It can be accessed HERE (pdf download)  (Figure 1)

Authors of this article observed a shortage of explicit mathematics instruction in commercially available programs.

When mathematics programs lack principles of explicit instruction it makes it difficult for even the most experienced of special educators to meet the instructional needs of students struggling with mathematics. Consequently, it may be necessary for teachers to “look under the hood” of mathematics programs.”

Explicit mathematics instruction should include:

1. Instructional scaffolding with carefully selected examples (that transition from least to most complex) and supports that are gradually withdrawn.

2. Student practice opportunities and timely feedback are essential in learning foundational skills. Students should be given opportunities to verbalize basic facts and procedures.

3. Review should be well designed and appropriately spaced over time to maintain skills and build procedural fluency.

Source:  A Guide for Evaluating the Mathematics Programs Used by Special Education Teachers

## What strategies work for students who struggle to learn math?

Below are links to three informative resources on the best practices for teaching students with mathematics difficulties and disabilities.

### Which Instructional Practices Most Help First-Grade Students With and Without Mathematics Difficulties?

(published June 25, 2014 in Educational Evaluation and Policy Analysis, a peer-reviewed journal of the American Educational Research Association)

Their research found that teacher-directed instruction is significantly more effective than other methods for students with mathematics difficulties.

Teacher-directed instruction was described as “Teachers initially demonstrate specific procedures for solving problems, and then provide students with repeated opportunities (e.g., worksheets, routine practice and drills) to independently practice these procedures.”

**********

### Assisting Students Struggling with Mathematics

(published by The Institute for Educational Sciences--the research arm of the U.S. Department of Education)

It recommends designing and implementing mathematics interventions including:

• Using explicit and systematic instruction during intervention.
• Instructing students to solve word problems based on common underlying structures.

On page 21 of this IES guide it reported strong evidence in support of the recommendation that:

Instruction during the intervention should be explicit and systematic.  This includes providing models of proficient problem solving, verbalization of thought processes, guided practice, corrective feedback, and frequent cumulative review.”

**********

### Mathematics Instruction for Students with Learning Disabilities

A meta-analysis evaluated the results of 42 interventions conducted with students with learning disabilities in math. Of all these interventions, it was determined that the two instructional components that resulted in statistically significant increases in effect sizes were teaching students to use heuristics and the use of explicit instruction.

The key elements of explicit instruction identified by the authors included teacher demonstrations of step-by-step processes to solve problems, the application of the strategies to a specific set of problems, and the requirement that students then use a specific step-by-step protocol to solve problems.

Gersten, Chard, et al. (2009) Mathematics instruction for students with learning disabilities: A meta-analysis of instructional components.  Review of Educational Research, 79(3), 1202-1242

A companion resource to this meta-analysis was published by the Center on Instruction.  It can be found here:

Mathematics Instruction for Students with Learning Disabilities or Difficulty Learning Mathematics: A Guide for Teachers