The IES Practice Guide for Assisting Students Struggling with Mathematics contains key research-based strategies for interventions and instruction. The key instructional strategies are listed below, with resources that can help you implement each of the strategies.

Visual representations

Intervention materials should include opportunities for students to work with visual representations of mathematical ideas and interventionists should be proficient in the use of visual representations of mathematical ideas.The documents listed below show how visual representations play an important role in moving students from concrete manipulatives to visual representations to symbolic/abstract procedures (C-R-A).

Interventions should include instruction on solving word problems that is based on common underlying structures. The panel recommends that interventions include systematic explicit instruction on solving word problems, using the problemsâ€™ underlying structure. Simple word problems give meaning to mathematical operations such as subtraction or multiplication. When students are taught the underlying structure of a word problem, they not only have greater success in problem solving but can also gain insight into the deeper mathematical ideas in word problems. The panel also recommends systematic instruction on the structural connections between known, familiar word problems and unfamiliar, new problems. By making explicit the underlying structural connections between familiar and unfamiliar problems, students will know when to apply the solution methods they have learned.

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.

Models of proficient problem-solving are aligned with instruction on the common underlying structure of word problems (see above).

Verbalization of thought processes means that both teachers and students explain the concepts behind how they solved problems or carried out procedures.

Guided practice with corrective feedback is like coaching: Practice problems should be ordered sequentially, interventionists should analyze mistakes that students make and help students see how they are going wrong. This usually does not involve doing the problem for the student (think about coaching) or giving them a verbal procedure that they might not be ready to understand. It means showing them why their approach does not work, in terms they do understand.

Frequent cumulative review is important because most people don't remember things that they don't use often.

An example involves the C-R-A for subtraction listed above. If a child does not see, on her own, how to break apart a ten-stack of cubes when needed (i.e. how to regroup), use the "I do it, we do it, you do it" approach. Explain your thought processes as you model the procedure. When doing it together, help the child explain what's happening when she needs help. When she does it alone, you have successfully transferred responsibility for understanding and doing the procedure to the student.

SUPPORTING STRUGGLING LEARNERS IN MATHEMATICSKey documents can be downloaded here.

Assisting Students Struggling with Mathematics: Response to Intervention (RtI) for Elementary and Middle SchoolsDeveloping Effective Fractions Instruction for Kindergarten Through 8th Grade(this is a large file)Mathematics Instruction for Students with Learning Disabilities or Difficulty Learning Mathematics: A Guide for TeachersDeveloping Computational Fluency with Whole Numbers in Elementary Grades, by Susan Jo RussellThe IES Practice Guide for Assisting Students Struggling with Mathematics contains key research-based strategies for interventions and instruction. The key instructional strategies are listed below, with resources that can help you implement each of the strategies.## Visual representations

Intervention materials should include opportunities for students to work with visual representations of mathematical ideas and interventionists should be proficient in the use of visual representations of mathematical ideas.The documents listed below show how visual representations play an important role in moving students fromconcrete manipulatives to visualrepresentations to symbolic/abstract procedures (C-R-A).## Common underlying structure of word problems

Interventions should include instruction on solving word problems that is based on common underlying structures.The panel recommends that interventions include systematic explicit instruction on solving word problems, using the problemsâ€™ underlying structure. Simple word problems give meaning to mathematical operations such as subtraction or multiplication. When students are taught the underlying structure of a word problem, they not only have greater success in problem solving but can also gain insight into the deeper mathematical ideas in word problems. The panel also recommends systematic instruction on the structural connections between known, familiar word problems and unfamiliar, new problems. By making explicit the underlying structural connections between familiar and unfamiliar problems, students will know when to apply the solution methods they have learned.

Children's Mathematics: Cognitively Guided Instruction, by Carpenter et. al. 1999## Explicit instruction

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.- Models of proficient problem-solving are aligned with instruction on the common underlying structure of word problems (see above).
- Verbalization of thought processes means that both teachers and students explain the concepts behind how they solved problems or carried out procedures.
- Guided practice with corrective feedback is like coaching: Practice problems should be ordered sequentially, interventionists should analyze mistakes that students make and help students see how they are going wrong. This usually does not involve doing the problem for the student (think about coaching) or giving them a verbal procedure that they might not be ready to understand. It means showing them why their approach does not work, in terms they do understand.
- Frequent cumulative review is important because most people don't remember things that they don't use often.

An example involves the C-R-A for subtraction listed above. If a child does not see, on her own, how to break apart a ten-stack of cubes when needed (i.e. how to regroup), use the "I do it, we do it, you do it" approach. Explain your thought processes as you model the procedure. When doing it together, help the child explain what's happening when she needs help. When she does it alone, you have successfully transferred responsibility for understanding and doing the procedure to the student.## Systematic curriculum

## Additional Resources

File Not FoundPowerpoint for Interventionist Workshop on Computation, April 23, 2013 PDF version of this powerpoint

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