Key+Strategies+for+Mathematics+Interventions

The Key Strategies described here are from the recommendations in the IES Practice Guide //Assisting Students Struggling with Mathematics: Response to Intervention (RtI) for Elementary and Middle Schools//. It can be downloaded from the Helping Struggling Learners page of this wiki.

A short version of the recommendations, with supporting implementation strategies, is available here: [|IES Practice Guide RtI Math - Checklist for carrying out the recommendations].

The [|Key Strategies workshop powerpoint] contains helpful examples. Additional resources from the presentation are included below each of the following recommendations.

** Recommendation 1. Screen all students to identify those at risk for potential mathematics difficulties and provide interventions to students identified as at risk.**
 * See the recommendations in the IES Practice Guide (short version or full version)

** Recommendation 2 **. **Instructional materials for students receiving interventions should focus intensely on in-depth treatment of whole numbers in kindergarten through grade 5 and on rational numbers in grades 4 through 8. These materials should be selected by committee.**
 * This means that intervention support programs should focus on developing fluency with addition, subtraction, multiplication and division of whole numbers, both fact fluency and multi-digit operations, in K-5, and on fluency with the use of fractions, decimals and percents in 4-8. Fluency must be broadly construed to include both the efficient use of procedures and an understanding of why the procedures work. Fluency is rooted in the flexible use of strategies.
 * [|IISD fluency packet] Strategies for helping students become fluent with "math facts"
 * [|Math across the curriculum] Problems for supporting fluency development in secondary schools
 * [|CGI problem sets], from //Children's Mathematics: Cognitively Guided Instruction//, by Carpenter et. al. 1999. The problems in these sets represent how students come to learn about whole number operations.
 * [|Multi-digit multiplication learning progression, examples and resources] Helpful for teaching about multi-digit multiplication.
 * [|Multi-digit division with examples] Helpful for teaching about multi-digit division.
 * [|Operations with Fractions & Decimals Packet] Student worksheets, teacher background information and assessments

** Recommendation 3 **. **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 discussed in Recommendation 4.
 * 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.
 * See Lattice Multiplication in the Arithmetic section at the Khan Academy website. This is not necessarily a perfect model of explicit instruction, but a start. He does verbalize his own thinking along with being clear about why he is doing various procedures.


 *  Recommendation 4. Interventions should include instruction on solving word problems that is based on common underlying structures. **
 * See the powerpoint for examples
 * The [|Problem Solving Toolkit] contains additional examples and other strategies for supporting students who struggle with problem solving


 *  Recommendation 5 . 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. **
 * Example 1: [|Various visual representations]
 * Example 2: [|5th grade decimal operations] This teaching strategy shows the use of an area model for decimal multiplication
 * Example 3: The concrete-representational-abstract learning progression (also called objects-pictures-symbols) incorporates visual representations in important ways. Here is an example: [|Objects-pictures-symbols from problem solving toolkit]
 * Example 4: [|CRA for multidigit subtraction]


 *  Recommendation 6 . Interventions at all grade levels should devote about 10 minutes in each session to building fluent retrieval of basic arithmetic facts. **
 * [|IISD Fact Fluency Packet] with teacher background information and teaching strategies


 *  Recommendation 7 . Monitor the progress of students receiving supplemental instruction and other students who are at risk. **
 * See the recommendations in the IES Practice Guide (short version or full version)


 *  Recommendation 8 . Include motivational strategies in tier 2 and tier 3 interventions. **
 * See the recommendations in the IES Practice Guide (short version or full version)