RtI Interventions for Math
Anyone well versed in Response to Intervention (RtI)for math is familiar with the recommendations of the Institute for Education Sciences’ “What Works” report, “Assisting Students Struggling with Mathematics: Response to Intervention (RtI) for Elementary and Middle Schools”, published in 2009. It’s the Department of Education’s main treatise regarding RtI.
In the report, a series of eight generalized intervention recommendations are presented and judged based on research-based evidence. Although all eight are valuable and need to be considered, only four are judged to have strong or moderate evidence to support them at the time of the report’s publication. (All four links go to the same report, but each recommendation’s specific page can be found separately within the report.)
Let’s look at those four-evidence based recommendations, and find specific strategies that fall into the generalized recommendation.
1. 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.
Students who have been classified as Tier 2 or 3 in RtI need their instruction to be organized and scaffolded. They lack the numeracy skills and background knowledge to engage in theoretical exercises with math.
Nothing is more systematic than the four-step approach to problem solving. Students seek to understand the problem, devise a plan to solve the problem, carry out the plan, and look back to analyze their result. Here is a Teaching Hacks article describing the problem solving process further.
2. Interventions should include instruction on solving word problems that is based on common underlying structures.
A stripped-down version of the Gradual Release Model, the “I do, We do, You do” strategy is effective in all levels of education. As RtI students require as much structure as possible, the strategy gives them an effective way to know what to expect from a lesson.
In word problems, not only can “I do, We do, You do” be used to solve problems, it can also be used to have students create their own word problems, reaching synthesis, a higher level of taxonomy. Students should start with sentences that involve a specific math operation and build from there. (McCarney, S.B., Cummins Wunderlich, K., Bauer, A. (1994). The Teacher’s Resource Guide: Columbia, MO.)
3. 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.
Graphics are important in math instruction, especially as the curriculum becomes more data-based under the Common Core State Standards. RtI students are not excluded from having to be able to read charts, graphs, and other math graphics.
Intervention Central has a great intervention that uses Question-Answer Relationships (QAR) to help students break down math graphics. In short, QARs come in four types:
- Right There questions are found explicitly in the graphic
- Think and Search are not quite as explicit, but still can be found in the graphic with some close analysis
- Author and You asks students to compare the data with their own life experiences and opinions
- On My Own are questions that only require the students’ knowledge and experience to answer
4. Interventions at all grade levels should devote about 10 minutes in each session to building fluent retrieval of basic arithmetic facts.
Rehearsal of math facts is a key step in the RtI process because many of the students who fall into Tier 2 or 3 status are missing key pieces of background information, usually in the form of math facts. Taking ten minutes each day to review these facts may be frustrating and boring, but there is a way to make flash card practice more effective.
Intervention Central has another strategy that uses flash card practice, but balances the facts in quickly recalled “known” facts and unknown facts. In short, unknown facts are modeled by a teacher or tutor and then presented with known facts in a sequence. Not only does this systematically build recall, it also builds confidence in the student because they are consistently getting cards correct throughout the process.
Learn more about RtI in the white paper: Math Intervention and the Promise of Adaptive Learning.