Institute of Education Sciences Assisting Students Struggling with Mathematics: Response to Intervention (RtI) for Ele

1. Institute of Education Sciences Assisting Students Struggling with Mathematics: Response to Intervention (RtI) for Elementary and Middle Schools Recommendation 3Instruction provided in math interventions should be explicit and systematic, incorporating modeling of proficient problem-solving, verbalization of thought processes, guided practice, corrective feedback and frequent cumulative review. Level of Evidence: Strong

2. Research to Support the Recommendation Based on a review of rigorous research, The National Math Advisory Panel defines explicit instruction as follows: • Teachers provide clear models (demonstrations) for solving a problem type using an array of examples. • Students receive extensive practice in using new strategies and skills. • Students are provided with opportunities to verbalize or “think aloud” about their work. • Students are provided with extensive corrective feedback on their efforts. In Explicit Instruction:

3. Research to Support the Recommendation Explicit and systematic instruction can significantly improve proficiency in word problem-solving and operations across grade levels and sub-groups. • Districts and schools should select materials with explicit and systematic instruction for math interventions • Professional development for intervention specialist should include training on the elements of explicit instruction

4. How to Carry Out the Recommendations

5. Be sure that instructional materials used for math interventions are systematic and explicit--or can easily be adapted for such teaching • Identify and teach pre-skills • Provide numerous applications of each concept (be prepared to present more examples than are in the teacher’s guide, as these materials often don’t provide enough examples) • Clearly provide step-by-step models of how to perform operations and the reasoning behind the steps. • Use “think-alouds” to let students know how you are thinking about the problem; ask students to “think out loud” as well.

6. 2. Provide students with opportunities to solve problems in a group and to communicate problem-solving strategies. • Use scaffolded practice: • Teacher demonstrates how to solve a problem type. • Teacher and students solve problems together. • Teacher reduces support, prompting as needed. • Students solve problems independently with teacher feedback. • Ask students to talk out loud about their problem-solving process and their rationale for it. • Provide specific feedback about what parts are right and what steps need to be corrected (and how to correct them).

7. Ensure that instructional materials include cumulative review in each session. • Provide problem-types from previous lessons • This helps maintain skills that were taught previously • If the materials don’t provide sufficient cumulative review, be prepared to insert your own examples into the lesson from previously taught problem types

9. Concerns & Considerations • Interventionists might not be familiar with using explicit instruction and might not realize how much practice is needed for students in tier 2 and tier 3 to master the material being taught. • As part of the training for teaching intervention programs, give participants hands-on experience with the materials so they can practice teaching from them • Provide positive and corrective feedback to participants as they practice teaching lessons from the program • Provide opportunities for interventionists to observe and discuss sample lessons together

10. Concerns & Considerations • Those teaching in the intervention might not be expert or feel comfortable with the math content. • Train interventionists to explain math content • Include math concepts, vocabulary, formulas, procedures, reasoning and methods • Use clear language understandable to students • This will increase student understanding and decrease their misconceptions

11. Concerns & Considerations • The intervention materials might not incorporate enough modeling, think-alouds, practice or cumulative review to improve students’ math performance. • Consider having a math specialist develop an instructional template which contains the elements of instruction identified above and which can be applied to various lessons. • If possible, have a math specialist coach new interventionists on how to use materials most effectively.