Assisting Students Struggling with Mathematics: Response to Intervention in Middle School

Presentation Highlights

Focus on rational numbers in grades 4-8

  • Many students in upper grades do not perform well in algebra
  • Rational number knowledge allows students to abstract to complex math
  • Starting early (4th grade) with rational number instruction should lead to better student performance in algebra later on

Use explicit and systematic instruction

  • Good instruction must be a key to developing understanding; it must be:
    • Mathematically precise
    • Developmentally appropriate (suitable for the students being taught)
    • Longitudinally transportable (still useful across the grades)
  • Students can’t afford to keep learning the same content in multiple grades

Teaching math vocabulary

Discussion of a professional development activity.

Use visual representation in teaching math

  • Visuals are good tools for scaffolding students’ understanding of concepts
  • Goal is to have students work with abstractions; support growth in understanding through the use of visual elements

Scaffolding from concrete to abstract ideas

  • Concrete representation (things you can touch) is used to lay the foundation
  • Visual representation (things you can see) is used as an intermediate step
  • Abstraction (numerical representation of quantity) is the final step

Considerations for using model representations in teaching math

  • Explicitly link the concrete and visual representations to the abstraction
  • Use consistent language in talking about the concepts
  • Provide ample opportunities to practice use of representation
  • Provide corrective and affirmative feedback on student responses
  • Select examples and non-examples carefully to support understanding

Recommendation 2

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.

Level of evidence: Low. This recommendation is based on expert opinion and professional consensus rather than on scientific research. Hence, the level of evidence is considered to be low.

Recommendation 3

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.

Level of evidence: Strong.

Recommendation 5

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.

Level of evidence: Moderate

  • Visual representations may include number lines, arrays and diagrams
  • If needed, physical manipulatives can be used to scaffold understanding from physical to visual to abstract representation of numbers

Resources and links cited in presentation

Beyond Slices of Pizza: Teaching Fractions Effectively [K-7]

“This webcast, sponsored by the Center for Comprehensive School Reform and Improvement at Learning Point Associates, showcases best practices for teaching fractions. Also available are classroom handouts and  additional video and other online resources for teaching fractions. This webcast can be accessed at (Note: Windows Media Player 9.0 or higher required for viewing video.)

(Note: This is a free and accessible resource from the Center on Instruction. It is available via their website. The Center on Instruction is a federally funded resource center which provides high quality resources for improving instruction across the curriculum.)