Response to Intervention Research, Series #4: Recommendation 3 – Model problem solving

Written By jmosier

On January 28, 2011

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Recommendation 3 – Model problem solving, verbalizing thought processes, guided practice, corrective feedback, and cumulative reviews

Connected to the CCSSO Standards and Instructional Recommendations

This is the fourth in a series of five postings that connect the Institute of Education Sciences (IES) practice guide recommendations, Assisting Students Struggling with Mathematics: Response to Intervention (RTI) for Elementary and Middle School Students with corresponding CCSSO Standards indicators, and an instructional look alike for that RTI recommendation.

The IES guide identifies eight recommendations that are designed to help teachers, principals, and administrators use Response to Intervention for early detection, prevention, and support of students struggling with mathematics. This guide is a synthesis of research that provides instructional recommendations in support of engaging those struggling mathematics students.

RTI Recommendation 3 – Model problem solving, verbalizing thought processes, guided practice, corrective feedback, and cumulative reviews

CCSSO Standards that correspond to the RTI recommendation  of verbalizing thought processes are  indicators as listed below. For the CCSSO Standards, verbalizing thought processes is a pervasive process that underscores the need for having students construct meaning about the mathematics through communicating what they know.

  • Explain correspondences between equations, verbal descriptions, tables, graphs, or draws diagrams.
  • Describe, analyze, compare, and classify shapes through building, drawing, and analyzing those shapes.
  • Draw, construct, and describe geometrical figures and describe the relationships between them.
  • Describe and compare measurable attributes.
  • Discuss, and use efficient, accurate, and generalizable methods for operating with numbers.
  • Explain why addition and subtraction, multiplication and division strategies work, using place value and the properties of operations.

What would verbalization of thought processes sound and look like instructionally?

In thinking through what verbalization of thought processes would sound and look like, I am reminded of a structure CTL uses in working with teachers. It is the research-based process of using the Gradual Release Model that support both students and teachers in verbalization of their thought processes.

Gradual Release Model: This model is an instructional structure used by students and teachers for verbalizing thought processes with the intent of having students construct meaning about the mathematics, build skill fluency, make connections, and use mathematical vocabulary for solving problems. It might be in the form of explaining the steps of an algorithm; defending why one strategy works, as well as, another in solving a problem; analyzing work so that errors could be corrected or discussing various ways to approach a problem; describing the attributes of a shape; and processing how to solve a problem.

The Gradual Release Model works because it provides an opportunity for supporting students as they:

  • need multiple strategies from which they can choose while solving problems, development of which can occur during the gradual release process.
  • cannot adequately learn a strategy by using it once and/or through watching someone else solve the problem. They construct meaning through multiple opportunities during the gradual release. process.
  • must have direct assistance in understanding the concept and making connections to other learning  before obtaining skill fluency, problem solving skills, and vocabulary for communicating understanding. Again, the process of gradual releasing the learning to students provide the opportunity for this to occur.
  • must experience a strategy multiple times, and reflect on the use of the strategy, before they are able to internalize it and eventually bring it to automaticity. The various stages of gradual release will provide that differentiated structure for supporting the multiple learning needs of students.

Generally, the gradual release model uses a series of steps that shift responsibility for learning from teacher to student with:

I do, you watch.

I do, you help.

You do and I help.

You do, I watch.

An illustration of the Gradual Release Model that capture various RTI Recommendations of – verbalization of thought processes, guided practice, working with visual representations, treatment of whole numbers is clearly demonstrated in the following YouTube video

Another clear resource to investigate would be from NCTM, Mathematics Teaching in Middle Schools, “Using Error Analysis to Teach Equation Solving,” Dec. 2006/January 2007, pp 238-242. This article provides student work and student dialogue as they analyze, within a safe environment, and verbalize thought processes through error analysis in solving algebraic equations.

What are other suggestions that you have to increase the student opportunities to verbalize their thought processes; why do you believe it is important; what are the benefits to student learning?