Math Interventions

When you write an intervention plan to support mathematical modeling, there are two main instructional approaches you might take. As you read about each approach, consider the following questions:

• What are the benefits and pitfalls of each approach?
• When might you want to use one approach over the other?

Explicit Instruction. Explicit Instruction includes the following components: activating prior knowledge, communicating the purpose of the lesson, teacher modeling, guided practice, and independent practice. This approach supports student mastery of more advanced modeling strategies through direct instruction and gradual release of the cognitive work from teacher to student. 

• When to use this approach: Explicit math instruction is particularly effective when intervening to support exceptional learners in learning how to execute a procedure correctly, in cases when students are skipping steps and/or executing steps the wrong way
• Potential Pitfall: There is a risk that a student might walk away from an explicit math intervention understanding the steps in the modeling procedure but not the mathematics underlying each step. In other words, the student may learn what to do but not understand why he's doing each step. This will limit the student's conceptual understanding

Inquiry-Based Instruction. Inquiry-based instruction is an approach to teaching in which students are asked to compare two different solutions to the same problem and make connections between the strategies. This approach supports student mastery of more advanced modeling strategies through guided discourse and puts the majority of the cognitive work on the student.

• When to use this instructional approach:  Inquiry-Based Instruction is particularly effective for teaching a more advanced strategy for solving a particular problem type, in a case when a student is taking a long time to solve a problem because he is using an inefficient strategy or making lots of mistakes due to a poor fit between the model and the problem situation. This approach supports student understanding of why the more advanced strategy works, which will support conceptual understanding 
• Potential Pitfall: The student might not understand how to accurately execute the procedure without explicit modeling and guided support after the guided discourse

Using Mathematical Modeling to Get Real With Students. (n.d.). Edutopia. Retrieved February 12, 2023, from https://www.edutopia.org/article/real-world-math-problem-solving

You can use either Explicit Instruction or Inquiry-Based Instruction when you intervene to support your student's modeling skills. The following lesson plan targets a modeling objective using Inquiry-Based Instruction. As you read this plan, consider:  

• How does this plan support objective mastery?

Modeling Intervention Plan

Art, E. (2017). Modeling lesson plan. New York, NY: Relay Graduate School of Education.