Math Interventions

In order to support your student's ability to apply math rules and concepts, it is important to use an inquiry-based approach that enables them to recognize patterns and make connections between new and previously learned material. This page includes intervention strategies that you can use to support your student's understanding of math rules and concepts. As you read, consider which of these interventions best aligns with the particular misconception your student is having. 

Explicitly Teach Why Math Rules & Concepts Help Us

Before you use an inquiry-based approach to intervene to support your students' understanding of mathematical concepts and ideas, you should start by explicitly teaching the student why it's important to understand the rules and concepts that are always true about math. This sounds like:

• Explain the Skill/Concept. Define mathematical rules and relationships, and explain the activity. ("When we solve math problems, it is important to identify rules that are always true. This will help us do math efficiently and check our work." "Today, we'll learn strategies to help us know which rules and relationships are true." )
• Model Skill with Examples. Think aloud about the importance of knowing math rules and relationships that are true.  ("When I read a math problem, I want to make sure I am solving it the most efficient way possible. Math rules and regularities help me do this. Imagine that I had to solve the problem: 1 +0 , 1 + 1, 1+ 2, 1 + 3, and so on. If I knew the rule that every time you add one to a number, you just count up one, I would be able to solve this quickly, and be confident in my answers.")
• Model Skill with Non-Examples. Think aloud about what happens when you aren't familiar with math rules and relationships. ("Imagine that I had to solve the problem again, but I didn't remember the rule.  If I spent the time counting on my fingers for every problem, it would take me a long time! But, if I knew the rule, I should have been able to solve it quickly, and be able to check my answers quickly. That's why knowing math rules and regularities is so important.")
• Practice the Skill. Engage in one or more of the activities below to practice the skill with your student, providing feedback as necessary. ("Now you try. I'm going to show you...")

Inquiry-Based Activity A: Pattern Recognition

If your student struggles to understand a mathematical rule, teach him to recognize the rule by looking for a pattern across a series of problems that adhere to that rule. First, introduce a set of problems that reveal a new (or previously learned) rule that the student has not yet mastered. Then, have the students solve the problems, prompting and questioning to support rule recognition. This might sound like, "I notice that when you add zero to 5, the sum is the same number, 5" or "What do you notice happens every time you add zero to a number?" (Clemens & Sarama, p. 192). Then, she encourages the student to "test out" their theory to see if the pattern or "rule" that they identified is true. This structure of practice and repeat continues until the student can explain and apply the rule fluently. Note: This strategy can be used for any math concept or principle, since every concept or principle can be demonstrated across multiple problems! 

Pattern Recognition in Action

As you read the following lesson plan, consider the steps the teacher takes to help the student notice the pattern.

Math Rule Lesson Plan

Pattern recognition template. (2016). Relay Graduate School of Education.

Inquiry-Based Activity B: Relational Thinking

If your student is having trouble understanding the fundamental properties of operations, teach him to use Relational Thinking (Carpenter et al., 2015). This strategy teaches a student to become more aware of the properties that he is using so that he can better draw connections between the different operations. 

Relational Thinking in Action

As you read the PDF below, consider: What kinds of questions is the teacher asking to help students make connections? How do these questions help enable a student to better understand operations?

Relational Thinking

Carpenter, T. P., Fennema, E., & Franke, M. L. (1996). Cognitively guided instruction: A knowledge base for reform in primary mathematics instruction. The Elementary School Journal, 97(1), 3-20. https://doi.org/10.1086/461846

Clements, D.H. & Sarama, J. (2009). Learning and teaching early math: The learning trajectories approach. New York: Routledge. 

Think about the following scenario, which takes place after a teacher has taught a student the rule that A x 0 = 0 by having the student identify a pattern across problem types.

     Teacher: "Let's practice applying the rule that any number times zero equals zero. What's
     10 times zero?
     Student: "10?"

In such a case, what might you do? 

When you are planning your lessons, you should anticipate that your student will make errors throughout. Here are a series of prompts that you can use to respond to errors. Keep in mind that all students are different, and that students might respond better to some types of feedback than to others.

If your student struggles to meet your objective, there are various techniques that you might try in order to adjust the activity so as best to meet your student's needs.