Math Interventions

The first step to modeling any problem is figuring out which information needs to be modeled. To do this, a student needs to identify which information is essential to solving the problem, as well as which information is unnecessary. This page includes strategies to support your students in this area. As you read, consider which of these interventions best aligns with the particular problem type with which your student is having difficulty.

Explicit Instruction

If you are intervening to support your students' ability to identify essential variables, you should start by explicitly teaching the skill. This sounds like:

• Explain the Skill/Concept. Define essential variables and explain activity. ("Essential variables are the numbers or the information in the story that we need to solve a problem. We need to identify this information so that we know which parts of the problem we should model." "Today, we will learn strategies for identifying the essential variables in our problem." )
• Model Skill with Examples. Think aloud about identifying essential variables.  ("When I read a problem, such as The boy had one apple. The girl had two apples. How many apples did they have all together? I need to figure out which information is essential to the problem. To do this, I'll need to first identify what the question is asking me: How many apples are there all together? I know that the boy had an apple, and the girl had two apples, so those are the essential variables I need to solve this problem. Therefore, these are the pieces that I will model.")
• Model Skill with Non-Examples. Think aloud, and use a model ineffectively. ("Now what if I used the blocks like this: The boy had one apple. The girl had two apples [Teacher grabs two blocks.] How many did they have all together? One, Two... Two apples. See how I only represented the girl's apples, not the boy's, with blocks? In this story, I needed to pick a block for every apple in the story.")
• 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 give you a problem...")

Activity A: SQR

If your student struggles to understand the essential information in a problem, and therefore struggles to model the problem, teach him SQR (Florida Department of Education, 2010). This strategy helps a student determine important and unnecessary information in a problem, which is a prerequisite for setting up a correct model. This strategy, originally develop by Leu and Kinzer (1991), has three essential parts: Survey (S), Question (Q), and Read (R), outlined below:

• Survey: The student reads the problem and paraphrases it in his own words.
• Question: The student questions the purpose of the problem by asking two question: What is being asked? What are you trying to figure out?
• Read: The student rereads the problem, eliminates unnecessary information, determines the exact information he is looking for, and devises a plan for modeling the strategy

SQR in Action
This example refers to the following problem.
Ronald has 2 kittens. Lupita has 5 kittens. All of these kittens like to play with string. How many more kittens does Lupita have than Ronald?

Teacher: Let's use the SQR model to identify the essential variables in the problem. This is a necessary step to figuring out which information we need to model.

First is S: I'll show you how I survey the problem and paraphrase it. This will help me ensure that I understand what the problem is asking. (Teacher reads problem.) Now, I'll paraphrase. Two children have different amounts of kittens. Ok, I understand that.

Now, I'll do Q: I need to see if I can figure out the question the problem is asking. (Teacher rereads problem.) Ok, the problem is asking me how many more kittens one child, Lupita, has than the other child, Ronald.

Now, on to R: I need to reread the problem and eliminate information I don't need, and determine the information that is necessary to make a model. I know that I'll need to model the kittens that Ronald has, which is 2, and the kittens that Lupita has, which is 5. It seems like the sentence about the kittens playing with string is unnecessary because I won't need this information to model the problem, so I can eliminate this sentence. Now, I'm ready to model this problem to solve it!

Florida Department of Education. (2010). Classroom Cognitive and Meta-Cognitive Strategies  for Teachers: Research-based strategies for problem-solving in mathematics, K-12. Retrieved from http://floridarti.usf.edu/resources/format/pdf/Classroom%20Cognitive%20and%20Metacognitive%20Strategies%20for%20Teachers_Revised_SR_09.08.10.pdf

Think about the following scenario, which takes place after a teacher has explicitly taught a student strategies to identify essential variables. This example refers to the following problem.

Ronald has 2 kittens. Lupita has 5 kittens. All of these kittens like to play with string. How many more kittens does Lupita have than Ronald?

     Teacher: "You've already completed the S and Q, now on to R. What unnecessary
     information can you eliminate that you won't need to model this problem?"
     Student: "It's all important. I just don't know how to model the string!" 

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.