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Math Interventions

Understanding the Problem

Understanding the problem is the first step in problem-solving. During this step, the student must be able to describe the problem and check his own understanding by talking it through and asking questions as he goes. This page includes intervention strategies that you can use to support your students in this area. As you read, consider which of these interventions best aligns with your student's strengths and needs in the whole-learner domains.

Explicit Instruction

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

  • Explain the Skill/Concept. Define understanding the problem, and explain the activity. ("The first step to problem-solving is to make sure we understand what the problem is asking us. We do this by talking through it to make sure we understand all of the pieces. We can also ask ourselves questions about what is happening or what we're trying to figure out." "Today we are going to learn how to think through a problem to help us understand it." )
  • Model Skill with Examples. Think aloud about talking through a problem to check for understanding.  ("Listen as I read this problem and make sure that I'm understanding what's happening. I'm going to read each sentence and make sure I understand what it is about. The problem is: The boy had one apple... okay, so the boy had an apple. The girl had two apples: This sentence tells me that the girl had two apples, which is more than the boy had. How many apples did they have together? The problem wants to know how many apples they had total, or together. I think that means I need to add up the amount that the boy has and the amount that the girl has. Now I understand what the problem is asking me.")
  • Model Skill with Non-Examples. Think aloud about using this strategy ineffectively. ("Now, I'm going to show you how I make a mistake and read a problem without making sure that I understand all of the parts. The boy had one apple. The girl had two apples. How many apples did they have together? The problem tells me that there is a boy and a girl in the story. They were eating apples together. But wait a second! I don't know what I'm trying to figure out! I only paid attention to certain parts of the story, and now I'm not set up to solve the problem. That's why we need to make sure to think through all of the parts of a 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: Teach Comprehension, Not Key Words

If the student is in the habit of underlining key words in a story or appears to be misunderstanding what a problem is asking because she is over attending to certain words in the story without trying to read and understand the problem holistically, teach this strategy. Teaching students to search for key words is not a recommended intervention strategy; therefore, it's important to intervene if you are working with a student who has been taught to attack word problems in this way. Burns (2007) writes, "Instruction of this type does little more than offer children tricks to find answers. Even worse, the implication is that getting the answer is most important and that relying on tricks is an effective strategy for finding those answers. This often results in children looking for tricks, rather than trying to make sense out of problems." Teach Comprehension, Not Key Words, helps students understand that, in order to solve a real-world problem, you need to understand the whole story.

Teach Comprehension, Not Key Words in Action
Tell the student who pulls out key words from the story that he'll be learning a better way to understand the story. Then, model thinking through the story, and ask how that type of understanding is different from just picking out key words. The below example refers to the following problem:

There were some birds on the telephone wire; 3 flew away, and now there are 9 on the wire and 3 on the tree. How many birds were on the wire before any flew away?

Teacher: Watch as I think through this story to make sure I understand:

There were some birds on the telephone wire  Okay, I get that. There were birds sitting on a wire.

3 flew away, now there are 9 on the wire and 3 on the tree — Three of the birds flew away, which means that there were probably more than three to begin with. There are now nine left on the wire. Okay, so three flew away, and nine are still on the wire. The three that flew away are now on the tree. Okay, so there are still nine on the wire. 

How many birds were on the wire before any flew away? So, the problem wants to me to figure out how many were there in the first place, before the 3 flew away. I understand what I have to do.

Teacher: Now, you try it!

Activity B: Unpack the Problem

If your student struggles to understand the context of the story problem, teach Unpack the Problem (Carpenter et al., 2015). This strategy helps a student to think through the story elements in the problem, and to consider the problem as a whole, rather than merely its component parts. 

Unpack the Problem in Action
As you read the scenario below, sourced from Carpenter et al. (2005), consider: What guiding questions does the teacher use to help the student unpack the problem?

UnpacktheProblem.pdf

Activity C: Reread and Retell

If your student is struggling to understand the story, teach him to Reread and Retell. In this strategy, the student rereads the story multiple times and then tries to tell the story in his own words, without looking back. Another variation of this strategy is for the teacher to reread the story (or teacher/student choral read the story multiple times) and then the student tells the story in his own words, without looking back.

Reread and Retell in Action
The below example refers to the following problem.

There were some birds on the telephone wire; 3 flew away, and now there are 9 on the wire and 3 on the tree. How many birds were on the wire before any flew away?

Teacher: Reread this story, and tell me what it is says in your own words.

Student reads story three times: Well, it tells me that there were some birds that were just hanging out on those wire things that are above the street. Then a couple of them, actually 3 of them, left the wire. But, there were still 9 there. The problem is asking me how many were there before the first 3 left. 

Response to Error: Understanding the Problem

Think about the following scenario, which takes place after a teacher has explicitly taught a student to check his understanding of the problem below. 

There were some birds on the telephone wire; 3 flew away, and now there are 9 on the wire and 3 on the tree. How many birds were on the wire before any flew away?

     Teacher: "Talk through the problem, and ask yourself questions as you go. This will help
     you make sure you understand the problem before you plan a strategy for solving it."


     Student: "It's ok. I get it. It's about birds on a telephone wire, and then some flew away."

     Teacher: "It sounds like you understand the characters in the problem, but do you
     understand the quantities or what the problem is asking you to figure out? You need to
     make sure you understand all parts of the problem in order to solve it."

     
     Student: "Sure, it says right here, "How many birds were on the wire before any flew
     away?" 

  
In such a case, what might you do? 

Feedback During the Lesson

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 others.

 

Level of Support Description of Scaffold Script
Smallest Scaffold Prompt. Ask the student what else happens in the story. "You told me what they are asking, but can you tell me what else happens in the story?" 
Medium Scaffold Back it Up. If a student is struggling to understand the whole story, back up your process. Ask the student to read from the beginning, and see if he can understand what is happening at each step. "I can see that you are stuck. Let's read from the beginning again and make sure that we understand each part as we go."
Highest Scaffold Model. If the student continues to struggle, model your own thinking. This will help a student understand how to think through the problem to make sure he understands it. "I can see that you are stuck. Let me show you how I start at the beginning and think through all parts of this problem to make sure I understand it." 

Strategies to Try After the Lesson

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

Activity Description of Strategy Script
All Activities You Think, I'll Write. If a student struggles to understand the problem, ask him to think aloud about it as you make notes. For example, as he says, "There are three birds," draw three circles. This way you are starting to visually represent parts of the problem, which will help him visualize what's happening. [Note: This will also help the student learn how to model story problems using pictures!] "As you read the problem, I'll draw what you say. Then, we'll check to make sure we understand each part."