Math Interventions

A student who has difficulty understanding the problem, planning and executing a solution, self-monitoring progress toward a goal, and evaluating a solution will benefit from intervention around the problem-solving process. The following interventions support students in internalizing this process from start to finish. This page includes intervention strategies that you can use to support your students in this area. Remember, if you're teaching a full process from start to finish, you probably want to use the Self-Regulated Strategy Development approach, which spreads explicit instruction of a full process across a series of intervention lessons. As you read, consider which of these interventions best aligns with your student's strengths and needs in the whole-learner domains.

Self-Regulated Strategy Development 

Self-Regulated Strategy Development (or SRSD) is one way to teach the problem-solving process. The SRSD model "requires teachers to explicitly teach students the use of the strategy, to model the strategy, to cue students to use the strategy, and to scaffold instruction to gradually allow the student to become an independent strategy user." (Reid, Leinemann, & Hagaman, 2013). The steps of teaching SRSD are slightly different from the steps of explicit instruction because, in SRSD, each step must be mastered before the next one is started. For example, you might spend an entire lesson on Developing Background Knowledge before moving on to Discuss It (see below). The longterm goal of SRSD is for students to be able carry out the strategy independently, and so time is dedicated to teaching each step of the strategy in such a manner as enables students to internalize the material. 

Teaching SRSD model requires six steps:

1. Develop Background Knowledge. Define the key ideas that students need to know in order to apply the strategy.
2. Discuss It. Tell the student what the strategy is called, and describe each step.
3. Model It. Use a think-aloud to demonstrate the strategy.
4. Memorize It. Internalize strategy.
5. Support It. Gradually release responsibility to students.
6. Independent performance. Give students opportunities to practice strategy without support.

SRSD Explicit Instruction Six-Step Model: 

To support your students' ability to apply SRSD, you should start by explicitly teaching the six-step model. Keep in mind that this type of explicit instruction may take place over a number of days. 

Step 1: Set the Context for Student Learning and Develop Background Knowledge. 

• Introduce Word Problem Mnemonics, and discuss the use of the mnemonic:"Today you will be learning a new trick to help you solve problems. This strategy is called CUBES." (Teacher gets out chart paper and markers and writes down C, U , B, E, and S vertically.) "CUBES is a self-regulated strategy, which means that you will learn to memorize the strategy and use it without my support. Let's go through each step of CUBES and see how it will help you go through the problem-solving process. First, C-Circle the Numbers" (Teacher write this next to C.) "U - Underline important words." (Teacher writes next to U.) B- Box the question" (Teacher writes next to B). E- Eliminate unnecessary information. S - Solve and Check. (Teacher writes these terms next to E and S). "Now, what do we need to know when we are doing CUBES?  We need to know which words are important. We also need to eliminate unnecessary information" (Teacher goes on to define these terms.)

Step 2: Discuss It. 

• Discuss the significance and benefits of using CUBES. Discuss and determine goals for using the strategy. At this point, students can examine their past work to set an individual goal: "So, how is a self-regulated strategy going to help us? Well, it gives us an easy way to remember the five steps to solving the problem. How else does it help us?" (Teacher elicits student responses.) "When we are using a SRSD, we ask ourselves questions to make sure we are following the steps. We call these self-statements.  My self-statements are 'What's my first step?' and 'What am I supposed to do now?' I ask myself self-statements so I can make sure that I am using each step of the strategy, and that I don't miss any steps." (Teacher and students discuss benefits of self-statements.)  "Now let's take some time to set goals for using this strategy...." (Teacher and students set goals, such as "students will each have two self-statements they use when employing the CUBE strategy.")

Step 3: Model It.

• The teacher models the strategy using think alouds and self-statements: "Watch as I show you what CUBES looks like when I use it. See if you can notice my self-statements. What am I supposed to do? I'm supposed to to follow the five steps to solve a problem. What is my first step? C. That's right, C. I need to circle the numbers. I'll do that now, and then check that off my CUBES list. (Teacher circles numbers). Okay, I'm going to check my CUBES list again. I've already completed C. Now, on to U. I have to Underline important words. (Teacher continues to model the entire CUBES process with 1- 3 problems. The session ends. Teacher starts Model It with new problems on Day 2.)

Step 4: Memorize It. 

• Students memorize the mnemonic and each of the steps of CUBES. The idea is that the students will not be able to implement the strategy if they cannot recall the steps. "Next, we are are going to take some time to memorize each step. What is C?" "Circle the numbers!"What is U?" (Teacher completes this process for all the letters. At this time, students also write the mnemonic down so they can use it as a reference. If they need to, they can come up with a beat or a chant to remember the mnemonic.)

Step 5: Support It.

• In step 5, the teacher gradually releases responsibility to the students. This is the most important stage, especially for struggling readers. In order for students to be able to implement this strategy on their own, they must be supported as needed. Graham, Harris, Mason, and Friedlander (2008), SRSD experts and authors, often tell their teachers, "Please Don't P.E.E. in the Classroom - Post, Explain, Expect. Success with SRSD depends on using all the stages for students who have difficulty with [reading]." SRSD instruction and implementation are only successful when students are given multiple opportunities to practice using their strategy with teacher support before trying it on their own. "Let's read the next problem and do CUBES together this time..."Teacher follows the steps of gradual release to transfer responsibility to students. The teacher first engages students with guided support. She might read the problem and allow students to complete different parts of the strategy. Then, students might do CUBES in groups. This part of the strategy might take multiple days, until students are effectively completing the strategy by using self-statements. 

Step 6: Independent Practice

• In the final step, students practice using the strategy independently. "Now, you are ready to use CUBES on your own! Remember to use your self-statements, like What do I do next? and What am I supposed to do now? and I'll look at my CUBES sheet to see what I do next. as you employ this strategy!" Teacher circulates and provides support for students who are not yet ready to work independently. 

Activity A: Word Problem Mnemonics

One way to support your student's problem-solving ability is to teach her a mnemonic for a series of steps to take whenever she encounters a story problem. The following brief, developed by the Evidence Based Intervention Network at the University of Missouri, describes this strategy. As you read, consider how each mnemonic breaks down the problem-solving process.

Click here to read the brief. 

Word Problem Mnemonics in Action

In the video below, Emily Art explicitly models how to use the word mnemonic, CUBES, to teach the problem solving process.

As you watch, consider: How do mnemonics support a student's ability to independently carry out the problem solving process?

Another strategy to use to teach your student the problem-solving process is called Self-Organizing Questions. Gifford (2005) advocates for teaching students a series of questions to ask themselves that will guide them through the problem-solving process. Read through each prompt below and consider its purpose. 

1. Getting to Grips: What are we trying to do?
2. Connecting to Prior Knowledge: Have we done anything like this before?
3. Planning: What do we need?
4. Considering Alternative Methods: Is there another way?
5. Monitoring Progress: How does it look so far?
6. Evaluating Solutions: Does it work? How can we check? Can we make it better?

 Self-Organizing Questions in Action 

Give the student a problem. Then, go through the six self-organizing questions to guide the student through the problem-solving process.
This example refers to the problem below. 

Lamont had 14 pumpkin seeds.
He also had 32 apple seeds.
He planted 41 of the seeds.
How many seeds did Lamont have left?

Teacher: We are going to use the self-organizing questions to solve this problem. Frank, what are we trying to do?

Frank: We are trying to figure out how many seeds Lamont has left, after he plants the pumpkin and apple seeds.

Teacher: Let's think about similar problems we've had in the past. Have we done anything like this before?

Frank: Yes, yesterday, we solved a problem about how many baseball and soccer balls Jamie had. 

Teacher: So, what do we need to do to plan to solve this problem?

Frank: We need to add up the total number of seeds, and then subtract how many he planted.

Teacher: Is there another way to solve this problem?

Frank: We could probably draw it, or use manipulatives to help us. 

Teacher: Okay, go ahead and execute it! How does it look so far?

Frank: It's working for me. I added the types of seeds together, which gave me 46. Then, I subtracted the 41 seeds he planted. That gave me 5 seeds leftover, which seems about right. 

Teacher: How can we check our answer?

Frank: I'll see if I can add it back up. My solution was 5, so I'll add that to 41, which gives me 46. Then, I'll add the number of seeds he had total, which gives me 46! So, it matches!

Activity C: Solve It

If your student has particular struggles with understanding the problem, use Solve It, which is an explicit approach to teaching the problem-solving process, with an emphasis on understanding what the problem is about. The following brief, developed by the Evidence Based Intervention Network at the University of Missouri, describes this strategy. As you read, consider how this approach supports student understanding of problems.

Click here to read the brief. 

Solve It in Action
Read the sample lesson plan (Montague, 2006) below to see what Solve It looks like in action. For your reference, click here to access a self-regulation script for students.

SolveItLesson.pdf

Think about the following scenario, which takes place after a teacher has explicitly taught a student to use the problem-solving process. The following example refers to the problem below. 

Lamont had 14 pumpkin seeds.
He also had 32 apple seeds.
He planted 41 of the seeds.
How many seeds did Lamont have left?

     Teacher: "Now that you understand the problem, what are you doing to do next?"
     Student: "Solve it! 41-32 = 9. He had nine seeds left." 

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.

Level of Support	Description of Scaffold	Script
Smallest Scaffold	Check your Resources. As you continue to use these interventions, your student should have the steps to the problem-solving process listed in his notebook.	"Look in your notebook: it seems like you skipped a step. Can you use the steps listed in your notebook to go through the problem-solving process?"
Medium Scaffold	Back it Up. If a student is struggling, back up your process. Ask the student to identify the next step he should take.	"Look in your notebook: what are the steps we take after understanding the problem and before solving the problem?"
Highest Scaffold	Model. If the student continues to struggle, model your own thinking. This will help a student understand how to use the problem solving process effectively.	"I can see that you are stuck. Let me show you how I go through each step of this problem-solving process."

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. 

Activity	Description of Strategy	Script
All Activities	Suggest Options. If your student rushes through a strategy by skipping the planning phase, encourage him to go back and select an attack strategy that matches the problem.	"Let's go back for a minute. It seems like you jumped to solving this problem using an equation. Let's read the problem again and consider whether an equation is the best strategy for solving this problem."