What evidence-based mathematics instructional practices can educators implement?
Page 8: Metacognitive Strategies
As you have now learned, students who struggle with mathematics tend to be poor problem solvers. They approach every mathematics problem using only a small number of strategies and often apply them inconsistently. Educators can begin to address these issues by teaching the students cognitive strategies that help them focus on relevant information, identify a given problem’s structure, and solve the problem. Such strategies include schema-based instruction, mnemonics, graphic organizers, and verbal rehearsal.
cognitive strategy
glossary
However, teaching students cognitive strategies alone is not enough to ensure that they will be implemented correctly or independently. This is especially the case for students with mathematics difficulties and disabilities, who tend to implement the same strategy for every problem, implement strategies without considering the problem type, or fail to use a strategy at all. To further support students during problem-solving, teachers should pair instruction on cognitive strategies with instruction on metacognitive strategies—strategies that enable students to become aware of how they think when solving mathematics problems. When these strategies are combined, students learn how to (1) consider the appropriateness of the problem-solving approach, (2) make sure that all procedural steps are implemented, and (3) check for accuracy or to confirm that their answers make sense. More specifically, metacognitive strategies help students learn to:
metacognitive strategies
glossary
High-Leverage Practice (HLP)
The content on this page aligns with:
HLP 14: Teach cognitive and metacognitive strategies to support learning and independence.
- Plan—Students decide how to approach the mathematical problem, first determining what the problem is asking and then selecting and implementing an appropriate strategy to solve it.
- Monitor—As students solve a mathematical problem, they check to see whether their problem-solving approach is working. After completing the problem, they consider whether the answer makes sense.
- Modify—If students determine that their problem-solving approach is not working or that their answer is incorrect, they can adjust their approach.
Research Shows
- When paired with cognitive strategies, metacognitive strategies have been shown to increase the understanding and ability of students with MLDs and disabilities to solve mathematics problems.
(Pfannenstiel et al., 2015) - Research has shown that when educators teach students to use metacognitive strategies in mathematics, students show significant improvement in math achievement as well as enhanced self-regulated learning and critical thinking skills.
(Hidayat et al., 2025; Sercenia & Prudente, 2023; Ishak et al., 2025) - Students develop procedural flexibility by breaking down complex problems through problem-solving.
(Tanola & Lomibao, 2024) - Middle school students who received cognitive and metacognitive strategy instruction outperformed peers who received typical math instruction.
(Montague et al., 2011; Pfannenstiel et al., 2015)
Types of Metacognitive Strategies
Metacognitive strategies that help students plan, monitor, and modify their mathematical problem-solving include self-instruction and self-monitoring. Not only are these strategies relatively easy for students to implement, but they also help students to become better independent problem solvers.
| Metacognitive Strategy | Definition | Examples |
|---|---|---|
| Self-instruction | Talking oneself through a task or activity (also known as self-talk) |
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| Self-monitoring | Checking one’s performance; often involves a checklist |
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Teaching Metacognitive Strategies
Teachers should use explicit instruction to help students understand how to use self-instruction and self-monitoring during the problem-solving process. To do this, teachers can:
- Provide students with a list of questions or prompts to ask themselves while they are engaged in the problem-solving process.
- Example questions: What information is relevant? Have I solved a problem like this before?
- Example prompts: Identify the relevant information. Use a visual to solve the problem.
- Model working through a problem using think-alouds, during which the teacher verbalizes thoughts while using self-instruction and self-monitoring throughout the problem-solving process.
- Provide sufficient opportunities for students to practice these metacognitive strategies with corrective feedback.
- Encourage students to use these strategies independently once they have achieved mastery.
Examples of Students Using Metacognitive Strategies
The videos below illustrate students using metacognitive strategies to solve mathematics problems. In the first video, in addition to self-instruction, an elementary student uses an age-appropriate self-monitoring checklist that includes visual cues for each step. Note that the student was explicitly taught how to use this checklist before using it to solve problems independently. In the second video, a high school student uses self-instruction and self-monitoring to solve a word problem.
Elementary School Example (time: 1:49)
Transcript: Metacognitive Strategies: Elementary School
Narrator: In this video, an elementary student uses metacognitive strategies while solving an addition problem. More specifically, he uses self-instruction and a self-monitoring checklist to guide himself through the problem-solving process. By doing so, he actively plans and monitors his work.
Student: I can’t figure out what three plus five is. What is it? Well, let me look at my checklist. First, it says, “Read the problem.” The problem says three plus five, so I’ve checked that. Now what is . . . now it says . . . my checklist says, “What is the problem asking?” It’s asking me to add three plus five.
Now, to draw a picture. One, two, three. One, two, three, four, five. Now it says, “Does my drawing match the problem?” Up here it says three plus five, so down here it says one, two, three, one, two, three, four, five. Now I have to solve it. So one, two, three, four, five, six, seven, eight. The answer to three plus five is eight.
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Read: Read the problem. |
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Ask: What is the problem asking? |
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Draw: Draw a picture. |
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Check: Does my drawing match the problem? |
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Solve: Solve it! |
High School Example (time: 2:54)
Transcript: Metacognitive Strategies: High School
Narrator: In this video, a high school student uses metacognitive strategies while solving a word problem. By using self-instruction and self-monitoring, she actively plans and monitors her work.
Student: First, I’m going to read the problem. “Mr. Smith, the principal, is standing on top of the high school. He is looking at a tree in the courtyard that is 30 feet away from the school. The angle from Mr. Smith’s feet to the base of the tree is 43°. Using this information, determine the height of the high school.”
So what am I missing? The problem says that the angle from Mr. Smith’s feet to the base of the tree is 43°. I’ve noticed that if you connect this point to this point, we have a right triangle. So while this angle is 43°, this angle right here is a right angle that’s 90°.
There’s a trick that I’m going to use that’s called SOH CAH TOA that you can use to find the sides and angles in a right triangle. The opposite side to 43° is 30 feet right here. So what do I need to find? I need to find the adjacent side. I’ll label it with an A. I’ll look at SOH CAH TOA, and I know that I need to find the tangent because tangent equals opposite over adjacent. Now all I have to do is plug in the information that I have in order to find A. Tangent of 43°, the angle, equals 30—that’s the opposite side—over A. And I find that 30 over 0.93 equals 32.25. So the height of this building is 32.25 feet.
Now that I’ve solved the problem, I ask, Does my answer make sense? Given the information from the problem, and with what I know about most buildings, 32 feet seems like a reasonable answer.
For Your Information
Although teachers can provide students with a generic list of questions or prompts to guide them through the problem-solving process, some students (such as those with mathematics difficulties and disabilities) might need more individualized support to address their specific learning challenges. The teacher can identify the student’s common error patterns by conducting an error analysis—a process by which instructors identify the types of errors consistently made by students when working mathematical problems. Using this information, teachers can develop a list of questions or prompts that students can use to address their specific needs. To begin with, many of these students might require a self-monitoring checklist, such as the one below, to guide them through the problem-solving process.
