What evidence-based mathematics practices can teachers employ?
Page 7: Metacognitive Strategies
As you have now learned, students who struggle with mathematics tend to be poor problem solvers. They approach every mathematics problems using only a small number of strategies, and even these strategies they apply inconsistently. Teachers can begin to address these issues by teaching the students cognitive strategies (e.g., schema-based instruction, mnemonics) that help students focus their attention on relevant information, identify a given problem’s structure, and solve the problem.
However, teaching students cognitive strategies alone is not enough to ensure that those strategies 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. If students are to be more successful, teachers should pair instruction on cognitive strategies with that of metacognitive strategies—strategies that enable students to become aware of how they think when solving mathematics problems. This combined strategy instruction teaches students how to consider the appropriateness of the problem-solving approach, make sure that all procedural steps are implemented, and check for accuracy or to confirm that their answers makes sense. More specifically, metacognitive strategies help students learn to:
How does this practice align?
High-Leverage Practice (HLP)
- HLP14: Teach cognitive and metacognitive strategies to support learning and independence
CCSSM: Standards for Mathematical Practice
- MP1: Make sense of problems and persevere in solving them.
- 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, as they work to solve a mathematical problem, students determine that their problem-solving approach is not working or that their answer is incorrect, they can adjust their approach.
- When paired with cognitive strategies, metacognitive strategies have been shown to increase the understanding and ability of students with mathematics learning difficulties and disabilities to solve mathematics problems.
(Pfannenstiel, Bryant, Bryant, & Porterfield, 2015)
- Middle school students who received cognitive and metacognitive strategy instruction outperformed peers who received typical math instruction.
(Montague, Enders, & Dietz, 2011; Pfannenstiel, Bryant, Bryant, & Porterfield, 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.
|Self-instruction||Talking one’s self through a task or activity (also known as self-talk)||
|Self-monitoring||Checking one’s performance; often involves a checklist||
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 her thoughts as she demonstrates 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)
High School Example (time; 2:55)
Diane Pedrotty Bryant, PhD
Project Director, Mathematics Institute for
Learning Disabilities and Difficulties
University of Texas at Austin
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 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.