Lesson 3: How can metacognitive development be integrated with mathematics instruction?

Objective

Learners will generate a list of strategies to develop metacognition in mathematics instruction and explain how and why those strategies will lead to improved outcomes of instruction for deeper understanding.

Case Study

Mrs. B begins teaching a lesson on how to add fractions with like denominators to a small group of 6th grade special education students who are all significantly below grade level in math. After direct instruction including both algorithmic steps (add the numerators and keep the denominator) and conceptual development (Why do we keep the denominator? Did the size of the pieces change?), Mrs. B begins circulating the room. She notices one student is adding the numerators and the denominators (1/5 + 2/5 = 3/10). What should Mrs. B do to help this student?


Look back at what you wrote as a response to the case study scenario in lesson two. What are three strategies that Mrs. B can use to help this student develop their metacognitive abilities in this specific context? Which components of metacognition do they address? Record your thoughts and save them for later.

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Introduction

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In this lesson, you will build on what you have learned in lessons 1 and 2. You will explore a variety of literature regarding strategies that can be used to develop metacognitive abilities both in general and within the context of mathematics instruction. You will also watch a video presentation regarding metacognitive development and instructional techniques. This lesson requires that you devote more time to reading and exploring than in the past lessons, so please plan accordingly! After reading and viewing the required material you will discuss your thoughts about what you have learned. You will continue working on your quick reference guide by adding a section that details a variety of strategies that your colleagues can use in their practice. You will reflect on your learning in this lesson. I encourage you to go beyond the resources I have required and explore further strategies that can be utilized to develop metacognition in mathematics instruction.

Please use the Strategies for Metacognitive Development Graphic Organizer to take notes as you investigate the material for this lesson.

File:Strategies for Metacognitive Development Graphic Organizer.pdf

Investigation

  1. Read: "Helping Students Self-Regulate in Math and Sciences Courses: Improving the Will and the Skill" http://dwb.unl.edu/chau/sr/self_reg.html
  2. Read: "Math MetaCognition" http://iamamathnerd.wordpress.com/2012/08/05/math-metacognition/
  3. Read: "Math Problem-Solving: Combining Cognitive & Metacognitive Strategies" http://www.interventioncentral.org/academic-interventions/math/math-problem-solving-combining-cognitive-metacognitive-strategies
  4. Read: "Metacognitive Strategies" http://www.coedu.usf.edu/main/departments/sped/mathvids/resources/metacognative.html
  5. Read: "Developing Metacognition" http://www.education.com/reference/article/Ref_Dev_Metacognition/
  6. Watch: "Meta-studying: Teaching Metacognitive Strategies to Enhance Student Success" http://www.youtube.com/watch?v=Tr37GOSEukw
  7. Discuss: How can metacognitive development be integrated with mathematics instruction? What strategies can be used to develop metacognition in students of mathematics? Which strategies would you choose to use and why? Use the Discussion page for Lesson 3 to discuss your thoughts on these questions. Your initial post should include an answer to these questions which draws on what you have watched and read and connects to your experiences as a student and teacher. Respond to at least two of your classmates' posts.

Application

You will continue creating a guide for your colleagues on how to integrate metacognitive development in mathematics instruction. To apply what you have learned in Lesson 3, you will create a section for your guide in which you will identify, explain, and give examples for at least 5 different strategies that can be used to integrate metacognitive development in mathematics instruction. In this section you must:

  • Identify at least 5 different strategies.
  • Explain how and why each of these strategies will lead to improved outcomes of instruction for deeper understanding.
  • Give an example for each of these strategies.

Reflection

Use the Discussion page for Lesson 3 to share your reflection on what you have learned and how you have learned it. Your reflection should include:

  • what you have learned about strategies that can be used to develop metacognition in mathematics instruction.
  • how you have learned it.
  • what you want to learn more about with regards to strategies that can be used to develop metacognition in mathematics instruction.

Navigation

Course Home Page: Integrating Metacognitive Development in Mathematics Instruction

Lesson 1: What is metacognition?

Lesson 2: How does metacognitive development impact learning in mathematics?

Lesson 4: What technological tools can be used to integrate metacognitive development in mathematics instruction?