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Integrating Metacognitive Development in Mathematics Instruction

Return to: ETAP 623 Fall 2012

Topic/Purpose

The title of the course I am developing is Integrating Metacognitive Development in Mathematics Instruction. This course will provide an introduction to the construct of metacognition and its value in the instruction of mathematics. The following questions will drive the design of this course:

  • What is metacognition?
  • How does metacognitive development impact learning in mathematics?
  • What can instructors do to integrate metacognitive development with mathematics instruction?
  • How can technology be incorporated in developing metacognitive skills in mathematics?

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Learning Outcomes

Learners will be able to:

  • identify the major components of metacognition and examples of each. (Verbal Information and Intellectual Skill)
  • describe the relationship between metacognitive development and learning in mathematics. (Verbal Information and Intellectual Skill)
  • utilize metacognitive questioning techniques and thinking aloud during mathematics instruction to promote the development of metacognitive abilities in students. (Verbal Information and Intellectual Skill)
  • demonstrate how technology can be utilized in developing metacognitive skills in mathematics. (Intellectual Skill)
  • choose to incorporate metacognitive development with mathematics instruction. (Attitude)

Needs Assessment

Instructional Problem

The Common Core State Standards in Mathematics have been adopted by the New York State Education Department. Fundamental to the Common Core State Standards are the Standards for Mathematical Practice, which include:

  • Make sense of problems and persevere in solving them.
  • Reason abstractly and quantitatively.
  • Construct viable arguments and critique the reasoning of others.
  • Model with mathematics.
  • Use appropriate tools strategically.
  • Attend to precision.
  • Look for and make use of structure.
  • Look for and express regularity in repeated reasoning.


Through a review of the literature on teaching math for understanding and informal observation of perceived challenges in teaching for understanding in accordance with the Common Core State Standards for Mathematics, it has become apparent that metacognitive abilities will affect a student’s ability to progress towards a deeper understanding of mathematical content. In the past, standards have focused on procedural knowledge of math skills. As such, K-12 teachers have focused their lessons on algorithmic proficiency. However, while students may master the use of an algorithm, they may not necessarily understand how or why the algorithm works. This lack of deeper understanding can cause a variety of issues from failure to connect important concepts to failure to recognize when the use of specific algorithms is appropriate. Teaching for understanding requires metacognitive development. Metacognition and mathematics are deeply related. While much of the research on metacognitive development in the past has focused on reading comprehension, current literature is beginning to address the importance of developing metacognitive abilities in line with progress in gaining a deeper understanding of mathematics.

The Nature of What is to be Learned

Through this mini-course, teachers of all levels in K-12 will learn about the basic components of metacognition and how they relate to the learning of mathematics. Teachers will also learn how to utilize several strategies to promote metacognitive development in tandem with a deeper understanding of mathematics.

About the learners

The learners in this mini-course will be K-12 mathematics teachers who are currently teaching with the Common Core State Standards. The learners will have practical experience with the teaching of mathematics and will be redesigning their instruction to address the new standards. Learners will have at least a Bachelor’s Degree in Education with a concentration in Mathematics, and may also have a variety of Master’s degrees as well. Therefore, it is predicted that learners will have the ability to monitor and self-regulate their learning and cognitive abilities. As this mini-course will be taken voluntarily, learners will be both intrinsically and extrinsically motivated. The successful completion of this course will lead to a deeper understanding and improved ability to incorporate metacognitive development in math instruction leading to improved outcomes of practice. It may also lead to salary advancement through professional development credits.


Instructional Context

This mini-course will be delivered online and will utilize a wiki in terms of presentation of content. This course will also utilize videos, graphics, and text accessed via the web. Each of the guiding questions from the topic proposal will be presented in a unit addressing that question. Learners will read, view, and listen to content, and do exercises relevant to the content being addressed.


Exploring Instructional Problem/Solutions

Learners will explore the instructional problems related to teaching for understanding in mathematics with a focus on integrating metacognition in math instruction. Learners will generate a variety of specific solutions relevant to their individual teaching contexts expanding on general solutions provided through the course content.

Goals

Learners will gain a deeper understanding of the construct of metacognition and how it relates to deeper learning in mathematics. Learners will create a variety of strategies specific to their teaching contexts to integrate metacognitive development with mathematics instruction.

Performance Objectives

  • Learners will identify the major components of the construct of metacognition.
  • Learners will relate each of the major components of the construct of metacognition to issues in learning and instruction of mathematics for deeper understanding.
  • Learners will identify strategies that can be utilized in integrating metacognitive development with mathematics instruction.
  • Learners will create a list of strategies specific to their instructional context and explain how and why those strategies will lead to improved outcomes of instruction for deeper understanding.
  • Learners will identify at least 2 different tools that can be utilized to develop metacognition in math instruction and justify the use of these tools in their specific instructional context.

Summary

In conducting this needs assessment several issues became apparent. The following questions arose from a review of the literature and informal observation of colleagues and peers who teach mathematics:

  • Do all mathematics teachers have a solid understanding of the construct of metacognition prior to designing instruction?
  • Can teachers identify the relationships that exist between each of the components of metacognition and student performance in mathematics?
  • Are teachers aware of a variety of strategies that can be used to develop metacognition in line with mathematics instruction?
  • How can teachers teach for deeper understanding if they are not aware of the metacognitive abilities students must possess to progress in gaining a deeper understanding of mathematics?

Ultimately, the solution to the instructional problem posed in this needs assessment requires that teachers of mathematics have a solid understanding of the components of metacognition, how each component relates to gaining a deeper understanding of mathematics, what strategies can be used to promote metacognitive development, and how to integrate these strategies with mathematics instruction.

Revised Performance Objectives

  • Learners will identify the major components of the construct of metacognition by naming metacognitive awareness which includes knowledge and experience as well as metacognitive regulation which includes goals and tasks through written response to questions.
  • Learners will identify real life examples of the major components of the construct of metacognition by distinguishing examples of each through answering multiple choice questions.
  • Learners will generate examples of various relationships between each of the major components of the construct of metacognition and issues in learning and instruction of mathematics for deeper understanding in the form of a written essay.
  • Learners will adopt the strategies of utilizing metacognitive questioning techniques as well as thinking aloud to integrate metacognitive development with mathematics instruction through the creation of short videos.
  • Learners will generate a list of strategies specific to their instructional context and explain how and why those strategies will lead to improved outcomes of instruction for deeper understanding.
  • Learners will identify at least 2 different tools that can be utilized to develop metacognition in math instruction and justify the use of these tools in their specific instructional context in writing.
  • Learners will choose to incorporate metacognitive development in mathematics instruction by utilizing the knowledge and techniques in this course within the context of their professional teaching positions.

Task Analysis

Please click on the following link to view the Unit 1 Task Analysis. File:Unit 1 Task Analysis C.Strattner.pdf

Please click on the following link to view the Unit 2 Task Analysis. File:Unit 2 Task Analysis C.Strattner.pdf

Please note that text in blue and orange sections are essential prerequisites.

Curriculum Map

Please click on the following link to view the curriculum map. File:Curriculum Map C.Strattner.pdf

Please note that text in light blue areas are supportive prerequisites.

Reflection and Revisions

As you can see from the final product of my course, several revisions were made to the unit and course objectives. As I delved deeper into the topic of metacognition in math, I made revisions to the course to reflect what I felt were the most pertinent knowledge and skills to be learned.

References and Resources

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Fisher R. (1998), ‘Thinking about Thinking: developing metacognition in children’, Early Child Development and Care, Vol 141 (1998) pp1-15. Retrieved from http://www.teachingthinking.net/thinking/web%20resources/robert_fisher_thinkingaboutthinking.htm


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Lai, E. R. (2011). Metacognition: A literature review. Pearson Education, Retrieved from http://www.pearsonassessments.com/hai/images/tmrs/Metacognition_Literature_Review_Final.pdf


Lang, J. M. (2012, January 17). Metacognition and student learning. The Chronicle of Higher Education. Retrieved from http://chronicle.com/article/MetacognitionStudent/130327/


Legg, A. M., & Locker, Jr., L. (2009). Math performance and its relationship to math anxiety and metacognition. North American Journal of Psychology, 11(3), 471-486.


Livingston, J. A. (1997). Metacognition: An overview. Retrieved from http://gse.buffalo.edu/fas/shuell/cep564/metacog.htm


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Math problem-solving: Combining cognitive & metacognitive strategies. (n.d.). Retrieved from http://www.interventioncentral.org/academic-interventions/math/math-problem-solving-combining-cognitive-metacognitive-strategies


Mayer, R. E. (2003). Learning and Instruction. Upper Saddle River, NJ: Pearson Merrill Prentice Hall.


McLoughlin, C., Lee, M. J. W., & Chan, A. (2006). Using student generated podcasts to foster reflection and metacognition. Australian Educational Computing, 21(2), 34-40. Retrieved from http://acce.edu.au/sites/acce.edu.au/files/pj/journal/AEC Vol 21 No 2 2006 Using student generated podcasts to fos.pdf


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Rahman, F., Jumani, D. N. B., Satti, M. G., & Malik, M. I. (2010). Do metacognitively aware teachers make any difference in students’ metacogniton?. International Journal of Academic Research, 2(6), 219-223. Retrieved from http://aiou.academia.edu/fazalurrahman/Papers/495213/DO_METACOGNITIVELY_AWARE_TEACHERS_MAKE_ANY_DIFFERENCE_IN_STUDENTSMETACOGNITON


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