Metacognition

First introduced by Flavell, metacognition is knowing about one's own cognitive learning processes. To learn more about his perspective, please look at one of his articles. Since then this important topic has garnered a lot of attention, as a result, a lot of research done to enhance students' learning. Considering the vast amount of resources that one could reach on the internet, and with the increase in the adoption of AI Tools, knowing one's own ways of learning, and shaping their own learning journey is becoming more important. Indeed, in the WEF Future of Jobs Report for 2023 (Figure 4.2, on p.38), self-awareness and lifelong learning skills are among the first five core skills for workers in 2023, which are

• Analytical thinking (cognitive skill)
• Creative thinking (cognitive skill)
• Resilience, flexibility, and agility (self-efficacy skill)
• Motivation and self-awareness (self-efficacy skill)
• Curiosity and lifelong learning (self-efficacy skill)

  Metacognitive skills also positively affect other core skills such as creative thinking and this will help our students not only during their studies but also in their jobs.

Useful Resources and Books

  I list several resources that I find useful while preparing a recent presentation below. I plan to add more details-reviews about them later. I also list some related research to Mathematics and teaching, in general.

Articles:

• Flavell, J. H. (1979), Metacognition and cognitive monitoring: A new area of cognitive–developmental inquiry. American Psychologist, 34(10), 906–911
• L. Brown, Metacognition, executive control, self-regulation, and other more mysterious mechanisms, in F. E. Winert & R. H. Kluwe (Eds), Hillsdale, NJ: Lawrence Erlbaum.
• D. Schraw and D. Moshman, Metacognitive Theories, Educational Psychology Review 7(4) (1995)​
• O. Nelson, Conciousness and Metacognition, American Psychologist 51(2)(1996) pp.102-116​

Books:

• J. van Velzen, Metacognitive Learning, Advancing Learning by Developing General Knowledge of the Learning Process, Springer (2016)
• J. van Velzen, Metacognitive Knowledge, Development, Application, and Improvement, Information Age Publishing (2017)​
• S. Y. McGuire, Teach students how to learn, Stylus (2015)

Mathematics and Metacognition:

• K.-L. Yang, Structures of cognitive and metacognitive reading strategy use for reading comprehension of geometry proof, educational Studies in Mathematics 80(3) (2012) 307-326​
• B. Kramarski, Enhancing Mathematical Reasoning in the Classroom: The Effects of Cooperative Learning and Metacognitive Training, American Educational Research journal 40(1) (2003) 281-310

Other Interesting Research:

• Y. S. Cho & K. Linderman, Metacognition-based process improvement practices, International Journal of Production Economics (211) (2019) 132-144​

Related Teaching Content:

• K. Krathwohl, A Revision of Bloom's Taxonomy: Overview, Theory into Practice 41(4) (2002) (attribute to State of Minnesota, 1998))​

Some Resources from Courses Taught

I share a few selected metacognitive resources that I prepared for students below.

Reflections on Midterms:

These worksheets were shared with students so that they can think about their performance in a recent midterm, analyze the factors, and develop a strategy to get better in other exams in the course. The second worksheet was based on the first one and updated in collaboration with Kaavya Sumit reflecting our reading and recent work on Metacognition.

Math 131-Reflections on Midterm 1 

Math 131-Reflections on Midterms (updated) 

Study Logs:

These logs are prepared so that students can analyze their study patterns and identify areas to improve on including background skills. Through these, they are encouraged to understand their mathematical cognitive structure and find gaps in their knowledge so that they can have a more efficient study time. The Review column in these worksheets list some skills and knowledge that are used while studying the topics.

Math 131-Formal Definition of Limit 

Math 131-Continuity 

Math 131-Higher Order Derivatives 

This page is still under construction and I hope more resources are available the next time you visit. Thanks for your visit.

Any opinions, ideas on this page represents only the author's perspective. Please let me know if you have any comments.