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Use of Student Mathematics Questioning to Promote Active Learning and Metacognition

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Book cover Selected Regular Lectures from the 12th International Congress on Mathematical Education

Abstract

Asking questions is a critical step to advance one’s learning. This lecture will cover two specific functions of training students to ask their own questions in order to promote active learning and metacognition. The first function is for students to ask themselves mathematical questions so that they learn to think like mathematicians who often advance knowledge by asking new questions and trying to solve them. This is also called problem posing, an important component of the “look back” step in the Polya’s problem solving framework. The second function is for students to ask their teachers learning questions during lessons when they do not understand certain parts of the lessons. Students who are hesitant to ask learning questions need to be inducted into the habit of doing so, and a simple tool called Student Question Cards (SQC) can help to achieve this objective. These SQC cover four types of mathematics-related learning questions: meaning, method, reasoning, and applications. In a pilot study involving Grades 4 and 7 Singapore students, every student was given a set of these laminated cards. During lessons, the teacher paused two or three times and required the students to select questions from SQC to ask to clarify their doubts. This reverses the normal roles of teacher and students during classroom interactions. Teachers and students in this pilot study expressed mixed responses to the use of SQC. These two functions of student mathematics questioning have the potential to promote active learning of mathematics among school students through strengthening their metacognitive awareness and control. To realize this potential, teachers need to pay due attention to the science, technology, and art of student questioning.

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Notes

  1. 1.

    http://english.chosun.com/site/data/html_dir/2011/12/07/2011120700522.html.

  2. 2.

    http://www.cut-the-knot.org/proofs/half_sq.shtml.

  3. 3.

    http://rescomp.stanford.edu/~cheshire/EinsteinQuotes.html.

  4. 4.

    See Chabris and Simons (2010) for further questions one can ponder over about this and other misleading claims.

  5. 5.

    http://einstein.biz/quotes.

  6. 6.

    http://www.peelweb.org/index.cfm?resource=about.

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Authors and Affiliations

  1. National Institute of Education, Nanyang Technological University, Singapore, Singapore

    Khoon Yoong Wong

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Correspondence to Khoon Yoong Wong .

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Editors and Affiliations

  1. Seoul National University, Seoul, Korea, Republic of (South Korea)

    Sung Je Cho

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Wong, K.Y. (2015). Use of Student Mathematics Questioning to Promote Active Learning and Metacognition. In: Cho, S. (eds) Selected Regular Lectures from the 12th International Congress on Mathematical Education. Springer, Cham. https://doi.org/10.1007/978-3-319-17187-6_49

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