teaching. The article argues that the coarse separation of "teachers' subject matter knowledge" and "formal disciplinary knowledge" is inherently problematic. Rather, they argue that mathematics-for-teaching is likely neither a matter of "more of" nor "to a greater depth than" of an in-service session, but rather a "branch of mathematics". They use classroom multiplication to illustrate four categories of elements involved in teachers’ mathematics-for-teaching, namely, “mathematical objects,” “curriculum structures,” “classroom collectivity,” and “subjective understanding”.
1. In the discussion of teaching multiplication, the authors assert that the understanding multiplication is not about how many figurative aspects of multiplication are taught but physical actions out of which multiplication arises. First of all, if this is the sudden conclusion of 24 experienced teachers after lengthy discussion of teaching multiplication in classroom, I would be disappointed at the quality of the mathematics courses which qualify those teachers. Strangely, I have to agree with the authors that we do need a special "branch of mathematics" for math teachers.
2. I found that the following illustration in the article was very intriguing especially when I realized that the stem splits to symmetrical halves: stable knowledge and dynamic knowledge.
Question: Compared to mathematicians, math teachers' expertise lies in the fact that their math is done through interactions with others. Should we value more their knowledge or their ability to engage students in meaningful discussion?
Good question. I think my value as a math educator is more closely related to the latter - my ability to engage students in discussion, along with my ability to inspire interest in mathematics and to help students make meaningful connections. My knowledge of mathematics is really not much greater than is expected of much of the general population who graduates high school, yet due to learning to teach it, and teaching most concepts many times over, I have a deep understanding of the structure of it, which allows me to be an effective educator.
ReplyDeleteThanks for the question! I agree with David, and believe that while there is a need for math educators to have a clear and accurate understanding of key concepts of mathematical knowledge, the value of math teachers lies in meaning-making for and with the unique profile of students that they work with. This may involve "prying apart concepts, making sense of analogies, metaphors, images and logical constructs that give shape to a mathematical construct" (p.301), interpreting concepts for and with the learners, suggesting idea connections within and across topics, or drawing out general principles that can then be applied to real world problems. I believe that a sense of confidence in the mathematical knowledge that one possesses will help provide greater security to a math educator, but being able to capture and re-communicate that meaning and understanding for and with students is of greater value for educators. As an educator, I believe that it is also our role to equip our students with sufficient knowledge and skills, both subject-specific and general, so that they can first come to a clarity of understanding on what is taught, and hopefully their own appreciation or perspectives on the subject.
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