Monday, 19 January 2015

Week 2: From Intended Curriculum to Written Curriculum: Examining the Voice of a Mathematics Textbook

Firstly - to Vanessa and Kerri, very sorry for this late post - I got a bit distracted over the weekend. Hopefully it wasn't too inconvenient for you

The author critically examines a disconnect between the NCTM's professional standards and the way that textbook authors present information. Some of the points she makes that I found most interesting:
  • When asking "questions", textbooks use imperatives (Do, Make, Study, Organize) to encourage them to discover mathematical concepts. There aren't really questions at all.
  • Texts make assumptions about student knowledge (eg. In your earlier work, you saw that linear relationships can be described by equations of the form y = mx + b). Is this really different from just stating mathematical facts?
  • If a teacher changes something in the textbook, it may diminish the authority of the textbook, but also imply that the teacher has knowledge about students' actual abilities and prior knowledge
This article brought to mind a lesson I learned from a department head in my first year of teaching. He reminded me that we do not teach textbooks; we teach curriculum. While this might be obvious to me now, and to many studying math education (and reading this blog). It was not obious to me as a first year math teacher, who observed most of my colleagues following textbooks very closely. I find many new textbooks overly conceptual and 'wordy' causing unnecessary confusion in students. Personally, I feel it is my job to create and find meaningful resources and explorations which will provide students with the opportunity to discover and engage with the prescribed mathematical subjects; all I hope for from a text is relevant and meaningful practice questions.

If I were to ask the author a question (which I suppose I may do,) I would be interested in her opinion on flipped classrooms - this is a model that is being explored in some schools where students are encouraged to do their learning at home, and their 'homework' at school. Students engage in a text or online resource to learn the material, and do the practice work in class with support of peers and teachers. This emphasized the importance of the text on initial learning, but allows students to have more support while attempting to analyze and expand upon their learning.
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2 comments:

  1. Vanessa Radzimski19 January 2015 at 17:01

    Hi David,

    It's interesting that you mention your experience working with textbooks, an in particular noticing your colleagues following textbooks very closely. I read an article over the weekend discussing how a seemingly perfect classroom can in fact be detrimental to student learning. This seems to be particularly relevant in the case of a textbook; the "perfect" learning device that has anything and everything a student needs to "succeed" in a course. To me, I find it exciting to push the textbook away and cause a bit of a mathematical mess. I personally think that it allows students to feel a little more connected to the mathematics, rather than feeling that it all comes from some superior authority.

    I would also be curious to hear her response on the flipped classroom. This is a big topic of discussion within university mathematics education, and a topic I'm quite divided on. I honestly don't know how I feel about it, and feel like I can't make a justified decision until I've actually tried it out (on one side or the other).

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  2. Keri Howard20 January 2015 at 09:21

    Seems like it was an interesting article! One of my professors last term said that if we needed a textbook to teach math, we shouldn't teach math at all. He was saying this more in terms of knowing the content, but I think this too applies to knowing your students. Textbooks weren't created for particular schools or particular classes or particular students. It is a teacher's job to find what works best for their students and themselves, and teach in that way.

    I like the idea of flipped classrooms, but I am not sure how practical it is for all students. I think this might only work with particular classes and/or students.

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