Teaching Mathematics: What, When and Why

An in-depth examination of mathematics education, topic by topic

Suggest discussion topics

Maybe you are teaching a topic for the first time and need guidance. Maybe you are a student who found a particular topic interesting, or difficult, or a waste of time. Maybe you are an old hand at teaching a topic and want to share what you have learned. By replying to this post you add that topic to the list from which we will select the next item for discussion.

At the start of your suggestion please give a question that explains what you want to discuss. For example: How to introduce algebra? When should we teach negative numbers? Why do we need to learn linear transformations?

If the list becomes unwieldy, I will try to arrange some voting system to choose the order of discussion.

tom's avatar

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tom

13 responses to “Suggest discussion topics”

  1. Terry Mills Avatar
    Terry Mills

    Congratulations on taking this on Tom. I look forward to reading many posts.

    For quite a few years I have been opposed to the teaching of statistics in the school mathematics curriculum. But just this week, I had an epiphany that has made me change my mind. It seems to me that, in essence, the curriculum is proposing the teaching of “exploratory data analysis” (EDA) as developed by John Tukey at Princeton about 50 years ago. EDA is a set of methods designed to assist in exploring data to lead to ideas for hypotheses that one could test more formally at a later date with more expertise. This strikes me as a worthy goal.

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    1. tom Avatar
      tom

      Hi Terry
      I too have been looking askance at the current statistics content. This looks like a very important question and anything Tukey has written is worth considering. Would you be prepared to write up an initial offering, explaining to us non statisticians?

      At Victoria University the stats guys put in a lot of effort to make a practical course which I guess had elements of data analysis along the Tukey lines. All gone now with the winding down of Science courses.

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      1. Terence Mills Avatar
        Terence Mills

        I gave this lesson to Year 9 students this week. The general aim of the lesson was to illustrate how box plots help us to explore data. More specifically, my hope was that working through the exercise will reinforce the students’ understanding of box plots. When I was planning the lesson, I thought that it might be too much for one lesson (70 minutes in my school) and they could finish it for homework. To my surprise, nearly all the students completed the work in about 60 minutes. I distributed the answers at the end of the lesson. ________________________________

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      2. Terence Mills Avatar
        Terence Mills

        Did the lesson appear on you website?

        Get Outlook for iOShttps://aka.ms/o0ukef ________________________________

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      3. tom Avatar
        tom

        Not sure what you mean Terry. The Victoria University course?

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      4. Terry Mills Avatar
        Terry Mills

        In my last email, I attached a lesson that I prepared on Exploratory Data Analysis. Did you publish this as well?

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      5. tom Avatar
        tom

        This is a reply for Terry Mills. Sorry Terry, the %$%$&$ WordPress site does not give me a reply button for your latest post. And up to now, all comments have also appeared in a special page for the site manager where I am given the option to reply directly. But now that page cannot retrieve your comment.

        In answer to your question: your post starting “I gave this lesson to Year 9 students this week.” had no attachment. I thought maybe you were saying “I gave a lesson to Year 9 students this week.” 😉 Possibly WordPress just deleted your attachment. If you send directly to me I will try to post it.

        Funny things are happening. I chose a setting that allows everyone to post without permission. But when Vicky posted earlier it was lying unpublished, waiting for my approval. Maybe because she had included a link to her website.

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  2. Adelaide Dupont Avatar
    Adelaide Dupont

    Geometry and visualisations, please.

    And how to show your work and why.

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    1. tom Avatar
      tom

      Welcome to this little site, Adelaide. Interesting suggestions, more general than I had in mind as topics, and more important. My unwritten rule is when someone suggests a discussion topic, I invite them to write the first post. A simple question is sufficient for an initial post, but you may like to explain your thoughts/experiences as well? I cannot give a timeline for when things will be published; I want to restrict the focus to one thread at a time.

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  3. Adelaide Dupont Avatar
    Adelaide Dupont

    Got it Tom!

    How do you construct a mathematical question and how is it similar and different to other questions that we may ask and answer in our lives?

    And how is a question different from a problem?

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  4. tom Avatar
    tom

    I see mathematics all around: the Essendon tactics in the game on TV, the germination rate of my snowpeas, the optimal use of my solar batteries. Perhaps I should get out more? But then we have the eddies in the creek, the springiness of the bridge over that creek, etc, etc.

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  5. Terry Mills Avatar
    Terry Mills

    On constructing mathematical questions. For some time, I have been opposed to the usual multiple choice questions. My reasoning is as follows. If I give the answer (c), then that tells you nothing about my learning. This week, my view has shifted. I like questions like this.

    Which of the following statements are true and which are false? Justify your answers.

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    1. Terry Mills Avatar
      Terry Mills

      Allow me to clarify my idea about questions that are similar to multiple choice questions (MCQs) but do not share the same difficulties. I now like questions like this.
      ——-
      Which of the following statements are true and which are false? Justify your answers.

      (A) Statement 1
      (B) Statement 2
      (C) Statement 3
      ——-

      All 3 statements deal with the same theme (e.g. quadratic functions, or correlation). Of course, there is nothing special about having 3 statements.

      More time would have to be allowed for such questions than one might allow for a normal MCQ. Two marks would be allocated for each part: 1 mark for the correct answer (true/false) and 1 mark for the justification.

      There is some subjectivity involved in allocating marks for the justification. However, I would take into consideration the year level of the students, and what we had covered in class up to the time of the assessment. I would have to frame questions so that students would not be tempted to write “I used my calculator”.

      I am not completely satisfied with the wording of “Justify your answers” and welcome any suggested improvements.

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