Maths Ed Fires Back

Today in The Conversation there is an article firing back at the open letter to ACARA:

The proposed new maths curriculum doesn’t dumb down content. It actually demands more of students

We haven’t read the letter, and we don’t know the authors, or of the authors. We’ll try to read the article and comment on the article soon, modulo home schooling and general exhaustion. For now, people can comment below (respectfully and on-topic and on-the-ball-not-the-man). We’ll be interested in what people think.

13 Replies to “Maths Ed Fires Back”

  1. The whole thing reads like a criticism of an imaginary maths education where prescribing mastery of fundamental and wide-ranging skills = students do not get better at maths (because they aren’t gaining “deeper understanding”, whatever that means). Marty, I appreciate (and support the sentiment) that you don’t want ad hominem comments, but my reaction is that the authors are not in touch with reality.

    eg:

    “For instance, a child will need to move from seeing a triangle as a pointy shape to focusing on the relationship between the length of sides and angles, as well as its properties (such as symmetry).”

    Since when did prior curricula just limit students to seeing a triangle as a “pointy shape”, or require that teachers only teach that?

    “Say a student reaches the hurdle of needing to focus on the relationships among properties of triangles, which is necessary before they can solve geometric proofs. Here, the proposed curriculum prompts teachers to consider a range of real-word [sic] examples. It also provides student-centred activities to support the kids in getting over the hurdle. ”

    Because real-world examples are the best way for students to learn that the area of a triangle is 0.5bh.

    On moving solving linear equations from Year 7 to Year 8, we have:

    “the proposed curriculum expects year 7 students to use “algebraic expressions to model situations and represent formulas. Students substitute values into these formulas to determine unknown values and interpret these in the context.”

    So, rather than confining students to solving simple linear equations, the new curriculum wants students to consider more complex relationships between numbers. It expects them to understand these, rather than showing them the trivial act of solving simple equations first.”

    So writing down an algebraic expression and substituting in a value leads to “understanding”, but solving 3x – 5 = 2 is “trivial”.

    On times-tables, we have:

    “The proposed [year 1] curriculum adds more detail, requiring students to:
    recognise, describe, continue and create growing number patterns formed by skip-counting, initially by twos, fives and tens starting from zero.
    Growing patterns this way is a building block for times tables. In this case, the two-times table.

    By year 4, students have progressed to dealing with more complex patterns and numbers, including those in multiplication tables. ”

    So in grade 1 students learn that counting by 2s gives 2, 4, 6, … but then they have to wait until grade 4 to learn their timestables.

    “Research also shows it is important to build a solid foundation from the early school years, while building students’ confidence and success from grade to grade.”

    Yes, but unfortunately that is not what the proposed curriculum will achieve.

    “Listening to students provides guidance for teachers in planning their lessons.”

    I guess we’ll need guidance from the students, because the curriculum provides little.

    “The proposed maths curriculum has the potential to provide a bridge between teaching, learning and assessment that should, in time, lead to improved maths outcomes.”

    Those phrases, “has the potential” and “in time” are doing some heavy-lifting. What’s that Keynes quote, again?

    1. It is bizarre that they think that they think solving a linear equation is trivial.

      Here is a linear modelling problem that I assume the national curriculum would like students to solve rather than just an equation. Guess how many year 9 students in a particular state got this correct? Just 7.2%. Students only needed to “skip count” and use some simple arithmetic – they event had calculators to help them. So how can you do such questions without being solid with arithmetic or straight away realising the patterns appear to be linear?

  2. I’ve read both and have two thoughts, one minor, one major:

    1 (minor) maybe this is good; the more people talk about the d(r)aft curriculum, the more people will think about it and express their thoughts to the relevant authorities before it is too late.

    2 (major) even if I agreed with the authors on “The Conversation” it still doesn’t help me understand what the d(r)aft curriculum is actually telling me to teach.

    3 (corollary to (2)) the authors of this reply seem to understand the d(r)aft curriculum well enough to be able to give a response to the open letter in language that I can understand. Maybe they can re-draft the d(r)aft curriculum and we can all have a second look at it…? (Yeah I know – unless hell froze over last week…)

    1. RF, I’m sceptical about your point #3. The article features the same vague, wishy-washy language that the curriculum uses. Now perhaps that is understandable given that it was published in TheConversation, but I would have thought that a good response to concerns about a lack of clarity and lowering of standards would have provided specific examples of where the curriculum prescribes in year level N that teachers teach concept X, along with examples of what students will do to demonstrate their learning of that concept. I note that the only time such an example is used, is when the authors are defending the delaying of teaching linear equations to Year 8 (solving x + 3 = 11).

      1. Fair point. I guess it is more of a gut-reaction: I read the article in the conversation and felt I (mostly) knew what the authors were trying to say. Whether or not I agree with them is irrelevant in this sense.

        After reading the ACARA d(r)aft curriculum I have no idea what I’m meant to be teaching nor when and I’ve been doing this for a number of years that I can only just count if I remove my shoes…

        And yes, the concept of what is or is not “trivial” is somewhere between the bizarre and the crazy.

  3. Thank you all for your comments. I haven’t had a moment, and so have still only skimmed the article.

    I have one, genuine question. Is is true that the authors defend delaying the solving of linear equations until year 8, while also referring to such solving as “trivial”? If so, can anyone indicate how the authors attempt to hold these two beliefs simultaneously?

    1. Perhaps (and yes I am being sarcastic) the two authors each hold one view and the editors didn’t see the need to check for internal consistency?

    2. Rereading that part of the article, now I wonder if the authors think that solving linear equations has *not* been delayed to year 8?

      They write “Another criticism is that the new curriculum *apparently* [my emphasis] delays linear equations from year 7 to year 8.

      But the proposed curriculum expects year 7 students to use “algebraic expressions to model situations and represent formulas. Students substitute values into these formulas to determine unknown values and interpret these in the context.

      So, rather than confining students to solving simple linear equations, the new curriculum wants students to consider more complex relationships between numbers. It expects them to understand these, rather than showing them the trivial act of solving simple equations first.”

      Perhaps the authors read “substitute values into formulas to determine unknown values” as including solving simple linear equations? But ACARA’s documentation on curriculum changes says “Focus in Year 7 is familiarity with variables and relationships. Solving linear equations is covered in Year 8 when students are better prepared to deal with the connections between numerical, graphical and symbolic forms of relationships”, which to me makes it pretty clear that whatever algebra students do in Year 7, they should only be solving linear equations until Year 8.

      So either the authors think that solving linear equations is NOT delayed until Year 8 (in which case, I think they do not know what is in the proposed curriculum). Or, they think that it is delayed, but that’s no big deal, because what is in the year 7 curriculum is more advanced / sophisticated, so the students will quickly pick up solving linear equations later on.

      1. Thanks, SRK. Whatever it is, it is mighty weird. As I note in a comment on my X = X post, the second elaboration includes “… solve equations from situations involving linear relationships”.

        So, the draft suggests there is *some* solving in “situations”, but it seems clear that this, by design and/or in practice, will be genuinely trivial, much less than a decent algebraic treatment of linear equations. And, if it means anything substantial, why did the authors quote the “expression” part of the draft, rather than the “equation” part.

  4. Deja vu.
    I have often remarked that when it comes to dumbing down the curriculum, Germany is 15 years ahead of Australia. 4 years ago 130 teachers and professors of mathematics wrote a letter condemning the loss of mathematical content in the curriculum (see https://www.tagesspiegel.de/downloads/19549926/2/offener-brief.pdf), and it was “answered” by 50 education scientists. The press observed that professors of mathematics were divided (because they failed to see that education scientists are not professors of mathematics). The letter had no further impact because everyone outside the profession of mathematicians and teachers seems to believe in the following axiom: education scientists can disprove claims using empirical studies. Same here: “based on research that demonstrates” etc. Oh, and of course the general attitude of the education scientists was the same over here: yes, students are not taught partial integration or equations involving square roots, but they learn other things that are much more important: modeling and mathematising.

    1. … but they learn other things that are much more important: modeling and mathematising.

      Except that they don’t.

      If you look at typical state-wide exams designed by the authorities working closely together with the curriculum authorities (all these institutes have the words “quality” and “competence” in their name), you’ll immediately notice that they do not even believe in what they say.

      These exams are indeed full of “modeling” and “mathematising”. However, none of that is ever expected to be carried out by the student. It is always given in the question, and sometimes (well, usually) weird or even plain wrong. If you’re familiar with the subject they are taken from (physics, biology, economics), trying to retrace the “modeling” is generally impossible. The actual “problem” to be solved by the student is to crunch a set of numbers into the given – not to be questioned – “model” and use the calculator to produce another set of numbers.

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