This is our final excerpt from Teaching Mathematics at Secondary Level Tony Gardiner’s 2016 commentary and guide to the English Mathematics Curriculum. (The first two excerpts are here and here.) It is a long and beautifully clear discussion of the nature of problem-solving, and its proper place in a mathematics curriculum (pp 63-73). (For Australia’s demonstration of improper placement, see here, here and here.)
Continue reading “Tony Gardiner on Problem Solving” →
Our first excerpt from Tony Gardiner’s Teaching Mathematics at Secondary Level is here. Our second excerpt is a short remark on “financial mathematics” in a mathematics curriculum (p 75). The relevance to Australia’s draft curriculum is obvious.
Continue reading “Tony Gardiner on Financial Mathematics” →
It’s been a while. We’ve been trying hard to get out a long, long post on ACARA and the draft curriculum. (Working title: Moby Albatross). We also had a great WitCH planned, but that was torpedoed by Simon the Likeable. For now, we’ll keep readers occupied with some excerpts from the writing of Tony Gardiner.
Gardiner is an English icon, sort of a one-man AMT, but without the foot-shooting. Previously, we wrote about Gardiner’s and Alenxandre Borovik’s beautiful (and free) book, The Essence of Mathematics Through Elementary Problems. Then a few weeks ago, we posted a “puzzle” from Gardiner’s book, Teaching Mathematics at Secondary Level.
Written in 2016, TMSL is Gardiner’s commentary and guide to the English Mathematics Curriculum, with a particular focus early secondary school (Key Stage 3). Although framed around a specific curriculum, much of TMSL is written from a more general perspective. In particular, Chapter 2.3 of TMSL is on problem solving and the manner in which problem solving can fit, or misfit, in a mathematics curriculum. We shall excerpt this chapter in three posts, beginning with two short passages and concluding with the main content of the chapter. Our first excerpt is on the importance of exactness in a mathematics curriculum (pp 73-75).
Continue reading “Tony Gardiner on Exactness and Approximation” →
Does anybody ever properly read Terms of Reference? Probably not, and in the case of ACARA’s Terms of Reference for their curriculum review, this was a fatal error. The Education Minsters who approved ACARA’s ToR screwed up. Royally.
Below, we work through the ACARA’s Terms of Reference, section by section, highlighting critical aspects to the review of the mathematics curriculum. We’ll indicate how the ToR gave, and continues to give, ACARA license to consciously and to thoroughly ignore mathematicians, as well as education ministers. We shall also indicate how, nonetheless, ACARA have violated their own Terms of Reference whenever and however it suited ACARA’s real agenda.
Continue reading “ACARA’s Terms of Reference” →
While we’re working away on ACARA, here’s another post to keep readers occupied. Below are released “benchmark” test items from TIMSS 2019. (Further details about the benchmarking can be found in the full report (pp 35-59, 172-198).
Continue reading “2019 TIMSS Sample Items” →
We’re working on a long ACARA post, which, hopefully, will be up in a day or so. In the meantime and as a bit of background for the coming post, readers may wish to have a wander through the Singaporean Primary Mathematics Syllabus.* (The syllabus begins with explanatory chapters, and the content description begins on page 34.)(Added 12/10/21 – The Secondary Syllabus 1-4 is here.)
Continue reading “The Singapore Mathematics Syllabus” →
We already had plans to start a new series of posts: Because it’s Funny. This was to begin with a different comedian, but Norm McDonald‘s dying kind of forced our hand. The characterisation “his cynicism was just a byproduct of his idealism” makes him our kind of guy. Below is a clip from Saturday Night Live. Continue reading “BiFF: Norm Macdonald and Pie Charts” →
(The preamble for this post is now a post-amble, at the end.)
(24/06/22) An update has been added to The ACARA Page. Continue reading “The Update Post” →