Send me a postcard, drop me a line
Stating point of view
Indicate precisely what you mean to say
Yours sincerely, wasting away
Give me your answer, fill in a form
Mine for evermore
Will you still need me, will you still heed me
I’m nineteen sixty-four
Below is a document from a foreign country, one of yesterday’s finds. We have our thoughts, and we shall update the post pretty soon. First, however, we’ll give people a chance to ponder. Think of it as a WinCH.
UPDATE (09/05/21)
Courtesy of the Evil Mathologre, the PDF below now has (somewhat clunky) OCR. That means you can search for words, such as “mathematising”.
Page 2:
“Thus the development of mathematical thought can be improved by placing greater emphasis, in our teaching methods, on induction and abstraction rather than deduction.”
And only a bit further on:
“It is the task of the primary school to prepare children by preserving and developing them with the opportunity to fully understand mathematical ideas.”
These two sentences, for me, pretty much set the whole document up for success. The number of times “understanding” is mentioned (and not “discovery”) is also impressive.
Thanks, RF. The document definitely includes some sense of “discovery”:
“The child needs adequate opportunity for experience and experimenting …”
Together with the emphasis on “understanding”, does that make the document ACARA-ish? If not, what’s the difference(s)?
In my opinion, this document (unlike ACARA documents) mention discovery as *one possible* method by which students learn rather than it being the *expected* method of delivery.
The difference, again opinion, is that ACARA suggests this is how learning should occur. This 1964 publication accepts that, alongside direct instruction, some students *might* learn ideas by self-discover and if this happens then great, but don’t expect every learner to be able to do this.
In short: ACARA doesn’t seem to trust teachers to be able to do their job without ACARA’s help. This may well be a symptom not a cause however.
Thanks, RF. Obviously I don’t for a minute think ACARA could appreciate, much less produce, that 1964 document. I’m just trying to tease out for myself why it is so different, particularly since some of the language is the same.
I agree, “discovery” has a much more circumscribed role in the 1964 document. I’m not sure, however, the 1964 guys trusted teachers less (or that they should have). The 1964 document isn’t exactly lesson plans, but it’s pretty prescriptive.
I’m suggesting that in 1964 the schools board (or whatever it was) trusted teachers MORE (actually, the word “more” is a bit superfluous…).
A long time ago in a galaxy far, far away…
“Any sufficiently advanced curriculum is indistinguishable from common sense”.
That is an interesting thought. I’m not sure I agree 100%, but I’m not sure I don’t.
I bought a book of chess problems recently – an old book – and it arrived yesterday. A previous owner had left his London bus tickets in the book. They generated nice thoughts.
The document talks about understanding before being able to have a automatic recall of mechanical processes: “As urderstanding develops and the ability to work in the abstract becomes evident, the response will increase in speed and become automatic without minimum drill”. They define drill as rote learning through doing lots of questions to memorise procedures through a shear number of repetitions. This sits well with me as the brain doesn’t retain things that it doesn’t understand, due to lack of meaning, and hence you cannot develop fluency in the procedures.
For that alone, I think it better than ACARA’s curriculum as it emphasises the importance of a teacher guiding students, as apposed to students discovering things for themselves. The document doesn’t discount students having oppertunities to discover things for themselves but seems to suggest they be carefully chosen situations. ACARA’s unstructured discovery method will leave students to develop misunderstandings that then then try to build more misunderstanding upon.
Thanks, Potii. That seems right. In the 1964 document, the “discovery’ seems localised, kind of “that’s the sort of thing we’re looking at”. But this exploration is quickly followed by the nailing down. And, yes, the document gives the lie to the standard claims that long-ago maths was just meaningless manipulation of symbols.
Re: the update. But is “mathematising” even a word? A sequence of letters, sure, but I’d hope Cambridge hasn’t inserted it into their tomes just yet.
(see https://dictionary.cambridge.org/spellcheck/english/?q=mathematising)
Just a matter of time (unfortunately) I guess.
Much like “numeracy” you think?
In my world, “numeracy” means “applied mathematics”, and now “mathematising” means “applying mathematics”.
Attached is a draft of my response to the revised curriculum. I made some changes on the screen before I submitted it.
tm_draft_ac
Terry, I don’t disagree with any of your criticisms. What, however, do you see as the value of your submission?
I felt that I had done something constructive. I also enjoyed using my very recent classroom experience in making comments.
My only suggestion that I expect to make a difference is to replace “New Guinea” by “Papua New Guinea”. We will see.
Several teachers have told me something like “I don’t have time to follow it”, or “It deals only with F-10 and I teach 11-12”. The powers-that-be could expect, and bank on, this general lack of interest.
I don’t think you’ve done something constructive.
I was suggesting that “numeracy” was a made up word much as “mathematising” is now.
If you make up words, you can define them however you like, and in the absence of a clear definition, can redefine the word (by implication) whenever and however it suits.
I think both words suck.
I agree. In fact, they are unnecessary – unless you want to change the direction of the debate. My theory is that “numeracy” is designed to avoid using the word “mathematics” because mathematics is hard.
People in education have a tendency to give new meaning to old words and then claim that the new meaning replaces the former meanings. In my MTeach I had to write an assignment about how I would deal with students who had special needs. Because there is such a wide variation in the mathematical ability of students, I developed an assignment about how to work with this variation. I was pretty excited because I had a great idea. But I thought that I would check with the lecturer. I was told that having very low mathematical ability is not the meaning of “special needs”. A student with “special needs” is not a student with special needs.
“Constructivism” is another example. I have often asked disciples of constructivism what does “constructivism” mean? I never get a satisfactory answer.
The use of jargon does a disservice to education.