How do you solve a problem like Hans Freudenthal?

The figure standing in the shadows of the draft Australian maths curriculum


Marty over at Bad Mathematics has posted about a meeting between ACARA, the body responsible for reviewing the Australian curriculum, and AMSI, the Australian Mathematical Sciences Institute. Basically, ACARA released a draft maths curriculum that a large number of experts objected to. AMSI initially welcomed the draft, but after consulting its members, eventually submitted a critical response, calling for the current review process to be halted.

According to Marty’s account, the meeting did not go particularly well. Marty appears to be in possession of a paper tabled by ACARA as a reply to AMSI’s concerns.

This reply is interesting. Apparently, all of the elaborations to the draft curriculum that push hard in the direction of inquiry, investigations and problem-based learning are optional, ergo the draft curriculum is neutral on teaching methods. However, as Marty points out, there is a lot of core content sitting in these elaborations and so this argument is untenable.

The reply also justifies ACARA’s various flawed proposals with reference to the ‘literature’, without specifying exactly what research they are referring to. AMSI recommended changing the vague strand name of ‘space’ back to the mathematical term, ‘geometry’, but ACARA are apparently holding firm. And there is a strange discussion of what is ‘essential’ in a mathematics curriculum. Basically, ACARA seem to interpret ‘essential’ to mean whatever it is they think should be in the maths curriculum.

However, perhaps the most interesting portion of the response is a section on the term ‘mathematising’. AMSI had written that, “Mathematising is a concept with which our highly qualified educators have no experience.” ACARA expressed surprise at this statement, apparently arguing that it is a, “…term that is widely used in the mathematics education literature,” and that, “The term mathematizing (mathematising) was introduced by the Dutch mathematician Hans Freudenthal as a component of Realistic Mathematics Education (RME) … It has also been associated with particular learning approaches identified in the literature as an essential component to building number sense and Numeracy capabilities.”

So, it originates with Hans Freudenthal. Interesting.

The fact that AMSI members, who I assume are the kind of folks who teach mathematics or engineering at university, have never heard of a late theorist who is popular among maths education academics, is not surprising. The former live in the real world of data, evidence and verifiable claims, whereas the latter live in a world of ideologically motivated supposition.

However, the ‘particular learning approaches’ that Freudenthal is associated with are precisely those approaches that ACARA keeps denying that it has build into its draft mathematics curriculum. For instance:

“According to the reinvention principle, a route to learning along which a student is able, in principle, to find the intended mathematics by himself or herself has to be mapped out (Freudenthal 1973b). To do so, the curriculum developer starts with a thought experiment, imagining a route by which he or she could have arrived at a personal solution.”

So, Freudenthal was a proponent of a form of discovery learning, an idea that he seems to base on the common misconception that the best way to teach mathematics is to ask student to copy the behaviour of expert mathematicians.

While I agree that learning approaches of this kind are extremely popular in the mathematics education literature, they are not an effective approach to maths teaching. Even if you disagree with me and believe discovery learning has a place, I think we can still agree that it should not be imposed on teachers, potentially against their own professional judgement, via the Australian curriculum. And, ACARA have repeatedly claimed that they are not attempting to impose a teaching style.

If so, mathematising and Hans Freudenthal must go.