# A revolution in teaching methods

### California’s new maths curriculum is about changing the way maths is taught

I recently wrote about the debacle of the proposed new Californian Mathematics Framework. I noted that Dr. Jo Boaler was involved in writing the new Framework and discussed some of the issues raised. I pointed to an open letter opposing the changes, signed by professors of maths and science, PhD students and other interested parties, and drew on some if its critique.

At the time, I was unaware of another open letter that had also been written opposing these changes, hosted by the *Independent Institute*. It is signed by a similar group of people and, if anything, takes a slightly stronger line.

In an encouraging sign that critics may be winning the argument, a group of researchers, teachers and organisations that includes Boaler (and Dan Meyer) have now signed their own open letter repudiating the *Independent Institute* letter.

Why is this an encouraging sign? Well, I have been critiquing Boaler’s ideas for nearly ten years and I cannot recall a response. And yet, at the time of writing, Boaler’s pinned tweet is a link to this letter and an invitation to sign. It seems that the stakes have been raised and critics can no longer be ignored.

As someone who has reviewed one of Boaler’s books and read several of her papers, I would not be surprised if she was responsible for drafting the letter. It has a similar tone - breathless, earnest and polemical. I also feel it misses, or perhaps distorts, its target - the *Independent Institute* letter.

For instance, the *Independent Institute *letter suggests that rather than focusing on stories of the marginalised people who have contributed to the development of modern mathematics, we should focus on the *mathematics* they developed:

*“The proposed framework… Encourages focusing on “contributions that historically marginalized people have made to mathematics” rather than on those contributions themselves which have been essential to the academic discipline of mathematics… We, the undersigned, disagree. Mathematics is a discipline whose language is universally accessible with good teaching. The claim that math is not accessible is an insult to the millennia of non-Western mathematicians and erases the contributions of cultures around the world to mathematics as we now know it.”*

The Boaler et al. letter interprets this as an, ‘offensive rejection of the contributions of marginalized people in mathematics.’ This is an extremely ungenerous interpretation.

Setting aside such issues, the substance of the Boaler et al. letter is highly revealing. Most of the time, I find advocates of inquiry learning, problem-based learning and so on, difficult to pin down. For instance, when the recent draft *Australian Curriculum: Mathematics* was released, we were reassured that it was not about imposing teaching methods *at all*, despite the document containing long preambles about problem solving, ‘mathematising’ and the importance of developing supposed problem-solving skills, as well as the many elaborations that described inquiry-style investigations (this document is now offline so I cannot link to it).

Boaler et al. have no such reservations. If it were perhaps wise to attempt to hide the extent of their pedagogical agenda, they are unaware of this:

*“The open letter represents a narrow view of mathematics, where the teacher and the textbook are the sole authority, and learning is focused on transmitting information from the teacher to the students (Freire, 1970; Lampert, 1990). This view of mathematics does not reflect the existing research, and it systematically acts as an unnecessary gatekeeper that denies many students access to rigorous mathematics courses that prepare them for career and college.” [My emphasis]*

Note that there is a reference to the late Brazilian theorist, Paulo Freire, who is inexplicably popular in American grad schools, but the part I have highlighted in bold has no reference associated with it. It is simply asserted that the kind of teaching described ‘does not reflect the existing research’, but, whatever that research is, we will never know.

Instead:

*“The draft Mathematics Framework embraces a multidimensional view of mathematics that values multiple strategies, emphasizes connections between ideas, and engages students in learning through making conjectures, exploring mathematical properties, explaining their reasoning, validating assertions, and discussing and questioning their thinking and the thinking of others (Lampert, 1990)”*

This approach is apparently supported this paper by Lampert, which, although interesting, is not designed to compare the effectiveness of different teaching methods and so cannot really support the claim. Instead, the Boaler et al. argument is the tired old call for a version of discovery learning where students have to figure some of the content out for themselves, learning *through* exploration rather than *from* a teacher. A large body of evidence suggests this is ineffective and that the reason it is ineffective is that it overloads the working memory of novice learners. Such a teaching style is likely to be most detrimental to those who are already the most disadvantaged because they have less to draw upon from long-term memory to mitigate the effects of this overload - achieving precisely the opposite of the aim of diversity and inclusion.

Boaler et al. have therefore laid their cards on the table. Theirs is the siren call to unstructured learning. Calfornia’s new framework is not just about Eighth Grade Algebra, important though that issue is. Boaler et al. want to plunge California back into an experiment with teaching methods that has repeatedly failed over the last 200 years.

And that’s worth objecting to.

Mathematics has always been a study undertaken by a leisured elite, in the richest and most free societies on earth.

"contributions that historically marginalized people have made to mathematics"

Yeah, name them.

Ada Lovelace was actually Ada King, Countess of Lovelace. I don't think she was terribly at risk of marginalisation. Rich and connected more like.

The great age of Islamic mathematics -- Al-Khwarizmi, al-Baghdadi etc -- weren't born street urchins. The were children of nobles, with lots of free time, who were living in the greatest power on earth at the time. They were the ones doing the marginalising back then. (They also kept slaves, but we won't mention that.)

Alan Turing went to Sherborne School and King's College. That's not how marginalised people are raised. True, he was actively gay, but what bearing does that have on his mathematics?

It's all a complete snow-job. People who know almost nothing about the mathematicians involved making up stories to fit their current political agenda.