Peter Sullivan is wrong about maths education

And he's roped in Dan Willingham

Photo by Chris Arthur-Collins on Unsplash

---

A colleague was passing the time, searching up content on the internet when he came across this presentation from Professor Peter Sullivan of Monash University in Melbourne and thought he would send it to me for my reaction. People do this. It amuses them.

It looks like the presentation was created in 2018 and the address bar linking to the Mathematical Association of Victoria (MAV) website suggests it was given at their annual conference.

I have been aware of Sullivan for some time. Trainee and graduate teachers always seem to have heard of him and I understand he was a strong influence on the writers of the doomed first draft of a recent revision of the mathematics component of the Australian Curriculum.

The presentation is a straight-up, full throated endorsement of ‘Inquiry based, student centred pedagogies’ — the kind of stuff that confuses students and is generally less effective than explicit teaching. It even includes a comical Brass Eye style OECD diagram (page three). In fact, the presentation goes on to quote a range of authorities, such as the OECD and the NCTM, who have a long and proud tradition of being wrong about mathematics education.

One authority that I am more inclined to listen to is Professor Dan Willingham, a cognitive scientist from the US. Sullivan quotes perhaps the best-known line from Willingham’s book, Why Don’t Students Like School — a recommended read if you have never encountered it. The slide on page six of the presentation reads:

“Memory is the residue of thought

From Daniel Willingham, professor of psychology at the University of Virginia.

Students remember what they have been thinking about, so if you make the learning too easy, students don’t have to work hard to make sense of what they are learning and, as a result, forget it quickly.”

To be fair, Willingham has stayed a safe distance away from debates about teaching methods, preferring to focus on content. It is perhaps Willingham, along with E D Hirsch, who have done the most to promote the idea that the curriculum should be knowledge rich, often by making the argument that the single most important factor in reading comprehension is background knowledge. Squeezing-out the teaching of knowledge in order to endlessly practice reading comprehension strategies is therefore self-defeating (although limited teaching of these strategies is worthwhile).

Sullivan’s deployment of Willingham in this way is a good example of an argument that arises periodically. People highlight Willingham, or perhaps research on so-called ‘desirable difficulties’, and suggest that we need to think hard about something in order to learn. Inquiry learning — or whatever it is called this week — makes students think hard and so that’s what we should do. QED.

This conveniently ignores the severe constraints on human working memory. We can only process about four discrete items at a time and inquiry-style teaching with novice learners pushes way beyond this limit.

Yes, some thinking is required to learn. This is why explicit teaching is highly interactive. Among other reasons, it forces students to engage with the content rather than daydream. And yes, if you have a task that is low in ‘element interactivity’ and therefore well within the four item limit, such as learning a list of capital cities, forcing a little more processing makes sense. Teaching maths to kids rarely fits into this category. Neither does much of the academic learning we do in school.

From a set of slides alone, it is hard to tell exactly where Sullivan’s presentation landed, so I searched for papers on the subject by Sullivan and found this short 2021 article from Australian Primary Mathematics Classroom which, if anything, is even more curious.

Implausibly written with seven co-authors, it effectively concedes the research evidence for explicit teaching, which the authors call ‘active’ teaching — probably after Brophy and Good’s characterisation of the findings of the process-product studies of the 1960s-1970s. Nevertheless, the authors think we should not do too much of it:

“While there are aspects of mathematics for which such approaches are suitable, there are risks that teaching in this way can make students dependent on the teacher, as opposed to encouraging students to think for themselves. This approach does not specifically make provision for the diversity of achievement and motivation found in most classrooms and, if this is the predominant method of instruction, it results in alienating many students.”

Why does an effective means of maths teaching alienate students? It’s not clear but appears to be based on the old progressivist manifesto.

Instead, teachers should consider using ‘Student Centred Structured Inquiry’ which the authors then describe at length. They imply that this will be better for building students’ independence and creativity but, as may be expected, they offer no empirical evidence to support this. Instead, we read that such an approach aligns with the aspirations of the oracles at the OECD and with Victoria’s High Impact Teaching Strategies. Which is debatable. The authors state that:

“Interestingly, there is still Explicit Teaching in this model although this happens after student experience with the task rather than before, and there are also Worked Examples although these come predominantly from the students.”

This is an interesting contortion. As I have argued before, you can call anything ‘explicit teaching’ if you wish, but the kind of explicit teaching that has an evidence base — the kind described by Brophy and Good — is a entire process were concepts are fully explained to students prior to them being required to use them, followed by a gradual release of control from teacher to student. Similarly, the kind of worked examples that have a strong evidence base are not ones that ‘come predominantly from students’. Frankly, any attempt to build a mathematics curriculum around such examples would either be a disaster or an elaborate and inefficient game of guess-what’s-in-my-head.

It is therefore worrying that such evidence-lite commentary appears to be so influential with those designing the Australian Curriculum and those training the next generation of Australian teachers.