What Does It Mean To Be An Education Expert? Part 1

What I was going to say about Jo Boaler in 2013

This is part one of a two-post series. I wrote the original version of these posts in 2013. I never finished or shared them. This may have been absent-mindedness on my part. I faced several personal and professional challenges that year. However, I think I hesitated because although I wanted to write about what was wrong with educational research in general, the post was mainly about one particular educationalist, Jo Boaler. I didn’t feel I could justify singling her out. In my view, her work was egregiously bad, and her influence was substantial. However, when you write 2000 words about one person, based largely on a single chapter of one of their books, the debate quickly becomes more about who has the right to criticise whom and what motivates the criticism. I wanted to discuss how poor-quality research and trendy ideas could be presented as authoritative in education. But the debate was likely to end up being about whether a teacher can criticise a professor of education, or whether a man can criticise a woman.

11 years on, it seems reasonable to focus on Jo Boaler. When I wrote this post, her work was a major influence on the education establishment and, therefore, teacher training and debate within the profession. However, it was difficult to demonstrate this to anyone who had not been trained to teach mathematics. Now, that influence is more public and more overtly political, with the US state of California forcing her ideology on schools. Her tactics for intimidating critics have been exposed after she threatened a black professor who criticised her with the police. The quality of her work is also in the public eye following an anonymous complaint to her university. In these circumstances, I don’t think I need to worry about being accused of having a personal grudge against her. But just in case, I will emphasise my main point here is not about her, but about how recognised experts in teaching a subject often have little expertise in either the subject or how to teach it.

What I wrote in 2013¹

A blogger I follow has uploaded a chapter from a book by Jo Boaler, a professor of mathematics education at Stanford and probably the leading figure in the field. 

And it’s awful.

Really awful.

Awful enough to raise questions about what it means to be an expert in the teaching of a school subject and the value of the work of such experts. In what follows, I don’t mean to suggest that all education experts are of the same quality. What I do mean to suggest is that there are education experts who do not deserve the trust of the profession, regardless of their position. This chapter, and its author, seem to illustrate that expertise in the academic field of education is not always what we might expect it to be.

1) Do you have to be an expert in a subject to be recognised as an expert in teaching that subject?

The first part of the chapter I linked to is an argument that mathematics is misrepresented in schools. 

The maths that millions of school children experience is an impoverished version of the subject that bears little resemblance to the mathematics of life or work, or even the mathematics in which mathematicians engage.

Now, of course, it is perfectly normal for progressive educators to concentrate on how a school subject is used in real life. Arguments that what is learnt in school should be relevant or practical are common. What is curious here, is the attempt to identify what mathematics is and how this is used to justify the claim there is a problem with the mathematics taught in schools.

In my different research studies I have asked hundreds of children, taught traditionally, to tell me what maths is. They will typically say such things as “numbers” or “lots of rules”. Ask mathematicians what maths is and they will more typically tell you that it is “the study of patterns” or that it is a “set of connected ideas”.² Students of other subjects, such as English and science, give similar descriptions of their subjects to experts in the same fields. Why is maths so different? And why is it that students of maths develop such a distorted view of the subject?

The ideas in this passage are enough to baffle anyone with a strong mathematical background. Maths at a higher level is about more than dealing with numbers. Children (or adults for that matter) may not realise this. However, I suspect that some number theorists might be surprised to hear it is wrong to think mathematics is about numbers. Even in areas of mathematics that don’t emphasise numbers, it’s hard to see how one could avoid considering “lots of rules”. Even a look at Wikipedia would suggest that this particular debate in mathematical philosophy cannot be squeezed into Boaler’s description. Logic and reasoning are repeatedly mentioned, yet logic cannot exist without rules. I have encountered mathematicians who claim that “patterns” are a defining feature of mathematics, but it is hard to imagine a mathematical concept of patterns that avoids the concept of rules. A “set of connected ideas” is a description so vague that it could describe any academic discipline. I don’t want to turn this post into an exploration of the philosophy of mathematics - I’m certainly not going to propose an alternative definition of mathematics - but I would challenge anyone to argue that the section I’ve quoted shows a reasonable grasp of what mathematics is. I would expect an undergraduate maths student to be able to do a better job of explaining what mathematics is.

Of course, perhaps we shouldn’t read too much into that passage. It could be an attempt to be clever, which has backfired, rather than a sign of conceptual confusion. However, having read this I cannot resist looking up Boaler’s academic credentials here and I see that she does not appear to have ever completed an undergraduate degree in mathematics.

From this, I conclude that no particular expertise in mathematics is necessary to be recognised as an expert in teaching mathematics.

2) Does the work of an education expert have to be well-researched?

The Golden Ratio (AI generated)

The next section of the chapter is more surprising. As an example of the true nature of mathematics, we have a section that goes from The Da Vinci Code (that well-known academic tome), through Fibonacci numbers, to the golden ratio.

...1.618, also known as phi, or the golden ratio. What is amazing about this ratio is that it exists throughout nature. When flower seeds grow in spirals they grow in the ratio 1.618:1. The ratio of spirals in seashells, pinecones and pineapples is exactly the same...

Remarkably, the measurements of various parts of the human body have the exact same relationship. Examples include a person’s height divided by the distance from tummy button to the floor; or the distance from shoulders to finger-tips, divided by the distance from elbows to finger-tips. The ratio turns out to be so pleasing to the eye that it is also ubiquitous in art and architecture, featuring in the United Nations Building, the Greek Parthenon, and the pyramids of Egypt.

Ask most mathematics students in secondary schools about these relationships and they will not even know they exist...

This is followed by a condemnation of the failure of maths teachers to teach this inspiring and important fact about the world. This surprised me because not long ago I read Dan Willingham’s (appropriately titled, in this context) When Can You Trust the Experts?³ The same details about the golden ratio came up there. However, it was not used as an example of what maths teachers should be telling pupils. It was used as an example of something quite different:

The Golden Ratio does exert a powerful and powerfully subtle influence on persuasion. Or it would if not for one small problem: The Golden Ratio theory is bunk. … Studies have been conducted in which people (ordinary people or professional artists and designers) are shown a large selection of rectangles and asked which they they find the most attractive. It’s not the case that people select the Golden Ratio rectangles. Another study examined the dimensions of 565 rectangular paintings by famous artists. Artists showed no predilection for canvas sizes that respected the Golden Ratio... And natural objects like the human body, faces and sea shells show lots of variability. It’s not the case that the most attractive show the Golden Ratio... Some of the Golden Ratio phenomena are accurate but trivial - trivial because examples that fit the Golden Ratio are emphasised, and examples that do not fit are ignored. Why evaluate the Parthenon and not the Pantheon? Why the Pyramid of Giza and not the Pyramid of Khafre? For that matter, why not the Roman Colosseum, the Taj Mahal, the Alhambra, or the Eiffel Tower? Then too a complex figure, like the Parthenon... has many measurable features that make it easy to pick and choose measurements that yield the desired ratio.

The level of background research in Boaler’s book was not sufficient to prevent her from repeating an urban myth.

In part 2, I will consider whether an education expert’s empirical work has to be of high quality, and whether education experts have to address criticism of their work.

1. I have tightened up the language where possible and removed errors as the original post was only a first draft. I have also changed links that no longer worked or were missing. The footnotes I have added are generally new.

2. One point I did not make in the original post is that the use of such questions is itself a dubious enterprise. It can only ever reveal slogans taught to the children; it is unlikely to reveal understanding. Defining disciplines is difficult, and philosophers of mathematics have some fundamental disagreements. What is being assessed in these children is what Barry Garelick calls “rote understanding”.

3. This is an affiliate link, i.e. if you use it to buy the book I will receive a small amount of money.