Jo Boaler is the Professor of Mathematics Education at Stanford University. She has become a familiar figure in the world of maths education and has a knack for publicity, often by taking quite radical positions on the teaching of mathematics.
For instance, Boaler has advocated against asking students to memorise multiplication tables and then testing students on this. Multiplication facts such as 6 x 6 = 36 are part of a larger set of ‘maths facts’ that teachers have traditionally asked students to learn by heart.
Part of Boaler’s argument is that maths facts are not as essential as this practice implies. She has claimed, for instance, that, “I have never memorised my times tables. I still have not memorised my times tables. It has never held me back, even though I work with maths every day.”
The other part of her argument is that timed tests of maths facts induces ‘maths anxiety’ – a debilitating condition that turns kids off maths and harms their performance. This claim has been the subject of quite a lot of interest because, initially, the citation trail ran cold. However, it now seems as if the basis for this claim is an article that Boaler authored in 2014. I have blogged about how I dispute that this article demonstrates that timed tests cause maths anxiety.
Indeed, my view is that maths facts are essential. By removing the need for a student to work out these simple calculations, the student is able to focus on other aspects of a problem. Given that total cognitive load is limited, this frees up resources, giving students a better chance of success and this should pay forward into a greater sense of self-efficacy in maths – one component of future motivation. If we wish to intervene with a group of students who are struggling with basic maths then a focus on memorising maths facts may be part of the solution.
Now, Boaler has co-authored an article for Time magazine with Tanya Lamar, a PhD student at Stanford. Paul Morgan, an education professor from Penn State College of Education, has pointed out on Twitter that there is a curious aspect to this piece.
The article is about the critical issue of teaching students who have a learning disability. After discussing a literacy intervention – which is interesting in its own right but I want to stick to the point – Boaler and Lamar state that, “A similarly promising study found that eight weeks of 40- to 50-minute sessions per day made children who had been diagnosed as having mathematics learning disabilities achieve at the same levels as a group of regular performers.”
There is no link to the study in the passage. However, later in the article, Boaler and Lamar mention students who are, “not good memorizers,” and that, “These students do not have less mathematics potential.” This time, they link to this paper which indeed involves an eight week intervention consisting of 40- to 50- minute sessions.
The paper, by Supekar and colleagues, is a foray into neuroscience and the participants underwent functional MRI brains scans prior to tutoring. I am yet to be convinced that neuroscience has much to offer that is of practical value to educators. The main effect seems to be lowering the power of studies by limiting the number of participants to a figure low enough to pass them all through an fMRI machine. Boaler and Lamar seem more impressed with neuroscience than I am, insisting that we need to understand that brain pathways can strengthen and form new connections. This seems to be just a fancy way of saying that people can learn things and I am pretty sure we knew that already.
The really interesting part of the paper is the description of the maths tutoring intervention. After brain scanning, participants:
“…subsequently went through an intensive 8-wk one-to-one tutoring program focused on number knowledge tutoring with speeded practice on efficient counting strategies. Tutoring was designed to facilitate fluency in arithmetic problem solving. Before and after tutoring, we recorded arithmetic strategy use as well as speed, accuracy, and performance efficiency of arithmetic problem solving in each child using standardized procedures.” [References removed]
Say what? Did the tutoring process really rely on ‘speeded practice’? Let’s read further. “The tutoring program combined conceptual instruction with speeded retrieval of math facts,” and, “Arithmetic verification tasks involving single-digit addition problems were performed during fMRI scanning and emphasized speeded performance.” Did any of this matter? Yes, because as the abstract states, “A significant shift in arithmetic problem-solving strategies from counting to fact retrieval was observed with tutoring. Notably, the speed and accuracy of arithmetic problem solving increased with tutoring, with some children improving significantly more than others.”
In summary, this study provides evidence to support the idea that, for students with learning disabilities at least, learning maths facts is important and speeded practice is a key component of this process.
Perhaps Boaler will now rethink her earlier views on this.