Fluency Without Fear: Research Evidence on the Best Ways to Learn Math Facts
Jo Boaler, Professor of Mathematics Education, co-founder youcubed, with the help of Cathy Williams, co-founder youcubed, & Amanda Confer, Stanford University
Jo Boaler, alongside Dylan Wiliam and John Hattie, probably have the highest ratios of “research papers that people assertively quote” : “research papers that people have actually read” amongst current educational researchers. This article is a good place to start to lower that ratio back to (at least!) 1:1. It’s a summary of Boaler’s research, and although it’s published on her public-facing website rather than as an academic paper in a journal, there are references at the end well worth following up.
The article starts with a story about Stephen Byers, a Government Minister in 1998. Being interviewed on BBC Radio Five about government plans to improve numeracy in schools, he was asked to multiply eight by seven. "Fifty-four," said the minister, whose job, ironically, was to raise standards in the classroom for reading, writing and arithmetic.
National ridicule occurred. "It is one of those character-forming events," he said. In contrast, David Cameron and Nicky Morgan both recently avoided answering times tables questions, with the implication that the public backlash and ridicule would be more than they were willing to stand. Boaler’s thesis is that it is time to rethink radically the way in which pupils acquire factual knowledge, especially now there is a greater emphasis upon memory and recall within both the primary and secondary curricula.
Boaler’s core principle is that “maths is a creative subject that is, at its core, about visualising patterns and creating solution paths”. She gives clear and concrete ideas of how to do this with a range of exercises and activity that, she believes, build mathematical understanding. By downloading the full pdf you can get full access to the activities. For example, asking pupils to identify how many ways there are of completing a calculation and then comparing them for efficiency. Activities such as this exemplify the value – and not insuperable challenge – of developing mathematical understanding through engaging activities rather than focusing upon mathematical rote learning.
Developing pupils’ fluency is one of the core aims of the new National Curriculum; however, there is a spectrum of fluency, from automaton-like recall (think The Terminator does times tables … oh actually he did, in 1990’s Kindergarten Cop) to deep conceptual understanding and number sense (which Robert Wilne discusses in a short piece for SSAT). In the article Boaler challenges the rote learning camp, and highlights what she identifies as the damage caused by such practice. Given the emphasis in the new GCSE curriculum that pupils develop “fluent knowledge, skills and understanding”, and the new directive in primary for the recall of times tables to 12 by the age of 9, it couldn’t be more timely that we take the time to understand, and reflect critically, on the arguments and evidence collated here.