Research in Action 10: When to tell and teaching algebra with Dave Hewitt


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Hello, and welcome to another episode of the Mr Barton Maths Podcast, with me Craig Barton.

This is an episode from the Research in Action mini series, where I interview a researcher from the Mathematics Education Centre at Loughborough University about their chosen area of interest, and the implications for maths teaching and learning.

On today’s episode I was lucky enough to speak to Dave Hewitt.

Dave gained his BA in Mathematics at the University of Warwick and completed a PGCE at the University of Exeter. He started out teaching in schools around the Bristol area for 11 years, including five as Head of Faculty. Dave then took up a position as Lecturer in Mathematics Education at the University of Birmingham, becoming Senior Lecturer in 2000. He received his doctorate from the Open University in 1994 under the supervision of Professor John Mason. In 2014 Dave moved to Loughborough to start up the new Mathematics PGCE course.

I have wanted to get Dave on the show ever since I became aware of his work. Regular listeners will know, I adore the Practising Mathematics book that he co-authored with former podcast guest, Tom Francome. And his articles for the ATM are always thought-provoking.

In putting together this Research in Action series, Colin Foster scheduled Dave in at the end as he thought we would have a lot to talk about. Ad he often is, Colin was spot on.

In this conversation we discussed:

  • When is a right to tell students something, and when should we let them play around and discover it for themselves?
  • We talk a lot on this show about the importance of memory, retrieval and rehearsal when learning mathematics. What else is missing?
  • One thing I struggle to get my head around is the role of subordination in developing fluency. Could Dave help me?
  • And then we dig deep into Dave’s approach for teaching algebra, and why he believes that “Arithmetic is impossible without algebra”

This was the 10th interview I did at the end of two gruelling – but thoroughly enjoyable – days. Thankfully Dave re-energised me, and this really is one of my all-time favourite conversations, and a fitting end of season finale for both the Research in Action series, the 5th year of this podcast, and 2020 in general.

Dave and Tom’s excellent book, Practising Mathematics, is available here
Dave’s work on Grid Algebra, along with some really useful videos, can be found here

Dave’s Big 3
1. Median by Don Steward
2. Douglas Hoffstater – Godel, Escher Bach?
3. A Gattegno Anthology – ATM



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