Dave Hewitt taught in schools for 11 years, including as Head of Department working with all-attainment classes from Years 7-11. Dave has since been working in teacher education for over 30 years, initially at the University of Birmingham and then setting up the mathematics PGCE at Loughborough University in 2014. Dave was last on the show back in 2020 when we discussed when to tell students how to do something. This episode is part of my 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. You can access the show-notes here: mrbartonmaths.com/blog/research-in-action-23 Time-stamps: Dave's background. (2:07) The law of efficiency and short term success. (7:36) The subordination of teaching to learning. (13:16) Children can abstract from a world of complexity. (19:49) Direct access to students. (25:15) Direct access vs. prior knowledge. (33:12) Assess the knowledge of your students. (41:32) The power of learning generated examples. (45:59) Not enough time for maths. (50:35) Teachers are not assessors. (55:19) Fluency-based learning. (1:00:02) Assessments are not just about assessment. (1:04:45) How to get students to explain things. (1:09:25) Discussing departmental meetings around the task. (1:14:51) How to assess where students are in the mind. (1:18:38) Being creative in the classroom. (1:24:21) What’s an example of something you’ve changed your mind about? (1:29:45) Building Thinking Classrooms. (1:32:36) The importance of enthusiasm and believing in mathematics. (1:38:47) Mimicry and direct instruction. (1:45:05)