Master Yoda chides Luke ” … all his life as he looked away to the horizon, never his mind on where he was … what he was doing … ”
Mindfulness is indeed a critical personal trait well worth instilling in our little padawans. But is mindfulness always on the beneficial end of the balance in the learning and doing of Mathematics? I contend that there is a time to let go … and trust the math, and that failing to do so can lead to … anxiety. And anxiety can lead to suffering. Indeed, there are strong empirical reasons to believe so, and that to think that some of today’s received wisdom about teaching math, seeking a sort of mindfulness, may result instead in unnecessary difficulty, incapacity — even hamper the intended end of understanding. I will explore some of these dimensions of mindfulness, memory, problem solving and critical thinking in mathematics, considering possible unintended consequences of cognitive-focussed instruction. Perhaps much to learn, you still have …
Rob Craigen holds a BSc. (Math, UBC), MMath (Waterloo), PhD (Pure Math, Waterloo); Director of the Manitoba Mathematical Competion; recipient of the Kirkman Medal (1994) for research in Combinatorics, a field of Pure Mathematics; taught for 26 years at universities in Alberta, California. His His concern for Math education grew out of exposure to the WNCP curriculum as he served for 4 years on the Provincial Math Curriculum Steering Commmittee. With Anna Stokke he cofounded the Western Initiative for Strengthening Education in Mathematics, a response on behalf of the professional mathematics community to changes in mathematics education across Western Canada over the past two decades.
Reputed to have been the largest and most expensive comparative study of teaching interventions in history (not to mention the most ironically-named), Project Follow Through (PFT) was a 10 year longitudinal study, during the 1970s, of the effectiveness of interventions for low-SES students in “communities at risk” across the U.S., comparing the performance of numerous models representing the leading schools of educational thought in that day. The performance of a “dark horse” model in the study surprised many. This is the story of what happened … and what happened afterwards.