Thinking with Experts

The title of this post is identical to the title of a chapter in new book by Annie Murphy Paul with some new ideas and data. The subtitle is The Power of Thinking Outside the Brain.

Cognitive apprenticeship is a term coined by Allan Collins, a professor emeritus of education at Northwestern University. Ms. Paul writes, “In a 1991 article written with John Seely Brown and Ann Holum, Collins noted a crucial difference between traditional apprenticeships and modern schooling: in the former, ‘learners can see the processes at work,’ while in the latter, ‘the processes of thinking are often invisible to the students and the teacher.’ Collins and his coauthors identified four features of apprenticeship that could be adapted to the demands of knowledge work: modeling, or demonstrating the task while explaining it aloud; scaffolding, or structuring an opportunity for the learner to try the task herself; fading, or gradually withdrawing guidance as the learner becomes more proficient; and coaching, or helping the learner through difficulties along the way.

Christoph Kreitz and his colleagues incorporated these features of traditional apprenticeships into their course redesign, reducing the amount of time students spent in lectures and increasing the length and frequency of small-group sessions led by tutors. In these sessions, students didn’t listen to a description of computer science concepts, or engage in a discussion about the work performed by computer scientists; they actually did the work themselves, under the tutor’s close supervision. The results of these changes were dramatic: the proportion of students failing the course shrank from above 60% to less than 10%.

The kind of shift Kreitz and his colleagues made at Potsdam is one that many of us will contemplate in coming years. All over the world, in every sector and specialty education and work are less about executing concrete tasks and more and more about engaging in internal thought processes. As Allan Collins observed, these processes are largely inaccessible in both novice and expert: the novice doesn’t yet know the material well enough, while the expert knows it so well that it has become second nature. This reality means that if we are to extend our thinking with others’ expertise, we must find better ways of effecting an accurate transfer of knowledge from one mind to another.”

Ms. Paul writes, “… reenacting the experience of being a novice need not be so literal; experts can generate empathy for the beginner through acts of the imagination, changing the way they present information accordingly. An example: experts habitually engage in ‘chunking,’ or compressing several tasks into one mental unit. This frees up space in the expert’s working memory, but it often baffles the novice for whom each step is new and still imperfectly understood. A math teacher may speed through an explanation of long division, not remembering or recognizing that the procedures that now seem so obvious to him were once utterly inscrutable. Math education expert John Mighton has a suggestion: break it down into steps, then break it down again—into micro-steps if necessary.

Though Mighton now holds a PhD in mathematics he struggled with math as a child. He succeeded by teaching himself how to advance one tiny move at a time—the method he advocates as the founder of a nonprofit educational organization, JUMP Math (the name stands for Junior Undiscovered Math Prodigies). When instructors make their expertise legible during the introduction, learners are able to master one small step, then another, and another, acquiring a solid understanding and gaining confidence as they go. The approach has allowed many JUMP participants, including some who struggled to grasp the most basic mathematical concepts in school, to achieve proficiency in the subject. An evaluation of the JUMP program, conducted by researchers from the University of Toronto and Toronto’s Hospital for Sick Children and published in 2019, provides support for Mighton’s method. By the second year of the study, JUMP students in grade three had made greater progress in problem solving, and JUMP students in grade six had made greater gains across a broad range of mathematical skills—calculations math fluency, and applied problems—than those who received traditional instruction.”