Posted by: Alexandre Borovik | August 18, 2014

## Educational value of deliberate mistakes

This recent story, Confuse Students to Help Them Learn, moved me to re-publish a post from my previous blog.

The Economist (22 Sept 2007), of all journals, published a long obituary of a parrot, Alex the African Grey, who became an ex-parrot on 6 September 2007, aged 31.

Alex the African Grey

The last time Irene Pepperberg saw Alex she said goodnight as usual. “You be good,” said Alex. “I love you.” “I love you, too.” “You’ll be in tomorrow?” “Yes, I’ll be in tomorrow”. But Alex (his name supposedly an acronym of Avial Learning Experiment) died in his cage that night, bringing to end a life spent learning complex tasks that, it had been originally thought, only primates could master.

In 1977, Dr Pepperberg bought a one-year old African Grey parrot at random from a pet shop. Then, for 30 years,

Using a training technique now employed on children with learning difficulties, in which two adults handle and discuss an object, sometimes, making deliberate mistakes, Dr Pepperberg and her collaborators at the University of Arisona began teaching Alex how to describe things, how to make his desires known and even how to ask questions.

And these are the key words which attracted my attention: making deliberate mistakes! In learning mathematics, detecting and correcting other people’s mistakes is a crucial but badly underrated component. We do not give our students a chance to analyse, criticise and correct each others’ work, and we do not reward them for detecting an error. Not surprisingly, our students’ progress is frequently less impressive than that of Alex:

By the end, said Dr Pepperberg, Alex … had a vocabulary of 150 words. He knew the names of 50 objects and could, in addition, describe their colours, shapes and the materials they were made from. He could answer questions about objects’ properties, even when he had not seen that particular combination of properties before. He could ask for things – and reject a proffered item and ask again if it was not what he wanted. He understood, and could discuss, the concepts of “bigger,” “smaller,” “same” and “different”. And he could count up to six, including the number zero.

Research publications on Alex:

Pepperberg, I.M., and Gordon, J.D. (2005). Number Comprehension by a Grey Parrot (Psittacus erithacus), Including a Zero-Like Concept. J. Comp. Psych, 2005, Vol. 119, No. 2, 197-209.

Pepperberg, I.M. (2001). Lessons from cognitive ethology: Animal models for ethological computing. Proceedings of the First Conference on Epigenetic Robotics, C. Balkenius, J. Zlatev, H. Kozima, K. Dautenhahn, & C. Breazeal, Eds., Lund University Cognitive Science Series No. 85, Lund, Sweden.

Pepperberg, I.M., Willner, M.R., and Gravitz, L.B. (1997). Development of Piagetian object permanence in a Grey parrot (Psittacus erithacus). J. Comp. Psych. 111:63-75.

[With thanks to Jeff Burdges]

## Responses

1. A reason to have students present work at the board (as in our Euclid course) is that other students may notice mistakes or at least may be more careful to look for them.