My Skinner Moment (updated 2024 reflection)

For a long time I really disliked the whole idea of Skinner's Behaviourism. This was a strong emotional feeling.

I saw behaviourism as drill and practice imposed by an authority figure, a teacher.

I came of age in the late 60s during the anti-Vietnam War movement. A stupendous social change occurred around about 1968. The government introduced their pull a birthday date marble out of a barrel military draft bill to send selected 18 yos to fight the Viet Cong. We began to question everything … racism, capitalism, imperialism, communism, Ho Chi Minh, Mao Tsetung, political power … everything. My friends were either locked up for 18 months for resisting the draft or went into the underground. There were many citizens quite happy to hide them.

Question everything.

With this backdrop do you think it would be likely that I would support a teaching methodology where the authority (the teacher) promoted relentless drill and practice. No way!

I also saw Skinner's absolute refusal to speculate on what happened inside the brain as a huge copout, as some sort of proof of the sterility of his whole approach.

As a methodology behaviourism seemed to symbolise the main thing that was wrong with School and Education. That it was BORING.

So, when I began teaching Maths and Science I followed authors who promoted creativity. An early interest in Science was 'The Act of Creation' by Arthur Koestler. Later, when computers entered education, I discovered the writings and Constructionist philosophy of Seymour Papert.

This history forms an emotional backdrop to this article. The action happened in 1996-97. When I realised that I had drifted into combining logo programming and behaviourist methods successfully in my classroom then it was a real shock, for a while I was in a state of disbelief.

So I had to write about it and theorise it. I'm still theorising it. For me this event was a difficult self reflection, an accomodation, where my view of the world suddenly crashed in the face of reality. This article covers a lot of ground - behaviourism, constructionism, learning maths, how to use computers in school, School with a capital 'S' (the institution of school and it's ingrained ways) and what works for the disadvantaged.

The Disadvantaged school setting:

Paralowie was / is a disadvantaged school in the northern suburbs of Adelaide, Australia ( 549 school card holders out of approx. 1100 students -- 1996 figures ). Although my new composite class was "extended" (representing the top 1/3 in ability at this year level) I didn't think the class was progressing particularly well in the 20 weeks I had taught them for up to the end of Term 3 before I started using the Quadratics software. I have already mentioned the poor skills of a substantial number of students when substituting negative numbers. Eg. substitute -2 into -2x^2 + 3x. Others resented the fact that they had been performing in the top half of their previous class but now were performing in bottom half of their new class. I had several requests from students to return to their previous class because the new work was "too hard". Poor attendance was a problem with about 3 students being away on a good day and up to 8 or 10 being absent on a bad day. Homework effort was poor from many because they had managed to get through with little homework in Years 8 and 9 and at any rate it is not cool to do homework. Moreover, in disadvantaged schools I find that it takes 2 to 3 terms for students to adapt and accept a new teacher and there is a continual behavioural testing out period during this time before things settle down.

THE PLACE OF BEHAVIOURISM IN SCHOOLS

(for instance, in the teaching of Quadratics)
A new reflection, rewritten April 2024

Introduction:

During 1996 and 1997 I wrote my own Quadratics drill and practice software in Logo to assist my teaching of the Quadratics topic to a Year 10 Pure Maths class.

The software was very successful in helping the students learn Quadratics (see companion article for evaluation of the software -- ‘Quadratics Software Evaluation’

Paradoxically, I became uneasy about the success of the software, as I came to realise that I was using Behaviourist methods successfully. My uneasiness came from the fact that as a Logo enthusiast I was committed to a Constructionist educationally philosophy which is way down the other end of the spectrum of teaching methodologies from where Behaviourism lies. At one point I desperately thought to myself, "I have become Skinner, is there any way out?"

My uneasiness led to further study and reflection of the nature of behaviourism, constructionism and school -- this is the resultant synthesis of my dilemma.

What is Behaviourism and what is it good for ?

Behaviourism is the idea that rewards strengthen certain behaviours. That is correct as far as it goes. But behaviourism has never explained how brains learn new ideas . On page 75 of ‘Society of Mind’, Minsky says:-

"Harvard psychologist B.F. Skinner ... recognised that higher animals did indeed exhibit new forms of behaviour, which he called 'operants.' Skinner's experiments confirmed that when a certain operant is followed by a reward, it is likely to reappear more frequently on later occasions. ... this kind of learning has much larger effects if the animal cannot predict when it will be rewarded. ....Skinner's discoveries had a wide influence in psychology and education, but never led to explaining how brains produce new operants ..... Those twin ideas - reward/success and punish/failure - do not explain enough about how people learn to produce the new ideas that enable them to solve difficult problems that could not otherwise be solved ..."

So behaviourist methods, like a computer drill and practice program, may work well for a prepackaged curricula, which is the norm in senior maths courses. I'll use the teaching of Quadratics at Year 10 level as an example of what I mean.

Does School have a mind of its own? Is quadratics real maths!

Seymour Papert (1993) talks about how School assimilates the computer to do things according to how School has traditionally done them, as though School is an independent organism with it own set rules, procedures and homeostasis. How does School manage to achieve this, using this case as an example?

1. By putting Quadratics into the Curriculum. Who ever questions that?
2. By buying maths textbooks with lots of Quadratics in them. Invariably these textbooks break down the complex topic of quadratics into small parts and then relentlessly drill the students in practising those parts until "understanding" is reached.
3. By telling students they have to do Pure Maths in Year 11 to obtain certain desired for academic and career pathways.
4. By creating a pre-Pure Maths extended class in Year 10 for the top group to prepare them for the "very important" Year 11 Pure Maths class.

This raises a big question which is hardly ever asked: Is learning Quadratics in this way, real maths, anyway? Well, clearly Quadratics is in the Curriculum because it is pregnant with maths skills. There are number skills of substitution and calculation (BEDMAS), there is graphing using the Cartesian co-ordinates, there is looking for the change in patterns as the 'a', 'b' and 'c' values vary. There is derivation of formula, like Axis of symmetry = -b / 2a. Then we have square roots, unreal numbers, the full quadratic formula ... there is even Halley's comet, parabolic reflectors and chucking a ball up in the air, not to forget "problem solving" ...... what a list. Clearly, no respectable maths teacher or School would take Quadratics out of the Curriculum !!

That is the case for Quadratics in the maths curriculum. Are you convinced?

But, is quadratics the sort of maths we really need in schools?

Papert argues (Mindstorms, Ch 2 Mathophobia) that school maths in general quadratics in particular are in schools largely for historical reasons that have now passed us by. School math does not fit well with the natural ways that children learn and so becomes a series of not fun hurdles which become harder and harder to jump.

In Papert’s view, Quadratics became important for School maths because it fitted into pencil and paper technologies which were the best ones available when the traditional Curriculum was formulated.

“As I see it, a major factor that determined what mathematics went into school math was what could be done in the setting of school classrooms with the primitive technology of pencil and paper. For example, children can draw graphs with pencil and paper. So it was decided to let children draw many graphs… As a result every educated person vaguely remembers that y = x^2 is the equation of a parabola. And although most parents have very little idea of why anyone should know this, they become indignant when their children do not. They assume that there must be a profound and objective reason known to those who better understand these things.”
- Mindstorms p. 52

Seymour’s main response to this was to create a Mathland where learning maths fitted more into children’s natural ways of learning. The first thing he put into his Mathland was turtle graphics / Logo. His broader agenda was to invent children’s maths with the following design criteria:

• appropriability principle … the serious maths of space, movement and repetition is appropriable to children
• continuity principle … with well established personal knowledge
• power principle… empower students to create personally meaningful projects
• principle of cultural resonance …the topic makes sense in a larger social context to children and adults

I have come to believe that the maths we need in schools involves self directed exploration, creating ones own projects, play and problem finding as well as problem solving. The problem with the current maths learning environment in secondary schools is that it is very strong on teaching maths skills but very weak in creating learning environments where students will come to enjoy maths and become self motivated in learning it.

So there is the case against quadratics. Are you convinced?

Alienation and social sorting:-

Not one student asked me, "Why do we have to do Quadratics?" or "How do they relate to real life?" questions that I would have found very difficult to answer. However, many students did say (and some more than once), "the work in this class is too hard, I want to go back to my other (not extended) class". This put a lot of pressure on me as the teacher. I was trying to set and maintain a higher standard of work to prepare students for Year 11 Pure Maths. But if I pushed to hard I would have students coming to me and asking to be moved out to an "easier" class. The losers in this process were the advanced section of the class who in effect were being held back by the tail. All of these problems were substantially overcome shortly after I introduced my quadratics software.

One of the social functions of Schooling is to condition the clients for their role and social niche in later life. Maths with its traditional emphasis on sacred knowledge (like Quadratics) and marks is particularly well suited for this. I can see these forces at work in the student responses in the previous paragraph. There was a passive acceptance of the right of School to put the Quadratics hurdle in place. The advanced element of the class believed they could jump this hurdle and were comfortable with that. The less skilled and motivated members of the class had strong doubts about their ability to jump the hurdle and tried to organise a soft option. Even though many students at Disadvantaged schools may reject School ("school sux") with varying degrees of hostility it does not seem there is significant group consciously rejecting the right of School to make fundamental judgements about their future social niche in life.

My Quadratics software resolved some of these problems for students by making it easier or perhaps more interesting to jump the hurdle. But in the process it begs the question of what School maths ought to look like this in the first place.

Student needs and Teacher deeds:-

The software seemed to meet the needs of many students in a Disadvantaged school who want to do well in a preparatory Pure Maths class at Year 10 level. Hurdles were jumped by many who without the software would have failed to jump them.

Although my own teaching mode is constructionist by preference I find that in Disadvantaged schools a fair bit of repetitive drill and skill is required anyway, more so than what is required in a middle class school. Otherwise students simply forget basic concepts. At any rate a balance between constructionist exploration and drill & skill is always required. In My Opinion.

Back then, the leading advocate of Computer Aided Instruction (CAI) in the USA was Patrick Suppes. I was helped by Papert's non dogmatic appreciation of what Suppes was trying to achieve, as expressed in 'The Children's Machine':-

"The concept of CAI, for which Suppe's original work was the seminal model, has been criticised as using the computer as an expensive set of flash cards. Nothing could be further from Suppe's intention than any idea of mere repetitive rote. His theoretical approach had persuaded him that a correct theory of learning would allow the computer to generate, in a way that no set of flash cards could imitate, an optimal sequence of presentations based on the past history of the individual learner. At the same time the children's responses would provide significant data for the further development of the theory of learning. This was serious high science." (164)

Papert goes onto explore his reasons for rejecting Suppes approach which is an argument that Relationship is more central to how our minds develop rather than Logic. See Ch. 8 'Computerists' of 'The Children's Machine' for the full argument. Also I’ve added a footnote on Minsky’s view of the limits of logical thinking.

I then turned to Cynthia Solomon who has documented Suppes work in greater detail and discovered something that was very interesting. Computer based drill and practice programs (developed to a fine art by Suppes) do work and in particular they work best for disadvantaged students and schools! These programs do not work as well for middle class students! (Solomon, pp. 22 & 27).

I interpret the finding by Suppes, as reported by Solomon, that CAI drill and practice assists the Disadvantaged but not the middle class students in this way:-

1. Middle class kids would be more likely to do their homework (put in the time at home to generate a significant number of parabolas so that the patterns would start to make sense) and so would not need the quick fix provided by a quadratics software program, so much.
2. Middle class kids question the system of School but are more likely to stay and perform within it.

Disadvantaged kids are more likely to question the system, reject it and drop out of it, either physically or mentally.

Almost 3 decades later: still trying to resolve this dilemma!

To restate the dilemma -- I didn't like behaviourist approaches but I worked hard to make one work and it worked well!

After this experience I didn’t abandon the Constructionist approach. But I did begin to study other learning theories seriously as well. The list is long so I won’t go into all that here.

My initial response was to take this sort of position: There are different methods of teaching which range along a spectrum from Constructionist to Instructionist. What a good teacher does is walk the walk along this continuum, knowing when to employ each method.

My Skinner moment persisted, as did my Papert moment.

Another way to look at it is that the learning environment rules. At Paralowie I was lucky to have a Principal, Pat Thomson, who understood the benefits of setting up teachers in classroom environments that they wanted. I was setup in a room with old XT computers that no one else wanted and ran the logo on 3.5 inch floppy discs. 1990s nirvana, for me.

Later when that Principal left that room was transformed and I was thrown into a different arrangement. In short, I diversified. I had no real choice.

Later still, as a late career thing, I decided to focus on working with aboriginal students, the most disadvantaged cohort in Australia. With that group I have tried different variation of Direct Instruction. I think the evidence shows that is needed. This is another can of worms that would take too long to discuss here.

Still later, I have recently discovered Diana Laurillard’s The Conversational Framework (reference) which I think successfully integrates a wide spectrum of learning theories. I will publish on that theory shortly.

Finally, Conrad Wolfram also sees the need for a radical reform of the Maths curriculum ('The Maths Fix' (2020)). The debate goes on.

References:-

Laurillard, Diana. The significance of Constructionism as a distinctive pedagogy. Proceedings of the 2020 Constructionism Conference (free download). The University of Dublin, Trinity College Dublin, IRELAND
Minsky, Marvin. The Society of Mind. Picador 1987
Papert, Seymour. Mindstorms: Children, Computers and Powerful Ideas (1980)
Papert, Seymour. The Children's Machine: Rethinking School in the Age of the Computer, 1993, Basic Books
Solomon, Cynthia. Computer Environments for Children: A Reflection on Theories of Learning and Education, 1986, The MIT Press, Cambridge, Massachusetts

Footnote:

Minsky (1987) defines logical thinking as follows:-

"The popular but unsound theory that much of human reasoning proceeds in accord with clear cut rules that lead to foolproof conclusions. In my view, we employ logical reasoning only in special forms of adult thought, which are used mainly to summarise what has already been discovered. Most of our ordinary mental work -- that is, our commonsense reasoning -- is based more on 'thinking by analogy' -- that is, applying to our present circumstances our representations of seemingly previous experiences." (329)