The gears of my childhood, again!

Lessons from the Gear Thinkers

I’ve been rereading Seymour Papert's Mindstorms. I thought I had understood it. But I needed the update. Recently, I’ve been part of a curriculum reform which overall has created waves. This was partly because of leadership errors (a mix of good and bad interventions) and partly because middle class parents complain when Schools depart from traditional structures.

Whilst I was writing my interpretation (here) of “The Gears of My Childhood” (Preface to Mindstorms) I discovered a bunch of other interpretations in Meaningful Making book 3 (free download!). Some of them I thought enhanced my interpretation of the "Gears" article. I’ll quote some extracts. Hopefully, this might encourage some to read the originals. Even though my main goal is to clarify my own thinking about what to learn from Seymour’s gears reflection.

Gears of Learning by Ridhi Aggarwal, p. 10

Children should be given the opportunity to explore their questions like babies explore the world around them ...

Children would learn by doing only when they make things that are answers to their own questions. Based on this idea, we started a Question Hour in which children could just share their daily curiosities about anything and everything. They raised questions and discussed possibilities, and then they explored the ideas by making things.

Papert reloaded by Federica Selleri, p. 14

As Papert said, we need to create and take care of the conditions in which the learning process takes place, because the creation of cognitive models is closely linked to the experience associated with them.

Therefore, it is important to pay particular attention to the context in which the experience takes place, and to design it in such a way that it can be about generating ideas and not about running into obstacles. This means thinking about the tools you want students to use, and trying them out for yourself to evaluate their possibilities, but listening to the students’ hypothesis about how things work and supporting their investigations.

What makes a project meaningful? by Lina Cannone, p. 16

I believe that a synergy between teacher and learner must be nurtured. We must abandon pre-planned activities and projects that ignore the participation of the learner. We must give way to the co-planning of activities

Finding my Gear at Twenty-Three by Nadine Abu Tuhaimer, p. 21

After graduation, I realized that my love for tinkering with objects outshined my love for programming,

At 24, I decided to take the “Fab Academy – How to Make Almost Anything” course. This is a six month long intensive program that teaches the principles of digital fabrication

Since then, I’ve been teaching in the Fab Academy program and trying to incorporate what I learned with the different educational programs I run at the Fab Lab where I work, the first Fab Lab in Jordan.

Making means heads and heart, not just hands by Lior Schenk, p. 22

Car child did not become car professional — he became a mathematician. He also became a cyberneticist and renowned learning theorist, responsible for both the 1:1 computing initiatives and the constructionist movements rippling across education to this day.

Gears were, he describes, “both abstract and sensory,” acting as “a transitional object” connecting the formal knowledge of mathematics and the body knowledge of the child.

This notion of knowing — what it means to know something, to learn, to develop knowledge formed the central thesis of Papert’s career. Knowledge is not merely absorbed through cognitive assimilation, but actively constructed through affective components as well. Papert would assert, in other words, that we learn best when we are actively engaged in constructing things in the world. Real, tangible things. Things you can hold, manipulate, and feel in order to make sense of them.

Papert’s successes, as he would ascribe, were not due to interacting with gears as objects — rather due to falling in love with the gears as more than objects, as a conduit across intellectual and emotional worlds.

As Dr. Humerto Maturana said, “Love, allowing the other to be a legitimate other, is the only emotion that expands intelligence.”

Time to Tinker by Lars Beck Johannsen, p. 28

I believe that we need to help our students discover their own gears, and help them channel it into their projects whenever possible. I also believe that it is a teacher’s task to help students develop new gears. Another task is being aware of the way you learn. If something is easy to you, it is natural to believe that it is also easy for everyone else, but that is not the case. We need to help our kids to discover their strengths!

There are a few things that could make this happen. One is knowing your students! Not just on a factual basis but also on a more personal basis. How would you otherwise discover, what makes them tick, what they love, who they are?

I strongly urge all the schools I work with to make time for more project based, constructionist, student-centered learning. The after-school programs, which most kids attend because the parents are working, also need to be a more inspiring place to spend your time. A place to tinker, do what you love, make stuff together with other kids, and have fun!

Between the garage and the electronics workshop, by Mouhamadou Ngom, p. 33

To conclude, I would say that the most important part of learning by doing is careful observation. My secret as a specialist in electro-mechanics is to take careful notes. For example, before disassembling a mechanism, I mark the intersections between the different gears. This is why I ask learners to observe well, to listen well, and to document their work.

Find your unique gear by Xiaoling Zhang, p.35

Dr. Papert’s experience makes me think that it might be a natural human instinct to love fiddling with objects as a prompt to explore the world around us. By building and playing with things, we are also building the connections between ourselves and the physical world. When it happens frequently and reliably, then it becomes a way of thinking. It makes it easier when we see consistency in the world to believe that there are laws behind seemingly superficial phenomena and to discover even more possibilities.

… every child or every person has their own unique “gear.” But can everyone find their gear? Or can we help them to find something that THEY love and can be applied as a bridge to understand more abstract ideas and the world. It seems that unique gear can’t be cloned or taught, but must be discovered

SUMMING UP, the lesson from the Gear Thinkers:

• Children should be given the opportunity to explore their questions
• We must give way to the co-planning of activities
• Listen to your students; pay attention to detail
• Be a trail blazer! Setup the first FabLab in your location
• Knowledge is actively constructed using hands, head and heart
• Love is essential for optimal knowledge growth (of the objects we work with as well as human-human)
• Know your students, personally
• Everyone has to find their own gear. They might need help with this
• Observe everything carefully

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)

Quadratics software evaluation

This was originally written in 1996. I also wrote an accompanying reflection at the time which I now think needs to be updated. So, I'm republishing this one with my new reflection, which is titled, "My Skinner Moment"

Paralowie R12 School
November 1996

I don't like drill and practice but it works, for some things

This year while teaching a Year 10 maths class I programmed my own Quadratics software in logo for student use.

The impact on the class was immediate and positive. Many students in the class had previously been bogged down in substituting negative numbers into quadratic expressions and getting nowhere fast. Suddenly, for them, things began to fall into place. Freed from the requirements of doing many rapid substitutions and calculations (generate table of values, draw graph, then start looking for patterns) they were suddenly able to see the relationship between the 'a', 'b' and 'c' values and the variation in shape of the parabolic curve. Rather than having to concentrate on the computation they could begin to concentrate on the patterns. By the 'a', 'b' and 'c' values I mean the values in this equation:- y = ax² + bx + c and how changing 'a', 'b' and 'c' will effect the parabolic curve.

I was so encouraged by this turn-around that I began to burn the midnight oil adding extra features to my software. This was an interactive process because I was perceiving students needs in lesson time and changing the software at night to meet those needs.

I hadn't anticipated that so many students in this "extended" class would have major difficulties with "basic" skills that "should" have been mastered in Years 8 and 9. Yet when I presented students with an equation like:-
y = 2x² - x + 3
and asked them to substitute x = -2 into it, then the success rate was not too high! So, one feature I added to my software was a drill and practice substitution into a quadratic equation. Students were given 'a', 'b' and 'c' values and an x value to substitute and required to calculate the value of the function, or the y value.

For example:
y = ax² + bx + c
if a = -1 b = 2 c = 3 and x = -1 then what is y ?

I found that the software released me from "lecture mode" and I was able to use much more time meeting some urgent needs of individual students while the others were happily occupied with the program. I could spend substantial slabs of time with a handful of students who really did need quite a lot of help. I could feel the mood changing in the class. Equations and parabolic graphs could be generated in seconds rather than many minutes. The students were able to concentrate on the structure of the parabola and how it was effected by changing a, b and c values without being tormented by their low skill level (in quite a few cases) in calculating the substitutions required to draw the curve. I did receive a lot of spontaneous positive feedback from students about the usefulness of the software.

Another thing I noticed was that the more able students in the class quickly mastered the program. They accepted it as a challenge to be quickly mastered and did just that. Then some of them would boast about it, "too easy sir", comments like that.

So, I began to add more advanced features to my program, to extend the advanced element further, to push out the leading edge. How do you find the axis of symmetry in all cases? How do you find the y value at the turning point? How do you find the x intercepts in certain specialised cases? We have not yet got to the stage of doing the full quadratic formula (that is part of the Year 11 Pure Maths course) but with the aid of my software I was fast approaching that point with the advanced element of the class. The leading edge was being extended, visibly.

So my program was catering for the needs of students across the whole ability range. It could do that because I was writing it and rewriting it on a weekly basis. I see that as a major advantage over a commercial product.

Some students were thrown in their pencil and paper work when the quadratic had a large 'b' value and they had mapped out a table of x values from +3 to -3 and the axis of symmetry might lie on the edge or outside of this domain. Lacking any knowledge of the overall structure of the curve (importance of axis of symmetry and turning point) their performance in mapping the correct graph was poor in quite a few cases.

My understanding and appreciation of this problem and other nuances of quadratics increased dramatically in the course of writing the software. For instance, initially I made the program draw the parabola by starting at one end and drawing to the other end. This created all sorts of problems at the limits because as the equation changed so did the limits. The effect was that some of my curves did not even begin to be drawn, I couldn't keep them on the screen. I eventually solved this frustrating problem by starting to draw the curve at the turning point of the parabola, drawing one side to the outer limits, then jumping back to the turning point and drawing the other side. This problem solving process reinforced in my own mind the central importance of axis of symmetry and turning point in the teaching of quadratics. The mechanical plotting of x values between +3 and -3 often just does not work in the case of quadratics with large 'b' values because the axis of symmetry has moved so far to the right or left.

All the signs of a class being turned around from just battling through to success were there to see. Students became more engaged in the tasks, they asked many more questions than previously, you could visibly see the confidence of many students increase, they became more animated and more positive in their relationship with mathematics and the teacher. Moreover, I felt that I could set more difficult and challenging questions in the program and subsequent tests than I would not otherwise have been able to do.

Looking in my marks book I can see that at least 7 students out of 27 have turned their results around from failing badly to pass marks and in some cases highly successful marks. I'll cite some statistics from my marks book to try to convince, you, the reader (who wasn't in the room to see the change) that a very significant turn around did occur. The Quadratics unit was a 6 week block. I did not use the computer software for the first two and a half weeks because I had not finalised it. In that first two and a half weeks I was mainly using lecture, textbook and homework mode. I also used one interesting activity from MCTP (Algebra Walk, pp. 213-18). In the third week I tested the students only on their ability to substitute values into an equation (two quadratics and one straight line) and plot the graph (first test). The results were poor, average class mark was 56%. I then introduced the Quadratic software and used it extensively for the next 3 weeks. In week 6 I tested the students twice. For test 2 they had to plot a quadratic again and also make predictions from other quadratic formulae about how altering 'a', 'b' and 'c' values would affect the y intercept, axis of symmetry and whether the curve was upright or upside down. This time the average mark for test 2 was 82%, a remarkable improvement over the first test.

For the final test (test 3) I offered students a choice - either do a pencil and paper version or a computer version. Nearly all students opted to practice for the test on the computer and 11 out of 27 choose to do their final test on the computer. One interesting aspect of this was that the computer test was set up for mastery learning. If a student got a question wrong they were invited to try again. They couldn't proceed to the next question until they got the previous one correct. Initially I had programmed it differently, that if a student gave a wrong answer, they got a "no" message and then the problem just disappeared and the next question appeared on the screen. However, when I was doing the test myself, I found this feature incredibly annoying, that when I got the wrong answer, I didn't have the opportunity to try again or to reflect on my mistake in any way. So I changed it. If the technology makes it easy then it seems silly not to use it.

So, conceptually, the final testing process for students who opted for the computer version was very different. They were being continually informed of their progress score as they went along. If they got a wrong answer they were required to persist until they got it right. In their final score this appeared as a larger denominator. If they did the test and didn't like their progress, they had the option of starting over again if time permitted. The program simply generated different questions (of the same type) each time it was run, so it was no difficulty for me to offer multiple chances for retesting.

There was some interesting discussion at the end by students about their reasons for which type of test they chose. Some high ability students said they found practising on the computer very useful but clearly saw it as risky to do their final test on the computer, given their established mastery of the pencil and paper medium. Other high ability students were confident enough to take that risk. Other students said they found it easier to solve the problems on the computer. Some made comments like "its faster". This was interesting because the same problems (actually the computer test had a greater variety of problems) were being set in both mediums but many students clearly felt that it felt very different and expressed preference for one over the other. Another factor was that doing the computer test was more public, less private. The room is set up with the computers around the walls so that all computer screens face towards the centre of the room. This made "collaboration" easier ("cheating") but also made mistakes more public.

A comparison between the final test results was also interesting. I offered 3 tests in total over 6 weeks of instruction (12 * 100 minute lessons), the first two tests were pencil and paper only but in the last test students were offered a choice (either computer or pencil and paper). Mainly due to high absenteeism only 17 out of the 27 class members sat for all 3 tests. Fortunately for the last test (test 3), this group of seventeen split themselves into roughly two equal groups, one group of 8 who chose to do the computer test, the other group of 9 who chose to do the paper and pencil test. For the previous two tests (tests 1 and 2) the percentage results of these two groups was roughly the same (71% versus 68% average). But for the final test (test 3) the group who chose the computer test scored an average of 95% compared with 68% for the pencil and paper group. Quite a difference !

I have explained above that the two tests were not really comparable (even though the questions were of the same type) because the computer based test provided instant feedback and monitored progress. Once again I would argue that it would be ridiculous not to incorporate these features into the computer program since they greatly assist in keeping students focused and motivated. This introduces formative elements into a summative test, which from a learning viewpoint is surely a good thing.

Here is an example of how students who did the pencil and paper test were disadvantaged. One question asked for the 'a', 'b' and 'c' values of this quadratic:
y = x² - 4

Two of the top students (averages in mid 90's for first two tests) in the class got confused on this question and made this elementary mistake:-
a = 1 (correct)
b = -4 (wrong, the answer is b = 0)
c = 0 (wrong, the answer is c = -4)

Since they made this mistake they also got wrong the y intercept, axis of symmetry and y value at turning point, losing 5 marks in total.

If they had been doing the computer test then they would have received instant feedback on their first error, b = -4, and would have easily corrected it (being in the high ability range), resulting in the loss of only 1 mark.

The program at this stage has these features as displayed in the main menu:-

• Practice number skills
• Vary 'a' value
• Vary 'b' value
• Vary 'c' value
• Do my own graph
• Work out the axis of symmetry
• Test
• Solve y = ax² - c
• Solve y = ax² + bx
• Solve y = (dx + e)(fx + g)

Final evaluation by students:-

I prepared a final evaluation sheet for students seeking their opinion of how they had learnt about quadratics. Twenty students successfully completed the final evaluation sheet. I asked them to evaluate 8 possible modes of learning according to this scale:-

1 = helped lots
2 = helped a fair bit
3 = helped a little bit
4 = didn't help at all

When I totalled the results the Quadratics software program came out on the top of the list: 10 students wrote that it helped lots, 8 said helped a fair bit, 2 said helped a little bit and none said that it didn't help at all.

"Indicate how much each of the following helped you learn Quadratics using this code. Write a number next to each statement below."

32 Quadratics software program
35 My own efforts in class
37 Help from friends, class mates
42 Help from teacher, one to one
49 Teacher explaining in front of the class
50 Doing lots of homework
54 Working through the textbook
71 Help from parents or other adults outside the class (eg. tutor)

APPENDIX: THE TESTS

Test 1 (end of week 3):

Average class mark = 56%

Plot these 3 graphs on the same set of axes. Show tables of values:-

y = 3x - 4
y = x² + 4x
y = -2x² + 2x - 1


Test 2 (week 6):

Average class mark = 82%

y = 2x² + 4x + 1
Find y when x = 1
What is the y intercept?
Calculate the axis of symmetry (Hint: AS = -b / 2a)
Is the graph upright or upside down?

y = x² - 2x - 3
Find y when x = 3
What is the y intercept ?
What is the axis of symmetry?

y = -0.5x² + x
Find y when x = -2
What is the y intercept?
Calculate the axis of symmetry.
Is the graph upright or upside down?

y = x² - 2x - 3
Calculate a table of values, eg. x = +3 to -3
Draw axes, plot the graph
What is the y intercept ?
Draw in the axis of symmetry.
Work out the x and y values at the turning point.
What are the x intercepts ? (there are two of them).

Test 3 (week 6) pencil and paper version.

Average mark for those who chose this test = 68%
Average mark for those who chose comparable computer test = 95%

y = -2x² + 2x + 1
x = -2
Calculate the y value

y = 3x² - x - 2
x = -1 Calculate the y value.
a = 2, b = 2, c = 0
Find the axis of symmetry.
a = -2, b = 4, c = 3

Find the axis of symmetry

y = x² - 4
Find the a, b and c values
Find the y intercept
Find the axis of symmetry
Find the y value at the turning point
Find the x intercepts

y = 2x² + 4x
Find the a, b and c values
Find the y intercept
Find the axis of symmetry
Find the y value at the turning point
Find the x intercepts

y = (x + 3)(x - 2)
Find the x intercepts
Then expand the brackets using FOIL and
Find the a, b and c values
Find the y intercept
Find the axis of symmetry
Find the y value at the turning point

Seymour Papert: The Gears of my Childhood

Original: The Gears of my Childhood

How can we restructure maths to make it more lovable and learnable!? What would success look like?

Seymour covers a lot of ground brilliantly in his 4 page Preface to Mindstorms! His personal learning story which then morphs into a pathway to universal powerful, learning opportunities

He traces his personal learning journey from early childhood when he played around with car gears in the back shed. Seymour fell in LOVE with the gears. He found “particular pleasure” in the differential gear due to its complexity, “the motion in the transmission shaft can be distributed in many different ways to the two wheels depending on what resistance they encounter”. He argues that this love affair became a vehicle for him to later on master school maths. “I clearly remember two examples from school maths. I saw multiplication tables as gears, and my first brush with equations in two variables (eg. 3x + 4y = 10) immediately evoked the differential.”

Another CRUCIAL piece of information about the gears. Good learning materials have a dual nature. They can carry both advanced maths ideas AND sensory motor ‘body knowledge’. You can be the gear.

So far, this is a story of one person’s unique pathway to maths mastery. But not everyone will fall in love with gears:

“One day I was surprised to discover that some adults – even most adults – did not understand or even care about the magic of the gears”

This led him to think:

“How could what was so simple for me be incomprehensible to other people?”

Seymour’s reflection on this question is revealing. He rejected the viewpoint of his proud father that he was clever because he knew people who could do other things he found hard who didn’t understand the differential.

But it slowly led him to what he still sees as the fundamental fact about learning: “Anything is easy if you can assimilate it to your collection of models. If you can’t, anything can be painfully difficult.”

This leads to further questions for educators: How can we create conditions where learners develop useful mental models? How do intellectual structures grow out of one another?

Having a physical manifestation helps here – be it a floor turtle, a Robocup competition vehicle made from LEGO or an attractive shape designed in Turtle Art and then 3D printed.

And to repeat: Seymour fell in love with the gears. He stresses that you need love. He gently criticises Piaget here who focused more on the cognitive than affect.

By the way, later the slogan became hard fun. Whether you prefer love, hard fun or play is ok the underlying message is the important thing: if we like it we will persist in learning it.

When computers came along Seymour envisaged that they could play the role for everyone that the gears played for him. His belief is that many more will fall in love with a cleverly constructed computer based learning environment that taps into natural ways of learning. Hence Seymour helped to invent Turtle Graphics. The computer (Protean machine) can take on a thousand different forms. It can be the universal machine for learners to fall in love with. An incredible leap! Profound yes, True? We shall see.

Of course, since the computer can take on a thousand different forms it can also be used in bad ways:

• Computer as universal machine
• Children’s learning machine
• Game playing machine
• School administrative systems
• Surveillance capitalism machine
• Tik Tok trivial and sinister machine
• Some blame social media for the mental health decline in youth (Jonathan Haidt, The Anxious Generation)

Spawner of revolutions …universal communication and computation (internet, smart phone – banned in schools because too distracting for the youth.

Seymour’s optimistic pathway is one amongst many. Creative learning systems are always there but never dominant in society overall.

I understood this part of Seymour’s message, that the turtle is body syntonic and offers an engaging, a path to mathematical abstraction. Logo / Scratch provides students with a far better chance of falling in love with maths.

What I didn’t grasp firmly enough was the embodiment aspect. I did run a LEGO TC logo group for a while in the 80s but drifted off that path because of the logistic / cost factors of establishing that in the curriculum. More recently, I've corrected that error, after reading Gershenfeld's book, Designing Reality.

In our age, where individual data points have taken on more importance how do we measure or evaluate the mental models that Seymour sees as the most fundamental measure of learning new, useful things? This question was unresolved in Seymour’s view:

“If any ‘scientific’ educational psychologist had tried to ‘measure’ the effects (of Seymour’s encounter with gears) he would probably have failed … A ‘pre-’ and ‘post-’ test at age two would have missed them.”

It’s hard to measure mental models! I see that as the most important challenge arising from Seymour’s article:

“Thus the “law of learning” must be about how intellectual structures grow out of one another and about how, in the process, they acquire both logical and emotional forms”

This is the subject of Marvin Minsky’s book Society Of Mind

Bits and Atoms, part one

- Towards a wider walls 21st C Maker Education curriculum pathway
- Wider walls means making the learning accessible to more citizens

Modern Maker Education has a history, philosophy, theory, practice and methods all of which have been dynamically developed over the past 50 years (refer Stager's book). This article outlines how to set it up and make it work in a big picture framework. The main aim is to provide a guide to teachers and school administrations interested in this pathway.

THE SPACE and MATERIALS

Paulo Blikstein argues the case for a dedicated Maker Space, aka Fab Lab:

“… after having conducted tens of robotics and invention workshops in schools, I was disappointed by the fact that students did not have a place to continue and deepen their projects – and projects would die after the workshop or the final expo. Schools manifest how they value a particular activity by building a space for it. If sports are important, schools build a gym and a basketball court. If music education is in demand, schools set up music rooms. Only then can like minded students gather together, hang out, do projects, talk about them, and create a productive subculture in schools. Unfortunately, I realized that there was no such space for engineering and invention. Even when schools had robotics labs, they were highly gender-biased and not inviting for most students. Robotics labs and science labs were not disruptive spaces anymore. Therefore in 2008 I started to work with schools around the world to establish digital fabrication labs – the FabLab@School project was born”
- Paulo Blikstein. The Democratisation of Invention (2013)

To setup a Fab Learn Lab or Maker Space we need a dedicated space, equipped with the right furniture, tools and storage. The room needs to be spacious with movable furniture. Beginning materials could be lots of cardboard, computers, 3D printers, microcontrollers and an equipment trolley. This is where my school's current maker space is at, including five Prusa 3D printers. Over time, the plan is to progressively expand into a full Fab Learn Lab with 5 types of machines (laser cutter, 3D printers, CNC routers, vinyl cutter and digital embroidery).

Much of the software is Free or Open Source (FOSS): MakeCode, Tinkercad, Prusa Slicer (if you have Prusa 3D printers), Scratch, Turtle Art … feel free to add to this list

THE THREE BETTERS: some materials are better for great learning

Harel and Papert (1990) argue that some materials are better with regard to the following criteria:

• appropriability (some things lend themselves better than others to being made one's own)
• evocativeness (some materials are more apt than others to precipitate personal thought)
• integration (some materials are better carriers of multiple meaning and multiple concepts)

This was said in connection with Idit Harel’s “Instructional Software Design Project”: a cross age tutoring project in which older students developed screens, using Logo, of fraction puzzles for younger student to solve. The better materials in this case being the learning design, computers and logo (an earlier version of Scratch). Of course, things have changed enormously since 1990. The atoms and bits are cheaper, better and more integrated than before. I argue that 21stC Maker Education is a modern embodiment of this educational philosophy. The materials outlined in this article are still better for achieving appropriability, evocativeness and integration than other materials.

THE HUMMING HOUSE METAPHOR

“low floor, wide walls, high ceiling, open windows”

This metaphor has been used as a descriptor for Scratch but it equally applies to a well constructed Maker Education curriculum. To explain:

• Low floor: develop an interesting project in 10 minutes, easily done using Scratch v3;
• Wide walls: Many diverse multimedia project pathways into any curriculum area and connections between software and hardware are available.
• High ceiling: In Scratch the priority has been on the wider walls but certainly the high ceiling (the ability to develop complex projects) is there as well. And there is a spin off from Scratch called Snap! where the powerful tools are more overt.
• Open windows: Collaboration, search and remix is a feature of the Scratch site, take someone else’s project and modify it

In the trade off between wide walls (project diversity) and high ceiling (project complexity) the emphasis ought to be on the wide walls, for most students. The goal is to get all students working on meaningful projects. A few will go on and master high levels of complexity in their making and coding. That opportunity is there too. (refer Resnick)

CAUTION: MOST CHILDREN ARE NOT HACKERS

Are all students makers in the age of social media? NO!

I have written a separate article about this (refer Kerr, thoughts on an article by Paulo Blikstein and Marcelo Worsley). The central point is that students often need support. If some don’t get it they will feel lost or frustrated. They drift into doing the less demanding parts of a task, eg. painting a project rather than tackling the coding. Without help (sink or swim approach) those who feel uncomfortable in a maker space can become disempowered.

Having recognised this there are different awareness's and strategies that improve the chance of success:

• include tasks that are meaningful to all students
• avoid too much “learn from failure” rhetoric
• find ways to get students out of their comfort zone. Setup collaboration so the lower ability in a pair is the driver)
• be aware that some groups expect to fail (stereotype threat (Cohen, Garcia, Apfel, & Master, 2006) which shows that individuals can perform below their ability level when they suspect that they belong to a group that historically does not do well at a particular activity)

THE PATHWAY

For most students there is lots of new learning involved. Here is a one pathway I have used suitable for Middle School students, say, Years 5 to 9, in my case Year 8s. There are other such introductory pathways, this is just one grape in a potential banquet:

(1) Work in a team to make a cardboard hat, then attach a microbit to code and power a half metre neopixel strip. Since it is a guided project the code will be supplied by the teacher. All groups will be supplied with basic introductory code (change the strip colours by pressing buttons) but then different groups will be shown how to develop more interesting effects (eg. rotating rainbows which respond to sound; neopixel strip lights that change colour one by one by pressing buttons or tilting the hat etc.).

(2) Work in a team to make an art machine. The machine has pegs to hold a couple of pens and is powered by a continuous micro servo (360 degree rotations). Once again the setup code is supplied. Then respond to challenges like: can you make the art machine draw a straight line.

There can be more introductory projects. But after a few like this students are ready to design their own projects.

DESIGN and REDESIGN: imitation, iteration and improvisation

When I trialled this approach recently with year 8s the sort of things they decided to build were a complete exo skeleton, a submarine made from geodesic domes, a sword and scythe weapon set, a mini computer, a dancing cactus and a couple of others.

Motivation was high for some groups:

• One student in the exo skeleton group made a shield at home and brought in DC motors extracted from remote control cars to augment his group's design.
• student in the weapon set group found the code for a flappy bird game and painstakingly copied it out for a microbit on the handle of their sword
• A student in the submarine group reported that she had spent about 10 hours at home making the triangles for her geodesic dome

All of the theories of design talk about the iterative stages of the design process. For example Mitch Resnick gives us this diagram to illustrate the process:

I began with guided design, then invited students to do their own design and then some (not all) of them during the process decided to redesign or improve their original design. I did not overtly teach this process. Rather some of the groups just decided to do it.

You could call this process imitation, iteration and improvisation (Designing Reality, 198). The process invites perseverance and resourcefulness.

I like Austin Kleon’s (“Steal like an Artist”) annotations on Mitch Resnick’s diagram:

TIME BLOCKS

Project based learning works much better with large blocks of continuous time – not one hour lessons but two, three or four hours (with 5 minute or recess / lunch breaks as normal). The difference this makes is remarkable. Some students became so engaged with their projects they were asking to work through their break times! The larger blocks of time enable both increased engagement by students on their projects, including the opportunity to improve their design along the way, and also increased opportunity for the teacher to build positive relationships. We are working as a team to build fun projects. Mitch Resnick’s Lifelong Kindergarten group calls this the 4Ps: Project, Passion, Peers and Play.

DESIGNERS NOTEBOOK

For each session (which varied between 2, 3 or 4 hours length) I told the groups to write out their plan in word and annotated pics at the start of each lesson (and to anticipate possible problems). Towards the end of a session I asked them to record their achievements, problems encountered and solved, who they had helped and who had helped them. So, by the end of the whole process they had a more or less comprehensive record. I also took photos of progress at significant points. One of my assessment goals was "Designers Journal and Teamwork". I think the quality of the journals did often reflect the Planning and Collaboration goals. One group was struggling to bring some disparate parts together into a coherent project. Their patchy journal keeping alerted me to this. On the other hand, some students were poor writers but compensated for this in their verbal presentations and questions to other groups when they presented.

THE ENDPOINT

The goal is for students to build personal or social meaning with engaging objects, microcontrollers and block code.

The end point should be some sort of display of products that have been created, a show and tell. I have seen this work. Teams that have planned their own project, worked hard, struggled with various problems and overcoming them, encouraging each other and then with pride displaying their final product to an audience. This might be on a small or large scale. When done on a large organised scale this is a Maker Faire.

The ultimate guideline in my view is eat your own dogfood! The teacher should also complete their own project, their own version of hard fun.

The experts who began all this have their own longer term, socially transforming goals:

• Neil Gershenfeld: to turn consumers into producers , How to make almost anything
• Adrian Bowyer (RepRap project) - to put the means of production into everyone’s hands

WHAT ARE THE STUDENTS LEARNING?

The students are designing and making artefacts, coding, designing and printing 3D objects, sharing ideas, collaborating and presenting their finished artefacts to an audience.

We can divide this along a constructionist to instructionist spectrum. The making and designing of artefacts was almost entirely student driven. With collaboration I did ask students who their preferred partners were and I set up the teams based on their selections. A couple of students asked to change teams early on and I said yes. With Makecode and Tinkercad (3D design) I did teach some introductory lessons. Particularly with Makecode my teaching was more on the instructionist end of the spectrum. But later on, when it came to completing some Makecode challenges I rearranged the seating and asked the stronger coders to help those who were having problems with it. To explain further would require a separate article.

REFERENCE

Listed in the order they are referenced in the text
Stager, Gary.20 Things to do with a Computer: Future Visions of Education Inspired by Seymour Papert & Cynthia Solomon's Seminal Work(2021)
Paulo Blikstein. The Democratisation of Invention (2013)
Harel, Idit. Software Design for Learning: Children's Construction of Meaning for Fractions in Logo Programming (MIT, June 1988)
Resnick, Mitchel. Designing for Wide Walls. (2020)
Kerr, Bill. Children are not Hackers, thoughts on an article by Paulo Blikstein and Marcelo Worsley.
Resnick, Mitchel. All I Really Need to Know (About Creative Thinking) I Learned (By Studying How Children Learn) in Kindergarten, pdf
Kleon, Austin. The creative learning spiral
Resnick, Mitchel. Lifelong Kindergarten: Cultivating Creativity Through Projects, Passion, Peers, and Play (2018)
Gershenfeld, Neil; Gershenfeld, Alan; Joel Cutcher-Gershenfeld. Designing Reality: How to Survive and Thrive in the Third Digital Revolution (2017)
Kerr, Bill. Own your own factory that makes more factories (about Adrian Bowyer, the founder of the RepRap project)

Books and articles I am reading 2024

The list will include some significant online articles too:

Dehaene, Stanislas. How We Learn: The New Science of Education and the Brain (2020)
Dennett, Daniel. Intuition Pumps and other Tools for Thinking (2013)
Gee, James Paul. Teaching, Learning, Literacy in our high risk, high tech world: A framework for becoming human (2017)
Gershenfeld, Neil. Self-Replicating Robots and the Future of Fabrication. Lex Fridman Podcast #380
Laurillard, Diana. Teaching as a Design Science: Building Pedagogical Patterns for Learning and Technology (2012). I really want to read this but too expensive at $219! link
Laurillard, Diana. The significance of Constructionism as a distinctive pedagogy. Proceedings of the 2020 Constructionism Conference. The University of Dublin, Trinity College Dublin, IRELAND
Papert, Seymour. Mindstorms: Children, Computers and Powerful Ideas (1980)
Resnick, Mitchel. Lifelong Kindergarten: Cultivating Creativity Through Projects, Passion, Peers, and Play (2018)
Taleb, Nassim, Nicholas. Antifragile: Things that Gain from Disorder (2013)
Wolfram, Conrad. The Maths Fix: An Education Blueprint for the AI Age (2020)

Previous: Books 2023

21stC Maker Education: The Big Picture

These are my more substantial, big picture, publications, gathered in one place (there are many other more detailed descriptions of particular apps or hardware toys I have made not listed here):

My Skinner Moment (April 2024)

Seymour Papert: The Gears of my Childhood (April 2024)

Bits and Atoms, part one (April 2024)

Educational Software: Designed by Kids for Kids (December 2023)

Turtle Art Tile Project: Series of articles (July-November 2023)
learning and teaching Turtle Art
Turtle Art Tile Project Conclusion
Turtle Art Tiles Project

The tower of AI babel (October 2023)

Children are not hackers (October 2023)

Student engagement is a variable (September 2023)

Papert's ideas: Mainly from Mindstorms (September 2023)

The Inevitable: Introduction (August 2022)

Innovative 21stC Maker Education Pathway (April 2022)
an innovative 21stC maker ed pathway (part two)
an innovative 21stC maker ed pathway (part one)

Whittlesea Tech School (April 2022)

innovation meets resistance: the war between ancients and moderns (April 2022)

Own your own factory, that makes more factories (March 2022)

Organising a 3D printer building activity (January 2022)

the 3 game changers: high level overview of the possibilities (September 2021)

21st Century Curriculum (September 2021)

Thoughts on reading Paulo Blikstein, the founder of the Fab Learn Schools Movement (August 2021)

dotted circles revisited (July 2021)

The Wider Walls in a book commemorating the 50th anniversary of the seminal paper by Cynthia Solomon and Seymour Papert, “Twenty Things to Do with a Computer.” (April 2021)

Self sufficient production (brief update of the Fab Lab proposal: April 2023)
Your town need a community Fab Lab (July 2021)

Maker Space and Middle School Curriculum Reform (June 2021)

don't separate the what from the how (January 2021)

Culturally Situated Design Tools: Dotted Circles Exemplar (December 2019)

The three game changers and disadvantaged youth (Nov 2019): presented to and discussed with Leon Tripp, Regional Youth Programs Coordinator, Southern Region, Department of the Chief Minister and Cabinet

integrating the digital technology curriculum with indigenous knowledge systems (October 2019)

how to evaluate construction kits: ten design principles (July 2019)

my evolving mangle -> ethnocomputing (July 2019)

Digital Innovation in Secondary Schools (July 2019) Submission to The Education and Health Standing Committee (a committee of the Western Australian Legislative Assembly) inquiry into Digital Innovation in Secondary Education

The teaching of coding (Jan 2019)

an old quote from Hal Abelson (December 2018)

technology as trickster, revisited (April 2018)

why software might be superior knowledge (April 2018)

ClimateTheMovie

ClimateTheMovie is good. Look it up. It is being banned on vimeo so I won't provide a link. The version I saw was put up on X by Tom Nelson.

Some new ideas (for me) in there too, eg. that supernova increase cloud cover on earth (climate is complicated).

As I watched it I wrote down the names of all the sceptics and looked them up. I've listed them below. Over 20 well informed people, some of them top scientists. Some of them are very interesting people, eg. Matthew Wielicki runs a substack called "Irrational Fear". I haven't read Stephen Koonin's book, 'Unsettled' but he was very good. Some of the interviewees had experienced being socially shunned, had their careers terminated. Lots of scientists around who can't tolerate differences of opinion. Not scientific.

My favourite sceptics were not even mentioned (Judith Curry, MIchael Shellenberger, Roger Pielke jnr and snr). There are LOTS of sceptics out there. I read Pielke jnrs book "The Climate Fix" years ago. But that was more about renewables not being able to do the job.

The "scientific" narrative that there is one major factor (CO2) controlling the climate is wrong but mainstream media has been pushing that for decades. Don't challenge the narrative, you will be cast out. Is global warming (annoying how the anthropenic is left out) an existential threat? I don't think so.

Why do they do it, the alarmists? The film's political narrative is that it's a money spinner (renewable energy) plus the Greens / IPCC have tapped into people's fear about growth, capitalism, environment with some pseudo scientific half truths. They want big government to control sensible pro growth people. Do I buy that? Yes and No. Middle class virtue signalling politics, tread lightly on the fragile Earth. How did it become so strong? Hard to figure. Stephen Koonin points out that even the IPCC is not as alarmist as it used to be. (also Judith Curry, but not in this movie)

Here's my list of thinking people from the movie:
Stephen Koonin, author 'Unsettled'
Dick Linzen, atmospheric physicist
Will Happer physicist
John Clauser, Nobel Prize winner
Ross McKitrick
Stephen McIntyre
Willie Soon
Patrick Moore
Nir Shaviv
Henrik Svensmark
Mathew Wielicki, "Irrational Fear" Substack
Roy Spencer
Sallie Baliunes
Claire Fox
Tony Heller
Austin Williams
Benny Peiser
Stephen Davies
Tom Nelson

EDUCATIONAL SOFTWARE: DESIGNED BY KIDS FOR KIDS

2023 introduction:

What did Seymour Papert give us? He gave us a series of microworlds where learning could flourish. Instances include turtle geometry, LEGO robotics and the "Instructional Software Design Project" (with Idit Harel). I became very interested in this, after reading MindStorms because it made my teaching of maths far more interesting and gave me the feeling that I was an innovator. Like many I found textbook maths rather boring.

Since then many new and fascinating microworlds have emerged. eg. the Turtle Art Tiles Project. As I see it the role of "constructionist educators" (a phrase that needs dynamic clarification IMO) is to evaluate in practice and then push these wonderful projects forward.

So, I’m reproducing this 1994 article of my efforts to imitate Idit Harels “Instructional Software Design Project”. I remember those Paralowie years evocatively - a "socially disadvantaged" school where I was encouraged to innovate by the Principal (Pat Thomson https://patthomson.net/author/patthomson/). I’ve reread this article carefully and think it stands up well as something that I might try again tomorrow if the conditions were right.

EDUCATIONAL SOFTWARE: DESIGNED BY KIDS FOR KIDS

Bill Kerr, Jan., 1994, Paralowie R12 School

Abstract:

Students at the Year 8 level used LogoWriter software to design computer screens to teach Year 3/4 students Fractions. Students were set the task of doing transformations between words, symbols and pictures using LogoWriter. They recorded their experiences in a journal and identified problems they encountered and solutions to those problems. They helped each other solve problems in Fractions, design and computer programming.

Outcomes from this learning sequence included expressive writing about mathematics, improved scores in a Fraction test, improved fluency in Logo programming, improved self management skills, increased cognitive resilience (overcoming frustration and not giving up), improved time management, and increased faith by the students in their own thinking patterns. Students remained motivated and interested in the Fractions topic for a 7 week block using this approach. The culture of mathematics was perceived by the students to be different and more interesting than traditional textbook maths. Some students dropped in at recess and lunch to work on their projects.

The final combined software product is a useful piece of educational software that can be utilised by other teachers for diagnostic purposes as well as being an exemplar of what can be achieved with LogoWriter when it is used in this way.

Pretest:

A pretest of 41 questions about Fractions (selected from Idit Harel's pretest -- see reference at end for this excellent resource) was administered to the Year 8 class at the beginning of the topic. The test involved a variety of Fraction transformations between words, symbols and pictures with multiple choice answers. Here is a sample of a couple of questions from the pretest:

The same test was then administered to the Year 3/4 students by the Year 8 students. The Year 8 students were asked to explain the questions to the Year 3/4 students if they did not understand them.

Introductory lessons:

As well as the Pretest other introductory lessons were held with the Year 8's to explain the nature of the Project and get the students started on the design project. This included:

• Conducting a class survey about the most difficult questions in the Fraction pretest. This simply required students to vote on the questions they got wrong and collating totals.
• Talking about the variety of word, symbol, picture transformations and asking the students to provide examples of them in a class group and then on their own. Explaining how to set out a multiple choice answer format with 5 choices, A to E.

• Leading the class in discussion on the following focus questions:
  • What would the Year 3/4 students find hard about fractions?
  • What computer screens could you design using LogoWriter to help the Year 3/4 students learn fractions?

Conceptually, the students were being asked to integrate their knowledge and learning about the 3 different areas of Fractions, Logo Programming and Instructional Design. Their brief is diagramatically represented below:

Information for a Logo novice

To create even a simple Logo screen involves a lot of mathematical learning. For instance, to create an equilateral triangle requires knowledge of the external angle of a triangle (120 degrees). To create a more complex design, such as a title page for the Project, requires more sophisticated manipulation of the turtle, for instance by using cartesian co-ordinates (Logo primitives, show pos and setpos[xvalue yvalue]). Conceptually, this is a fourth transformation of Fraction representations in addition to the word, symbol and picture transformations described above.

Regular lesson format

After the introductory lessons the class then gradually settled into a regular lesson format that went as follows:

• Start (5 min.): Write down todays plans about screen designs.
• Middle (40 min.): Programming Fraction screens on the computer using LogoWriter
• End (5 min.): Write down how it went today with an emphasis on:
  • What problems did you have?
  • What you did to solve problems?
  • Who did you help today?

The teacher kept his own journal at the same time as the students. During the middle part of the lesson (40 min.) the teacher mainly worked as a facilitator, moving from group to group, answering questions and helping students design and program their screens.

When students completed a Fraction screen then they would go to the Year 3/4 room and ask their partners to return with them to complete the problem on the screen. The teacher would often intervene after this to assist the Year 8 students to evaluate their screens. Did the Year 3/4's find them too easy or too hard? Were there any confusing design aspects of their screens (such as confusing a picture of 3/4 (three-quarters) with 1/4 (one-quarter))? What would be an appropriate question to ask the Year 3/4 students next? The Year 8's were then offered a copy of the pretest to go through it again with the Year 3/4's so as to discover what they understood and did not understand.

This part of the programme carried on for about 5 weeks at 4 lessons a week. In that time each group (1 or 2 students per group) had designed between 1 and 4 Fraction screens. Some groups designed special title pages and special answer pages as well.

Here is a design problem that arose in the course of one lesson. The Year 8 Designer intended C to be shaded 3/4 in white and the correct answer to be E. However the Year 3/4 student saw C as shaded 1/4 in the darker colour. After the ambiguity was pointed out by the teacher the Year 8 Designer altered the question to, "What picture shows 1/4 shaded in white?"

The cultural setting

Although this Project used computing technology extensively, it was culturally driven not technology driven. The elements of the cultural setting included the skills and style of the teacher, the background of the students, some important elements of the Paralowie R12 School environment and finally the computing hardware that was available. Paralowie R12 School

Paralowie School is located in one of the lowest socio-economic regions of Australia. Absenteeism and lateness to lesson by students are chronic problems in the School and a variety of programmes already exist to meet special student needs. Students in the school are under some pressure NOT to embrace the traditional culture of maths and science since they are likely to be labelled "squares" by their peers. However, it was noticeable that some of the students from different cultures (eg. Serbian, Vietnamese) overtly rejected this cultural stereotype. The School Administration supports innovative teaching practice and so I have been encouraged to pursue my investigations into the effectiveness of transforming a maths learning culture into something more relevant and meaningful to students by using the LogoWriter medium. However, Logo is NOT an established part of the whole school culture at this stage. The Year 8 class is part of the new Paralowie Middle School (Years 6-9). As such I taught the class for 10 lessons a week (4 Maths, 4 Science and 2 Personal Development). This enabled me to establish closer personal relationships with many of the students than is normally possible for High School teachers.

Teacher input into the class culture

The central element of my teaching style can be described by the metaphor of relationship. I believe that learning occurs best when students develop a positive relationship with the teacher, their classmates and the subject matter, in this case maths. I select teaching materials with the idea of building a positive relationship at the forefront. This is a central reason for using Logo, for Logo is closely associated with an educational philosophy of making Maths personally meaningful or appropriable. My students would see me as an evangelical promoter of Logo and someone who can answer any question they have about it. Other maths teaching materials that I use extensively are Australian developed "hands on" products called RIME (Reality in Maths Education) and MCTP (Maths Curriculum and Teaching Program).

Students

This Year 8 class had a high proportion of English as a Second Language students of a variety of backgrounds. 5 students had Khmer background, 2 were Australian Aboriginal, 2 Latin American, 1 Vietnamese, 1 Vietnamese / Maltese, 1 Serbian and the remaining 13 were Anglo-Saxon Australian.

Each student brought into the classroom certain cultural attitudes -- attitudes to mathematics and Fractions that have developed over 8 years of Schooling, attitudes to computers ranging along a continuum from extreme reticence (initially) to extreme interest, attitudes about being put into the role of being expected to teach younger kids, attitudes about how to be "cool" in the classroom. I would loosely and simplistically group my students as follows:

• Achievers: I classify 8 students out of the 24 in this category, 4 girls and 4 boys.
• Artistic: One student (boy) used LogoWriter mainly as a means of artistic expression by designing a very attractive title page about Fractions as his first and main priority.
• Socials: I identified 6 students in this group, 5 girls and 1 boy. For these students their most important lesson is lunch and recess where they can pursue personal relationships and do things that are "cool" such as smoking or leaving the school grounds without permission (breaking the rules).
• Strugglers (4 girls and 5 boys): This is a mixed group that I believe are not achieving a great deal for a variety of reasons such as a difficult family situation or a poor mastery of the English language (ESL) or missing out significantly in their earlier schooling or learning styles that have not been catered for.

Although I believe that this Project could succeed in many classes it is worth stressing that it did succeed in this class with its high proportion of Socials and Strugglers (15 out of the 25 students)

Hardware

At the time of this project there were 17 computers in the room shared between 24 students. Hence some students had to double up on the computers. The computers are mainly ageing XT's (5 years old) with a variety of monitor formats. All of the computers were old and some were unreliable. Time and work was sometimes lost because of mechanical failure. Only 8 out of 17 computers had colour screens which was a big drawback because the students love to use colour.

Background knowledge

In Logo: Students had very little knowledge (if any) of Logo at the beginning of the school year. During 1994 they had been exposed to it in a fairly intensive way over 3 terms (10 weeks per term) as part of the Maths course prior to commencing this project. A closed book test held during Term 3 indicated that students knew between 12 and 68 LogoWriter primitives each, with a mean score of 38 primitives.

In Fractions: Students came from a variety of feeder schools with diverse curricula and teacher expertise in maths. Initially knowledge in Fractions was ascertained by a Fraction pretest (taken from Idit Harel's thesis). Scores in the pretest varied between 13 and 36 out of 41 with a mean of 25 out of 41.

Assessment

Students were assessed for this unit of work as follows:

1. Quality of their written journals, marked about every 1.5 weeks.
2. The number of problems identified in their journals and the number of solutions to the identified problems
3. How many times they helped other students as recorded in the journals
4. Quality of the Logo Fractions screens that students designed
5. How many screen that were designed (ie. how many times that Year 3/4 students were invited to the room).
6. Post test of Fractions (same as the pretest)
7. Open book test at end with this question:
   Place Logo primitives into groups or categories of your own choosing.

Post-test results for Fractions test for Year 8 class:
out of 41

	Pre	Post
Lowest	13	17
Highest	36	41
Mean	25	31

This improvement occurred over 7 weeks without any organised formal instruction from the teacher to the whole class about how to solve Fraction problems. Twelve students improved their score substantially (between 5 and 18 extra), 8 marginally (between 1 and 4 extra) while 4 obtained the same score or less.

Samples of students work

From the journal of Ngoc Tran 9/11/94

"I have brought 3 girls up from Ms Munro's class, and show them my animation on computer of Fraction, and they all got incorrect answers by guessing. One of my year 8 friend who not bad at maths but couldn't even get it right, the problem is that they cannot recognize the equal shapes or areas."

By the design of her question, Ngoc is clearly identifying a common problem students have about Fractions, that the parts have to be divided into equal areas.

From the journal of Daniel Curnow Monday 21/11/94

"Today I am going to make a harder procedure maybe one that the younger kids found hard in the test they had. The last procedure we did the younger kids found it easy but it took a while before they got the answer. They said that they did not know that one fourth is the same as one quarter."

Daniel's screen:
WHICH SHOWS 1/4?

• A. THREE FOURTHS
• B. ONE THIRD
• C. TWO FIFTHS
• D. ONE QUARTER
• E. NOT GIVEN

Daniel is reflecting on as aspect of language in maths. Students sometimes become confused when different words are used to represent the same value, in this case one fourth and one quarter.

From the journal of Sarah Scott Monday 14/11/94

"I showed them (the Year 3/4 students) my screen and they found it easy. I showed them the fractions test and pointed out the hard ones and they knew the answers to all of them. I don't know what screen to do that they wont find easy. I will design that screen in planning tomorrow."

Tuesday 15/11/94

"Today I will ask Mr. Kerr what type of screen I can do now since I am not sure. I just thought of one."

Sarah's was paired with a talented student in the Year 3/4 class who had found her previous screens easy to solve. Sarah thought up this more difficult screen without teacher help so as to offer the Year 3/4 student a real challenge. Her journal entry clearly documents the problem and the moment of creation.

DISCUSSION

Rich Learning Outcomes

As well as the learning about Fractions my strong impression was that significant amounts of learning were also occuring in such diverse areas as:

• Collaboration with other students
• Design skills
• Self management skills
• Fluency in logo programming
• Expressive writing about mathematical and technical issues
• Cognitive resilience (ie. learning not to give up)
• Time management
• Faith in own thinking
• Developing teaching skills such as empathy with Year 3/4 students, planning, reflection and explaining.

It's hard to prove this and unfortunately you, the reader, were not there. Also the merits of the whole approach rests or falls on this claim. The best I can do is to refer you to Idit Harel's thesis for a far more comprehensive documentation of these claims.

What follows is a discussion of some of the claims and connected issues.

Improved Fraction Knowledge

How come students improved their Fraction knowledge (shown by the Pre and Post test results) without being formally instructed in Fractions?

The environmental framework was constructed by the teacher by setting the students a teaching task, a design task and a medium to work in. These were non negotiables but beyond that the students had the freedom to do their own thing. Students were put into the role of a teacher and all teachers know that having to teach a topic is a very good way to learn it. Students were set the task of doing transformations between words, symbols and pictures using LogoWriter. The LogoWriter procedures written by the students became a fourth type of transformation that kept students focused on the manipulation of Fractions. They were learning in constructionist fashion using Logo as a medium over an extended period of time. By constructionist I mean active, self directed exploration providing the opportunity for internal representations of fractions to evolve.

Dealing with complexity

A complex learning sequence where students designed computer screens to teach other students Fractions was completed successfully by the class. The students did not find it particularly difficult or confusing to be learning different skills at the same time. The teacher did not have to nag the class to get on with their work, apart from the occasional individual exception. By and large students self managed their own progress with the teacher (or another student) acting as a helper or facilitator when they became "stuck" with a particular problem.

Inclusive learning activity

All of the students, except two latecomers to the class, contributed to the final instructional software design product. Most of the students designed and made their own screens. The quality of the final screens varied considerably but the final collective class product is a useful piece of instructional software. Some students copied designs from the pretest, which was made readily available throughout. The teacher did not interfere if students chose to do this interpreting it as a lack of confidence that would be overcome in time.

Individuality was expressed

Some students displayed their individuality, initiative and skill by designing special features, such as:

• Attractive title pages, designed using LogoWriter
• An elaborate answer screen where a truck backed up to pickup a "YOUR RIGHT" shape and towed it across the screen
• Flashing colour screens. One group discovered this by accident and it quickly spread throughout the class.

The teacher did not ask students to do any of this but did approve and encourage it when it happened.

Motivation

Motivation and interest in the Project by both students and the teacher remained high throughout the whole 7 week block. Usually, the teacher could work intensively with a small group of students with his back turned to most of the class. I have taught the same class using other more teacher directed methods and found this method the most effective for maintaining motivation and interest over an extended time period.

Problem Finding and Solving

Nearly all of the students systematically identified and recorded problems that occurred in the course of their work and solutions to many of those problems. According to my records, in the course of the Project 123 problems were identified by the students and solutions to 47 of those problems were recorded. The sort of problems that were identified included programming problems, technical problems, design problems, maths problems and personal problems.

Appraising

Students appraised the suitability of the product they made for the target audience (Year 3/4 students) and in many cases made plans to improve t

heir subsequent designs to better fit the target audience. eg. in some cases the first design was too easy for the particular Year 3/4 partner and so a more complex question was designed next time. This is a similar process that real life teachers go through in learning how to teach effectively.

Improved Fluency and Confidence in Technological Competence

Students became more fluent in their use of Logo primitives so that certain strings became second nature to them. For example, I have seen one particular programming sequence that involves trialling something on the front of the LogoWriter page in the command centre and then selecting, copying and pasting it to the flip side, which involves about 12 different keystrokes in correct order, gradually become second nature to a large proportion of the class. This is just one illustration of the improvement in programming fluency and increasing confidence of students in working with complex technology that could be readily observed in the classroom. Students, to varying degrees, developed a positive relationship with the computer and a sense of self as a technically competent person.

Expressive Writing about Maths and Technology

Students wrote systematically about mathematical and technical questions and in many cases included how they felt about these events. They wrote with feeling about technical questions and their collaboration with other students.

Genuinely Useful End Product

The "final" product is educationally valuable. The student software designs have been compiled and edited by the teacher and some of the more enthusiastic students. It is envisaged that the end product will be a useful diagnostic tool for maths teachers as well as an exemplar of what can be done with LogoWriter.

The "final" product could be developed and refined further in the future, simulating within the School the process that commercial software developers have to go through. It might even be possible to work on the product over an extended time with a select group of students to improve the software to commercial standard and then market it.

CONCLUSION

Methodology: Objects to think with

Teachers face the task everyday of how to make their subjects relevant and interesting to their students and this is seen to be a particular problem with maths. One way to look at this is from the point of view of objects to think with. The teacher and students co-construct a learning environment that is replete with "objects to think with". These "objects" include:

• The challenge of teaching others and designing screens for this purpose using Logowriter
• The structure of fractions and their transformations (words, symbols, pictures)
• Other students, eg. best friends, class experts, the Year 3/4 students
• Teacher (Is he/ she approachable, friendly and skilled?)
• Journal reflections

Taken together these objects represent the ISDP (Instructional Software Design Project)

Harel and Papert (1990) argue that some materials are better with regard to the following criteria:

• appropriability (some things lend themselves better than others to being made one's own)
• evocativeness (some materials are more apt than others to precipitate personal thought)
• integration (some materials are better carriers of multiple meaning and multiple concepts)

When used in the way described above LogoWriter is a most effective learning medium to think about Fractions and Design according to these criteria.

References

The approach adopted in this learning sequence was inspired from Idit Harel's PhD thesis titled: Software Design for Learning: Children's Construction of Meaning for Fractions in Logo Programming (MIT, June 1988). I obtained a copy of the thesis for US$20 by writing to:
Epistemology and Learning
MIT Media Lab
E15-309
20 Ames Street
Cambridge, MA 02139

Idit Harel's thesis was subsequently published as a book called Children Designers (1991), published by Norwood: Ablex.

Harel, I. & Papert, S. (1990) Software Design as a Learning Environment. Interactive Learning Environment, 1, 1-32

Kafai, Yasmin B., Minds in Play: Computer Game Design as a Context for Children's Learning (1993). This thesis is available from the same 'Epistemology and Learning' address given above for the Idit Harel thesis.

Acknowledgments

Helen Munro, teacher of the 3/4 class at Paralowie R12 School in 1994, for her flexibility and collaboration