building the logo turtle

Seymour Papert started lots of things!

“How to build a programmable floor turtle” is on Josh Burker’s (JoshB) site: LogoTurtle

INSPIRATION

Going back roughly 50 years, the inspiration originally came from Seymour Papert’s Logo floor turtle which accompanied the Logo programming language, developed for children.

I was further inspired on reading Neil Gershenfeld’s account in his book, Designing Reality, of a conversation he had with Seymour, back then:

“As fab labs started doubling and the Fab Academy began to grow, Seymour came by to see me to talk about them. I had considered the whole fab-lab thing to be an historical accident, but he made a gesture of poking his side. He said that it had been a thorn in his side that kids could program the motion of the turtle but could not make the turtle itself. This had been his goal all along”
Designing Reality, p. 29

Another goal I have is learning more electronics in a practical way. So, I was on the look out for a meaningful project to help me achieve that.

These factors pushed me over the edge. I decided to build the Logo Turtle!

Following the links in JoshB’s article I bought the materials from adafruit, Core Electronics and some other online and local stores.

There were some mishaps along the way. eg. it’s much better if you can get the 2xAA battery holders with a hole in the middle for the flat head screws. After some searching I found an Adelaide store, Altronics, which had these.

I wrote to Josh and his advice was that I should make a Printed Circuit Board (PCB) since the breadboard approach produced unreliable results. He sent me the Gerber files that I needed for that.

I downloaded a free open source viewer, Gerbv to view the files.

I asked for advice on the Adelaide Maker Space forum about how to get the PCB made and some helpful people suggested a couple of companies. I went with PCBWay and they made the PCB for me.

I have my own 3D printer so I printed the parts in PETG. All the links for that are in the JoshB article.

HELP

I’m an electronics novice so I had trouble finding some of the equivalents between the breadboard design and the PCB design. Fortunately I found Tony Onofrio, a friend in the Adelaide Hackerspace group. He translated the fritzing diagram on JoshB’s article into a PCB diagram for me.

Unfortunately, the link to the LogoTurtle software on JoshB’s article is broken. But I wrote to Josh and he sent me the files. Following his instructions (downloading drivers and Java) I tested the LogoTurtle software on the metro mini board and this was successful.

The software is a Logo implementation in Java. The logo files are text files which you download to the metro board. I didn't understand how it was working but spoke to David, a Java programmer at the Hackerspace group and he explained some of it to me.

The next step was soldering the parts onto the PCB board. This was hard for me since I’m a novice at soldering. Again Tony helped out by giving me some lessons in soldering. The order in which I soldered the parts on was: (1) resistors x 2 (2) Darlington driver, note the notch (3) Metro Mini (4) header pins 2 x 5 then x 3 (5) photocell (6) switch

Having done all this I was ready to attach the PCB to the turtle. I soldered the 4 battery leads, plugged in the stepper motor 5 pin connectors and inserted the 4xAA batteries.

I found some pens with the correct diameter at Office Works and placed one in the pen holder on a sheet of paper. I flicked the switch to turn on the metro power, indicated by a green light and pressed the reset button

Hallelujah, the turtle drew a square! Logo.jar runs the test.txt file by default.

to startup
square
end

to square
pd
wait 1000
repeat 4 [fd 100 rt 90]
pu
alloff
end

But note the angles are not quite 90 degrees. Using trial and error, I changed the angle to 85 degrees and it drew a pretty good square

JoshB’s solution here is to add a shim to alter the angle of the stepper motors reproduce. I tried this but it didn’t make any difference.

I wrote to JoshB again and he suggested I alter the sys.txt file where the logo drawing procedures are stored as text files.

So I altered the rt and lt turn procedures by multiply and angle by 85/90. This then drew a perfect square.

to rt :n
make "n :n * 235 / 100 # (the multiplying factor was altered from * 25 / 10)
repeat :n [rstep- lstep+]
alloff
end

I then tried a pentagon, square and triangle combined:

The more ambitious rotating octagon worked well first up:

Then I made a similar change to the arcrt (arc right) and arclt (arc left) procedures and then I could draw near perfect circles and arcs.

An interesting feature of the design is the photo resistor. When exposed to the light the resistance goes down. This photocell is plugged into A0 on the Metro Mini, so you can introduce this value into the code to achieve variations based on light intensity.

Following JoshB's notes I established the A0 values for a bright flashlight were roughly 960, for normal light 830 and with curtains drawn about 565. So I ran the following procedure in normal mode and flashlight mode which modified the size of a circle:

to startup
wait 1000
let [n a0 / 10]
repeat 10 [
arcrt 50 :n
make "n a0 / 10
]
alloff
end

So far, so good. I could draw closed shapes with the LogoTurtle.

But to draw people's initials, for example, you need to be able to lift the pen (logo command pu) and put it down again (pd) at the right times. This requires fitting a servo to lift the pen. I also added a weight to the pen to ensure it drew firmly on the paper when down.

Here are a couple of initials I drew, using the alphabet file from JoshB's LogoTurtle Curriculum. I presented these to a couple of members of the Hackerspace group who have been helping me:

REFERENCE

Josh Burker's original article: LogoTurtle
LogoTurtle Curriculum (lots of great ideas here)

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

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

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

PAPERT'S IDEAS: MAINLY FROM MINDSTORMS

I first published this in October 1991. Have the ideas of Piaget, Papert, Minsky, Solomon, Turkle stood the test of time? Yes. But still more does need to be said ...

MISSING OUT ON THE MINDSTORMS

Before I read Mindstorms and had only read about Mindstorms I gained the impression that Papert's educational philosophy was open ended discovery learning and that was about it.

Some of the articles that I have since read about Logo or about Papert's philosophy convey just this sort of impression. They talk vaguely about the "Logo philosophy" and about how some teachers who use Logo are aware and others are not aware of it.

It could be that either some Logo commentators do not understand Papert or, alternatively, they water him down so as to make him appear more respectable. I don't think that this is right. If Papert's ideas are important then we ought to find out what he is on about and if they inspire us, passionately propagate them. After all, ideas when they are put into practice do change the world, either for better or for worse.

At best, some writers about Logo talk about the importance of Logo to problem solving, debugging (children reflecting constructively about their "mistakes") and using Logo to develop learning about learning and all that guff. In other words, the sort of reflections on Logo that often pass for informed educational comment are so consistent with current modern educational thinking they would scarcely cause a ripple in the mind of the informed teacher. No Mindstorms here!

In my view the central tenants of Papert's thesis are educationally, socially and politically somewhat more radical. So, what is Papert really on about?

CONSTRUCTIONISM

Papert's beliefs are rooted very firmly in Piaget's findings about children's learning. Papert worked with Piaget for 5 years, applying his own expertise in maths to help build Piaget's theories. Two points from Piaget stand out:

• Children build or construct their own intellectual structures.

From this point arises the obligation of the modern teacher to restructure traditional subjects such as maths to fit the child. Hence, Papert has restructured maths by inventing the computing language logo to fit the natural development of the child.

• Children build on what they know. Piaget's term for children's continual balancing of existing cognitive structures with new experiences is equilibration.

From this point arises the obligation of the modern teacher to investigate the cognitive structures of their students and to interact with those cognitive structures in a subtle, not a heavy handed manner.

Piaget found that incredible amounts of learning occur without formal teaching. In his work, Papert tries to discover and promote the factors that are causing this "hidden" learning and also asks: Why is it that learning often does not occur with formal teaching (and often does occur without formal teaching)?

MATHSLAND: RESTRUCTURING TRADITIONAL KNOWLEDGE

Piaget was not an educational psychologist but a genetic epistemologist. These obscure words are highly significant. Papert has recently moved to a new lab at MIT which has been named the Learning and Epistemology Group. Clearly epistemology is central to the concerns of Piaget and Papert. So, what is epistemology and what is genetic epistemology?

Piaget has recognised it as a mistake to separate the learning process from what is being learned. The study of what is being learned is epistemology. Hence, a genetic epistemologist is a person who investigates the evolution of the structure of knowledge in the minds of young people!

This is a much more dynamic conception than a traditional psychology of the learning process which passively accepts the traditional structure of knowledge as a given. Piaget and Papert are suggesting that there is a dialectical relationships between knowledge and people. Papert quotes Warren McCulloch tellingly to make this point:

"What is a man so made that he can understand number and what is number so made that a man can understand it." (Mindstorms, p. 164)

In looking at learning it is not enough to look at "learning how to learn" (ie. concentrate on the learner) but we need to study the basic structure of the subject itself. Papert investigates the basic structure of mathematics in some detail including a critique of the formal logical thinking emphasised in Bertrand Russell's Principia Mathematica and the "new math" of the 1960s/70s. In Piaget/Papert's view the basic structure of maths is derived from the thinking of the Bourbaki school: order, proximity (topology), combination (algebra).In Papert's view it is not natural that advanced maths ideas are inaccessible to most. What Papert has tried to do is restructure maths so as to accommodate the natural tendencies of the child. Instead of mathophobia Papert hopes to create a mathsland where it will be natural to learn maths, like learning to speak French in France.

Logo was designed with this philosophical/mathematical background in mind. Logo was developed as a language so that mathematically naive users could learn how to program and control the computer as well as more sophisticated users.

TOOLS, CULTURE AND PEOPLE

Change is inevitable but widespread change will only occur when there are significant changes in the wider culture. This applies to both social change and change in patterns of intellectual development.

The printing press on its own did not create poetry, but by spreading poetry around it helped to create new poets. The steam engine on its own did not create the industrial revolution. Tools are made by people and when tools call out for revolution they will speak through people.

Computers will not create an educational revolution. Forget about computers (for a minute!); culture is central to change! Papert is not a mechanical technological determinist. He is more on about reconceptualising traditional subject domains and using, in this instance, the computer as a tool to help do this.

This is a vitally important point when we come to evaluate the effectiveness of logo for if logo is implemented as a technical act (in a formal, teacher centred, Instructionist classroom) then obviously Papert's beliefs are not being given a fair trial. Papert has clearly rejected this technological determinism:

"Technocentrism refers to the tendency to give a ...centrality to a technical object - for example computers or Logo ... (this) betray(s) a tendency to reduce what are really the most important components of educational situations - people and cultures - to a secondary, facilitating role. The context of human development is always a culture, never an isolated technology ..." (Papert, quoted in Solomon, p.128)

Since culture is central to change then it follows that a teacher ought to aspire to be an anthropologist. The computer is merely one important recent addition to the cultural landscape. The question that the anthropologist/teacher ought to focus on is which cultural materials are relevant to intellectual development

The computer will not replace the teacher. On the contrary, teachers will have to become more skilled to incorporate the new technology into the overall educational context:

• Skilled in modern learning theories and psychology
• Skilled in relating to a variety of children
• Skilled in detecting new, important elements of their student's culture
• Skilled in cross curricular applications
• Skilled in computing
• Able to apply a variety of skills creatively

These skills are necessary for a modern educational system. Currently, one of the main problems with regard to developing creative applications of computers in education is training teachers with these skills. But lets not blame the teachers for this when education departments and governments are not providing the time, the infrastructure or the educational insights to make it all possible.

Papert has proposed a new field of teacher training called humanistic computer studies, where:

"In my vision of this field its professionals will need special combinations of competences. Apart from a foundation in scientific knowledge and technological skill they will need high degrees of psychological sensitivity and 'artistic' imagination. For the ones who will make the greatest social contribution will be those who know how to mold the computer into forms which people will love to use and in ways which will lead them on to enrichment and enhancement...." (from Solomon, p.133)

THE ROLE OF THE COMPUTER

If culture is central then what is the role of the technology? The new technology provides the underlying basis for a radical change in the educational and social system. Computers are obviously an important new part of our popular cultural landscape and everyone agrees that their influence will grow in the future.

However, the point is that the future possible pathways for education and society are manifold and that these decisions will be made in the cultural and political arenas - popular culture often determines political expediency. Logo taught in a constructionist framework represents a great educational opportunity but unless cultural persuasion and political pressure is brought to bear on the formal education system then the opportunity will be lost.

In today's world computers will usher in new cultural change but the sort of change that occurs will be fought out socially, in the world of business (how can productivity be maximised?), in the world of institutionalised education, in schemes for alternative schools, in the home with PC's, in the Arcades with the latest computer games. There is no social inevitability about the future pattern of usage of computers.

Computers may be used to mechanically increase productivity by crunching words, numbers and data. Others will use them as an expressive and creative tool to develop individuals with new insights into traditional subject domains, including human psychology. As a tool the computer is versatile enough to do both! Alan Kay has claimed that the computer can be used to simulate anything:

"...[the computer] is a medium that can dynamically simulate the details of any other medium, including media that cannot exist physically ... it has degrees of freedom for representation and expression never before encountered and as yet barely investigated." (Sunrise Notes Number 2, June 1990, p.29)

Papert says that the role of the new technology is twofold: both instrumental and heuristic.

Instrumental simply means that as computers become cheaper, more powerful and more popular they will carry and spread the ideas and social relations embedded within them amongst larger and larger groups of people. Papert expresses the instrumental role of computers spreading ideas around very powerfully with the metaphor "computer as pencil".

The heuristic influence of computers is a more complex and surprising idea.

Computing science is not fundamentally a technical science of computers. Rather, most of it is the science of descriptions and descriptive languages. Hence computing science (especially AI research) has something to offer learning theory, since descriptive languages are used to talk about learning. At an elementary level it is clear that concepts such as input, output, feedback, subprocedures (modularisation), recursion, debugging and extensibility could provide at least part of a framework for explanations of biological and human behaviour.

Papert and Minsky argue that ideas from computing science are instruments of explanation of learning and thinking. More, they are instruments of changing, altering the way in which we learn and think. In this way computing science and AI Research has ushered in a whole new theory of human psychology as outlined by Minsky in Society of Mind.

PAPERT'S CRITIQUE OF THE EDUCATION SYSTEM

Those who invented the automobile didn't do so by an in depth study of the horse and buggy! This is Papert's comment on the educational horse and buggy!

Papert is scathing of the established education system. He perceives our present schooling process as a technical act under the guiding methodology of Instructionism.

Although instruction is fine and an inevitable part of everyone's everyday learning this is different from Instructionism which is the entrenched methodology of a central person or curriculum transmitting pre-established pieces of information to an essentially passive, captive audience. Papert is against the teacher as technician under the control of the curriculum, against centralised control, against hierarchy, against the whole notion of a centralised curriculum and against accountability and national testing based on the above precepts. In short, Papert is swimming against the current winds of educational tightening up in this country but in doing so he is giving us some powerful weapons to effectively oppose the current disastrous, straight-jacketing trend. Papert's weapons are the ideas outlined above, computer software (logo) and computer hardware (LEGO).

In a dynamic, living culture there is little place for a centralised curriculum because the culture will generate its own interesting, unpredictable challenges on a day to day basis. Attempts to impose a curriculum onto this culture would only serve to cramp the style and creative interest of those who work within the culture.

Instructionism is misguided because it treats children as empty vessels to be filled up with knowledge. Instructionism ignores Piaget who emphasises that children construct their own internal mental worlds by integrating new information with already established structures (equilibration).

Hence, Piaget's findings and not computers as such are at the centre of Papert's radical critique of the education system. Papert would oppose the use of computers for Computer Aided Instruction (CAI) such as maths drill as a band-aid to patch up a basically sterile system.

In opposition to Instructionism, Papert advances the guiding principle of Constructionism for creating a humane and enriching education system. The learning environment is about building and creating things, eg. building rich cognitive structures internally and building things like LEGO machines externally. In this environment the teacher is first and foremost a fellow learner (who might spend more time instructing others simply because he/she may know more).

There is nothing new in Papert's critique of the education system up until now. In the history of education there has always been alternative schools with an emphasis on freedom. These movements have never really caught on partly because "...they were unable to handle the more formal aspects such as mathematics or grammar or many parts of science."(Papert, address to WCCE, 1990). So, what is new in Papert's vision is the use of modern technology (computers with logowriter and LEGO TClogo) to make possible interesting constructivist maths, science and grammar for perhaps the first time ever, historically.

CONCLUSION

Many teachers are enthusiastic to start with. Then, after ten years many teachers are burnt out Instructionist hacks, despite their best intentions. Don't blame the teacher, blame the system.

Fundamentally, Papert influences us because, if we really listen to him, he politicises the educational debate in a highly practical way. Papert has taken the most traditional subjects - maths and science - and has begun to restructure them to fit the user. Papert and his supporters have created an interesting maths-land and science-land that are both user friendly and powerful learning environments.

Hence, Papert and the MIT group are creating conditions that make it possible for people to become passionate about educational options. LEGO TClogo is something that you can take home and happily play with! It is hard to be passionate about maths drill and practice style textbooks, or Instructionism - broadcasting essentially the same lesson year after year, marking Common Tests, or whether Sarah was really worth a low A or a high B. Constructionism and Logo is different. It fits the user and has no ceiling in terms of expertise.

Papert's ideas have the power to change lives and to change whole education systems (eg. Costa Rica). Of course this will require a tremendous and possibly protracted educational/political struggle since the Instructionist model casts such a long shadow. As in all meaningful struggles the outcome is far from certain.

Since Papert's ideas are revolutionary they are not for the faint hearted. It is very difficult to mentally step outside of a system you are working in, that you are part of, that you help to reproduce by your day to day actions and then to turn around and to say that it is fundamentally at fault. It is easier for Papert to make this critique than it is for a practising classroom teacher. In the final analysis, Papert invites us to have the courage to embark on the adventure of tearing down the old ways while creating the new ways of teaching and learning.

REFERENCES:

Papert, Seymour. Mindstorms: Children, Computers and Powerful Ideas. Harvester Press, 1980.

Papert, Seymour. Peristroika and Epistemological Politics. Address to the 5th World Conference on Computers in Education, Sydney, Australia, July 1990.

Solomon, Cynthia. Computer Environments for Children: A Reflection on Theories of Learning and Education. The MIT Press, 1987

Turkle, Sherry. The Second Self: Computers and the Human Spirit. Simon and Schuster, New York, 1984.