Missing in Australia: 21st C Maker Ed Jobs

Fab Learn Jobs Board

This Job Board is open to "educational makerspaces around the world" but for some strange reason I never see Australian jobs advertised here. Oh, yes, I am being ironic and rhetorical. IMO an important reason, although not the only one, is that we have a one size, (doesn't) fits all, national standards based curriculum called ACARA.

Why aren’t jobs like this being advertised in Australia? Or, if I have missed them then please show me where they are?

Posted March 21, 2024
Westfield State University:
Research, Innovation, Design and Entrepreneurial (RIDE) Center Coordinator
General Statement of Duties: Full time salaried position

The RIDE Center coordinator will support the Executive Director in managing the equipment, space, and programming. The space includes a design studio and MakerSpace with 3D printers, Adobe and other equipment software, laser cutter, woodworking, sewing, computer programing, vacuum formers, and circuitry tools. They will help to coordinate and contribute to a positive user experience, managing classroom, student, and community visits and activities, helping with scheduling events, communication, student support, preparation of reports/assessments, administrative/office tasks, and other RIDE center needs. They will assist with coordination of student interns, work study, and graduate assistants, and community engagements associated with RIDE centers. They will assist the Executive Director with RIDE expositions, workshops, speaker series, and other events, as well as training students, faculty, staff, and community on equipment and software use within the center.

Posted March 21, 2024
St Mary’s School in Orange County

St. Mary’s School is an independent day school that serves over 700 students, Pre-K through Grade 8, in Aliso Viejo, CA. As the only independent school in Orange County that offers the international baccalaureate (IB) program from primary school through middle school, St. Mary’s is committed to a globally-minded and innovative curriculum that, in many ways, stands alone within the educational landscape in Orange County. St. Mary’s students are prepared not only for the next steps in their educational journey, but also to become courageous, caring, global citizens and enlightened leaders of tomorrow.

This summer, construction will begin on a 28,000 square foot facility which will include a design center comprising five specialty labs and a gallery space. The director of the design center will lead the transition into this new space, oversee the design center and its resources, and collaborate with faculty and academic leadership to fully integrate design thinking with St. Mary’s outstanding IB and design-centered curriculum. The director of the design center will report to the director of technology and innovation, and will bring an expertise in design thinking and a relational approach to leadership to the role. St. Mary’s looks forward to welcoming the director of the design center to start July 1, 2024, or later by mutual agreement.

Posted June 1, 2023
Lab Instructor for The da Vinci Lab (DVL) for Creative Arts & Sciences

St. Stephen’s Episcopal School-Houston is looking for a full-time Lab Instructor for The da Vinci Lab (DVL) for Creative Arts & Sciences (DVL) – a makerspace for students in 1st  to 8th grades. The goal of the program is to offer a creative space for students that inspires collaborative learning and cross-pollination of learning techniques and creative skills. The Lab Instructor teaches maintenance and use of equipment, sets and delivers the yearly curriculum for DVL, and records the ways in which learning and making take place within the space.

Posted June 1, 2023
Maker Space Manager, UC Santa Barbara Library

Responsible for the day-to-day operational management of a new Library service for UCSB students to engage in making activities. Develops opportunities for experiential and project based learning with digital and non-digital creative technologies for varying skill levels. Maintains high levels of customer service in the delivery of Makerspace services. Supervises student assistants in providing peer-to-peer support for project design and creation and ensuring safe use of equipment. The inaugural Makerspace Manager will be an integral part of ensuring a smooth launch of the Makerspace and for informing the development of its service portfolio.

Posted February 28, 2022
Location: Cincinnati, Ohio, U.S.A.
Position Overview:

Seven Hills Middle School seeks an inspiring, high-energy, and passionate teacher to serve as Director for our signature Innovation Lab.  Housed in a specially designed makerspace in our new, state-of-the-art Middle School building, the Innovation Lab program engages students in a series of sequenced projects designed to foster design thinking skills. In an empathy-based approach, students consider the needs or challenges faced by others as they work in project teams to conceptualize, design, prototype, test, fail, iterate, and, in many cases, present their fabrications to authentic audiences.

In preparation for these projects, students learn a series of fabrication and design skills. Sixth-grade students develop basic skills as they work with hand, power, and digital tools on projects that include designing for others. Seventh-grade students dive more deeply into the engineering design process. They explore and develop spatial reasoning, empathy, and creative thinking skills as they take on a series of challenges. An eighth-grade Computer Science elective course teaches students to use loops, variables, functions and conditionals to build efficient and adaptable computer programs. Students also design, build, and program robotic devices. In addition to teaching courses, the Innovation Lab Director supports student-driven projects each day during lunch. All student projects increase in scope, complexity, and sophistication as they acquire new skills, but the basic formula is to help students learn to understand and empathize with challenges faced by others and to use their creativity and imagination to design effective solutions.

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)