Mathematicians from South Africa

"Should the computer program the kid or should the kid program the computer?"

"Now, given that picture of a rapid change of society, one would expect to see a rapid evolution of the institutions charged with preparing the young for it. We do not see this. We see a much slower rate of evolution of the school and that means we're seeing a bigger and bigger gap between school and society. This gap is what I believe is responsible for the deterioration of performance in our schools and our educational systems. Because the children can see this; they can see that school is irrelevant. They feel that the pace of school and the mood of the school culture is out of sync with the society in which they live. And so it becomes harder and harder to get them to buy into the idea that school is satisfying their needs, that school is a bridge to the 21st century, as our political leaders keep on reiterating."

"Many children who grow up in our cities are surrounded by the artifacts of science but have good reason to see them as belonging to "the others"; in many cases they are perceived as belonging to the social enemy."

"In my vision, space-age objects, in the form of small computers, will cross these cultural barriers to enter the private worlds of children everywhere. They will do so not as mere physical objects. This book is about how computers can be carriers of powerful ideas and of the seeds of cultural change, how they can help people form new relationships with knowledge that cut across the traditional lines separating humanities from sciences and knowledge of the self from both of these. It is about using computers to challenge current beliefs about who can understand what and at what age. It is about using computers to question standard assumptions in developmental psychology and in the psychology of aptitudes and attitudes. It is about whether personal computers and the cultures in which they are used will continue to be the creatures of "engineers" alone or whether we can construct intellectual environments in which people who today think of themselves as "humanists" will feel part of, not alienated from, the process of constructing computational cultures."

"In many schools today, the phrase "computer-aided instruction" means making the computer teach the child. One might say the computer is being used to program the child. In my vision, the child programs the computer and, in doing so, both acquires a sense of master over a piece of the most modern and powerful technology and establishes an intimate contact with some of the deepest ideas from science, from mathematics, and from the art of intellectual model building."

"A programming language is like a natural, human language in that it favors certain metaphors, images, and ways of thinking. The language used strongly colors the computer culture. It would seem to follow that educators interested in using computers and sensitive to cultural influences would pay particular attention to the choice of language. But nothing of the sort has happened. On the contrary, educators... have accepted certain programming languages in much the same way as they accepted the QWERTY keyboard. An informative example is the way in which the programming language BASIC has established itself as the obvious language to use in teaching children how to program computers... Today, and in fact for several years now, the cost of computer memory has fallen to the point where any remaining economic advantages of using BASIC are insignificant. Yet in most high schools, the language remains almost synonymous with programming, despite the existence of other computer languages that are demonstrably easier to learn and are richer in the intellectual benefits that can come from learning them. The situation is paradoxical. The computer revolution has scarcely begun, but is already breeding its own conservatism."

"BASIC is to computation what QWERTY is to typing. Many teachers have learned BASIC, many books have been written about it, many computers have been built in such a way that BASIC is "hardwired" into them. In the case of the typewriter, we noted how people invent "rationalizations" to justify the status quo. In the case of BASIC, the phenomenon has gone much further, to the point where it resembles ideology formation. Complex arguments are invented to justify features of BASIC that were originally included because the primitive technology demanded them or because alternatives were not well enough known at the time the language was designed."

"One might ask why the teachers do not notice the difficulty children have in learning BASIC. The answer is simple: Most teachers do not expect high performance from most students, especially in a domain of work that appears to be as "mathematical" and "formal" as programming. Thus the culture's general perception of mathematics as inaccessible bolsters the maintenance of BASIC, which in turn confirms these perceptions."

"It is not uncommon for intelligent adults to turn into passive observers of their own incompetence in anything but the most elementary mathematics. Individuals may see the direct consequences of this intellectual paralysis in terms of limiting job possibilities. But the indirect, secondary consequences are even more serious. One of the main lessons learned by most people in math class is a sense of having rigid limitations. They learn a balkanized image of human knowledge which they come to see as a patchwork of territories separated by impassable iron curtains."

"An unknown but certainly significant proportion of the population has almost completely given up on learning. These people seldom, if ever engage in deliberate learning and see themselves as neither competent at it nor likely to enjoy it. The social and personal cost is enormous... Deficiency becomes identity: "I can't learn French, I don't have an ear for languages;" "I could never be a businessman, I don't have a head for figures;"... These beliefs are often repeated ritualistically, like superstitions... Although these negative self-images can be overcome, in the life of and individual they are extremely robust and powerfully self-reinforcing. If people believe firmly enough that they cannot do math, they will usually succeed in preventing themselves from doing whatever they recognize as math. The consequences of such self-sabotage is personal failure, and each failure reinforces the original belief. And such beliefs may be most insidious when held not only by individuals, but by our entire culture."

"Our children grow up in a culture permeated with the idea that there are "smart people" and "dumb people". The social construction of the individual is as a bundle of aptitudes. There are people who are "good at math" and people who "can't do math." Everything is set up for children to attribute their first unsuccessful or unpleasant learning experiences to their own disabilities. As a result, children perceive failure as relegating them either to the group of "dumb people" or, more often, to a group of people "dumb at x" (where, as we have pointed out, x often equals mathematics). Within this framework children will define themselves in terms of their limitations, and this definition will be consolidated and reinforced throughout their lives. Only rarely does some exceptional event lead people to reorganize their intellectual self-image in such a way as to open up new perspectives on what is learnable."

"I have asked many teachers and parents what they thought mathematics to be and why it was important to learn it. Few held a view of mathematics that was sufficiently coherent to justify devoting several thousand hours of a child's life to learning it, and children sense this. When a teacher tells a student that the reason for those many hours of arithmetic is to be able to check the change at the supermarket, the teacher is simply not believed. Children see such "reasons" as one more example of adult double talk. The same effect is produced when children are told school math is "fun" when they are pretty sure that teachers who say so spend their leisure hours on anything except this allegedly fun-filled activity. Nor does it help to tell them that they need math to become scientists---most children don't have such a plan. The children can see perfectly well that the teacher does not enjoy math any more than they do and that the reason for doing it is simply that it has been inscribed into the curriculum. All of this erodes children's confidence in the adult world and the process of education. And I think it introduces a deep element of dishonestly into the education relationship."

"The kind of mathematics foisted on children in schools is not meaningful, fun, or even very useful. This does not mean that an individual child cannot turn it into a valuable and enjoyable personal game. For some the game is scoring grades; for others it is outwitting the teacher and the system. For many, school math is enjoyable in its repetitiveness, precisely because it is so mindless and dissociated that it provides a shelter from having to think about what is going on in the classroom. But all this proves is the ingenuity of children. It is not a justifications for school math to say that despite its intrinsic dullness, inventive children can find excitement and meaning in it."

"Frank Rosenblatt... invented a very simple single-layer device called a Perceptron. ...Unfortunately, its influence was damped by Marvin Minsky and Seymour Papert, who proved [in Perceptrons: An Introduction to Computational Geometry (1969)] that the Perceptron architecture and learning rule could not execute the "exclusive OR" and therefore could not learn. This killed interest in Perceptrons for a number of years... It is possible to construct multilayer networks of simple units that could easily execute the exclusive OR... Minsky and Papert would have contributed more if they had produced a solution to this problem rather than beating the Perceptron to death."

"MORAL REALITY AND MORAL FACTS -- https://www.whyarewehere.tv/people/george-ellis/"

"WHAT IS FINE-TUNING? -- https://www.whyarewehere.tv/people/george-ellis/"

"TOP-DOWN CAUSATION -- https://www.whyarewehere.tv/people/george-ellis/"

"THE ETERNAL TRUTHS OF MATHEMATICS -- https://www.whyarewehere.tv/people/george-ellis/"

""On the limits of quantum theory: Contextuality and the quantum–classical cut", Annals of Physics 327 (2012) 1890–1932"

"Above all he believes that these mathematically based speculations solve thousand year old philosophical conundrums, without seriously engaging those philosophical issues. The belief that all of reality can be fully comprehended in terms of physics and the equations of physics is a fantasy."

"You cannot do physics or cosmology without an assumed philosophical basis. You can choose not to think about that basis: it will still be there as an unexamined foundation of what you do."

"Attempts to explain values in terms of neuroscience or evolutionary theory in fact have nothing whatever to say about what is good or bad. That is a philosophical or religious question (scientists trying to explain ethics from these kinds of approaches always surreptitiously introduce some unexamined concept of what is a good life by the back door)."

"Actually philosophical speculations have led to a great deal of good science. Einstein’s musings on Mach’s principle played a key role in developing general relativity. Einstein’s debate with Bohr and the EPR paper have led to a great of deal of good physics testing the foundations of quantum physics. My own examination of the Copernican principle in cosmology has led to exploration of some great observational tests of spatial homogeneity that have turned an untested philosophical assumption into a testable – and indeed tested - scientific hypothesis. That’ s good science."

"Because I had to choose some teaching subjects, I chose mathematics."

"As a mathematician, your work consists of building a knowledge base, almost like building a house of bricks,each layer of bricks you lay has a solid foundation underneath it with no holes, gaps, or errors."

"I always loved mathematics, and was inspired by particular teachers in both primary and secondary schools, and so I went to University to study mathematics."

"I gave “extra mathematics lessons” while I was doing my degree and enjoyed this (as well as earning quite well from it) and so went on from a B Sc to do my professional teaching diploma."

"Psychology was my second major – this also wasn’t in my original plan – I had thought I would do Applied Maths, but I enjoyed Psychology in first year and so continued, and then enjoyed work on child development, learning and so on."

"I moved into teaching – rather than set out to teach, or work in education. When I began my working career as a secondary mathematics teacher, I had no intention of becoming an academic and researcher in education. My first post was in a so-called ‘coloured’ school in Cape Town, a school with a strong political identity tied to the Unity Movement."

"We need really curious leaders"

"because then you don’t make assumptions, you don’t take diversity views for granted."

"Once you get a big role, that's the starting line, not the finishing line. So it's really, how do you understand what the need is from your organization and in society?"

"If you don't know as a leader what your license to operate is from society, then you've got tunnel vision. So it's understanding the context, what society expects, what the organization needs, and having to adapt yourself and evolve.” Asked about the way forward"

"You have to be vulnerable. You have to recognize you don't know the answers. Good ideas can come from anywhere"

"Broadly my time is shared between supporting the professional development work we do in schools, and doing and supporting the research that is linked to this work, with a large proportion of time supporting full time doctoral students in the project. I teach less than I did before. I travel internationally a fair amount, to conferences and for other international work I do."

"I think our whole field of educational research in South Africa is relatively young. There is so much we need to know more about, and from the empirical base of our schools, classrooms and learners. I think the transition years from primary into secondary mathematics what teachers need to know and do to teach across subjects at that level are very poorly understood. This is critical in mathematics where the move to greater abstraction and working with symbolic forms emerges. It is also a critical point where we need to know more about what it means to learn and teach mathematics in a dominant minority but extremely powerful language (English)."

"Interesting as I think about this, Eva Hoffman’s Lost in Translation had an immense effect on me. I happened to read this while I was working on my PhD, and it provided a different gaze on what it meant to learn and live in a language that was not your mother tongue, or as she called it, the language of her heart and emotions. I have since read much of her work, the most powerful of which was After Such Knowledge: Meditations on the Holocaust. The latter, a philosophical and social commentary rather than an academic text, has contributed significantly to my understanding of the social world, as well as some of my own location in history."

"Most influential at the start of my academic career was Lev Vygotsky’s work: Mind in Society and Thought and Language. As a mathematics education researcher I am always working between educational theory and literature in mathematics education. With my early work on teaching mathematics in multilingual classrooms, David Pimm’s book Speaking Mathematically was pivotal in turning my attention to mathematical language more generally. More recently, with my interest in mathematical knowledge in and for teaching and particularly what is produced as mathematics in teacher education practice, influential resources are Basil Bernstein’s Pedagogy, Symbolic Control and Identity, and Anna Sfard’s Thinking as Communicating and then the extensive work done by Deborah Ball in the past decade. I could go on, as I enjoy reading, and spend time relaxing with whodunnit."

"Hearing from a young age that you are a “words person” can heighten your anxiety about math. As a result, you may avoid it."

"In science stories, math helps the reader understand real-world phenomena."