Tag Archives: math

Programming, Math, and Computational Thinking: on education

Actually, this post will feature a few reads and resources for you that are part of a theme – the need to change K-12 education to face the realities of today and tomorrow, instead of preparing them for a world that has already turned. To do so will require children to gain a working understanding of the use of, and creation of, software. This is as important today as reading, writing and mathematics and it helps provide invaluable tools to build on, and strengthen, those foundational parts of children’s education.

Google Edu serves a terrific resource for educators and students that brings together many of these concepts – “Exploring Computational Thinking”. The lesson plan includes Python exercises that help illustrate computational thinking while strengthening math skills.

Why this is important

Over 10 years ago Lawrence Lessig exclaimed, “The Code Is the Law”, and in a series of articles, presentations, and an influential book spread the idea among the digerati, but interestingly enough, those outside of technology didn’t adopt the idea as a truism.

Douglas Rushkoff recently released his most recent book, “Programed or be Programmed” that took the concept further and declared a course of action for future educators.

Kevin Slavin: Kevin Slavin: How algorithms shape our world:

YouTube: “TED: Conrad Wolfram: Teaching kids real math with computers”:

A Mathematician’s Lament: on education

Paul Lockhart wrote an accessible read on what is wrong with math education and the popular perception of math that is reinforced in culture that has been shared on the Web in quite a few corners. It deserves a wider read: “A Mathematician’s Lament”:

The art of proof has been replaced by a rigid step-by step pattern of uninspired formal deductions. The textbook presents a set of definitions, theorems, and proofs, the teacher copies them onto the blackboard, and the students copy them into their notebooks. They are then asked to mimic them in the exercises. Those that catch on to the pattern quickly are the “good” students.

The result is that the student becomes a passive participant in the creative act. Students are making statements to fit a preexisting proof-pattern, not because they mean them. They are being trained to ape arguments, not to intend them. So not only do they have no idea what their teacher is saying, they have no idea what they themselves are saying.

Even the traditional way in which definitions are presented is a lie. In an effort to create an illusion of “clarity” before embarking on the typical cascade of propositions and theorems, a set of definitions are provided so that statements and their proofs can be made as succinct as possible. On the surface this seems fairly innocuous; why not make some abbreviations so that things can be said more economically? The problem is that definitions matter. They come from aesthetic decisions about what distinctions you as an artist consider important. And they are problem-generated. To make a definition is to highlight and call attention to a feature or structural property. Historically this comes out of working on a problem, not as a prelude to it.

The point is you don’t start with definitions, you start with problems. Nobody ever had an idea of a number being “irrational” until Pythagoras attempted to measure the diagonal of a square and discovered that it could not be represented as a fraction. Definitions make sense when a point is reached in your argument which makes the distinction necessary. To make definitions without motivation is more likely to cause confusion.


Kevin Devlin: “Lockhart’s Lament – The Sequel”

Slashdot: “A Mathematician’s Lament — an Indictment of US Math Education”

G.H. Hardy:

A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.

Martin Gardner RIP

Unfortunately I did not know of Martin Gardner’s work until watching the embedded video. He inspired many and I’ll be looking to read some of his books, articles, and trying to learn some magic myself. We can all use a little magic.

Boing Boing: RIP Martin Gardner

Douglas Hofstader: Martin Gardner: A Major Shaping Force in My Life

The Nature of Things / Martin Gardner from Wagner Brenner on Vimeo.

Educational video on ‘Quants’ and their role in the financial crisis

YouTube: “Quants: The Alchemists of Wall Street (Marije Meerman, VPRO Backlight 2010)”

Related: “The Modelers’ Hippocratic Oath”: I will never sacrifice reality for elegance without explaining why I have done so….I understand that my work may have enormous effects on society and the economy, many of them beyond my comprehension.

Quotes from Paul Lockhart’s terrific essay about the state of Mathematics education in America

Paul Lockhart’s terrific essay about the state of mathematics education and what should be done: A Mathematician’s Lament (25 page must read PDF):

G.H. Hardy’s excellent description:

A mathematician, like a painter or poet, is a maker
of patterns. If his patterns are more permanent than
theirs, it is because they are made with ideas.

So mathematicians sit around making patterns of ideas. What sort of patterns? What sort of ideas? Ideas about the rhinoceros? No, those we leave to the
biologists. Ideas about language and culture? No, not usually. These things are
all far too complicated for most mathematicians’ taste. If there is anything
like a unifying aesthetic principle in mathematics, it is this: simple is
beautiful. Mathematicians enjoy thinking about the simplest possible things,
and the simplest possible things are imaginary.

By removing the creative process and leaving only the results of that process, you virtually guarantee that no one will have any real engagement with the
subject. It is like saying that Michelangelo created a beautiful sculpture,
without letting me see it.

By concentrating on what, and leaving out why, mathematics is reduced to an
empty shell. The art is not in the “truth” but in the explanation, the
argument. It is the argument itself which gives the truth its context, and
determines what is really being said and meant. Mathematics is the art of
explanation. If you deny students the opportunity to engage in this activity–
to pose their own problems, make their own conjectures and discoveries, to be
wrong, to be creatively frustrated, to have an inspiration, and to cobble
together their own explanations and proofs– you deny them mathematics
itself. So no, I’m not complaining about the presence of facts and formulas in
our mathematics classes, I’m complaining about the lack of mathematics in our
mathematics classes.

If teaching is reduced to mere data transmission, if there is no sharing of
excitement and wonder, if teachers themselves are passive recipients of
information and not creators of new ideas, what hope is there for their
students? If adding fractions is to the teacher an arbitrary set of rules, and
not the outcome of a creative process and the result of aesthetic choices and
desires, then of course it will feel that way to the poor students.

Teaching is not about information. It’s about having an honest intellectual relationship with your students. It requires no method, no tools, and no training. Just the ability to be real. And if you can’t be real, then you have no right to inflict yourself upon innocent children. In particular, you can’t teach teaching. Schools of education are a complete crock. Oh, you can take classes in early childhood development and whatnot, and you can be trained to use a blackboard “effectively” and to prepare an organized “lesson plan” (which, by the way, insures that your lesson will be planned, and therefore false), but you will never be a real teacher if you are unwilling to be a real person. Teaching means openness and honesty, an ability to share excitement, and a love of learning. Without these, all the education degrees in the world won’t help you, and with them they are completely unnecessary.

It’s perfectly simple. Students are not aliens. They respond to beauty and
pattern, and are naturally curious like anyone else. Just talk to them! And
more importantly, listen to them!

Read the whole thing. This essay has reinforced some beliefs of mine about software engineering, teaching and parenting.

Slashdot has a decent thread on the piece.