Einstein on his school experience

One had to cram all this stuff into one’s mind, whether one liked it or not. This coercion had such a deterring effect that, after I had passed the final examination, I found the consideration of any scientific problems distasteful to me for an entire year … is in fact nothing short of a miracle that the modern methods of instruction have not yet entirely strangled the holy curiosity of inquiry; for this delicate little plant, aside from stimulation, stands mainly in need of freedom; without this it goes to wreck and ruin without fail. It is a very grave mistake to think that the enjoyment of seeing and searching can be promoted by means of coercion and a sense of duty. To the contrary, I believe that it would be possible to rob even a healthy beast of prey of its voraciousness, if it were possible, with the aid of a whip, to force the beast to devour continuously, even when not hungry – especially if the food, handed out under such coercion, were to be selected accordingly.

Seeing that even almost a hundred years later it is almost unchanged gives one an idea of how little effort has gone into changing how we learn.

Genetics and human nature

Usually, in the discussion regarding human nature, there is a group of academics who would like to put all the differences amongst humans to non-genetic components. That is to say, the cultural heritage plays a much more important or the only important role in the transfer of characteristics. In the case of education, this is one of the most contested topics. The nature-nurture debate as it is known goes to the heart of many theories of human behaviour, learning and cognition. The behaviourist school was very strong until the mid 20th century. This school strongly believed that the entirety of human learning is dependent only on the environment with the genes or (traits inherited from the parents) playing little or no role. This view was seriously challenged on multiple fronts with attacks from at least six fields of academic inquiry: linguists, psychology, philosophy, artificial intelligence, anthropology, and neuroscience. The advances in these fields and the results of the studies strongly countered the core aspects of behaviourism. Though the main thrust of the behaviourist ideas seems to be lost, but the spirit still persists.  This is in the form of academics who still deny any role for genes, or even shun at the possibility of genes having any effect on human behaviour. They say it is all the “environment” or nurture as they name it. Any attempt to study the genetic effects are immediately classified as fascist, Nazi or equated to social Darwinism and eugenics. But over several decades now, studies which look at these aspects have given us a mounting mountain of evidence to lay the idea to rest. The genes do play a definitive role and what we are learning is that the home environment may not be playing any role at all or a very little role in determining how we turn out. Estimates range from 0 to 10%. The genes, on the other hand, have been found to have about 50% estimate, the rest 40% being attributed to a “unique”  environment that the individual experiences.   Though typically, some of the individuals in academia argue strongly against the use of genetics or even mention of the word associated with education or any other parameters related to education. But this has to do more with their ideological positions, which they do not want to change, than actual science. This is Kuhnian drama of a changing science at work. The old scientists do not want to give up on their pet theories even in the case of evidence against them. This is not a unique case, the history of science is full of such episodes.

Arthur Jensen, was one of the pioneers of studying the effect of genetic heritability in learning. And he lived through the behaviourist and the strong nurture phases of it. This quote of his summarises his stand very well.

Racism and social elitism fundamentally arise from identification of individuals with their genetic ancestry; they ignore individuality in favor of group characteristics; they emphasize pride in group characteristics, not individual accomplishment; they are more concerned with who belongs to what, and with head-counting and percentages and quotas than with respecting the characteristics of individuals in their own right. This kind of thinking is contradicted by genetics; it is anti-Mendelian. And even if you profess to abhor racism and social elitism and are joined in battle against them, you can only remain in a miserable quandary if at the same time you continue to think, explicitly or implicitly, in terms of non-genetic or antigenetic theories of human differences. Wrong theories exact their own penalties from those who believe them. Unfortunately, among many of my critics and among many students I repeatedly encounter lines of argument which reveal disturbing thought-blocks to distinguishing individuals from statistical characteristics (usually the mean) of the groups with which they are historically or socially identified.

–  Arthur Jensen, Educability and Group Differences 1973

As the highlighted sentence in the quote remarks, the theories which are wrong or are proven to be wrong do certainly exact penalties from their believers. One case from history of science being the rise and rise of Lysenkoism in the erstwhile USSR. The current bunch of academics who strongly deny any involvement of genes in the theories of human learning are no different.

Implicit cognition in the visual mode

Images become iconified, with the image representing an object or
phenomena, but this happens by enculturation rather by training. An
example to elaborate this notion is the painting Treachery of
Images by Belgian surrealist artist René Magritte. The painting is
also sometimes called This is not a pipe. The picture shows a
pipe, and below it, Magritte painted, “Ceci n’est pas une pipe.”,
French for “This is not a pipe.”

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When one looks at the painting, one
exclaims “Of course, it is a pipe! What is the painter trying to say
here? We can all see that it is indeed a pipe, only a fool will claim
otherwise!” But then this is what Magritte has to say:

The famous pipe. How people reproached me for it! And yet, could you
stuff my pipe? No, it’s just a representation, is it not? So if I had
written on my picture `This is a pipe’, I’d have been lying!

Aha! Yess! Of course!! you say. “Of course it is not a pipe! Of
course it is a representation of the pipe. We all know that! Is this
all the painter was trying to say? Its a sort of let down, we were
expecting more abstract thing from the surrealist.” We see that the
idea or concept that the painting is a \emph{representation} is so
deeply embedded in our mental conceptual construct that we take it for
granted all the time. It has become so basic to our everyday social
discourse and intercourse that by default we assume it to be so. Hence
the confusion about the image of the pipe. Magritte exposes this
simple assumption, that we so often ignore. This is true for all the
graphics that we see around us. The assumption is implicit in all the
things we experience in the society. The representation becomes the
thing itself, for it is implicit in the way we talk and communicate.

Big B and D

When you look at a photo of something or someone, you recognize
it. “This is Big B!” you say looking at the painting! But then you
have already implicitly assumed that the representation of Big B is Big B. This implicit assumption comes from years of implicit training from being submerged in  the sea of the visual artefacts that surround and drown us. This association between the visual representation and the reality it represents had become the central theme of the visual culture that we live in. The training that we need for such an association comes from the peers and mentors that surround us from the childhood. The meaning and the association of the images is taught/caught over the years, so much so that we assume the abstract association is the normal way things are. In this way it becomes the implicit truth, though when one is pressed, the explicit connections are brought out.

Yet when it comes to understanding images in science and mathematics, the same thing doesn’t happen. There is no enculturation of children into understand the implicit meaning in these images. Hardly there are no peers or mentors whose actions and practices can be imitated by the young impressible learners. The practice which comes so naturally in other domains (identifying actor with a picture of the actor, or identifying a physical space with a photo) doesn’t happen in science and mathematics classrooms. The notion of practice is dissociated from the what is done to imbibe this understanding in the children. A practice based approach where the images become synonymous with their implied meaning is used in vocabulary might one very positive way out, this is after all practitioners of science and mathematics learn their trade.

Mathematical Literacy Goals for Students

National Council of Teachers for Mathematics NCTM proposed these five goals to cover the idea of mathematical literacy for students:

  1. Learning to value mathematics: Understanding its evolution and its role in society and the sciences.
  2. Becoming confident of one’s own ability: Coming to trust one’s own mathematical thinking, and having the ability to make sense of situations and solve problems.
  3. Becoming a mathematical problem solver: Essential to becoming a productive citizen, which requires experience in a variety of extended and non-routine problems.
  4. Learning to communicate mathematically:  Learning the signs, symbols, and terms of mathematics.
  5. Learning to reason mathematically: Making conjectures, gathering evidence, and building mathematical arguments.
National Council of Teachers of Mathematics. Commission on Standards for School Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Natl Council of Teachers of.