Reforming Education–Concepts

There is an interesting concept in teaching the concepts of math and science in early education.  Children as young as kindergarteners can learn the basic concept of number though simple experiential learning.  A 4-year old can learn that four popsicle sticks are always four sticks, no matter how they are arranged; or the equally important concepts of unity (the number 1) or zero by applying the same techniques.  As simple as it seems, learning the very underlying principles of mathematics – one thing is very different from many things; and no things counts as much as one thing or many things is critical not only for mathematical reasoning, but all reasoning. 

An article in the Wall Street Journal today (11/29) gives other examples of work done by the Early Mathematics Project of the Erikson Institute.

“Math instruction is omnipresent if not always apparent…It shows up when [a student] mimics a teacher’s syncopated clapping pattern….The students don’t know it, but they are learning fundamental math concepts such as connecting numerals to quantity, building patterns, and the idea that adding something or someone creates a larger number.

“’Now I work to make [students] mathematical thinkers and I want them to be able to tell me why and how they know things’, said [a teacher in the Erikson Project].

An Erikson professor…said proper math instruction [at an early age] helps students develop reasoning and logical thinking skills that prepare them to learn any subject.

[The Director of the Project] said the Project is designed to teach mathematical thinking rather than basic math procedures. Instead of learning, for example, to recognize the numeral 4 and it comes between 3 and 5, Erikson wants to understand that 4 represents a quantity and has meaning”

It is clear from this Project and others like it that very young children can understand and master basic concepts – not just mathematical ones, but even metaphysical ones.  I remember taking my 3-year old daughter up on the roof of our apartment building.  She loved to wander around amongst the pipes and cables, and was especially interested in holes.  She would look down the air pressure pipes and say “hole”.  When we walked along sidewalks and over grates, she would say “hole”.  I then realized that she understood the basic nature of a hole – that a hole was a hole no matter where it was found – and I encouraged her whenever we went out.  I then explained to her that a hole could be two-dimensional, but it still had the same basic properties as a three-dimensional hole – you could put your finger through it rather than down it, pour water through it rather than down it.  It was a hole.  She had learned a basic, fundamental rule – how to group objects into categories, and how to apply one definition to all objects that fell within that grouping.  She and other children her age and younger can learn when a thing is a thing and when it is not perhaps the essential building block of perception.

My daughter learned because of some natural hardwiring and intelligence (If Chomsky is right, and we are hardwired for language; and if language and thought are functions of each other - there can be no thought without language and vice-versa – then the ability to conceptualize may also be hardwired), and teaching.  I took every opportunity to strengthen in her what I knew was a particular intellectual ability.  There is no reason why we cannot do the same thing in formal education.

My son was in the third grade, and he had a love of raptors – eagles, hawks, any bird of prey.  I think it was part of the boy-dinosaur phenomenon, and through him I learned all about these elegant and fierce birds, how they are grouped, and most importantly when a bird of prey is a raptor, and when it is something else that resembles a raptor – like an owl – but is not in the same phylogenetic category. We went through all the raptors and discussed those that were clearly in the middle of the category – i.e. no doubt about classification – and those that were outliers about which there was still academic discussion.

The point was even at 8 years old, my son was forming the foundation of solid scientific inquiry.  Classification is at the heart of science, and the work of Linnaeus (plants) and Darwin (animals and everything) were based on that simple intellectual principle.

Causality and inductive reasoning can also be taught in the earliest grades.  If you place an apple on the edge of a table and push it off so it drops to the floor, you can ask the child “How did the apple get onto the floor?” to which you will usually get the correct answer.  However, when you place an apple on the floor near the table, and ask a different child how did it get there, you are encouraging and teaching deductive reasoning.

I have written earlier about the importance of encouraging behavioral abilities such as risk taking and innovative thinking in early education.  Children can learn about the importance of taking risks, setting goals, failing, and regrouping to succeed just by playing on the jungle-gym.  How much higher can I climb without falling?  If I fall, will I get hurt?  Bobby climbed to the top.  How was he able to risk falling and succeed in the climb.  Unfortunately because of liability concerns, old-fashioned, risky jungle-gyms are being dismantled in favor of safe equipment, and little learning can take place.

Similarly innovative thinking can be stimulated at a very young age.  In addition to learning simple facts of math, reading, history, and nature, children can be challenged to come up with something new – something based on perception, but equally a part of their imagination.  For example, “Look at a picture of a bird, then change something about it so that it can do something a bird cannot do”.  Or, display a number of randomly selected items that do not resemble any specific object – that is, they do not look like hammers, spoons, etc.; but have basic structural features that might allow them to serve as these tools and utensils.  “Take any object you see on the table, and tell me what it could be used for”.  The examples and ideas are far too many to list.

Learning how to compete is an intrinsic part of any early education whether it is specifically encouraged or not.  Grades reflect competition, even though in today’s PC atmosphere they are explained as useful tools for self analysis only.  Learning how to compete as a group with other groups on a design challenge is another story altogether.  That is two groups of children are given the same problem to solve with blocks.  “Which can be the first group to make something that moves?”.  This learning can be the basis for entrepreneurship and management. 

All of the above discussion has not point unless this type of education has a purpose.  Of course it is important to learn for the sake of learning, but we live in an increasingly competitive world and there are fewer chances for “its own sake”.  Our schools are not turning out the economically productive and civically aware citizens that are needed.  Strong cognitive skills, especially reasoning, are necessary for everything; but they are particularly important in being able to organize, manage, and utilize data; to be able to tell reliable information from that which is not; to judge the veracity of a source, etc.  The same reasoning is necessary to judge the reasonableness of a political statement, to sift through noise, rumor, innuendo, and speculation to get to the truth. 

There is no doubt that young children also need to have the very practical skills to thrive in the 21st century – to learn how to navigate through a complex, virtual world which will soon cease to resemble that of today; but they cannot really apply these tools, these new technologies unless they can think about how best to apply them in a cost-effective way.  This requires the same critical thinking that we use today.

In the same edition of the Wall Street Journal today, I saw an article about how Toyota has changed its assembly line.  Instead of cars coming down the line head to tail, they changed them so that they come down parallel to each other.  This, the Japanese found, cut down production time because it reduced by seconds the time it took for a worker to go from one car to another.  Some engineer looked at the assembly line, used his critical, analytical, and creative faculties and made a quantum leap – a drastic, dramatic change, the first after 100 years of car making.   It is this skill – looking at a familiar object, routine, or event and jumping way beyond tweaking, adjusting, or modifying – that can be taught in kindergarten and should be.

This article will be published in THE REAL STORY www.realstorypublishing.com