Harvard Educational Review


VOLUME FORTY  NUMBER TWO                                                                       

MAY 1970  


Illiteracy in America

Paulo Freire

David Harman

Carol Chomsky



Neil Postman

Jane w. Torrey

Wayne O’Neil

Caleb Gattegno

Armando Martinez

Frank and Robert Laubach



Jeanne Chall

David Harman

Ephraim Isaac

Dorothy Jones

Frank Laubach

Robert Laubach

Wayne O’Neil


The Problem of Reading is Solved


Schools for the Future Foundation, Inc.

Dr. Caleb Gattegno holds that reading is a relatively simple process of matching the sound system of a language with its written system.  Children can be easily taught to do this, helped by color-coded instructional material, since they internalized the algebraic and temporal structure of their language when they learned to talk.

As a scientist I came to the problem of reading as I did to problems in the field of mathematics or physics, by first defining them and then attempting to find solutions.

There is indeed a problem of reading and it can be formulated as follows: “how to provide awareness that a system of signs isomorphic to the system of sounds of one’s language exists and can play a certain number of the roles of the system already owned?”

Looking carefully at the two systems we find,

a)     that since the first is in time, the second must also display temporal features and hence the signs, which are space forms, must be aligned (the line being an isomorphic system to time, intervals on this line represent durations).

b)    that since time is irresversible, we must choose a direction on the line to display this property.  A succession of lines, usually parallel, is needed to accommodate greater durations of speech.

Inventors of writing have shown awareness of the temporal nature of speech and of the capacity of the straight line to be used as an isomorphic system.  They have also been aware that, with a small number of distinct sounds and an algebraic procedure, one can produce any number of combinations and permutations.

Speech itself displays some algebraic structures which can be taken advantage of when, instead of one sign for each word or idea (as in Chinese and hieroglyphic ideograms), one attempts to render sounds by associating one sign to each sound and conversely.  Although not many languages with a past have managed to preserve this one-one correspondence, we can safely assume that enough correspondence existed initially to make it possible to render evident the algebraic rules which, from the small number of signs selected initially, would produce the representations of all the words of the language.

A careful study of speech and of some “phonetic” languages such as Hindi would soon reveal that the algebra in question uses four operations: substitution, addition, reversal, and insertion.  It is unnecessary to use subtraction though some cases can be perceived as implying it. 

It is obvious that vowels and syllables can be abstracted from the whole of one’s speech.  Their combinations and permutations blended in time produce the words we wish to utter.  Therefore vowels and syllables are the units of speech, not consonants.

Having found that the awareness of algebra and the awareness of time were essential in the production of speech and its written form, it became clear that to teach people to read was to give them the rules which they themselves could use to obtain, from as little data as was necessary the totality of the language.

The concept of restricted language helped to devise the progressive solution.  It is possible to display all the conventions of writing if one uses two vowels and designates as “words” sequences of these two sounds uttered as one unit.  Thus if a (as in at) and i (as in if) are the two selected sounds for which these signs are chosen, it is possible to form temporal sequences by pointing at them in turn, or repeatedly, and produce: a, i, aa, ii, ai, ia, iai, iia, aai, aia, etc. from which “sentences” can be formed which can be “read,” written, dictated:


                                    -ia        a          aa         i           ai         i           ii          a

                                    -aia       ia         a          ai         aaa       iai        aa         etc…..


Here we provide alignment, separation by a blank of successively distinguishable words, sequencing from left to right and top to bottom above the line, and a different sign for a different sound – ie., each of the conventions of written English.  These conventions learned independently of meaning, have a meaning of their own.

The first group of restricted languages is formed of a few vowels.  To form syllables, we can introduce consonants, not giving them a sound, but showing how they affect each vowel so as to form a number of syllables. These can now be blended with each other or with vowels to form new words and sentences in the new restricted language, whose meaning emerges if the melody of the languages integrates them.  For example: at, it, us, as, is, provide as is, it is, is it, it is us, is it as it is, and so on.

It becomes clear that the powers we all used as infants to break the speech code of our milieu can be used to reach the written code.  Indeed, young children have been able to approach the written word in this way to break the code of the traditional orthography.  They are helped to recognize through color the identity of sounds, but they learn to read essentially because we respect the algebraic and temporal nature of speech, which are already a part of their awareness.  In the case of English it is necessary to provide three groups of restricted languages:

  • one - to display that a system of signs can be used to elicit production of sounds that strangely remind one of English,

  • one - to survey the totality of the sounds of English, and

  • one - to survey the totality of the spellings of English.

In each group the successive languages integrate the preceding one.  Reading with comprehension follows.  Vocabulary increases when meanings are introduced deliberately or result unequivocally from the context.

“Word attack” is another way of naming the algebraic passage from vowels and syllables to words, and from one word to another.  As more and more spellings are met, the increased mastery of the process permits a shifting from elaborate analysis to a quick survey of probabilities and the selection of a sound that meets morphological demands as well as contextual exigencies.  In this approach, learners have full responsibility all through their apprenticeship.  The presentation makes sense to them all the time since it starts with them and their experience and calls in all their gifts.  No distraction or interference is allowed in.  The teacher becomes a silent guide, challenging with his pointer, but also suggesting exciting games which provide intellectual instruments as well as a sense of power over the new medium.  Generally, if learners enter the games, the problem of reading for them is solved in a few hours and reading as a skill becomes an automatic function as for adults. 

With regard to the problem of illiteracy we come to the following conclusions. 

First, illiteracy cannot be the result of the nature of the skill to be mastered.  Possibly what is causing illiteracy is the fact that the simple process of learning to read is interfered with by so many “bright ideas” and so many distractions that many sensitive children become confused and lost and give up.

Second, remediation in reading can be most easily achieved by stressing the isomorphism of the sound and written systems and by letting students construct sequences of words and sentences as appropriate representations for the sounds uttered in the environment.  This task may only require 20 hours or less.

Finally, illiteracy can be wiped out at a far smaller cost than any wild dreamer has ever dreamed.  I am prepared to do the computation if asked.

Sima Gandhi