1973 book why johnny cant add

Kline makes a pro-applied argument, which in the long run is not what truly beautiful Math is about, I wholeheartedly agree that it's trough intuitive approach we first come about it and as the target group of this book is schoolchildren, it is only thoughtful to use natural ideas and curiosity supplied by the physical world to guide them through their first steps.

Then, however, the distinction has to be made and it's with the purist side of the pool that I stick e. As While M. Aug 04, Dale rated it liked it Recommends it for: various.

Shelves: education. It's old, but still scary. As the parent of a crowd of math-phobic, or at least math-disliking, kids, I wondered why math seems so hard for them, and so pointless. Some of it I recognised as techniques used when I was in school graduated high school in - this book was published in , although we never went quite as far with it as this book suggests.

Some good points. A bit of an overtone of hysteria, but then if the examples given are actually accurate, perhaps not overstated. Un libro aparentemente anticuado pero que da mucho que pensar.

Desafortunadamente, dedica mas tiempo a exponer los problemas que a discutir soluciones. Liquidlasagna rated it it was amazing May 26, Chong rated it liked it Jan 02, Darren rated it really liked it Nov 22, Molly rated it really liked it Apr 11, Aisley Joy rated it really liked it Aug 27, Craig rated it liked it Feb 25, Frix Lupio rated it it was amazing Sep 05, Glenn Daniel Marcus rated it really liked it Jan 01, Eka Fatma rated it really liked it Jan 12, Gordon Horne rated it liked it Jan 13, Lauren Hug rated it it was ok Jul 09, Jim D'Ambrosia rated it liked it Apr 02, John Pattillo rated it really liked it Mar 23, Armani rated it liked it Aug 20, Marco rated it really liked it Oct 08, Sang rated it really liked it Dec 22, Everett Dumont rated it liked it Apr 12, Don Beniking Jr.

James Nickel rated it it was amazing Jun 05, Alejandro rated it really liked it Sep 19, Brian rated it liked it Jun 22, Chiung-yi Tseng rated it really liked it Dec 08, There are no discussion topics on this book yet.

Be the first to start one ». Readers also enjoyed. About Morris Kline. Morris Kline. Morris Kline was a Professor of Mathematics, a writer on the history, philosophy, and teaching of mathematics, and also a popularizer of mathematical subjects. Have glimpses that would make me less forlorn. Let us look into a modern mathematics classroom. No, reproves the teacher, the correct answer is because the commutative law of addition holds.

Evidently the class is not doing too well and so the teacher tries a simpler question. The teacher is aghast. The students are now wary of replying, but one more courageous youngster does do so: "I am Robert Sinith. The teacher looks incredulous and says chidingly, "You mean that you are the name Robert Smith? Of course not. You are a person and your name is Robert Smith. Now let us get back to my original question: Is 7 a number? The symbol 7 is a numeral for the number.

The teacher sees that the students do not appreciate the distinction and so she tries another tack. Then she answers her own question: "Of course not! But the numeral 3 is half of the numeral 8, the right half. The students are now bursting to ask, "What then is a number? This is extremely fortunate for the teacher, because to explain what a number really is would be beyond her capacity and certainly beyond the capacity of the students to understand it.

And so thereafter the students are careful to say that 7 is a numeral, not a number. Just what a number is they never find out. The teacher is not fazed by the pupils poor answers. She asks, "How can we express properly the whole numbers between 6 and 9? A teacher thoroughly convinced of the vaunted value of precise language, and wishing to ask her students whether a number of lollipops equals a number of girls, phrases the question thus: "Find out if the set of lollipops is in one-to-one correspondence with the set of girls.

Bent but not broken, the teacher asks one more question: "How much is 2 divided by 4? I subtracted 4 from 2 and got minus 2. It wouId seem that the poor children would deserve some relaxation after school, but parents anxious to know what progress their children are making a1so query them.

Flabbergasted, he re-phrased the question: "But how many apples are 5 apples and 3 apples? The child didn't quite understand that "and" means plus and so he asked, "Do you mean 5 apples plus 3 apples? Another father, concerned about how his young son was getting a1ong in arithmetic, asked him how he was faring. I just add and get the right answer, but she doesnt like that. We shall examine the major features in greater detail in due course and we sha1l consider their merits and demerits. Though the traditional curriculum has been affected somewhat in recent years by the spirit of reform, its basic features are readily described.

The first six grades of the elementary school are devoted to arithmetic. In the seventh and eighth grades the students take up a bit of algebra and simple facts of geometry such as formulas for area and volume of common figures. The first year of high school is concerned with elementary algebra, the second with deductive geometry, and the third with more a1gebra generally called intermediate a1gebra and with trigonometry. The fourth high schooi year usually covers solid geometry and advanced algebra; however, there has not been as much uniformity about fourth-year work as there has been for the earlier years.

Several serious criticisms of this curriculum have been voiced repeatedly. The first major criticism, which applies to algebra in particular, is that it presents inechanical processes and therefore forces the student to rely upon memorization rather than understanding.

The nature of such mechanical processes can readily be illustrated. Let us consider an arithmetical example. This number is One then divides 4 into 12, obtains 3, and mu1tiplies the numerator 5 of the first fraction by 3. Siniilarly one divides 3 into 12, obtains 4, and multiplies the numerator 2 of the second fraction by 4. The result thus far is to convert the above sum into the equal sum. A good teacher would no doubt do his best to help students grasp the rationale of this process, but on the whole the traditiona1 curricu1um does not pay much attention to understanding.

It relies upon drill to get, students to do the process readily. After students learn to add numerical fractions they face a new hurdle when asked in a1gebra to add fractions where letters are involved. Though the saime process is used to ca1cu1ate. Again the curriculum relies upon drill to put the lesson across. The students are asked to carry out the additions in nurmerous exercises until they can perform them readily.

Hence the students are faced with a bewildering variety of processes which they repeat by rote in order to master them. The learning is almost always sheer memorization. It is a1so true that the various processes are disconnected, at least as usually presented. They rarely have much to do with each other. They are like pages torn from a hundred different books, no one of which conveys the life, meaning and spirit of mathematics.

This presentation of algebra begins nowhere and ends nowhere. After a year of such work in algebra the traditiona1 curriculum shifts to Euclidean geometry. Here mathematics sudden1y becomes deductive. They then prove theorems by applying deductive reasoning to the axioms. The theorems follow each other in a logical sequence; that is, the proofs of later theorems depend upon the conclusions already established in the earlier theorems. The sudden shift from mechanical algebra to deductive geometry certainly bothers most students.

They have not thus far in their mathematics education learned what "proof" is and must master this concept in addition to learning subject matter proper. The concept of proof is fundamnental in mathematics, and so in geometry the students have the opportunity to learn one of the great features of the subject. But since the final deductive proof of a theorem is usually the end result of a lot of guessing and experimenting and often depends on an ingenious scheme which permits proving the theorem in the proper logical sequence, the proof is not necessarily a natural one, that is, one which would suggest itself readily to the adolescnt mind.

Moreover, the deductive argument gives no insight into the difficulties that were overcome in the original creation of the proof. Hence the student cannot see the rationale and he does the same thing in geometry that he does in algebra. He memorizes the proof. Another problem troubles many students.

Since algebra is also part of mathematics, why is deductive proof required in geometry but not in algebra? This problein becomes more pointed when students take intermediate algebra, usually after the geometry course, because there proof is again abandoned in favor of techniques.

With or without proof, the traditional method of teaching results in far too much of only one kind of learning - memorization. The claim that such a presentation teaches thinging is grossly exaggerated.

By way of evidence, if evidence is needed, I have challenged hundreds of high school and college teachers to give open book examinations. This suggestion shocks them. But if we are really teaching thinking and not memorization, what could the students take from the books? The traditiona1 curriculum has also become too traditional.

Some topics that received considerable emphasis for generations have lost significance but are still retained. One example is the solution of triangies in trigonometry. Here, given some parts - sides and angles of a triangle, the theory shows how to.

This topic, which had far more relevance when trigonometry was taught primarily to prospective surveyors, should have been deemphasized long ago.

Another example is the computation of irrational roots of polynomia1 equations. The method usually taught, called Horner's rnethod, requires several weeks of class tinre and does not warrant it.

However, the latter can be factored if we are willing to introduce irrational numbers. Beyond the few defects we have already described, the traditional curriculum suflers from the gravest defect that one can charge to any curriculum - lack of motivation.

It has no value other than as a tool for learning other things, namely more advanced, conceptual math. She would know, unlike many modern math educators, that the point is not to understand arithmetic, but to use arithmetic in order to understand. You learn arithmetic, not in order to think about arithmetic, but in order not to think about it. No one believes that a carpenter is made better able to build a house by contemplating the complex process by which his tools are made.

No one believes that you can become a better writer by learning more about how the alphabet system was developed. T o think too much about the things that are supposed to help you think can be positively detrimental. The precise opposite is the case. Civilization advances by extending the number of important operations which we can perform without thinking about them. They are the ones who sent men to the moon and who pioneered the computer revolution. They followed the great German scientists of the nineteenth century whose classical education enabled them to conduct the relativity and quantum revolutions in physics, and the development of genetics in biology.

I asked my father one time whether he took calculus in high school. Poor man. Originally published in The Classical Teacher Spring edition. He holds a B.

He is widely-quoted on educational issues and other issues of public importance, and is a frequent guest on Kentucky Educational Television's "Kentucky Tonight," a weekly public affairs program. His articles on current events have appeared in numerous newspapers, including the Louisville Courier-Journal and the Lexington Herald-Leader. You must be logged in to post a comment. Remember me Log in. Lost your password? If you are having trouble logging in, you may need to delete any site cookies in your browser for memoriapress.

What Is Classical Education? Winter Letter from the Editor: Spring July 31, at pm Log in to Reply. Jan England says: Very enjoyable and informative reading.