Morris Kline in his book Why Johnny Can’t Add: the Failure of the New Mathematics discusses issues regarding modern mathematics. He argues that modern mathematics merely introduces further confusion in the way mathematics is taught even though it was formed to correct errors in the traditional way that mathematics was taught.
The book starts with a catchy introduction about how mathematics is taught using the new curriculum. Mr. Kline clearly drives home the point that modern mathematics confuses those who are taught under this curriculum. He mentions a teacher teaching mathematical concepts to students. Yet even though the teacher introduces many concepts during his lecture, he only leaves the students more confused than before he started the lecture.Mr. Kline mentions that traditional mathematics has its share of faults which prompted the move for the mathematics teaching reform. He stresses that traditional mathematics stresses on mechanical ways of solving problems instead of making students understand, which should be the goal in all types of teaching.
Students end up memorizing steps and proofs without really understanding what the point was in solving mathematical problems.Further on he discusses the origins and evolution of the new mathematics. Mr. Kline’s exposition on the subject is detailed and comprehensive despite the fact that he mentions only the contribution of only a few groups which were committed to revamp the traditional curriculum. Many other groups contributed to the work that ultimately became modern mathematics, but the author argues that these works tended to be imitations of each other.
Thus these groups can be considered to form a single movement that produced modern mathematics.In the succeeding chapter, modern mathematics is shown to be ineffective as a substitute for traditional mathematics. Whereas in the traditional method learners of mathematics mostly relied on rote memory, modern mathematics more often than not just confuse its learners. The author made his point very clear with his exposition on the deductive approach to solving problems.The deductive approach relied too much on rules and logic. This might be a good thing if the rules were at least made clear beforehand, but modern mathematics did not properly define such rules. The learner is also faced with a ton of them to use.
Such structure based on rules and logic is then contrasted to the fact that the masters of mathematics from antiquity up to more recent times relied on intuition in solving mathematical problems. Modern mathematics in effect leaves the learner to memorize proofs instead of really understanding concepts thus defeating the purpose for which modern mathematics was made.Other problems the author exposes in the book with regard to modern mathematics are rigor and language. It seems that modern mathematics is obsessed with making problems that have to be solved by as much rigor as possible.
It is also obsessed with trying to make problems as rigid as they can come with respect to language. It makes it a point to leave no room for ambiguities. At this part, it can be seen that the author has a keen way of showing the absurdity of such an assumption.
Students end up being more confused. Readability and even comprehensibility of mathematics texts are sacrificed. With such language the author argues that only experts would understand the text, but such texts are forced into novices.The insular way of promoting mathematics is also a point in the author’s case against modern mathematics. Mathematics divorced itself from fields where it is being useful.
The author expresses alarm at this trend by arguing that students have become less appreciative of the subject. They don’t see math applied to relevant situations. The situation is further aggravated by the introduction of new concepts such as set theory, matrices, symbolic logic, abstract algebra, and congruence. Such subjects are used almost purely in the study of pure mathematics unadulterated by fields such as engineering and astronomy!Formulators of the new mathematics curriculum did this in an attempt to present mathematics in a logical and orderly manner. Yet the author argues to his readers that what this does is just further confuse learners under this new curriculum.Nevertheless, the strongest argument Mr. Kline has against modern mathematics is the way it was developed and eventually accepted.
There were no experiments to test whether the new curriculum would be better than the old or traditional curriculum. They were directly imposed upon students. Nevertheless, Mr. Kline does admit that testing for positive results or even negative results of the teaching modern mathematics can be difficult. Courses that claim to be modern may just be mixtures of traditional and modern concepts. Only “smart” students may have been enrolled under the new mathematics while those who were not as smart were left with the traditional method.The author, however, points out criticism from those who worked with the development of new mathematics to clamor for a change in how mathematics is to be taught. To give a darker tone to the new mathematics curriculum, the author mentions ulterior motives.
Teachers who may have struggled with topics suddenly see easy and logical proofs as teaching tools. This may seem easy to them who have some mathematics background, but it may not be the same case for first time learners. Teachers who wanted to be recognized began writing modern mathematics textbooks. Publishers who wanted to profit from the controversy joined in. Soon there was no turning back.
Students are now stuck with modern mathematics.The book shows that the author was passionate in his campaign for a reform in the teaching of mathematics. The traditional methods were not sufficient.
Thus it was replaced by the new mathematics curriculum. Yet the new mathematics still did not make the cut. In fact it merely added more confusion in the teaching of mathematics. His use of exposition plus some sarcasm and good natured humor and common sense forms an informative and interesting text.The text also makes readers into thinkers.
In a world where modern mathematics has largely replaced traditional mathematics, one is left wondering with many questions after reading the book. What if I learned mathematics in the traditional way? Could I have loved math then? Should we reform modern mathematics as Mr. Kline argues in the book? Would it even make a difference if the way of teaching mathematics is to be reformed? Would there come a time when ordinary students would eventually love math?Yet in conclusion, even though the book is almost light in its approach to the subject, it does it with a readability that warrants attention to its arguments.