Issue 107 / September - October 2015
Why Math Education?
Bruce J. Parker
In this article, we will discuss why math education is a very crucial component of the core K-12 and college curricula. We will underline the controversial aspects of the topic which have been discussed for many years, and try to answer the arguments of both sides by outlining the importance of math education in modern society.
Many students in elementary, middle, and high school have problems with math classes. Many students and their parents often ask why math is an important part of the curriculum for all levels of their education. Most of the time, the main complaint is, "Why do we have to take so many 'useless' math courses? There is no direct or immediate use of most of the material we learn in our math classes." Even though this assertion seems to be right for the "direct/immediate use" aspect at first sight, we will try to go deeper and consider the question from a different point of view.
An anecdote from recent US math education history proves the controversial nature of the subject. The paper, "A Brief History of American K-12 Mathematics Education in the 20th Century"1 by David Klein gives a good account of the developments in US math education in the 20th century. In the early 1900s, one of the nation's most influential education leaders, William H. Kilpatrick, rejected the notion that studying mathematics contributed to mental discipline. He even defended his view that mathematics is harmful rather than helpful to the kind of thinking necessary for ordinary living. At the time, his opinions about the teaching of math and algebra were supported by many experts. For example, in the 1920s, Commissioner of Education for the state of Massachusetts, David Snedden, said that, "Algebra...is a nonfunctional and nearly valueless subject for 90 percent of all boys and 99 percent of all girls--and no changes in method or content will change that." Hence, at the period, the students were taught basic math skills which would have immediate practical applications. However, after World War II, policymakers began to advocate for a stronger math curriculum, a movement motivated by the space race of the 1950s. But later, and especially in the 1990s, the controversy of the "math wars" among parents, professional educators, and mathematicians was raised again. With the involvement of many educators and mathematicians, the US' math curricula and textbooks were remodeled to provide students with stronger math skills, which are essential in global competition.
The importance of math in the core curriculum
The aim of the core curriculum for K-12 (and for college) is to prepare people for life; to cultivate the verbal, numerical, and visual skills necessary to analyze and synthesize information; and to foster an understanding of the intellectual and cultural wealth of modern society. This basic education aims to provide the members of society a basis and medium to communicate, to live together, and to advance within the society.
If we take out one or two of the courses like literature, arts, social science, or the natural sciences from the core curriculum, it is not hard to see that students would definitely miss out on some of our rich human experiences; it would be hard for them to adapt to the society in some ways, since they would have no idea about some very basics elements of that society. Beyond this direct implication, each of these courses affects people in a deeper way, encouraging them to explore who they are, and to be a "more complete" member of society. These courses enrich and deepen our understanding of what our surroundings are and how they function in the world. For example, if literature was taken out from the core curriculum, as an immediate consequence, it would weaken students' communication skills with other people; and moreover, people would miss out on the first chance of interaction with an excellent medium to express human feelings, experiences, and imagination. If we took out the natural sciences, most of us would be ignorant about why and how many things came to be. The deeper effect would be that it would cause people to get used to ignorance, as there would be many things around them which they had no idea about.
Now, let's go back to the original question. What if we took out math from the core curriculum? No one opposes the need for basic math at the elementary school level, as it gives basic knowledge of numbers, counting, etc., which are undeniably very basic skills in a person's life. So the question is, "Do we really need to have math in middle and high school, as well as college curriculums, as a required component?" This is not a meaningless question as we do not see "the direct use" of the contents of these courses in practical life. To answer this question, we first need to understand what these contents are about, and what they enable us to do.
First, we must ask: "What is mathematics?"
There are many definitions. We can cite some of them here. According to Aristotle, "Mathematics is the science of quantity." Benjamin Pierce defined math as, "...the science that draws necessary conclusions." Lastly, Walter Warwick Sawyer thought that, "Mathematics is the classification and study of all possible patterns."
For our purpose, though, we will use the following intuitionist definition: "Mathematics is a mental activity which consists in carrying out, one after the other, those mental constructions which are inductive and effective." This means that by combining fundamental ideas, one reaches a definite result.
Math trains the brain
By using the definition above, we can argue that even though the mathematical content in the core curriculum may not have direct use for many jobs and practical applications in life, studying math should be considered as training the brain to comprehend complicated ideas, and to deduce or construct new knowledge in every aspect of life by reflecting on and relating the given information.
In other words, studying math (independent from the content) trains the brain in logic, order, and pattern recognition, all of which are essential to understanding and arguing about ideas everywhere. The most common analogy for this situation is that "studying math contributes to strengthening one's 'brain muscles' very effectively, like running strengthens one's leg muscles." Studying math makes people smarter, and helps them solve complicated problems and analyze tough situations from different parts of life. These skills are undeniably very important for any person, and everyone wants to strengthen these skills through their education to prepare for their mature life. Hence, if we can prove our claims above about studying math, we can present a convincing argument to show the necessity of math education in our core curriculum.
Of course, we cannot give a 100% solid proof that studying math improves one's ability to comprehend or better analyze the complicated situations we confront in our work and daily life; or to deduce new relations and make smarter decisions. However, if we go back to the example of running and how it enhances one's leg muscles, we can point out the similarities of these processes.
If one considers any math problem from any level, it always describes a situation with given statements A, B, and C; it asks when the statements A, B, and C are true, whether a new statement, D, is also true? From elementary school to the PhD and research levels, any math problem can be described in these terms.
Doing this in an abstract setting might make it complicated at first sight, but this property provides math with great advantages. First of all, it makes math universal for any time and place. A mathematical truth is absolute (if a,b,c are assumed to be true, it is impossible that d is false); after being settled, the statement is true at any time and any place in the world. If you asked the question "whether A & B & C implies D or not" five centuries ago, it still makes sense today; and the answer will still be true in the future. If you ask the same question in the USA, Europe, or Africa, it undeniably has the same answer. Since the whole setting is abstract, the answer does not depend on time or place. Furthermore, because of this universal property, by using a good idea, a kid might solve a nice math problem, while many smart people cannot. This makes math very interesting and intriguing. It is not a coincidence that the youngest university professors are mathematicians.
Now, let's go back to our original question. For an untrained person, running a couple of miles in his or her first attempt would be quite hard, but with a few months exercise, they can get used to the distance, and run it very easily. Furthermore, it improves his other athletic skills, and gives a good base to adapt to other sports. Like this example, studying math is good training for the brain to analyze situations, to understand deeper concepts, and to find connections. In K-12 education, the aim is to prepare students for their mature life, and to give a good background for their future jobs. The math content up to the high school level is from research that is at least 3-4 centuries old; many of the formulas are over a thousand years old. Because of the universality of such formulas, if any number of kids or teenagers talks about the same problem, they can communicate with each other without any problem, across national, ethnic, and linguistic boundaries. Hence, math provides us an ideal environment in which to train the brain.
The abstract setting is ideal
The next question would be, "Is math the only (or best) way to work out one's mind? Would we ask everyone to run laps on a track if some students prefer to exercise by swimming, cycling, weightlifting, or rock climbing? We have already answered this question above, but it would be better to underline some points again. Of course, other courses like natural sciences, social sciences, literature, etc. will help students to train their brains, too. However, as we emphasized earlier, math provides us an excellent workout environment because of its abstract property. For a given, complicated math problem, one must separate the problem into simpler pieces, and see the relation between these pieces. After comprehending the whole complicated scenario with this process, he or she comes up with a new idea to deduce the answer. This training subconsciously equips people with the skill to approach the different complicated situations in their lives, and to come up with a solution. In other fields/courses, the answers and solutions are not absolute, and most of the time there may not be only one good answer. This ambiguity could undermine the training which we want to achieve.
On the other hand, because of the universal property of math, a great variety of subjects and questions have accumulated over the past centuries. These abundant and rich resources have been collected in different parts of the world at different times by the people who would like to understand the patterns and relations around them, and who enjoy to travel in this abstract world. Hence, math consists of a great wealth of subjects and problems, which have naturally developed through the work of very intelligent people who have sought answers to the puzzles posed by both nature and the human mind. This property makes math the best way to train the human mind, and it offers a rich platform for all levels and ages.
In short, math provides the mind with the skills to question and analyze, to find connections between events, and to make deductions with the given information. These are unquestionably essential skills for any life.
Direct and practical outcomes
Besides the profound effects mentioned above, math education also has very direct and practical effects in our lives. In this century, even many entry-level jobs require good math skills. With the advances in technology, good math skills became very handy in everyday life. As job descriptions change over time, the necessity for good math skills becomes more urgent.
Many college majors like engineering, economics, finance, medicine, and natural sciences demand a solid math background. In other words, if you don't acquire the basic math skills in your basic education, it will be impossible to get a degree in these fields, and to get a decent job related to these subjects.
Math education as a part of a K-12 core curriculum has been a controversial issue for centuries. One side sees math education as a "luxury," whereas the other side believes that it's one of the most essential components of a well-rounded education. This side ÔÇô correctly, I believe ÔÇô feels that math trains the human mind to comprehend, question, and analyze complicated ideas. In our changing times, math education becomes more and more important as it gives a necessary background for many professions, from entry level to advanced research positions.
1. Klein, David. "A Brief History of American K-12 Mathematics Education in the 20th Century," in Mathematical Cognition: A Volume in Current Perspectives on Cognition, Learning, and Instruction, p. 175-225.