Math Phobia

< 33.2 Math Savants | Topic Index | 33.4 Concepts &amp; Conventions >

In the last 2 decades, two phrases have entered the vocabulary of many math educators- Math Phobia &amp; Dyscalculia. Why is phobia only associated with math? Why don&rsquo;t we hear of history or language phobia? In this article we will try and understand this phenomenon.

There are two inter-related reasons. First is not understanding that math is qualitatively different from other school subjects and the second is inappropriate pedagogy used in math education, because of this misunderstanding.

Math Is Different

Most people realize that out of all the subjects learnt in school, math is different. Everyone can easily describe what they are learning in Science or Social Studies. But most have difficulty even to describe what is it that they are learning in math. Numbers, Operations and Geometry is what most can come up with. They are also not able to pinpoint the nature of their difficulties with math. It is natural that they are unable describe the reasons for the same.

To understand how math is different, we need to go into the components of any subject that is to be learnt.

What are Subjects made of?

Learning of any subject can be classified into the following components – Concepts, Skills &amp; Information.

Concepts are mental abstractions, which need to be constructed in our mind, by experience &amp; introspection. Ideas of prime &amp; the operation of subtraction are two examples. They may be mirrored by physical entities &amp; events but cannot be directly &ldquo;perceived&rdquo; or &ldquo;pointed out&rdquo;. You cannot show what the &ldquo;prime-ness&rdquo; is. We can only point out a few numbers which have this quality. Concepts are the most difficult tom learn.

Skills are to be learnt by practicing them. They can be physical or mental. Performing a long division or colouring a map are examples.

Information are &ldquo;bytes&rdquo; of information to be remembered or memorized. The names of types of triangle or the birth year of Akbar are examples. We may not even know if a piece of information is true or false. Different pieces of information that we learn, may not even be related to one another. Information is the easiest to learn.

Each of these components also needs a different way of learning. Information can be lectured &amp; remembered. Skills have to be practiced and mastered. Concepts have to be Understood.

Difference Between Subjects

Let us represent the number of concepts, skills &amp; information in 4 common subjects taught in school. The numbers are indicative. The purpose of the table is mainly to understand the difference between the 4 subjects.

Information is maximum in Social Studies followed by Science. By Science we mean science as taught in schools where the emphasis is on information about the definitions, discoveries &amp; inventions. So, both become subjects with a lot of memorization. Information is the easiest component of learning.

Skills are maximum is language where without listening, speaking, reading and writing skills, a language cannot be mastered. Though skill of experimentation is a major part of science, in schools, laboratory work is not given real importance. Math also needs a lot of skills to be practiced.

Concepts are the most difficult aspect of learning as it involves a lot of thinking &amp; abstraction. Language has the least number of concepts which is basically grammar &amp; phonic rules. Social Studies has very deep concepts which do not form part of the school curriculum. Math has the highest level of concepts.

Math is Different &amp; Difficult

Math is concept heavy. Concepts are abstract mental ideas which need a lot of experience, modelling and introspection for understanding. Concepts have to be &ldquo;caught&rdquo; by the learner. They cannot be directly &ldquo;taught&rdquo;. These elements make it a difficult subject to understand. There is no clear understanding of what &ldquo;understanding&rdquo; is.

Another difficulty is that all math concepts are related across the curriculum and also related hierarchically across grade levels. We can think of the math curriculum as a pyramid built with playing cards, stacked one on top of another. The weakness of even one card at the lower level will weaken the entire structure. It is similar to the saying that a chain is as strong as its weakest link. A weakness in subtraction will affect understanding of division, fractions, algebra etc.

A further difficulty is that abstract ideas in math start right from the preschool stage. Understanding a number is the first hurdle.

How Math Needs to be Taught?

For effective learning of math, there has to be equal emphasis on conceptual understanding, inculcating the appropriate learning habits of mind, procedural fluency and problem-solving skills. In the initial years, focus has to be on understanding and not on speed of execution. Children need to be acknowledged for small gains rather being chided for failures. Multiple opportunities need to be given for trying again. Basic ideas in math like numbers, shapes &amp; operations were developed by observing patterns in the world around us. Hence in Pre-School and Primary schools, these ideas can be taught to children using the environment around us and our daily life experiences.

But very soon, these basic concepts start developing into complex ones. Continuous layers of abstraction get added on like the layers of skin in an onion. Hence along with teaching of these basic ideas, the very process of thinking about these ideas and the inter-relationships between them should also be developed. If these faculties are not developed, very soon these concepts will become so abstract that students would not be able to understand them.

Beginnings of Math Anxiety &amp; Phobia

If the teaching of math is not appropriate, the students&rsquo; non-understanding keeps on increasing, as the complexity of the concepts keeps on increasing. A learning psychologist has compared the mental state of a student who cannot understand what is happening in the class, to that of a novice swimmer who struggles just to keep his nose above water!

The problem starts with teachers in preschool & primary who are not well trained in understanding & teaching math. Math curriculum in preschool & primary is seen to be just learning numbers & operations. Hence the wrong notion that any one can teach any subject in these years. This in turn leads to appointment of teachers who have little or no experience in teaching math and no training to speak of. So math anxiety starts from the primary school.

In addition, negative comments about weaker students, reduce the self-confidence of students. Hence each math class brings a lot of anxiety. Anxiety itself reduces the motivation to learn and hence further reduces the capacity to focus and learn. For many students the level of anxiety keeps on building up leading to the psychological condition of a phobia. The fact is that being “bad at math” has very little to do with innate intelligence and everything to do with psychology and self-confidence.

What is the Way Out?

Since Math Phobia is a condition which develops over a number of years, there is no short-term solution to it. In the long run, there are several interconnected strategies which could be adopted.

Appropriate Pedagogy

Concepts cannot be directly pointed out. They have to be demonstrated in a variety of ways so that the student can catch them. My guru used to say &ldquo;Concepts are not taught. They are caught&rdquo;. So, the concept of an even number should be shown to students by equal sharing which is a daily even they are familiar with. This can be done using simple manipulatives. Just providing a definition (that an even number is divisible by 2) may not produce understanding.

A Math Activity Centre with plenty of manipulatives and models is extremely necessary for children to &ldquo;practice &amp; explore&rdquo; math.

Some examples of skills in math are computations and constructions in geometry. In general skills have to be practiced in a variety of ways. But math skills are intimately woven with underlying concepts. They have to be practiced with understanding of the concepts. Mastering addition of 2 digit numbers needs a clear understanding of the place value concept. Practicing them mindlessly may lead to mistakes when the procedure needs to be modified to suit the situation. My guru used to say &ldquo;drilling may produce only holes and not understanding&quot;.

Information in math is mostly the symbols, names &amp; definitions. Many names used in math are never heard by students outside the math classroom – obtuse, coprime etc. Some have different meanings when used in daily life – interest, imaginary etc. In such cases, students have to be helped in absorbing these names &amp; their connotations by repeatedly using them in context in class for extended periods of time.

Appropriate Agewise Pedagogy

Children do an average of 15 years of schooling, during which they go through several stages of mental &amp; emotional development. Developmental Psychology tells us that until the age of 10, their ability to understand abstraction is limited.

Hence as children proceed through different class levels, the method of teaching should change to be in consonance with their mental ability to learn complex concepts, skills &amp; information.

Unfortunately, we see that, in our schools, all subjects at all class levels are taught using the same process – lecture, blackboard, chalk, duster, students cramped in rows, textbooks, classwork, homework, examinations, pass/fail, report cards.

Teacher Training

Such changes in pedagogy require a sea change in our teacher development &amp; certification courses and on-the-job training.

Primacy of the Primary

The strong foundation for developing the motivation and competency to learn math has to be laid in the primary school. Hence in the Primary School the curriculum has to be reduced and teachers have to ensure that each and every child who leaves Primary school attains at least 80% understanding of the entire curriculum. A pass mark of 40 or 50% is inappropriate in math in primary school.

Assessments

Formal examinations, which reduce the number of teaching periods, should be replaced up to Primary with class tests and that too of the Formative type. Methods of assessment should be broadened to include oral, practical &amp; project assessments. Timed tests should be reduced to the minimum. The textbook should become a reference, rather than a &ldquo;bible&rdquo;.

In this digital &amp; knowledge society all children must be given an opportunity to learn &amp; enjoy math which is going to be extremely necessary for them to lead an empowered life.

< 33.2 Math Savants | Topic Index | 33.4 Concepts &amp; Conventions >