Most people are quite capable of success in maths if presented with opportunities to succeed, an open mind and a belief that one can do maths, and of course a readiness to put in some work. But performance is often undermined by faulty beliefs regarding the subject and one’s own abilities. A believe in certain myths can hamper both effort and self-confidence. Self limiting beliefs should be examined and exposed for what they are, mistaken ideas, in order that students can acquire a more productive approach to mathematics.
“There is one best way to do maths problems”
Maths problems can usually be solved in many different ways. There is no one best way. There are a variety of tools to assist with the process. The myth that there are always specific steps to use for a particular problem can discourage flexible thinking and rigid adherence to procedures and algorithms can stifle creative approaches to mathematics. That does not mean it is not useful to have set procedures to follow, but one should understand when to use them and why.
“Using Tools Is Cheating”
Using tools to make a task simpler is just common sense. Without them, life could be more difficult. There is nothing wrong with counting on fingers as an aid to doing arithmetic. This actually indicates a greater understanding of arithmetic than if everything were memorized. The calculator is a powerful tool when used appropriately. It greatly speeds up and simplifies the work where a lot of calculation is involved, but you still need to know what calculations to do, and how to enter them into the calculator. Unfortunately it seems to be quite common for teachers to assume that students automatically know how to use their calculator correctly, and so many do not receive the required instruction. Look up tables allow us to take advantage of the work already done by someone else. In “real life” why would we want to reinvent the wheel?
“Maths is Mostly Memorizing”
Memorizing a procedure to solve a particular type of problem can be effective as long as the information given is sufficient to find that required by merely plugging numbers into the procedure. However, there’s usually more than one way to solve a problem. If the wording of the question is not given in a familiar format or needs other things to be worked out along the way that we are generally given, then memorizing procedures is not as effective as understanding concepts.
We need to apply thinking skills and creative thought to get a better understanding of maths. Every now and then we should experience “Aha” moments, where suddenly a number of things come together and suddenly make sense. The most important aspect to learning maths is understanding. After solving a maths problem, ask yourself are you merely applying a series of memorized steps/procedures, or do you really ‘understand’ how and why the procedure works. How do you know it’s right? Is there more than one way to solve this problem?
Excessive memorization is boring, discourages flexible thinking and can lead to frustration when a learner is confronted with a new problem. Some memorization is useful and at times even necessary but it should be supported with background knowledge, so that concepts make sense to you, and rules and formulae are understood. In practise most formulae that you will need are given in look up tables or booklets that are easily accessible. Those doing Junior or Leaving Certificate exams will have them available to them during the exams in the official Formulae & Tables booklet.
Keep giving more drill and repetition questions until students get it.
All too often, students receive worksheets with with excessive drill and repetition, leading to overkill and negative attitudes towards maths. If a concept isn’t understood after being presented to a student several times, it’s time to find another method of teaching it. As Albert Einstein said, “Insanity: doing the same thing over and over and expecting different results.”
“Mathematicians find it easy to do problems quickly in their heads”
Solving new problems or learning new material is often difficult and time consuming. The only problems mathematicians do quickly are those they have done before. Speed is the result of experience and practice. It is not a measure of ability. Giving up if you can’t solve a problem within five minutes is foolish. Students need to develop perseverance. Sometimes it is necessary take a problem home and “sleep on it”.
Maths is Only Computation
Maths is not just all about numbers and simple calculations. It is about problem solving. Some of the most interesting maths problems don’t come with numbers that can be immediately crunched. Solving these problems is how students develop mathematical skill.
You need left brain dominance to be good at maths
There will be opposing views on any topic, and the process of human learning is no exception. Some theorists believe that some people are wired with better maths skills than others. They think that logical, left-brain thinkers tend to have stronger maths ability than artistic, intuitive, right-brainers. So left-brain dominant students may grasp concepts quickly while right-brain dominant students don’t.
The “myth of ability” can lead to accepting less than a student’s full potential. Students should be convinced that they are fully capable of learning and doing maths. False self limiting beliefs lead to a lack of self-confidence. But self-confidence is one of the most important determining factors in mathematical performance. Even if some find it easier than others, that does not mean the others can not do maths.
The Gender Myth
Research has failed to show any difference between men and women in mathematical ability. There may sometimes be some social conditioning, with cultural pressures on women “to be less interested” in mathematical careers.
“Who Needs Maths Anyway”
Some who find maths difficult, may rationalize that only a few fields — like engineering — require maths skills, in order to downplay its importance in their own minds. But we use maths in eveyday life. And many career fields — from Agriculture to Zoology — use quite a lot of maths. In studying maths, we learn a way of thinking that is a valuable transferable skill. In today’s information age, mathematics is needed more than it ever was before, and problem solving skills are highly prized by employers . We all need to study an appropriate level of maths.
Maths requires logic, not Intuition or Creativity.
Intuition is the cornerstone of doing maths and solving problems. Mathematicians always think intuitively first. Most people have mathematical intuition; they just have not learned to use or trust it. It is amazing how often the first idea you come up with turns out to be correct. Maths also involves creativity. It requires imagination, intellect, intuition, and an aesthetic sense about the rightness of things.
You must always know how to get the answer and it must be exactly right.
Getting the answer to a problem and knowing how the answer was derived are independent processes. If you are consistently right, then you know how to do the problem. There is no need to explain it.
The ability to obtain approximate answers is often more important than getting exact answers. The difference between an approximate answer and the “exact” answer is often insignificant and the additional effort required to get the exact answer might not be justified. At other times we make assumptions which limit the accuracy of the answer. For example, we often give an answer to a specified number of decimal places. However, in exams you do what ever the examiner expects from you.
Maths is done by working intensely until the problem is solved
Perseverance is important in studying maths but if you “come up against a brick wall” then leaving the problem and returning to it later allows your mind time to assimilate ideas and develop new ones. Often, upon coming back to a problem, a new insight is experienced which unlocks the solution.
The myth of coverage.
According to this myth, if material is “covered” in class, students will learn it. This myth can cause teachers to feel pressured to teach huge amounts of material at speed. This fosters a curriculum that is superficially broad, and encourages speed rather than deep understanding. But covering too many topics too quickly hinders learning because students acquire disorganized and disconnected facts and organizing principles that they cannot make meaningful. If students learn ideas and procedures by rote, without understanding, they quickly forget them, so the ideas must be repeatedly retaught. Where rote learning and understanding are combined students can develop and interrelate new concepts. They accumulate an ever-increasing network of well-integrated and long-lasting mathematical knowledge. So while curricula that emphasize deeper understanding may cover fewer topics at particular grade levels, they enable students to learn more material in the long run, because topics do not need to be repeatedly taught. When studying maths it can be a case of “less haste and more speed”, particularly earlier on.
The Magic Key Myth
There is no magic key or general insight into understanding all maths problems. No formula, rule, or general guideline will suddenly unlock the mysteries of maths. If there is a key to doing maths, it is in overcoming anxiety about the subject, dispelling restrictive myths, and applying the same effort and skills you use to do everything else.