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Mathematics Concepts and Skills: Repetion in Maths

Over the last couple of decades there has been a decreasing emphasis on the importance of repetition of mathematics concepts and skills in the learning of this subject. The emphasis has shifted more toward thinking skills and "working outside the square", meaning being able to apply problem solving skills to real life situations. This has been accompanied by an increase in the amount of written material in secondary school math textbooks and a decrease in the amount of repetitive exercises where only the basic mathematical skill is practiced.

This is good in theory, but continually declining standards of mathematics in Australia and the US indicate that this approach to maths is not as good as it seems. The problem lies with its fundamental assumption that students already possess the basic skills needed for problem solving. In maths, it is not possible to "work outside the square" unless one is competent with all the skills contained within the square. For example, a student will not be able to solve a problem concerning the amount of wire needed to fence Farmer Brown's paddock unless they can accurately calculate perimeter first.

Being able to complete repetitive textbook exercises does not guarantee success in application problems. What it does do is give students the tools they need to tackle problems beyond the textbook. Attempting to solve abstract problems without a solid skill base is like building a house on sand; it is a futile exercise.

This situation can be compared to physical training. One can understand the benefits of being able to build muscle through exercise, but unless you do this you will fail when it comes to the application task of weight lifting. Math works the same way. Repetition of basic skills builds the skill so that it becomes a reflex. When a skill is a reflex it can be applied to other situations. Posessing the skill does not guarantee success in the application, but it does allow for that success.

The role of repetition of basic skills in maths needs to be re-examined in the context of primary and lower secondary education. Without a firm foundation of numeracy skills to build on, students will continue to struggle with maths throughout their school careers.

Roger Vanderlely.

Free math resources and science experiments are available at my website, http://www.green-planet-solar-energy.com.  Many of these can be downloaded and saved to your computer for your free ongoing use.

About the Author

I am currently teaching maths and science in a Victorian secondary college.

Are some people just bad at Mathematics or is it a mental problem with me?

I graduated from high school taking the minimal math required to graduate. It was very basic Mathematics and I was lucky to pass it. On the other hand, my Science classes were a total interest of mine and I recieved A's in the classes.
What is the deal. I am going to have to take math to get into Chemistry, and I am afraid I will not be able to pass the classes. It is so hard for me. I struggle and it is scaring me to enroll in college Math. Whats the deal and how do I get good grades? I feel totally stupid. Its embarrasing. Do other people struggle like this?

I've seen a lot of people coming in from high school to college and the majority do not have the skills to go into college math and must take remedials. MOST people have to take basic arithmetic or beginning algebra first. The good news is that those developmental classes really do work to bring you up to college level. Its like anything else, if you are interested in it then you will do better. Chemistry has about college algebra level work in it, physics is the worst as far as involving math, but you can do it if you really want to work.

Unfortunately, science and math are tied together in college and most science majors require a minimum of calculus. This means you better learn to like math. If you are willing to work at the math you can do it. The question is "is it worth it to you?". Don't be scared because you are in the same boat as everyone else in those classes. By the way most colleges won't let you get in over your head in math classes, you'll be tested and put where you belong.