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Mathematics Concepts and Skills – Repetition in Math
Over the past two decades, there has been less and less emphasis on the importance of repetition of mathematical concepts and skills in learning this subject. The emphasis shifted more to thinking skills and “working outside the square”, that is, the ability to apply problem-solving skills to real-life situations. This has been accompanied by an increase in the amount of written material in high school math textbooks and a decrease in the amount of repetitive exercises where only basic math skill is practiced.
That’s fine in theory, but the continued decline in math standards in Australia and the United States indicates that this approach to math isn’t as good as it looks. The problem lies in its fundamental assumption that students already have the basic skills needed for problem solving. In mathematics, it is not possible to “work outside the square” unless you are proficient with all the skills contained within the square. For example, a student will not be able to solve a problem regarding the amount of wire needed to fence Farmer Brown’s paddock unless they can first accurately calculate the perimeter.
Being able to perform repetitive exercises in textbooks does not guarantee success in application problems. What it does do is give students the tools they need to solve problems beyond the textbook. Trying to solve abstract problems without a solid foundation of skills is like building a house on sand; it is an exercise in futility.
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, you will fail when it comes to the application task of weightlifting. 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. Possessing the skill does not guarantee success in the application, but it does enable that success.
The role of rehearsing basic math skills needs to be reconsidered in the context of primary and lower secondary education. Without a solid foundation of numeracy skills to build on, students will continue to struggle with math throughout their school careers.
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