Mathematics Concepts and Skills

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.




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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. Possessing 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.