the last two decades has been declining emphasis on the importance of repetition of math concepts and skills in learning this stuff. The focus has shifted more towards thinking skills and “working outside the square,” which means to be able to apply problem solving skills to real life situations. This has been in contact with the increase in the volume of written material in secondary mathematics textbooks and a decrease in the amount of repetitive exercises where only basic math skills are practiced.
This is good in theory, but a steady decline in standards of mathematics in Australia and the United States suggest that this method of mathematics is not as good as it seems. The problem lies with the basic assumption that students already have the basic skills needed to solve problems. In mathematics, it is not possible to “work outside the square” unless one is a town with all the skills within the square. For example, a student will not be able to solve the problem regarding the amount of wire needed to fence fence Farmer Brown, unless they can accurately calculate the perimeter first.
Freedom to complete repetitive textbook exercises does not guarantee success in the application problem. What it does do is to give students the tools they need to address problems outside the textbook. Try to solve abstract problems without a solid knowledge base is like building a house on sand; it is a futile exercise.
This situation can be compared to physical training. Can understand the benefits of being able to build muscle through exercise, but if you do this you will fail when it comes to application task weight lifting. Math works the same way. Repetition builds on basic skills so that it becomes reflex. When skill is action that can be applied to other situations. Possessing the skill does not guarantee success in the application, but it is expected that success.
role repetition of basic skills in mathematics should be reviewed in conjunction with primary and lower secondary level. Without binding basis math skills to build on, students will continue to struggle with mathematics throughout their school careers.