Fractions: What Happens between Kindergarten and the Army? This article deals with the idea that the way that children learn about fractions and other mathematical concepts might actually be hurting them. The concern is that traditional teaching methods are not really the best for children. This is evidenced by the fact that children who are asked to solve problems with fractions do not often do so in a way that would be traditionally accepted in the mathematics community. In other words, children as young as kindergarten can sometimes solve even rather complex problems dealing with fractions, but they go about it in a totally different way then what would be traditionally accepted. This study was done by several teachers who became interested in the fact that children were not really fostering any kind of understanding of mathematics. It appeared that children who first start kindergarten have quite a bit of understanding of mathematics, and this includes fractions. Unfortunately, by the fifth or sixth grades it appears that many of these same children are no longer able to solve problems as easily as they could in kindergarten and first grade. Obviously, this is a great concern for the teaching community, as it indicates that children are actually being harmed rather than helped by the current instructional system.

Since the particular group of teachers that did this study was interested in improving the way that they taught fractions and how students learned, they began to study exactly how children solve fractional problems when they have had little to no instruction in that area. Several meetings ensued where the group of teachers considered these problems and wanted to know what happens between the students in kindergarten who can solve problems and those in adult life who often struggle with them. As math teachers, they work with fractions on a daily basis and have no difficulty in solving complex problems. However, they began to realize as they studied their students more and more that the students...

They would traditionally be required to do this if the fractions had different denominators. After they did this, they would need to add these improper fractions together and then divide to get an answer that included both a whole and a fraction. This has long been the traditional method for teaching children how to do fractions and it remains in schools all across the world today. However, those students in lower grades that solved fractional problems on their own did not use this approach. They did not understand about improper fractions and how to divide them to get the right answer. Instead, they chose an approach that was not traditional but did work for a relatively large percentage of the students.
What they did was fascinating, and it interested the teachers who performed the study a great deal, because it indicated to them that perhaps they are not helping their students out by teaching them the traditional way to do fractions. It only appears to confuse them and undermine the basic understanding that many people have that fractions are part of a whole. The way that young students solved these problems was by taking the fractions and borrowing bits and pieces of them to create a whole and parts that make more sense. The problem that was given to the students from kindergarten through sixth grade was 2 1/2 plus 3/4. Traditional solutions to this problem involve a lot of mathematics and calculation to arrive at 3 1/4. However, students instead drew pictures of wholes and parts and even borrowed part of one side of the equation to make up a whole for the other side. For example, many children took 1/4 from the 2 1/2 and added it to the 3/4. They then had 2 1/4 plus 1, and they added these together to come up with 3 and 1/4 which, of course, was the right answer. This was obviously not…