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Understanding fractions

It is about the understanding of fraction. The topic is literature review on student understanding of fraction. In this assignment we have to talk about:
What is the range of views held by learners?
What are some difficulties experienced by students about this topic in learning it and why, or alternative concepts, ways of thinking.

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What are some difficulties experienced by students about this topic in learning it and why?
Fractions can be difficult for some, as some find it hard to comprehend the structure of how fractions work. In reality, fractions are not difficult at all. "A fraction describes a part of a whole when the whole is cut into equal parts. Fractions can also be a part of a group. For example, if there is a group of fruit: 3 oranges and 4 apples, what fraction of the group are apples? Four sevenths. There are seven parts, and four apples. What is the fraction for the oranges? Three sevenths. They are fractions that are not one whole, it's just a part of the whole." (Think Quest 2009) This explanation is in laymen's terms to better assist one having difficulty with the subject.

To further assist the students in their studies, fraction games can help. "By working game activities, students have opportunities to think about how fractions are related to a unit whole, compare fractional parts of a whole, and find equivalent fractions, as discussed in the Number and Operations Standard. The Role of the Teacher is to communicate about mathematics through the aid of fraction games. The third part, Communication among Students, shows how activities like this allow students to use communication as a tool to deepen their understanding of mathematics, as described in the Communication Standard. In the fourth part, Reflecting on Practice, the teacher reflects on her own mathematical learning that occurs as a result of using activities like this game with her fifth-grade students." (Bennett 2009)

These games are an important factor in expanding the knowledge of the students and advising the students that fractions can be fun. The communication standard of this process enables the student to look at fractions as part of a "game theory" versus a mathematical theory to better broaden the student's thinking. Once the thinking is broadened, and the fear of fractions has past, the students can actually excel in their mathematical studies.

Research on this subject is significant. The Teaching and Learning Research Brief (2006) discussed a major factor in understanding the issues have with fractions. The main difficulty factor is "Research on fractions has shown that many of the mistakes which pupils make when working with fractions can be seen as a consequence of their failure to understand that natural and rational numbers involve different ideas. One well-documented error that pupils make with fractions is to think that, for example, 1/3 of a cake is smaller than 1/5 because 3 is less than 5." The root of the problem appears to be with the way the problems are taught. Diagrams are the main source for teaching one how to better understand the process of fractions.

When teaching and comprehending fractions, it must be taught that the higher the number the smaller the fraction; the lower the number, the larger the fraction. The students must be taught to think in reverse when ...

Solution Summary

The solution discusses students understanding fractions.