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Marina Kurvits

on 5 May 2010

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STUDENTS` UNDERSTANDINGS OF
RATIONAL NUMBER REPRESENTATIONS
Jüri Kurvits
Tallinn University / University of Helsinki
The 10th INTERNATIONAL CONFERENCE
TEACHING MATHEMATICS: RETROSPECTIVE AND PERSPECTIVES
14-15 May, 2009, Tallinn
Teachers spend many classroom hours developing proficiency with fractions, decimals and percents, but they are teaching big number of rules, focusing only on algorithmic and problem-solving proficiency which can leave many students without a conceptual understanding of rational numbers and the relationships among fraction, decimal, and percent representations (Stohl H.D., 2002). 1.Transition from whole numbers to rational numbers and misunderstandings that occur in this process.

2.Student’s understandings of the connections among rational number different representation forms.

3.The development of multiplicative reasoning.

A full understanding of rational numbers for any middle grade student involves an understanding of rational numbers in all of its representations and students’ ability to operate effectively with rational numbers depends on knowing interconnections among different representations of rational numbers (numeral and pictorial). numeral fraction decimal percent pictorial fraction “In the preschool years, a child learns to count by matching one number name to each object in the set being counted. The unit “one” always referred to a single object. When the child begins to study fractions, however, the unit may consist of more that one object or it is might be a composite unit, that is, it may consist of several objects packaged as one. Furthermore, that new unit is partitioned (divided up into equal parts) and a new kind of number is used to refer to parts of that unit.” (Lamon, 1999) Many students were introduced to fractions by dividing up a single pizza. Teachers and textbook authors did not realize that by always using the same unit – one pizza – students were getting the idea that a unit was always a single pizza.
When teaching common fractions it is usually shown as a part of a whole and to visualize the fractions only constructions similar to those depicted in Figure 1 are used. As a result many students develop an understanding that a common fraction is always smaller than one and that some sort of an object (a circle or a rectangle divided into equal parts) can represent the whole. It is important to point out that this kind of introduction of rational number is grounded in additive thinking (Moss J, 2005). Figure 1 “…the relationship between equivalent fraction representations. For

example, to understand number , it is necessary that the student

focus on the relative amount represented by the various shaded

regions described by , as shown here, without regard for the size,

shape, color, orientation, location, number of equivalent parts in each

partition, and so forth.“ (Lamon, 1999)

eight tests