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Hea-Jin Lee and Irina Boyadzhiev use technology to target misconceptions
Introduction
According to the Common Core Standards, students in Grades 3 and 4 are in the exploratory and experiential stage. In Grade 3 students are introduced, for the first time, to the part-whole concept of a fraction and are to be exposed to, and to experience, fractions with various manipulatives. A fraction is formally established as a number in Grade 4, and students begin to learn all four arithmetic computations with fractions to solve problems. In Grade 4, it is suggested that there is a move from providing multiple models to using an exclusive model for a fraction. More sophisticated interpretations of a fraction begin to emerge in Grade 5. The content of fractions becomes even more complicated in Grades 6 and 7 and includes the full development of fraction division. The applications of fractions lead to the concepts of percentage, ratio, and rate in Grade 7.
Studies of fractions blame the confusing meaning of fractions, the inappropriate use of a model or manipulative, and ambiguous teaching as the causes of student misconceptions. McNamara and Shaughnessy (2010) suggest that students struggle with fractions, because a fraction has many meanings, for example part-whole, measurement, division, operator, and ratio which is written in a new way. In addition, some criticize teachers for not focusing on a conceptual understanding of fractions that may lead students to attempt to link their existing knowledge of whole numbers to fractions.
With regard to the use of models, a fraction can be modeled by using discrete objects, or continuous models (length, area, and volume). Each model has pros and cons depending on the level of the curriculum. Using discrete objects is an appropriate way for to introduce unit fractions to 3rd graders but this has limits. For example, one can only discuss how many, not how much, and it is unnatural to discuss 1/3 with two pencils as the whole. Continuous models require teaching that is well planned. A commonly observed mistake is to let a geometric shape to be the whole, rather than the area of the shape. This leads to confusion; such as a fraction is a geometric shape not a number, or that equal parts means congruent....