Rationale
Fractions are typically a difficult concept for students. Fractions are particularly challenging for fourth graders for several reasons. Fourth graders not only have to conceptualize fractions, but also calculate and solve word problems using them. Working with fractions requires knowledge of multiplication and division. These operations are relatively new skills in fourth grade.
Additionally, solving simple word problems with whole numbers is a weak area for most students. Accuracy plays a role in being successful. Fourth graders' basic skills are still developing, so students tend to make frequent errors. The rigor of problem solving increases when the problems are multistep, involve multiplication or division, or fractions. Sometimes in fourth grade, students are faced with problems involving all of these skills. There are many factors that contribute to great effort needed to become successful with fractions.
Developing the students' confidence and even an affinity for working with fractions is an especially challenging task for the teacher. For many students, fourth grade provides the first experience to compare and compute with fractions. A bad experience can affect students negatively for a long time or possibly for the rest of their lives. Also, an inadequate foundation and understanding of rational numbers can hinder students' ability to understand higher mathematical and scientific concepts. Therefore it is crucial for students to develop a robust understanding of rational numbers at an early age.
My curriculum unit is designed to teach myself, other teachers and most importantly the students ways to approach fractions without relying on memorizing the "rules" that are typically taught in the United States. The curriculum unit is designed to develop deep, conceptual knowledge and lead the students to discover the algorithms themselves. Developing a strong foundation and understanding of rational numbers is an important component of the curriculum unit. Students typically extend their knowledge of whole numbers to rational numbers. They think of multiplication as repeated addition and generalize that multiplication always makes the product larger. Similarly, students think of division as a model of sharing and incorrectly assume that division always leads to a smaller answer. Both of these ideas only hold true for whole numbers. According to Susan J. Lamon, "In the world of rational numbers, both of these models are defective" 1. I plan to create a curriculum unit that is not limited by a few defective models, but full of a variety of models to build my students' conceptual understanding of rational numbers.
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