The present study examined preservice elementary teachers' performance on the problems of multiplication and division of fractions and compared their performances and analyzed the misconceptions. An instrument including 11 fraction multiplication and division tasks was given and the task involved three contexts: making own story problem,…

In the body of knowledge in mathematics education research, fractions are one of the researchers' concerns. The reason is because fractions are very difficult for students to understand. This study explores elementary school students' knowledge and obstacles in dealing with the multiplication of fractions. This study employs descriptive…

The purposes of this study are to report current Preservice Teachers' (PTs) decimal abilities regarding the types of error patterns that they commit and to analyze characteristics of the errors in the problems posed for multiplication and division in decimals. We have determined common concept- and procedure-based errors made by the PTs. 37 PTs in…

Attending to the whole unit that a number refers to in a mathematical problem situation and showing flexibility in coordinating different units are foundational for mathematical understanding. In this study, we explored teachers' attention to and flexibility with referent units in situations involving fractions and fraction multiplication. Using…

This study investigates college students' understanding of arithmetic fraction operations as defined by the Common Core State Standards in grades three through six Mathematics. This study is meant to extend upon an extensive body of research regarding elementary and middle grades students' understanding of fraction operations and see if recognized…

This dissertation case study examines how teachers' levels of units coordination afford their ability to reason multiplicatively and fractionally, as well as use their mathematics knowledge for teaching to analyze student multiplicative and fractional reasoning, when a two-year intervention is put into place to evoke new mathematical reasoning.…

The number one plays a special role in mathematics because it is the identity element in multiplication and division. The present findings, however, indicate that many middle school students do not demonstrate mathematical flexibility representing one as a fraction. Despite possessing explicit knowledge of fraction forms of one (e.g., 95% of…

This paper presents an analysis of fractions errors displayed by learners due to deficient mastery of prerequisite concepts. Fractions continue to pose a critical challenge for learners. Fractions can be a tricky concept for learners although they often use the concept of sharing in their daily lives. 30 purposefully sampled learners participated…

"A critical pillar of a strong PreK-12 education is a well-qualified teacher in every classroom" (Conference Board of Mathematical Sciences, 2012, p. 1). In order for teachers to help students build procedural fluency from conceptual understanding and meet the standards set forth by governing agencies, prospective teachers will need deep…

The purpose of this study was to examine adult developmental mathematics (ADM) students' knowledge of fraction addition and subtraction as it relates to their demonstrated fraction schemes and ability to disembed in multiplicative contexts with whole numbers. The study was conducted using a mixed methods sequential explanatory design. In the first…

In this study, we considered how middle school teachers understood the relationship between fractions and ratios. We used two instruments to collect data from 11 teachers and relied on Knowledge in Pieces as a lens for considering understandings teachers have and how coherent those understandings are. From our analysis, we developed three main…

This study investigated how pre-service teachers' fractional concepts are related to solving problems involving advanced fractional knowledge. 96 Participants took a written test including three fractions questions about fraction concept, fraction comparison, and multiplicative relationship involving fraction quantities and composite units. The…