This study compares the effects of a concrete-representational-abstract (CRA) intervention against a modified CRA-Integrated (CRA-I) intervention using a pretest-posttest design with random assignment of matched pairs to intervention conditions. The researchers designed both interventions to improve participants' understanding of and ability to…

Understanding related to fraction concepts is a critical prerequisite for advanced study in mathematics such as algebra. Therefore, it is important that elementary students form conceptual and procedural understanding of fractional numbers, allowing for advancement in mathematics. The concrete-representational-abstract (CRA) instructional sequence…

With the advent of mobile technologies, well-designed fraction apps can be used to help children gain fraction knowledge, a challenging topic for both teachers and students. The present pilot study adopted a quasi-experimental design to investigate whether children can learn fraction concepts equally well if half of the lesson time (20 min) is…

This study describes a teaching process that offers teachers and pupils ways of constructing the division operation through illustration based on defining the reference unit (divisor), the reference whole1 and the dividend. We introduce a computerized dynamic environment, using an Excel spreadsheet, in which both teachers and pupils can…

This article describes a study of how Chinese preservice teachers unpacked a learning goal pertaining to adding fractions and understanding the concepts underlying the operation. Based on work in the USA by Morris, Hiebert, and Spizter ("Journal for Research in Mathematics Education," 40(5), 491-529, 2009), 50 Chinese preservice teachers…

Research has shown that fraction magnitude and whole number division are important precursors to learning and understanding fractions. Deaf and hard-of-hearing (DHH) students are consistently challenged with learning fractions from K-12 through college. Sixty DHH college students were tested for both their understanding of magnitude between two…

I examined how well a self-diagnosis activity engages students in knowledge-integration processes, and its impact on students' mathematical achievements. The self-diagnosis activity requires students to self-diagnose their solutions to problems that they have solved on their own--namely, to identify where they went wrong and to explain the nature…

Fractions are an important part of the primary school mathematics curriculum, being introduced to children in the Slovenian educational system during the second grade (at age seven). For clarification of terms it is worth mentioning that the term "fraction" is only introduced in the sixth grade. Before that, the term "equal parts of…

This study investigated how six Year Four (9-10 years old) students interacted with a dynamic (zoomable) digital number line to demonstrate knowledge and understandings of decimal fractions. Results from a task-based interview indicated that the zoomable number line is able to assist students in developing conceptual understandings of decimal…

Findings are presented from an analysis of how six future middle-grade teachers reasoned with strip diagrams and a variable parts perspective on proportional relationships to develop and explain equations in two variables. One equation was for two quantities varying together and one was for a line through the origin in a coordinate plane. Both…

The article deals with mathematical literacy in relation to mathematical knowledge and mathematical problems, and presents the Slovenian project NA-MA POTI, which aims to develop mathematical literacy at the national level, from kindergarten to secondary education. All of the topics treated represent starting points for our research, in which we…

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…

The programmed instruction helps each student gain knowledge with different time or sequences, depending on available knowledge, ability, and learning speed. With this method, students can perform self-evaluation and self-regulation in learning activities. This article presents the application of the programmed instruction method in designing the…

Implementation of the Common Core Mathematical Standards and Practices (CCSS) has emphasized the importance of instruction that develops both procedural knowledge and conceptual understanding. Novice teachers have experienced the implementation of the CCSS during their PreK-12 experience, as well as within their teacher preparation program. It may…

Identifying components of teaching that make a difference in children's learning is an ongoing challenge in our field. Focusing on teaching that is responsive to children's fraction thinking, we decomposed responsiveness into the instructional practices of questioning to support and extend children's thinking, noticing children's thinking, and…