In the present study, we illuminate students' multiplicative reasoning in the context of their units-coordinating activity. Of particular interest is to investigate students' use of three levels of units as given material for problem-solving activity, which we regard as supporting a more advanced level of multiplicative reasoning. Among 13 middle…

Previous research on the role of prior skills like proportional reasoning skills for the development of mathematical concepts offers conclusions such as "more (prior skills) is better (for later learning)." Insights, which prior skill "level" goes along with which "level" of learning outcomes, may advance the…

There is strong evidence from research conducted in the United States that fraction magnitude understanding supports mathematics achievement. Unfortunately, there has been little research that examines if this relation is present across educational contexts with different approaches to teaching fractions. The current study compared fourth and…

This paper describes the authors' journey in designing a linear representation that aligns mathematics and music to support fractional reasoning. The three authors, guided by the theoretical framing of realistic mathematics education, engaged in a task design process over a 12-month period to develop integrated resources. Data were collected in…

The aim of this study is revealing the strategies used by 5th-grade students in comparing fractions. In line with this purpose the study is based on qualitative research. Participants of the study conducted with convenient sampling method are seventy 5th-grade students. The students have been asked six questions which necessitate comparison of…

Although students' nonstandard strategies have great importance in understanding students' thinking and creating effective mathematics classrooms, much remains unexplored in the literature. This study investigated 22 middle school teachers' reasoning about a student's nonstandard strategy for the division of fractions. The data were collected…

In this paper, we analyse the results of an experience designed and implemented to evaluate the epistemic and cognitive conflicts identified in the study of proportionality, carried out by a group of 21 students in their last year of primary education. Initially the students exhibit difficulties to recognize situations where proportionality can be…

This study aimed at: (1) determining whether the Concrete-Pictorial-Abstract (CPA) strategy has a positive effect on students' mathematical conceptual understanding (MCU) and students' mathematical representation (MR) on fractions; (2) describing how CPA strategy can improve students' MCU and students' MR on fractions. This research used a mixed…

One of the subjects that constitute a problem for adult students of mathematics is the understanding of fractions and proportions. These notions are interrelated with proportional reasoning which was the focal point of our study. Using a mixed methods approach, we tried to assess the proportional reasoning of adult students during problem solving.…

The importance of mathematical reasoning is unquestioned and providing opportunities for students to become involved in mathematical reasoning is paramount. The open-ended tasks presented incorporate mathematical content explored through the contexts of problem solving and reasoning. This article presents a number of simple tasks that may be…

In this paper, we report on how Year 5 and 6 students (10 to 13 years old) solve reverse fraction problems; that is, where students are required to find the quantity of an unknown whole given a known partial quantity and its equivalent fraction of the unknown whole. To what extent do students' solutions generalise fraction structures that indicate…

When teachers conduct a universal screening in mathematics, they identify students who are struggling with mathematical content and adjust their instruction. In this mixed-methods study in Kolkata, India, teachers piloted a screening tool at the beginning of the academic year in 5th grade to determine students' (n = 171) understanding of…

Background: Fractions continue to pose a critical challenge for students and their teachers alike. Mathematics education research indicates that the challenge with fractions may stem from the limitations of part-whole concepts of fractions, which is the central focus of fractions curriculum and instruction in the USA. Students' development of more…

Many researchers argue that a deep understanding of fractions is important for a successful transition to algebra. Teaching, especially in the middle years, needs to focus specifically on those areas of fraction knowledge and operations that support subsequent solution processes for algebraic equations. This paper focuses on the results of Year 6…

All students should have opportunities to develop their ability to reason mathematically. Gersten and Chard (1999) support this stance with respect to students with learning disabilities: "Even if students are not automatic with basic facts, they still should be engaged in activities that promote the development of number sense and…