Fractions are a fundamental component of the school mathematics curriculum, and most students achieve proficiency in these concepts during their elementary education. However, a significant proportion of students still encounter challenges in this area even after entering secondary education, necessitating additional support to prevent further…

This single-case study investigates the effectiveness of video modeling for teaching the Look, Ask, Pick (LAP) strategy to three seventh-grade students with learning disabilities. The participants watched video segments explaining the technique to solve fraction problems. Results from the intervention revealed substantial performance improvements…

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…

One of the attributes of rational numbers that make them different from integers are the different symbolic modes (fraction, decimal and percentage) to which an identical number can be attributed (e.g. 1/4, 0.25 and 25%). Some research has identified students' difficulty in mental calculations with rational numbers as has also the switching to…

In the present study, we tested the hypotheses that: a) there are individual differences in secondary students' conceptual and procedural fraction knowledge, and b) these differences are predicted by students' approach (deep vs. surface) to mathematics learning. We used two instruments developed and evaluated for the purposes of the study which…

Background: Mathematics education is a significant issue in the South African context. Learners' achievement levels are markedly low as suggested by both national and international studies. The teaching and learning of fractions in particular have been identified as challenging. Aim: The aim of this article is to share some of the outcomes derived…

Purpose: Most literature has focused solely on either knowledge about number sense or understanding of fractions. To fill the research gap, this study examined pupils' abilities in both number sense and fractions. In particular, it investigated Year 4 and Year 5 pupils' use of strategies in developing their fraction sense. Methodology: This study…

Ratio-proportion is one of the topics that middle school students have difficulty in comprehending. This study aims to determine the learning difficulties that seventh-grade students face while learning about ratio-proportion. Three commonly used strategies to solve ratio-proportion problems are buildup, unit ratio and cross-multiplication. The…

Gap reasoning is an inappropriate strategy for comparing fractions. In this article, Patrick Sullivan and Joann Barnett look at the persistence of this misconception amongst students and the insights teachers can draw about students' reasoning.

There has been a controversial debate if individuals solve fraction comparison tasks componentially by comparing the numerators and denominators, or holistically by considering the numerical magnitudes of both fractions. Recent research suggested that expert mathematicians predominantly use componential strategies for fraction pairs with common…

Thus far, it is unclear how students can learn most effectively from their own errors. In this study, reflections on the rationale behind self-made errors are assumed to enhance knowledge acquisition. In a field experiment with pre/post/follow-up design, the authors practiced fractions with 174 seventh- and eighth-grade students who were randomly…

The key purpose of this study was how we taught the use of benchmark strategy when comparing fraction for fifth-graders in Taiwan. 26 fifth graders from a public elementary in south Taiwan were selected to join this study. Results of this case study showed that students had a much progress on the use of benchmark strategy when comparing fraction…

This guidance report focuses on the teaching of mathematics to pupils in Key Stages 2 and 3. It is not intended to provide a comprehensive guide to mathematics teaching. We have made recommendations where there are research findings that schools can use to make a significant difference to pupils' learning, and have focused on the questions that…

Reports the results of a study on students from Grade 4 to Year 10 (n=1853) where the larger number from pairs of decimals was chosen. Test results and interviews were used for data collection. Presents a detailed description of more than 10 ways in which students interpreted decimal numbers. Contains 11 references. (Author/ASK)

Describes a method for teaching multiplication of fractions based on Piaget's constructivism. Instead of teaching the algorithm of multiplying the numerators and denominators, students are presented with many problems and ask to invent their own ways of solving them. (DDR)