Researchers from multiple disciplines have found that fractions and algebra knowledge are linked. One major strand of research has identified children's "units coordination" structures as crucial for success with fractions and algebra via multiplicative reasoning, whereas a second strand of research points to "magnitude…

Researchers from multiple disciplines have found that fractions and algebra knowledge are linked. One major strand of research has identified children's "units coordination" structures as crucial for success with fractions and algebra via multiplicative reasoning, whereas a second strand of research points to "magnitude…

Procedural flexibility is an important skill for algebra. Although prior work has focused on measuring students' procedural flexibility using arithmetic problems, word problems may also capture students' flexibility because of their open-ended nature. To date, no published study has examined the use of word problems as another measure of…

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…

This study investigated children's knowledge of the addition of fractions with unlike denominators. It focussed on the strategies used by children to add fractions with unlike denominators. A cross-sectional survey of Grade 8 children in schools in two districts in Ghana was used. A test on the addition of fractions with unlike denominators was…

This study revealed the fractional number sense form associated with daily life and the number sense of 8th-grade students with high academic success. This study aimed to determine fractional number sense which in eighth graders with high academic performance. This study has a qualitative patterned. The sample consisted of 20 students from the…

Urban school districts have seen low scores on NWEA Map math scores (Education Recovery Scoreboard, 2024). To foster and promote urban youths' capabilities to learn mathematics, a new method to teach, enhance, and remediate understanding of fractions was developed, Fractions and Signed Numbers Workshop (FracSi). It utilizes the approach of an…

Fractions are foundational for success in algebra and STEM, but they are notoriously difficult for students. In past work, two separate branches of research from psychology and math education have studied fractions knowledge using different, isolated approaches. In this dissertation, I synthesize research from both fields about proportional…

We examined the development of numerical magnitude representations of fractions and decimals from fourth to 12th grade. In Experiment 1, we assessed the rational number magnitude knowledge of 200 Chinese fourth, fifth, sixth, eighth, and 12th graders (92 girls and 108 boys) by presenting fraction and decimal magnitude comparison tasks as well as…

Background: Concerning students' difficulties with fractions, many explanatory approaches are based on the distinction between conceptual knowledge and procedural knowledge. For further research in this field, it is thus crucial to make these constructs accessible to valid measurement. Aims: In this study, we aim at developing a test instrument…

Learning rational number concepts is acknowledged as an important task but many learners find it difficult to make sense of them. This paper reports on a case study of the learning in a short (nine-lesson) learning programme for Grade 8 learners in a Namibian school, which sought to use visual models (circle area, bar area and number line) to…

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…

Without a conceptual understanding of fraction magnitude, students have difficulties understanding more advanced mathematics in high school and beyond. The purpose of this study is to highlight 4th and 8th grade students' misconceptions in fraction magnitude using the Trends in International Mathematics and Science Study 2015 data. The study is…

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…

There is an ongoing need to support students' learning of linear functions, and the study of slope makes up a foundational component of this learning. We applied techniques from systemic functional linguistics to document the meanings that were established through spoken interaction between a student and her tutors during discussions of slope. We…