From Non-symbolic to Symbolic Proportions and Back: A Cuisenaire Rod Proportional Reasoning Intervention Enhances Continuous Proportional Reasoning Skills

The persistent educational challenges that fractions pose call for developing novel instructional methods to better prepare students for fraction learning. Here, we examined the effects of a 24-session, Cuisenaire rod intervention on a building block for symbolic fraction knowledge, continuous and discrete non-symbolic proportional reasoning, in children who have yet to receive fraction instruction. Participants were 34 second-graders who attended the intervention (intervention group) and 15 children who did not participate in any sessions (control group). As attendance at the intervention sessions was irregular (median = 15.6 sessions, range = 1–24), we specifically examined the effect of the number of sessions completed on their non-symbolic proportional reasoning. Our results showed that children who attended a larger number of sessions increased their ability to compare non-symbolic continuous proportions. However, contrary to our expectations, they also decreased their ability to compare misleading discretized proportions. In contrast, children in the Control group did not show any change in their performance. These results provide further evidence on the malleability of non-symbolic continuous proportional reasoning and highlight the rigidity of counting knowledge interference on discrete proportional reasoning.

A systematic review on teaching fraction for understanding through representation on Web of Science database using PRISMA

Through a search executed on Web of Science database with general keywords pertaining to ‘teaching fractions’ or ‘understanding fractions’ and ‘representation’, this study utilized PRISMA’s procedure in analysing previously published articles. This review reveals seven articles in inclusion criteria and seventeenth articles in exclusion criteria with reasons. The included articles were reviewed for (a) studies characteristics, (b) instructional focus, (c) representation elements: real-world situation, manipulative aids, pictures, spoken and written symbols, and (d) the outcomes of each study. The metadata was analysed to organise the outcomes. Most of these articles focus on grade 3 and above and Western countries’ urban area. The result indicates most studies emphasize both conceptual and procedural understandings. Multi representations utilize sequential or parallel concept related to fractions improve students’ knowledge, particularly in understanding fractions. Meanwhile, developing fraction learning through multiple explicit representations at the initial Grade level of fraction instruction is for elementary school. However, less attention has been given to explicit representations in learning fractions at such a level.

From non-symbolic to symbolic proportions and back: a Cuisenaire rod proportional reasoning intervention enhances continuous proportional reasoning skills

The persistent educational challenges that fractions pose call for the development of novel instructional methods to better prepare students for fraction learning. Here, we examined the effects of a 24-session, Cuisenaire rod intervention on a building block for symbolic fraction knowledge, continuous and discrete non-symbolic proportional reasoning, in children who have yet to receive fraction instruction. Participants were 40 second graders divided into three groups: the Full intervention group who attended nearly all the sessions (n = 14), the Partial intervention group who participated in a small number of sessions (n = 11), and Control group (n = 15). Children in the Full intervention group increased their ability to compare non-symbolic continuous proportions in representations in which they did not receive any practice (annulus-shaped figures). However, contrary to our expectations, children in this group also decreased their ability to compare misleading discrete proportions. In contrast, children in the Control group did not show any change in their performance, and children in the Partial intervention group showed a similar, but not significant pattern of effects as the Full intervention group. These results provide further evidence on non-symbolic continuous proportional reasoning’s malleability and highlights the rigidity of counting knowledge interference on discrete proportional reasoning.

Anchoring Problem-Solving and Computation Instruction in Context-Rich Learning Environments

Middle school students with learning disabilities in math (MLD) used two versions of Enhanced Anchored Instruction (EAI). In one condition, students learned how to compute with fractions on an as-needed basis while they worked to solve the EAI problems. In the other condition, teachers used a computer-based instructional module in place of one of the EAI problems to deliver formal fraction instruction. The results indicated that students in both instructional formats improved their fraction computational skills and that formal instruction provided an added benefit. Both instructional conditions improved students' problem-solving skills by about the same amount. The findings suggest that combining formal fraction instruction with EAI is a viable way to improve the problem-solving and computational skills of students with MLD.