Solving Fraction Problems Research Articles

Strategic Development for Middle School Students Struggling With Fractions

Research has suggested that different strategies used when solving fraction problems are highly correlated with students’ problem-solving accuracy. This study (a) utilized latent profile modeling to classify students into three different strategic developmental levels in solving fraction comparison problems and (b) accordingly provided differentiated strategic training for students starting from two different strategic developmental levels. In Study 1 we assessed 49 middle school students’ performance on fraction comparison problems and categorized students into three clusters of strategic developmental clusters: a cross-multiplication cluster with the highest accuracy, a representation strategy cluster with medium accuracy, and a whole-number strategy cluster with the lowest accuracy. Based on the strategic developmental levels identified in Study 1, in Study 2 we selected three students from the whole-number strategy cluster and another three students from the representation strategy cluster and implemented a differentiated strategic training intervention within a multiple-baseline design. Results showed that both groups of students transitioned from less advanced to more advanced strategies and improved their problem-solving accuracy during the posttest, the maintenance test, and the generalization test.

Measuring fraction comparison strategies with eye-tracking

Research suggests that people use a variety of strategies for comparing the numerical values of two fractions. They use holistic strategies that rely on the fraction magnitudes, componential strategies that rely on the fraction numerators or denominators, or a combination of both. We investigated how mathematically skilled adults adapt their strategies to the type of fraction pair. To extend previous research on simple fraction comparison, we used a highly controlled set of more complex fractions with two-digit components. In addition to response times, we recorded eye movements to assess how often the participants fixated on and alternated between specific fraction components. In line with previous studies, our data suggest that the participants preferred componential over holistic strategies for fraction pairs with common numerators or common denominators. Conversely, they preferred holistic over componential strategies for fraction pairs without common components. These results support the assumption that mathematically skilled adults adapt their strategies to the type of fraction pair even in complex fraction comparison. Our study also suggests that eye-tracking is a promising method for measuring strategy use in solving fraction problems.

Exploratory Study of Informal Strategies for Equal Sharing Problems of Students With Learning Disabilities

Little to no information exists explaining the nature of conceptual gaps in understanding fractions for students with learning disabilities (LD); such information is vital to practitioners seeking to develop instruction or interventions. Many researchers argue such knowledge can be revealed through student’s problem-solving strategies. Despite qualitative differences in thinking and representation use in students with LD that may exist, existing frameworks of student’s strategies for solving fraction problems are not inclusive of students with LD. This exploratory study extends existing literature by documenting the strategies students with LD use when solving fraction problems. Clinical interviews were conducted with 10 students across the third, fourth, and fifth grades ( N = 10). Results indicate students with LD used similar strategies as previously reported in research involving non-LD students, although the dominant strategy utilized was less advanced and the range of strategy use was relatively compact. Researchers suggest the nature of conceptual gaps students with LD display in their understanding of fractions originates from a malleable source. Implications for instruction and assessment are presented.

Making Conceptual Knowledge Connections to Clear Misconceptions in Fractions in Primary Classrooms

This study aimed at investigating the effect of making conceptual knowledge connections through multiple representations in clearing misconceptions in the study of fractions. The study used a quasi- experimental research design with a pre-test- intervention- post-test format where in 40 students of Grade 4 of a primary school in New Delhi were randomly selected. The students in the control group were taught fractions using the conventional approach where as the experimental group was exposed to an instructional program that utilized a problem solving approach. The emphasis during the intervention program was on making connections among various mathematical representations to develop fraction number sense and operation sense among children. The treatment group was immersed in fraction instructions for six weeks and problem contexts were used each and every day to clear misconceptions. The effect of making conceptual knowledge connections in fractions and the performance of the students in solving fraction problems were assessed with a pre-test and post-test. For better understanding of the thinking processes and working patterns of the children while dealing with fractions, the classes were regularly observed by the researcher and interviews with 5 students each in the control and experimental groups were conducted by her. The findings of the study indicated that the students who received the treatment had significantly higher scores, used manipulatives more meaningfully when posed with fraction problems and had lesser misconceptions suggesting deeper conceptual understanding of fractions.

The relation between ability to draw equally divided figures showing fractions and performance in solving fraction problems

The relation between ability to draw equally divided figures showing fractions and performance in solving fraction problems

Childirens Strategies for Solving Fraction Problems: A Comparision of Primary and Intermediate Grades

Childirens Strategies for Solving Fraction Problems: A Comparision of Primary and Intermediate Grades

Partitioning: An Approach To Fractions

Recent research reports show that students have difficulty solving fraction problems when using physical models or diagrams whether the units are sets of objects (Hunting 1983) or regions (Kieren, Nelson, and Smith 1985). These reports show that students are not familiar with fraction models, a finding that suggests that they do not have sufficient experience with nonsymbolic work in fractions. Competence in representing fractions concretely or pictorially would facilitate solving fraction problems and could serve to verify computations with symbolic fractions.