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Topic Specificity of Students' Conceptual and Procedural Fraction Knowledge and Its Impact on Errors
Katja Lenz; Frank Reinhold; Gerald Wittmann – Research in Mathematics Education, 2024
When learning about fractions, teaching usually follows certain topics -- e.g. part of the whole, fraction equivalence, and size comparison. Not yet answered is whether students' conceptual and procedural knowledge of fractions is coherent between those topics. To answer this question, we performed a latent profile analysis of data from N = 1005…
Descriptors: Fractions, Error Patterns, Mathematics Instruction, Concept Formation
Rodríguez-Martínez, José Antonio; González-Calero, José Antonio; Olmo-Muñoz, Javier; Arnau, David; Tirado-Olivares, Sergio – British Journal of Educational Technology, 2023
This study analyses the potential of a learning analytics (LA) based formative assessment to construct personalised teaching sequences in Mathematics for 5th-grade primary school students. A total of 127 students from Spanish public schools participated in the study. The quasi-experimental study was conducted over the course of six sessions, in…
Descriptors: Foreign Countries, Elementary School Students, Grade 5, Mathematics Instruction
Morano, Stephanie; Flores, Margaret M.; Hinton, Vanessa; Meyer, Jillian – Exceptionality, 2020
This study compares the effects of a concrete-representational-abstract (CRA) intervention against a modified CRA-Integrated (CRA-I) intervention using a pretest-posttest design with random assignment of matched pairs to intervention conditions. The researchers designed both interventions to improve participants' understanding of and ability to…
Descriptors: Students with Disabilities, Intervention, Mathematical Concepts, Concept Formation
Kara, Fatma; Incikabi, Lutfi – International Electronic Journal of Elementary Education, 2018
The current study aims to show the transition skills of sixth grade students between the representations (numerical, model, number line and verbal) given in addition-subtraction operations in fractions and to analyse the ability of the students to construct each representation type. In this research, case study method was used in terms of the…
Descriptors: Grade 6, Foreign Countries, Mathematical Concepts, Addition
Loc, Nguyen Phu; Tong, Duong Huu; Chau, Phan Thai – Educational Research and Reviews, 2017
In Vietnam, primary school students explicitly learn the concept of fraction in Grade 4 and 5. Because this concept is introduced to them intuitionally, it is difficult for them to understand and apply it. Base on this point, we believe that the students will commit many errors when solving exercises related to this concept. The survey of 478…
Descriptors: Foreign Countries, Elementary School Students, Fractions, Mathematical Concepts
Bossé, Michael J.; Bayaga, Anass; Fountain, Catherine; Lynch-Davis, Kathleen; Preston, Ron; Adu-Gyamfi, Kwaku – International Electronic Journal of Elementary Education, 2018
This study applies the Mathematics Acquisition Framework (MAF) (Bossé, Ringler, Bayaga, Fountain, & Young, 2018) to investigate fifth- through seventh-grade students' comprehension of fractions and decimals and examines how students build understanding of mathematical principles and concepts regarding fractions and decimals. Based on case…
Descriptors: Mathematics Education, Grade 5, Grade 6, Grade 7
Lewis, Katherine E. – Learning Disability Quarterly, 2016
Although many students struggle with fractions, students with mathematical learning disabilities (MLDs) experience pervasive difficulties because of neurological differences in how they process numerical information. These students make errors that are qualitatively different than their typically achieving and low-achieving peers. This study…
Descriptors: Learning Disabilities, Mathematics Instruction, Neurological Impairments, Statistical Analysis
Resnick, Lauren B.; And Others – 1988
Considered is a conceptual analog of buggy algorithms and rule-based mathematical development. The investigations consider whether children's efforts to make conceptual sense of new mathematics instruction in terms of their available knowledge may sometimes lead them to make systematic errors. In particular, the possibility is explored that…
Descriptors: Arithmetic, Concept Formation, Decimal Fractions, Educational Research

Hart, Kathleen – Mathematics in School, 1978
Thirty-five secondary school children were interviewed on a one-to-one basis using questions which involved concepts considered as basic to the notion of ratio. One implication of the study is that a doubling ability is no indication of the ability to tackle other ratio questions. (MN)
Descriptors: Concept Formation, Educational Research, Error Patterns, Fractions

Hart, Kathleen – Mathematics in School, 1987
A brief overview is given of a research project funded to investigate the cause and cure of errors in ratio and proportion, algebra, and fractions. Choosing pertinent information, interviewing students, listing significant features, developing lessons, and testing the materials are considered. (MNS)
Descriptors: Algebra, Concept Formation, Curriculum Development, Educational Research

Resnick, Lauren B.; And Others – Journal for Research in Mathematics Education, 1989
Documented are major categories of errors that appear as children learn decimal fractions. Then the conceptual sources of these errors are established. Different curriculum sequences influence the probability that these classes of errors will appear. They can be used as diagnostic tools to detect children's understanding of mathematics topics.…
Descriptors: Cognitive Structures, Concept Formation, Decimal Fractions, Diagnostic Teaching