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Pedersen, Pernille Ladegaard; Bjerre, Mette – Educational Studies in Mathematics, 2021
In this study, we present a mathematical analysis distinguishing two conceptions of equivalence: "proportional equivalence" and "unit equivalence." These two conceptions have distinct meanings in relation to equivalent fractions: one is grounded in proportionality, while the other is grounded in equal wholes. We argue that (a)…
Descriptors: Fractions, Mathematical Concepts, Mathematics Instruction, Concept Formation
Copur-Gencturk, Yasemin – Educational Studies in Mathematics, 2021
Teachers' understanding of the concepts they teach affects the quality of instruction and students' learning. This study used a sample of 303 teachers from across the USA to examine elementary school mathematics teachers' knowledge of key concepts underlying fraction arithmetic. Teachers' explanations were coded based on the accuracy of their…
Descriptors: Fractions, Mathematics Instruction, Arithmetic, Teaching Methods
Street, Karin E. S.; Malmberg, Lars-Erik; Stylianides, Gabriel J. – Educational Studies in Mathematics, 2022
Self-efficacy in mathematics is related to engagement, persistence, and academic performance. Prior research focused mostly on examining changes to students' self-efficacy across large time intervals (months or years), and paid less attention to changes at the level of lesson sequences. Knowledge of how self-efficacy changes during a sequence of…
Descriptors: Self Efficacy, Longitudinal Studies, Attitude Change, Mathematics Instruction
Xie, Jinxia; Masingila, Joanna O. – Educational Studies in Mathematics, 2017
Existing studies have quantitatively evidenced the relatedness between problem posing and problem solving, as well as the magnitude of this relationship. However, the nature and features of this relationship need further qualitative exploration. This paper focuses on exploring the interactions, i.e., mutual effects and supports, between problem…
Descriptors: Fractions, Mathematics Instruction, Teaching Methods, Problem Solving
Chow, Alan F.; Van Haneghan, James P. – Educational Studies in Mathematics, 2016
This study reports the results of a study examining how easily students are able to transfer frequency solutions to conditional probability problems to novel situations. University students studied either a problem solved using the traditional Bayes formula format or using a natural frequency (tree diagram) format. In addition, the example problem…
Descriptors: Probability, College Students, Mathematical Formulas, Bayesian Statistics

Streefland, Leen – Educational Studies in Mathematics, 1982
A process of teaching fractions is detailed that respects pupil ideas and concept images and builds on these in a way that helps children to develop personal algorithms. This approach is an attempt to get away from perceived one-sided views found in most textbooks. (MP)
Descriptors: Algorithms, Educational Research, Elementary Education, Elementary School Mathematics

Bell, Alan; And Others – Educational Studies in Mathematics, 1981
An experiment is described which started with exploratory interviews, evolved to design and administration of diagnostic tests, and led to the preparation and use of calculator-enriched teaching materials. (MP)
Descriptors: Decimal Fractions, Diagnostic Teaching, Educational Research, Elementary Secondary Education

Bell, Alan – Educational Studies in Mathematics, 1993
Three teaching experiments are reported which study aspects of a diagnostic teaching methodology. An experiment in the field of directional quantities showed a positive relationship between the intensity of discussion and amount of learning; one on fractions and another on geometric reflections showed good two-month retention under the…
Descriptors: Cognitive Development, Diagnostic Teaching, Discussion (Teaching Technique), Fractions

Pirie, Susan; Kieren, Thomas – Educational Studies in Mathematics, 1992
Proposes and describes four teachers' beliefs necessary in creating constructivist classroom environments. Presents the background, description, and analysis of seven teaching episodes that examine the mathematical understanding actions of pupils in classrooms in which teachers exhibit these beliefs in an effort to verify the necessity of the…
Descriptors: Beliefs, Classroom Environment, Constructivism (Learning), Creative Thinking