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Caitlin R. Bowman; Dagmar Zeithamova – Journal of Experimental Psychology: Learning, Memory, and Cognition, 2023
A major question for the study of learning and memory is how to tailor learning experiences to promote knowledge that generalizes to new situations. In two experiments, we used category learning as a representative domain to test two factors thought to influence the acquisition of conceptual knowledge: the number of training examples (set size)…
Descriptors: Classification, Learning Processes, Generalization, Recognition (Psychology)
Karina J. Wilkie – Mathematics Education Research Journal, 2024
Quadratics provide a foundational context for making sense of many important algebraic concepts, such as variables and parameters, nonlinear rates of change, and views of function. Yet researchers have highlighted students' difficulties in connecting such concepts. This in-depth qualitative study with two pairs of Year 10 (15 or 16-year-old)…
Descriptors: Algebra, Mathematics Instruction, Mathematical Concepts, Grade 10
Zeycan Kama; Mine Isiksal Bostan; Zelha Tunç Pekkan – Journal of Pedagogical Research, 2023
This study investigates sixth-grade Turkish students' pattern-generalization approaches among arithmetical generalization, algebraic generalization, and naïve induction. A qualitative case study design was employed. The data was collected from four sixth-grade students through the Pattern Questionnaire (PQ) and individual interviews based on the…
Descriptors: Grade 6, Generalization, Rote Learning, Algebra
Hogue, Mark; Scarcelli, Dominic – International Journal of Mathematical Education in Science and Technology, 2022
Tangent lines are often first introduced to students in geometry during the study of circles. The topic may be repeatedly reintroduced to students in different contexts throughout their schooling, and often each reintroduction is accompanied by a new, nonequivalent definition of tangent lines. In calculus, tangent lines are again reintroduced to…
Descriptors: Calculus, Mathematics Instruction, Teaching Methods, Mathematical Concepts
Lee, Mi Yeon; Lee, Ji-Eun – Journal of Mathematics Teacher Education, 2023
In this study, hypothetical samples of students' work on a task involving pattern generalizations were used to examine the characteristics of the ways in which 154 elementary prospective teachers (PSTs) paid attention to students' work in mathematics. The analysis included what the PSTs attended to, their interpretations, and their suggestions for…
Descriptors: Generalization, Mathematics Instruction, Learning Processes, Thinking Skills
Mizrap Bulunuz; Betül Kuralay – Online Submission, 2023
Mole, molar mass and the Avogadro number are used constantly to measure the amount of substance in chemical changes. However, students have difficulty in understanding these concepts because they are not familiar with measuring very small amounts of matter that cannot be seen and weighed in daily life, like atoms. The mole concept was developed to…
Descriptors: Formative Evaluation, Science Instruction, Scientific Concepts, Concept Formation
Sievers, Carolin; Bird, Chris M.; Renoult, Louis – Learning & Memory, 2019
Repeated study typically improves episodic memory performance. Two different types of explanations of this phenomenon have been put forward: (1) reactivating the same representations strengthens and stabilizes memories, or (2) greater encoding variability benefits memory by promoting richer traces. The present experiment directly compared these…
Descriptors: Memory, Concept Formation, Prediction, Cognitive Processes
Relaford-Doyle, Josephine; Núñez, Rafael – International Journal of Research in Undergraduate Mathematics Education, 2021
This paper describes a study that used a novel method to investigate conceptual difficulties with mathematical induction among two groups of undergraduate students: students who had received university-level instruction in formal mathematical induction, and students who had not been exposed to formal mathematical induction at the university level.…
Descriptors: Concept Formation, Mathematical Concepts, Difficulty Level, Undergraduate Students
Rupnow, Rachel; Randazzo, Brooke – North American Chapter of the International Group for the Psychology of Mathematics Education, 2022
Isomorphism and homomorphism appear throughout abstract algebra, yet how algebraists characterize these concepts, especially homomorphism, remains understudied. Based on interviews with nine research-active mathematicians, we highlight new sameness-based conceptual metaphors and three new clusters of metaphors: sameness/formal definition, changing…
Descriptors: Mathematics Instruction, Teaching Methods, Algebra, Concept Formation
Ünlü, Emre; Diken, Ibrahim Halil – International Technology and Education Journal, 2022
The prerequisite for teaching many skills and behaviors to children with intellectual disabilities is that the child has acquired the basic concepts. Teaching concepts plays a very active role in the independence of the child with intellectual disabilities and in the acquisition of higher level skills that they will learn in the future. The…
Descriptors: Students with Disabilities, Intellectual Disability, Educational Technology, Technology Uses in Education
Wilkie, Karina J. – Educational Studies in Mathematics, 2021
Teachers whose mathematical meanings support understanding across different contexts are likely to convey them in productive ways for coherent student learning. This exploratory study sought to elicit 67 secondary mathematics pre-service teachers' (PSTs) meanings for quadratics with growing pattern creation and multiple translation tasks. A…
Descriptors: Equations (Mathematics), Secondary School Mathematics, Preservice Teachers, Mathematics Skills
Bowman, Caitlin R.; Zeithamova, Dagmar – Journal of Experimental Psychology: Learning, Memory, and Cognition, 2020
Building conceptual knowledge that generalizes to novel situations is a key function of human memory. Category-learning paradigms have long been used to understand the mechanisms of knowledge generalization. In the present study, we tested the conditions that promote formation of new concepts. Participants underwent 1 of 6 training conditions that…
Descriptors: Concept Formation, Generalization, Discrimination Learning, Classification
Saba, Janan; Hel-Or, Hagit; Levy, Sharona T. – Interactive Learning Environments, 2023
This paper presents the design and initial learning research with the MMM modeling platform, seeking to advance middle school students' learning through constructing computational models of complex physical and chemical systems. A complexity-based structure of an MMM interface is introduced. It suggests that a complex system can be described and…
Descriptors: Motion, Chemistry, Physics, Grade 7
Connections between Empirical and Structural Reasoning in Technology-Aided Generalization Activities
Yao, Xiangquan; Elia, John – International Electronic Journal of Mathematics Education, 2021
Mathematical generalization can take on different forms and be built upon different types of reasoning. Having utilized data from a series of task-based interviews, this study examined connections between empirical and structural reasoning as preservice mathematics teachers solved problems designed to engage them in constructing and generalizing…
Descriptors: Mathematics Instruction, Generalization, Preservice Teachers, Mathematics Teachers
Hunter, Jodie; Miller, Jodie – ZDM: Mathematics Education, 2022
A key aspect of young children's development of algebraic reasoning is the process of visualising and identifying structures to both abstract and generalise. There has been a growing body of research focused on how students form generalisations, this article adds to the existing body of research by examining how young culturally diverse students…
Descriptors: Mathematics Instruction, Mathematical Logic, Generalization, Low Income Students