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Scheiner, Thorsten; Pinto, Marcia M. F. – For the Learning of Mathematics, 2022
Earlier approaches to sense-making in mathematics have looked at the ways students comprehend a mathematical concept. Recent research suggests that some students make sense not only of mathematical objects that have a being, but also of objects that have yet to become. In such cases, learning mathematics is not just an act of comprehending a given…
Descriptors: Mathematics Instruction, Mathematical Concepts, Concept Formation, Learning Processes
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Ana Patricia García-Amado; Maythe García-Rivero; José Luis Cruz-Canales; Rubén Abraham Moreno Segura; Asuman Oktaç – For the Learning of Mathematics, 2024
The aim of this study is to explore the possibility of introducing the general notions of function and inverse function through a mathematical activity on linear functions, focusing on the quantitative meaning associated to the connection between a relation and its inverse. We present a genetic decomposition, that is, a viable cognitive path for…
Descriptors: Mathematics Instruction, Teaching Methods, High School Students, Student Attitudes
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Luz, Yael; Yerushalmy, Michal – Journal for Research in Mathematics Education, 2023
We report on an innovative design of algorithmic analysis that supports automatic online assessment of students' exploration of geometry propositions in a dynamic geometry environment. We hypothesized that difficulties with and misuse of terms or logic in conjectures are rooted in the early exploration stages of inquiry. We developed a generic…
Descriptors: Algorithms, Computer Assisted Testing, Geometry, Mathematics Instruction
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Aydin-Güç, Funda – Journal of Inquiry Based Activities, 2021
This article presents theoretical knowledge, sample activities, and reflections from the implementation process on how teachers can benefit from the Variation Theory to help students enhance their mathematical comprehension. In this context, "congruence of triangles" was conceptualized as an object of learning. Critical aspects were…
Descriptors: Educational Environment, Learning Theories, Geometry, Geometric Concepts
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Antonides, Joseph; Battista, Michael T. – North American Chapter of the International Group for the Psychology of Mathematics Education, 2022
Over half a century has passed since Bruner suggested his three-stage enactive-iconic-symbolic model of instruction. In more recent research, predominantly in educational psychology, Bruner's model has been reformulated into the theory of instruction known as concreteness fading (CF). In a recent constructivist teaching experiment investigating…
Descriptors: Mathematics Instruction, Teaching Methods, Constructivism (Learning), Educational Psychology
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Abassian, Aline; Safi, Farshid; Bush, Sarah; Bostic, Jonathan – Investigations in Mathematics Learning, 2020
This article presents a review of literature exploring five different perspectives on mathematical modeling in mathematics education. Because there is not a single agreed-on definition of what mathematical modeling is or how it should be done, a focused and extensive review of mathematical modeling is essential. The five broad classifications…
Descriptors: Mathematics Instruction, Mathematical Models, Teaching Methods, Social Influences
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Oktaç, Asuman; Trigueros, María; Romo, Avenilde – For the Learning of Mathematics, 2019
Certain aspects of theoretical frameworks in mathematics education can remain unexplained in the literature, hence unnoticed by the readers. It is thus interesting to participate in a dialogue where they can be discussed and compared in terms of the aims, objects studied, results and their relation to teaching. This study is focused on how APOS…
Descriptors: Mathematics Instruction, Learning Theories, Knowledge Level, Constructivism (Learning)
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Thanheiser, Eva; Melhuish, Kathleen – ZDM: The International Journal on Mathematics Education, 2019
Prospective elementary school teachers (PTs) come to their mathematics courses fluent in using procedures for adding and subtracting multidigit whole numbers, but many are unaware of the essential features inherent in understanding the base-ten place-value system (i.e., grouping, place value, base). Understanding these features is crucial to…
Descriptors: Preservice Teachers, Elementary School Teachers, Number Concepts, Number Systems
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Dello Iacono, Umberto; Ferrara Dentice, Eva – International Journal of Mathematical Education in Science and Technology, 2022
This work refers to a research project named 'Math walks', whose aim is to investigate a few students' common conceptions and difficulties related to symmetries as well as to guide the student in the transition from visualization to conceptualization. As far as this issue is concerned, we designed a learning activity (LA) according to Dina van…
Descriptors: Mathematics Instruction, Teaching Methods, Learning Activities, Visualization
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Pujawan, I. Gusti Ngurah; Suryawan, I. Putu Pasek; Prabawati, Dewa Ayu Ari – International Journal of Instruction, 2020
Spatial ability is an ability to visualize an object in space. In learning geometry, the spatial ability is required to solve geometric problems. One of the learning models that can be applied in the learning process to improve students' spatial ability is Van Hiele learning model. Van Hiele learning model is a learning model based on Van Hiele…
Descriptors: Spatial Ability, Instructional Effectiveness, Teaching Methods, Geometric Concepts
Watson, Jane; Fitzallen, Noleine – Mathematics Education Research Group of Australasia, 2021
Statistical terms are used in everyday language and, at times, used in non-statistical ways. It is often assumed students understand statistical terms because of their common use; however, research into their understanding of specific statistical terms is scant. This report focuses on 58 Year 3 students' responses to the basic question, "What…
Descriptors: Mathematics Instruction, Grade 3, Elementary School Students, Data Analysis
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MacDonald, Beth L.; Boyce, Steve; Hunt, Jessica H.; Byerley, Cameron; Moss, Diana L.; Bertolone-Smith, Claudia – North American Chapter of the International Group for the Psychology of Mathematics Education, 2019
Students' construction, coordination, and abstraction of units underlie success across multiple mathematics domains. Structures for coordinating units underscore notions of numbers as composite units (e.g., five is a unit of five and five units of one). In this working group, we seek to facilitate collaboration amongst researchers and educators…
Descriptors: Mathematics Instruction, Concept Formation, Numbers, Researchers
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Vos, Pauline; Frejd, Peter – Journal on Mathematics Education, 2022
Many students do not experience usefulness in mathematics. To address this problem, we offered them a mathematical tool, Sankey diagrams, which is a flow chart appearing in news media to visualize social, industrial or environmental processes. We carried out an Educational Design Research (EDR) to develop and evaluate lesson materials about…
Descriptors: Instructional Design, Mathematics Instruction, Visual Aids, Lesson Plans
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Björklund, Camilla – Scandinavian Journal of Educational Research, 2018
This is an empirical inquiry concerning children's concept development and early mathematics teaching. The intention is to broaden the understanding of preschool children's perceptions of the concept "half" (as 1 of 2 equal parts of a whole), in designed mathematics teaching settings. Three teachers working with 4-5-year-old children…
Descriptors: Teaching Methods, Preschool Education, Preschool Children, Mathematics Instruction
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Alex, Jogymol K.; Mammen, Kuttickattu J. – EURASIA Journal of Mathematics, Science & Technology Education, 2016
This paper reports on one part of a large study which attempted to identify the linguistic and hierarchical characteristics of van Hiele theory amongst grade 10 learners. The sample consisted of a total of 359 participants from five purposively selected schools from Mthatha District in the Eastern Cape Province of South Africa. The performance of…
Descriptors: Foreign Countries, Grade 10, Geometric Concepts, Secondary School Students
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