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Kartal, Ozgul; Morrissey, Susie; Popovic, Gorjana – The Mathematics Educator, 2020
According to the Association of Mathematics Teacher Educators (AMTE, 2017), teachers should first try to see problems through their students' eyes, anticipate, understand, and analyze students' varied ways of thinking, and respond appropriately. In this study, we engaged preservice teachers (PTs) in planning to implement problem-solving tasks;…
Descriptors: Elementary School Teachers, Preservice Teachers, Problem Solving, Intervention
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Kuzle, Ana; Glasnovic Gracin, Dubravka – The Mathematics Educator, 2020
For many decades, the amount of geometry curriculum worldwide has been cut, mathematics curricula have lacked diversity of geometrical phenomena, and geometry teaching has been reduced to a somewhat eclectic mix of activities. Recently, new trends have begun to counteract these tendencies by framing new curricula around fundamental ideas. The…
Descriptors: Geometry, Mathematics Instruction, Mathematics Curriculum, Freehand Drawing
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Liang, Biyao; Castillo-Garsow, Carlos – The Mathematics Educator, 2020
Contributing to research on students' multifaceted meanings for angles (e.g., angles as ray pairs, as regions, and as turns), we report on three undergraduate students' meanings for central and inscribed angles in circles. Specifically, we characterize how these meanings govern their mathematical activities when engaging in a circle geometry task,…
Descriptors: Mathematics Instruction, Undergraduate Students, Concept Formation, Geometric Concepts
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Zwanch, Karen – The Mathematics Educator, 2019
The purpose of this research is to construct a preliminary genetic decomposition delineating the mental constructions underlying probabilistic independence. This delineation is considered within the framework of APOS theory. While the use of the term independence in probability is often conflated with causation, the definition relies instead upon…
Descriptors: Mathematics Instruction, Probability, Mathematical Concepts, Developmental Stages
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Rhodes, Ginger; Hallman-Thrasher, Allyson; Schultz, Kyle T. – The Mathematics Educator, 2019
This article examines the professional vision of mathematics teacher developers during a professional development experience that featured observations of a content course for elementary teachers. The researchers examined whether these mathematics teacher developers viewed the demonstration class as an analysis class serving as a site for…
Descriptors: Mathematics Teachers, Teacher Educators, Preservice Teacher Education, Teacher Attitudes
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Kuzle, Ana – The Mathematics Educator, 2019
Despite the important role that metacognition plays in school mathematics, attention has only recently turned to primary grades. The aim of this exploratory qualitative study was to find out to what extent 6 second graders engage in metacognitive behaviors during mathematics problem-solving. The analysis was based on the adaptation of the…
Descriptors: Grade 2, Metacognition, Problem Solving, Mathematics Instruction
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Poulsen, Seth – The Mathematics Educator, 2019
Methods of causal inference are not widely used by education researchers, even though they can be extremely useful tools for eliminating selection bias and confounding factors in empirical studies. For example, researchers have established that taking additional math classes in high school is strongly correlated with success in college and higher…
Descriptors: High School Students, Secondary School Mathematics, College Students, College Mathematics
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Taylor, Cynthia E.; Smith, Ryan C. – The Mathematics Educator, 2019
In this study, we examined five mathematics teacher educators' (MTEs') interpretation of the situative perspective, who self-identify as holding that perspective. Furthermore, we share how they designed and facilitated their secondary mathematics methods course pertaining to the activities they identified as most important for the course. We…
Descriptors: Secondary School Mathematics, Secondary School Teachers, Mathematics Teachers, Teacher Educators
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Prasad, Priya V.; Barron, Victoria – The Mathematics Educator, 2019
Students' ability to reason for themselves is a crucial step in developing conceptual understandings of mathematics, especially if those students are preservice teachers. Even if classroom environments are structured to promote students' reasoning and sense-making, students may rely on prior procedural knowledge to justify their mathematical…
Descriptors: Preservice Teachers, Mathematics Teachers, Mathematics Instruction, Knowledge Level
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Dorko, Allison – The Mathematics Educator, 2019
Generalization is critical to mathematical thought and to learning mathematics. However, students at all levels struggle to generalize. In this paper, I present a theoretical analysis connecting Piaget's assimilation and accommodation constructs to Harel and Tall's (1991) framework for generalization in advanced mathematics. I offer a theoretical…
Descriptors: Mathematics Education, Generalization, Piagetian Theory, Learning Theories
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Winsor, Matthew S.; Kirwan, J. Vince; Ssebaggala, Lawrence – The Mathematics Educator, 2018
The structures of secondary mathematics teacher preparation (SMTP) programs in the United States are not well documented. This study sought to identify baseline data for SMTP programs. Survey data was collected from 86 different institutions regarding their SMTP programs. Results indicated that most SMTP programs are housed in mathematics…
Descriptors: Secondary Education, Mathematics Instruction, Preservice Teachers, Mathematics Teachers
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Tekin-Dede, Ayse; Bukova-Güzel, Esra – The Mathematics Educator, 2018
The purpose of this study was to introduce a rubric named "Rubric for the Assessment of Modeling Skills" for assessing cognitive modeling skills and explaining the rubric's development process. The dimensions of the rubric are understanding the problem, simplifying, mathematizing, working mathematically, interpreting and validating.…
Descriptors: Scoring Rubrics, Mathematics Instruction, Grade 6, Grade 11
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Donaldson, Brianna; Nakamaye, Michael; Umland, Kristin; White, Diana – The Mathematics Educator, 2018
The Math Teachers' Circle (MTC) model is a widely implemented form of professional development that invites teachers to become practitioners of mathematics, thereby developing their fluency with mathematical practices. This article presents comparative case studies investigating the self-reported experiences of several MTC-participating teachers…
Descriptors: Teacher Effectiveness, Mathematics Teachers, Mathematics Instruction, Teacher Participation
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Kosko, Karl W.; Singh, Rashmi – The Mathematics Educator, 2018
Multiplicative reasoning is essential for students' engagement with various mathematical concepts. Although the field's understanding of children's multiplicative concepts has grown over the past 30 years, relatively few studies have examined the development of multiplicative concepts with whole numbers, and even fewer have studied this phenomenon…
Descriptors: Mathematics Instruction, Mathematical Concepts, Concept Formation, Multiplication
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Norton, Anderson; Ulrich, Catherine; Bell, Martha Ann; Cate, Anthony – The Mathematics Educator, 2018
The emerging field of mathematics educational neuroscience provides researchers with new approaches to understanding mathematical development, as well mathematics itself. This paper focuses on the role of the hand in constructing mathematics through activity. We rely on Piaget's distinction of three kinds of activity: sensorimotor activity,…
Descriptors: Mathematics Instruction, Mathematics Activities, Neurosciences, Piagetian Theory
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