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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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Thomas, Jonathan; Jong, Cindy; Fisher, Molly H.; Schack, Edna O. – The Mathematics Educator, 2017
For the past two decades, the development of preservice elementary teachers' mathematical knowledge and skills has been central to mathematics education research. Two frameworks that researchers have drawn upon to examine such development are mathematical knowledge for teaching and professional noticing (of children's mathematical thinking). We…
Descriptors: Pedagogical Content Knowledge, Preservice Teachers, Elementary Education, Mathematics Education
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Sawyer, Amanda Gantt – The Mathematics Educator, 2017
I investigated a reform based teachers' beliefs about the nature of mathematics, teaching mathematics, and learning mathematics, and the factors leading to their formation. I interviewed and observed a reform-based elementary mathematics teacher with 13 years' experience teaching first grade. She held a Platonist/problem solver view of…
Descriptors: Elementary School Teachers, Mathematics Teachers, Teacher Attitudes, Beliefs
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Harkness, Shelly Sheats; Brass, Amy – The Mathematics Educator, 2017
Mathematics methods textbooks/texts are important components of many courses for preservice teachers. Researchers should explore how these texts are selected and used. Within this paper we report the findings of a survey administered electronically to 132 members of the Association of Mathematics Teacher Educators (AMTE) in order to answer the…
Descriptors: Textbook Selection, Preservice Teacher Education, Teacher Educators, Teacher Surveys
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