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Li, Yeping, Ed.; Lewis, W. James, Ed.; Madden, James J., Ed. – Advances in STEM Education, 2018
This book is inspired by Roger E. Howe's contributions to the international communities of mathematics and mathematics education. Renowned for his research contributions in the fields of representation theory, automorphic forms, harmonic analysis, and invariant theory, Dr. Howe has also fundamentally deepened our understanding of the mathematics…
Descriptors: Mathematics Education, Educational Research, Mathematics Instruction, Interdisciplinary Approach
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Wu, Hung-Hsi – Advances in STEM Education, 2018
We describe the mathematical content knowledge a teacher needs in order to achieve a basic level of competence in mathematics teaching. We also explain why content knowledge is essential for this purpose, how Textbook School Mathematics (TSM) stands in the way of providing teachers with this knowledge, and the relationship of this concept of…
Descriptors: Mathematics Instruction, Mathematics Teachers, Pedagogical Content Knowledge, Knowledge Level
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Friedberg, Solomon – Advances in STEM Education, 2018
Post-secondary mathematics faculty members have an important role to play in the preparation of future mathematics teachers at all levels and in the support and professional development of in-service mathematics teachers. This work can be demanding and time-consuming and constitute a significant professional contribution. Some departments now…
Descriptors: Mathematics Teachers, College Faculty, College Mathematics, Teacher Role
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Askey, Richard – Advances in STEM Education, 2018
Two content topics will be described. One deals with geometric measurement: length, area, and volume. These are important topics and they have not been learned very well. In particular, what types of relations can one consider when dealing with these three aspects of geometric measurement? The second topic is fractions, and different views of what…
Descriptors: Knowledge Level, Geometry, Measurement, Geometric Concepts
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Madden, James J. – Advances in STEM Education, 2018
Ratio and proportion have been part of school mathematics since the earliest manifestations of anything like school math in the Middle Ages. In this paper, I compile and comment on statements from primary sources of the last 2300 years to exhibit ideas that appear to have influenced the treatment of these topics in schoolbooks today. Historical…
Descriptors: Mathematics Instruction, Pedagogical Content Knowledge, Mathematical Concepts, Mathematics Teachers
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Bass, Hyman – Advances in STEM Education, 2018
Number and operations form the backbone of the school mathematics curriculum. A high school graduate should comfortably and capably meet an expression like, "Let f(x) be a function of a real variable x," implying that the student has a robust sense of the real number continuum. This understanding is a central objective of the school…
Descriptors: Number Concepts, Numbers, Mathematics Instruction, Computation
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Beckmann, Sybilla; Kulow, Torrey K. – Advances in STEM Education, 2018
Findings are presented from an analysis of how six future middle-grade teachers reasoned with strip diagrams and a variable parts perspective on proportional relationships to develop and explain equations in two variables. One equation was for two quantities varying together and one was for a line through the origin in a coordinate plane. Both…
Descriptors: Preservice Teachers, Middle School Teachers, Visual Aids, Mathematical Concepts
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Cuoco, Al; McCallum, William – Advances in STEM Education, 2018
Building on the work of Schmidt et al., we propose a definition of curricular coherence for K-12 mathematics that encompasses both the arrangement of topics, which we call coherence of content, and the habits of mind the curriculum fosters in students, which we call coherence of practice. We give examples to illustrate each. [For the complete…
Descriptors: Elementary Secondary Education, Mathematics Education, Mathematics Curriculum, Alignment (Education)
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Dwyer, Jerry; Schovanec, Lawrence – Advances in STEM Education, 2018
Research mathematics departments promote scholarly activities primarily focused on traditional mathematical research. These departments also have a role to play in advancing high-quality teaching, student mentoring, K-12 outreach, and the mathematical education of preservice teachers. A significant number of faculty pursue these activities and…
Descriptors: Elementary Secondary Education, Higher Education, Preservice Teacher Education, College Faculty
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Usiskin, Zalman – Advances in STEM Education, 2018
Almost 50 years ago, Arthur Coxford and I developed a high school geometry course in which geometric transformations were fundamental to the mathematical development. Properties of reflections and size changes (dilations) were taken as postulates and used to deduce properties of symmetric figures, the traditional theorems of triangle congruence…
Descriptors: Geometry, Mathematics Instruction, Geometric Concepts, Secondary School Mathematics
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Lai, Yvonne; Carlson, Mary Alice; Heaton, Ruth M. – Advances in STEM Education, 2018
Skillful teaching involves seeing mathematics in ways that are coherent and making decisions during planning and teaching. In particular, teaching requires making decisions about what connections to make, when to make them, and how students might make them. We posit that it is important for teachers and teacher educators to understand the…
Descriptors: Mathematics Education, Mathematics Instruction, Elementary School Teachers, Planning
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Fuson, Karen C. – Advances in STEM Education, 2018
Howe (2014, Three pillars of first grade mathematics, and beyond. In: Li Y. & Lappan G. (eds), Mathematics curriculum in school education, Springer, Dordrecht, pp 183-207) identified three pillars of first grade mathematics and beyond that described central mathematical and sense-making aspects of major Common Core State Standards Math…
Descriptors: Elementary School Mathematics, Common Core State Standards, Mathematics Instruction, Addition
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Cohen, Amy – Advances in STEM Education, 2018
Education is a complex process involving teachers and learners within surrounding institutional and social environments over which neither group has extensive control. However, complexity is not an excuse for despair or inactivity. We will not make progress unless each of us contributes what we can and does so without waiting for someone else to…
Descriptors: Mathematics, Professional Personnel, Mathematics Education, Teacher Education
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Ewing, John – Advances in STEM Education, 2018
K-12 mathematics education has undergone many changes over the past decades, sometimes driven forward by mathematicians, sometimes by mathematics educators. Those two groups have often disagreed, but we are now in a more cooperative period in which experts on both sides seem to agree more and argue less. But in reaching this rapprochement, we have…
Descriptors: Mathematics Education, Mathematics Teachers, Expertise, Elementary Secondary Education
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Uzzo, Stephen Miles, Ed.; Graves, Sherryl Browne, Ed.; Shay, Erin, Ed.; Harford, Marisa, Ed.; Thompson, Robert, Ed. – Advances in STEM Education, 2018
This volume represents both recent research in pedagogical content knowledge (PCK) in science, technology, engineering and math (STEM), as well as emerging innovations in how PCK is applied in practice. The notion of "research to practice" is critical to validating how effectively PCK works within the clinic and how it can be used to…
Descriptors: Pedagogical Content Knowledge, STEM Education, Theory Practice Relationship, Educational Research
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