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Izsák, Andrew; Beckmann, Sybilla; Stark, Joy – Cognition and Instruction, 2022
The present study is motivated by a significant body of research documenting teachers' perennial difficulties with a critical swath of topics related to multiplication. In response, we track how Nina, a future middle grades mathematics teacher, made progress constructing explanations across topics by reasoning with measurement-based definitions of…
Descriptors: Multiplication, Mathematics Instruction, Pedagogical Content Knowledge, Middle School Teachers
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
Izsák, Andrew; Beckmann, Sybilla; Kulow, Torrey – Mathematics Teaching in the Middle School, 2018
This article explores teaching practices described in NCTM's Principles to Actions: Ensuring Mathematical Success for All. Common factors, common multiples, strip diagrams, and double number lines are discussed in this, the third installment in the series. [For the second installment in this series see "Connecting the Dots: Building…
Descriptors: Problem Solving, Mathematics Instruction, Teaching Methods, Middle School Students
Beckmann, Sybilla; Izsák, Andrew – Journal for Research in Mathematics Education, 2015
In this article, we present a mathematical analysis that distinguishes two distinct quantitative perspectives on ratios and proportional relationships: variable number of fixed quantities and fixed numbers of variable parts. This parallels the distinction between measurement and partitive meanings for division and between two meanings for…
Descriptors: Mathematics Education, Mathematical Concepts, Multiplication, Measurement
Izsák, Andrew; Kulow, Torrey; Beckmann, Sybilla; Stevenson, Dean; Ölmez, Ibrahim Burak – Mathematics Teacher Educator, 2019
We report results from a mathematics content course intended to help future teachers form a coherent perspective on topics related to multiplication, including whole-number multiplication and division, fraction arithmetic, proportional relationships, and linear functions. We used one meaning of multiplication, based in measurement and expressed as…
Descriptors: Mathematics Instruction, Multiplication, Division, Mathematical Concepts
Stevenson, Dean L.; Beckmann, Sybilla; Johnson, Sheri E.; Kang, Rui – North American Chapter of the International Group for the Psychology of Mathematics Education, 2018
We have extended two perspectives of proportional reasoning to solve problems based in probability. Four future middle grade teachers were enrolled in a mathematics content course that emphasized reasoning about multiplication with quantities. The course expected future teachers to generate and explain methods for solving proportions. Probability…
Descriptors: Problem Solving, Probability, Middle School Teachers, Preservice Teachers
Lloyd, Gwendolyn; Beckmann, Sybilla; Zbiek, Rose Mary; Cooney, Thomas – National Council of Teachers of Mathematics, 2010
Are sequences functions? What can't the popular "vertical line test" be applied in some cases to determine if a relation is a function? How does the idea of rate of change connect with simpler ideas about proportionality as well as more advanced topics in calculus? Helping high school students develop a robust understanding of functions requires…
Descriptors: Calculus, Misconceptions, Mathematics Instruction, Mathematics Teachers
Woodward, John; Beckmann, Sybilla; Driscoll, Mark; Franke, Megan; Herzig, Patricia; Jitendra, Asha; Koedinger, Kenneth R.; Ogbuehi, Philip – What Works Clearinghouse, 2012
The Institute of Education Sciences (IES) publishes practice guides in education to bring the best available evidence and expertise to bear on current challenges in education. Authors of practice guides combine their expertise with the findings of rigorous research, when available, to develop specific recommendations for addressing these…
Descriptors: Mathematics Instruction, Problem Solving, Educational Research, Evidence
What Works Clearinghouse, 2012
Instructional tips help educators carry out recommendations contained in IES Educator's Practice Guides. The tips translate these recommendations into actionable approaches that educators can try in their classrooms. These tips are based on a practice guide authored by Sybilla Beckmann, Mark Driscoll, Megan Franke, Patricia Herzig, Asha Jitendra,…
Descriptors: Mathematics Instruction, Problem Solving, Evidence, Teaching Methods
What Works Clearinghouse, 2012
Instructional tips help educators carry out recommendations contained in IES Educator's Practice Guides. This summary describes the research evidence that supports the use of the instructional tips in classrooms and is based on a practice guide authored by Sybilla Beckmann, Mark Driscoll, Megan Franke, Patricia Herzig, Asha Jitendra, Kenneth R.…
Descriptors: Mathematics Instruction, Problem Solving, Evidence, Teaching Methods