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Direct linkBeckmann, 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; 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
Download full textStevenson, 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
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
