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Direct linkBradshaw, Laine; Izsák, Andrew; Templin, Jonathan; Jacobson, Erik – Educational Measurement: Issues and Practice, 2014
We report a multidimensional test that examines middle grades teachers' understanding of fraction arithmetic, especially multiplication and division. The test is based on four attributes identified through an analysis of the extensive mathematics education research literature on teachers' and students' reasoning in this content…
Descriptors: Middle School Teachers, Numbers, Arithmetic, Multiplication
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
Download full textIzsák, Andrew; Beckmann, Sybilla; Bradshaw, Laine – North American Chapter of the International Group for the Psychology of Mathematics Education, 2016
The present study extends recent advances coordinating research on cognition and psychometric modeling around fractions. Recent research has demonstrated that the Diagnosing Teachers' Multiplicative Reasoning Fractions survey provides information about distinct components necessary for reasoning in terms of quantities when solving fraction…
Descriptors: Thinking Skills, Growth Models, Outcome Measures, Preservice Teachers
