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Bishop, Jessica P.; Lamb, Lisa L.; Philipp, Randolph A.; Whitacre, Ian; Schappelle, Bonnie P. – Research in Mathematics Education, 2018
We share a subset of the 41 underlying strategies that comprise five ways of reasoning about integer addition and subtraction: formal, order-based, analogy-based, computational, and emergent. The examples of the strategies are designed to provide clear comparisons and contrasts to support both teachers and researchers in understanding specific…
Descriptors: Thinking Skills, Numbers, Numeracy, Comparative Analysis
Polotskaia, Elena – International Journal for Mathematics Teaching and Learning, 2017
The main goal of this paper is to show how Vasily Davydov's powerful ideas about the nature of mathematical thinking and learning can transform the teaching and learning of additive word problem solving. The name Vasily Davydov is well known in the field of mathematics education in Russia. However, the transformative value of Davydov's theoretical…
Descriptors: Models, Mathematics Instruction, Foreign Countries, Problem Solving
Boudreaux, Grant; Beslin, Scott – Australian Senior Mathematics Journal, 2013
The purpose of this article is to examine one possible extension of greatest common divisor (or highest common factor) from elementary number properties. The article may be of interest to teachers and students of the "Australian Curriculum: Mathematics," beginning with Years 7 and 8, as described in the content descriptions for Number…
Descriptors: Numbers, Foreign Countries, Fractions, Mathematical Formulas