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Prospective teachers’ understanding of the multiplicative part-whole relationship of fraction
(2016)
The part-whole multiplicative relationship, as a topic that gives rise to the concept of fraction, is fundamental in education at the primary school level, and must therefore be included in training courses for prospective ...
The Number Line as a Representation of Decimal Numbers: A Research with Sixth Grade Students
(International Group for the Psychology of Mathematics Education, 2004)
One of the aims of mathematics instruction is to achieve the understanding of mathematical concepts through the development of rich and well organized cognitive representations (Goldin, 1998; NCTM, 2000; DeWindt-King, & ...
Primary school students’ structure and levels of abilities in transformational geometry
(2014)
This paper used CFA analyses to investigate the factors and structure of transformational geometry concepts ability. The results suggest that the three geometric transformations (translation, reflection and rotation) consist ...
An empirical taxonomy of problem posing processes
(2005)
This article focuses on the construction, description and testing of a theoretical model of problem posing. We operationalize procesess that are frequently described in problem solving and problem posing literature in order ...
CERME7 Working Group 7: Mathematical potential, creativity and talent
(2012)
WG7 was a new CERME WG, whose purpose to draw the attention of the mathematics education community to the field of mathematical potential, creativity and talent, and to encourage empirical research that will contribute to ...
Knowledge construction and diverging thinking in elementary & advanced mathematics
(1999)
This paper begins by considering the cognitive mechanisms available to individuals which enable them to operate successfully in different parts of the mathematics curriculum. We base our theoretical development on fundamental ...
Examining number sense and algebraic reasoning through cognitive styles
(2013)
Recently, a new cognitive style approach was introduced, which refers to two types of visualizers. This approach is based on neuropsychological evidence and neuroimaging results, which suggest the existence of two distinct ...
The embodied, proceptual, and formal worlds in the context of functions
(2005)
In this study we use Tall et al.’s (2000) theory on mathematical concept development, which describes three worlds of operations, the embodied, the proceptual and the formal (Tall, 2004; Tall, 2003; Watson, Spirou, & Tall, ...
The structure of prospective kindergarten teachers' proportional reasoning
(2011)
Lamon (Teaching fractions and ratios for understanding. Essential content knowledge and instructional strategies for teachers, 2nd edn. Lawrence Erlbaum Associates, Mahwah, 2005) claimed that the development of proportional ...
Proofs through exploration in dynamic geometry environment
(2004)
The recent development of powerful new technologies such as dynamic geometry software (DGS) with drag capability has made possible the continuous variation of geometric configurations and allows one to quickly and easily ...