Marios Pittalis

Tracing Students’ Modeling Processes in School

In this study, we report on an analysis of the mathematization processes of one 6th and one 8th grade group, with emphasis on the similarities and differences between the two groups in solving a modeling problem. Results provide evidence that all students developed the necessary mathematical constructs and processes to actively solve the problem through meaningful problem solving. Eighth graders who were involved in a higher level of understanding the problem presented in the activity employed more sophisticated mathematical concepts and operations, better validated and communicated their results and reached more efficient models. Finally, a reflection on the differences in the diversity and sophistication of the constructed models and mathematization processes between the two groups raises issues regarding the design and implementation of modeling activities in elementary and lower secondary school level.

Augmenting mathematics with mobile technology

This chapter describes two case examples of the use of mobile technology for mathematics. Building on the assumption that mobile learning has a positive effect on student attitudes and academic outcomes including STEM subjects (Hsi, 2007; Wu et al., 2012) we develop a theoretical lens for future studies for ‘mobile mathematics’. The two case examples describe how mobile technology could provide opportunities for ‘mathematics outside the classroom’. The first example describes a dynamic Ferris wheel, the second a static cathedral. Both examples demonstrate how ‘geo-location’ and ‘augmented reality’ features allow mobile technologies to bridge formal and informal mathematics learning (Lai et al., 2016).

A Longitudinal Study Revisiting the Notion of Early Number Sense: Algebraic Arithmetic AS a Catalyst for Number Sense Development

ABSTRACT The aim of this study was to propose a new conceptualization of early number sense. Six-year-old students’ (n = 204) number sense was tracked from the beginning of Grade 1 through the beginning of Grade 2. Data analysis suggested that elementary arithmetic, conventional arithmetic, and algebraic arithmetic contributed to the latent construct early number sense, and the invariance of the model over time was validated empirically. Algebraic arithmetic represents the dimension of early number sense that moves beyond conventional arithmetic and encompasses an abstract understanding of the relations between numbers. A parallel process growth model showed that the three components of number sense adopt a linear growth rate. A structural model showed that the growth rate of the algebraic arithmetic component has a direct effect on the growth rate of conventional arithmetic, and subsequently the growth rate of conventional arithmetic predicts the growth rate of elementary arithmetic.