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This research investigates elementary mathematics teachers' competencies to implement neuroscience theory (NS) of mathematical cognition into their classroom practices during and after, participation in a professional development (PD) course. We examine the teachers' familiarity with Approximate Number System (ANS), relevant to elementary school level, and build their competencies to implement this NS concept into teaching. Data for this qualitative study were collected from the reflective reports written by nineteen female elementary mathematics teachers (aged 25–40) and were analysed using two complementary methodologies: content and linguistic analyses. Our findings indicate that the teachers acquired NS knowledge, and their competencies evolved from listing the facts and analysing their meanings to weighing possible applications and attempts to integrate newly acquired knowledge into their teaching. This study seeks to contribute to the field of professional teacher development by demonstrating how teachers can lend meaning to theoretical knowledge they obtain in a PD course, in meaningful ways by connecting it with their classroom teaching practices.

One of the key courses in the mathematics teacher education program in Israel is arithmetic, which engages in contents which these pre-service mathematics teachers (PMTs) will later teach at school. Teaching arithmetic involves knowledge about the essence of the concept of "number" and the development thereof, calculation methods and strategies. properties of operations on different sets of numbers, as well as the properties of the numbers themselves. Hence, the question arises: how to educate PMTs in order to supplement their mathematical knowledge with the required components? The present study explored the development of arithmetic thinking among preservice teachers intending to teach mathematics at elementary school. This was done by matching the van Hiele theory of the development of geometric thinking to arithmetic. Analysis of findings obtained both in the present study and in many studies of geometry teaching indicates that this approach to considering the learners' level of thinking development might lead to meaningful learning in arithmetic course for PMTs.

The results of international experience and research in the teaching and learning of mathematics, on a global level, have influenced school mathematics curriculum with the emergence of a relatively uniform mathematics curriculum, comprising an internationally accepted core of mathematical knowledge and skills (e.g. Cai & Howson, 2013). From a distance, this perspective has some footing since it regards common topics and notions as they might be presented within national curriculum documents. However, such 'zooming out' may ignore cultural factors and local conditions, including teaching practices, classroom norms, and assessment methods. These forms of variation need closer scrutiny (e.g. Hiebert et al., 2003;Guberman & Abu Amra, 2018).Considerable variations are also found when specific curriculum issues are considered. For example, within the mathematics curriculum for basic education in many countries, the topic of Statistics focuses on describing, representing, and interpreting data (e.g. Biehler et al., 2018), but there are considerable differences in how statistical content is approached, especially through the use of technology and real-world data (e.g. Ben-Zvi et al., 2018). Furthermore, the ways in which mathematical literacy or computational/algorithmic thinking are defined and included in