The main aim of this review is to systematize and present evidence from recent scientific studies regarding the role of early mathematical competencies in later mathematics achievement, as well as to analyze characteristics of educational and family environments that facilitate the development of these competencies in children. Presented longitudinal studies provide clear evidence that early math competencies significantly predict later mathematical outcomes. Reviewed studies also suggest that how adults and children interact in terms of mathematics activities is related to children’s mathematics development. In both formal education and family environment, adults who use everyday situations and activities for reasoning, communicating, and mathematical thinking seem to be the most important factor for fostering early math competencies. These findings are also discussed in the context of BiH where most children do not attend formal early education.

A wide range of mathematical ideas could be used to develop and justify a formula for calculating the area of trapezoid. Those ideas lead to different strategies for finding out area of trapezoid that we classify in three groups: decomposing, enclosing and transforming strategies. Those strategies should be part of mathematics content knowledge for teaching. In this study we trace a change in structure of mathematics content knowledge of nine pre-service mathematics teachers as a result of using GeoGebra applets that visualize different approaches in finding out the area of trapezoid. We argue that engaging pre-service mathematics teachers to develop and justify formula for calculating the area of trapezoid using GeoGebra applets is a worth task that enhances pre-service mathematics teachers’ content knowledge for teaching. Our experiment confirmed that the use of Geogebra encourage pre-service mathematics teachers to uncover new ideas that lead them towards clearer justifications and easier way of proving formula for area of trapezoid. Keywords: Area of trapezoid, GeoGebra, content knowledge for teaching