Our work focuses on the transition from high school to university in the field of calculus. In France, recursive sequences are studied as one of the classical exercises in both institutions. Their studies use different theorems and notions, such as functions, convergence, monotonicity, induction, etc. The work expected at this transition requires…

This paper discusses the significance of model-based teaching on the topic of ionic and metallic bonding in Year 12 Chemistry in a New Zealand secondary school. Based on the conceptualization of the sub-macro level understanding of the bonding structure and properties of ionic and metallic compounds, models and drawings were used as an effective…

Learning mathematical thinking and reasoning is a main goal in mathematical education. Instructional tasks have an important role in fostering this learning. We introduce a learning sequence to approach the topic of integrals in secondary education to support students mathematical reasoning while participating in collaborative dialogue about the…

According to Geary's evolutionary approach, humans are able to easily acquire primary knowledge and, with more efforts, secondary knowledge. The present study investigates how primary knowledge contents can facilitate the learning of formal logical rules, i.e., secondary knowledge. Framing formal logical problems in evolutionary salient contexts…

Twenty years ago when the author was student teaching, he quickly learned what geometry teachers and researchers (e.g., Senk 1985) have long known: High school geometry students struggle with proof. Throughout his career, he has tried to create instructional materials to make proof more accessible to his students. From field-testing materials with…

This study used a multiple probe across participants design to examine the effects of concrete-representational-abstract sequence of instruction on solving equations using inverse operations with high school students with mild intellectual disability. Results demonstrated a functional relation between the Abstract sequence of instruction and…