Students’ Learning with the Connected Chemistry (CC1) Curriculum: Navigating the Complexities of the Particulate World

The focus of this study is students’ learning with a Connected Chemistry unit, CC1 (denotes Connected Chemistry, chapter 1), a computer-based environment for learning the topics of gas laws and kinetic molecular theory in chemistry (Levy and Wilensky 2009). An investigation was conducted into high-school students’ learning with Connected Chemistry, based on a conceptual framework that highlights several forms of access to understanding the system (submicro, macro, mathematical, experiential) and bidirectional transitions among these forms, anchored at the common and experienced level, the macro-level. Results show a strong effect size for embedded assessment and a medium effect size regarding pre-post-test questionnaires. Stronger effects are seen for understanding the submicroscopic level and bridging between it and the macroscopic level. More than half the students succeeded in constructing the equations describing the gas laws. Significant shifts were found in students’ epistemologies of models: understanding models as representations rather than replicas of reality and as providing multiple perspectives. Students’ learning is discussed with respect to the conceptual framework and the benefits of assessment of learning using a fine-tuned profile and further directions for research are proposed. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.

Intuitive vs analytical thinking: four perspectives

This article is an attempt to place mathematical thinking in the context of more general theories of human cognition. We describe and compare four perspectives—mathematics, mathematics education, cognitive psychology, and evolutionary psychology—each offering a different view on mathematical thinking and learning and, in particular, on the source of mathematical errors and on ways of dealing with them in the classroom. The four perspectives represent four levels of explanation, and we see them not as competing but as complementing each other. In the classroom or in research data, all four perspectives may be observed. They may differentially account for the behavior of different students on the same task, the same student in different stages of development, or even the same student in different stages of working on a complex task. We first introduce each of the perspectives by reviewing its basic ideas and research base. We then show each perspective at work, by applying it to the analysis of typical mathematical misconceptions. Our illustrations are based on two tasks: one from statistics (taken from the psychological research literature) and one from abstract algebra (based on our own research).