Physics experts and students commonly use a variety of representations when working with partial derivatives, including symbols, graphs, and words. One especially powerful representation is the contour graph. In open-ended problem-solving interviews with nine upper-division physics students, we asked students to determine derivatives from contour…

Approximate mathematical treatments are commonly taught in undergraduate chemistry, but the validity ranges of these approximations have rarely been properly defined. We present error contour plots of commonly used quadratic approximations for calculating equilibrium proton concentrations of monoprotic acids. Students and instructors can easily…

Change over time is a crosscutting theme in the sciences that is pivotal to reaction kinetics, an anchoring concept in undergraduate chemistry, and students' struggles with rates of change are well-documented. Informed by the education scholarship in chemistry, physics, and mathematics, a research team with members from complementary disciplinary…

Previous studies have identified physics students' difficulties with graph slope and area under a graph in different contexts. In this study we compared physics and nonphysics (psychology) students' understanding of graphs; i.e., we evaluated the effects of concept (graph slope vs area under graph), type of question (qualitative vs quantitative),…

In this article we propose that educational game design should work to create games as objects-to-think-with--games that engage players in the exploration of and experimentation with personally interesting questions around domain-relevant representations. We argue that this design focuses on developing tools and interactions that the player can…

This article describes how two teachers implemented a 5E lesson in a third-grade classroom where the students had been working with forces/motion and investigating things that move like pendulums, swing sets, and various toys. The lesson was included as part of a larger unit on motion. The desired outcome for this lesson was for students to…

The incorporation of engaging and meaningful learning experiences is essential for the enhancement of critical thinking and the development of scientific literacy. The study engaged several groups of students in activities designed to elicit their understanding of a graphical representation of motion, and to determine the kinesthetic effect of…

Flavio Azevedo, Peggy Martalock and Tugba Keser have initiated an important conversation in science education as they use sociocultural theory to introduce design based scenarios into the science classroom. This response seeks to expand Azevedo, Martalock and Keser's article "The discourse of design-based science classroom activities" by…

Cross-grade studies are valuable for the development of sequential curriculum. However such studies are time and resource intensive and fail to provide a clear representation to integrate different levels of representational complexity. Lin (Lin, 2006; Lin & Chiu, 2006; Lin, Chiu, & Hsu, 2006) proposed a cladistics approach in conceptual…

Mobile device accelerometers are a simple and easy way for students to collect accurate and detailed data on an amusement park ride. The resulting data can be graphed to assist in the creation of force diagrams to help students explain their physical sensations while on the ride. This type of activity can help students overcome some of the…

This is our fourth paper in our five paper series describing our national study of general education astronomy students' conceptual and reasoning difficulties with cosmology. While previous papers in this series focused on the processes by which we collected and quantitatively analyzed our data, this paper presents the most common pre-instruction…

Current educational reform calls for increased integration between science and mathematics to overcome the shortcomings in students' quantitative skills. Data Nuggets (free online resource, http://datanuggets.org) are worksheets that bring data into the classroom, repeatedly guiding students through the scientific method and making claims…

The aim of this study is to scrutinize the characteristics of conceptual meaning making when students engage with virtual worlds in combination with a spreadsheet with the aim to develop graphs. We study how these tools and the representations they contain or enable students to construct serve to influence their understanding of energy resource…

Working with evidence is a fundamental part of scientific enquiry. Children should be taught to consider evidence and evaluate it. They should make simple comparisons, comparing what happened with what they expected to happen, and try to explain what happened through drawing on their knowledge and understanding. In this article, the author…

We apply a "tutorial design process", which has proven to be successful for a number of physics topics, to design curricular materials or "tutorials" aimed at improving student understanding of important concepts in a university-level introductory materials science and engineering course. The process involves the identification…