Time is an important but complex area of learning for students in the primary years. This study sought to develop a tool which would provide a clear picture of students' understanding of what constitutes time and how time is related to clock and calendar use. Four major components of time, Awareness of time, Succession, Duration, and Measurement…

The aim of this paper is on the one hand to discuss from an APOS (Action-Process-Object-Schema) theory perspective the mental constructions involved in the learning of linear algebra, through examples concerning the linear transformation concept and related notions. On the other hand, methodological issues related to the design of research…

When establishing connections among representations of associated mathematical concepts, students encounter different difficulties and successes along the way. The purpose of this study was to uncover information about and gain greater insight into how student processes connections. Pre-calculus students were observed and interviewed while…

Classical mechanics challenges students to use their intuitions and experiences as a basis for understanding, in effect to approach learning as "a refinement of everyday thinking'' (Einstein, 1936). Moving on to quantum mechanics (QM), students, like physicists, need to adjust this approach, in particular with respect to the roles that…

Relating mathematical concepts to graphical representations is a challenging task for students. In this paper, we introduce two visual strategies to qualitatively interpret the divergence of graphical vector field representations. One strategy is based on the graphical interpretation of partial derivatives, while the other is based on the flux…

Based on the findings of a larger study on middle school students' problem solving behaviors, we identified three sub-components for understanding the iteration of unit area in this paper: the mechanism of iteration, an identical unit, and the specificity of the identical unit. A three-stage progression on the acquisition of these components is…

This chapter presents the bottlenecks identified by seven faculty members from diverse disciplines and an inductive content analysis of their Decoding interviews. Representative quotations illustrate themes in the interviews and we consider the implications for both faculty development and pedagogical research.

In this study I investigate Saldanha and Thompson's (1998) claim that conceptualizing a coordinate pair in the Cartesian coordinate system as a multiplicative object, a way to unite two quantities' values, supports students in conceptualizing graphs as emergent representations of how two quantities' values change together. I presented three…

This study investigated relationships between the thinking processes that 28 undergraduate chemistry students engaged in during guided discovery and their subsequent success at reasoning through a transfer problem during an end-of-semester interview. During a guided-discovery laboratory module, students were prompted to use words, pictures, and…

The purpose of this exploratory study was to investigate the cognitive processes used by individuals who read a refutational text about physics and demonstrated conceptual change learning. Four high school readers whose initial conceptions differed from the scientific conception of Newton's first law thought aloud while reading a refutational…

One of the goals of college-level introductory biology is to establish a foundation of knowledge and skills that can be built upon throughout a biology curriculum. In a reformed introductory biology course, we used iterative model construction as a pedagogical tool to promote students' understanding about conceptual connections, particularly those…

Darwinian evolution is difficult to understand because of conceptual barriers stemming from intuitive ideas. This study examined understanding of evolution in 52 students (M = 14.48 years, SD = 0.89) before and after a guided field trip to a natural history museum and in a comparison group of 18 students (M = 14.17 years, SD = 0.79) who did not…

We review and extend existing frameworks on modeling to develop a new framework that describes model-based reasoning in introductory and upper-division physics laboratories. Constructing and using models are core scientific practices that have gained significant attention within K-12 and higher education. Although modeling is a broadly applicable…

This study sought to identify specific types of discussion-based strategies that two successful high school physics teachers using a model-based approach utilized in attempting to foster students' construction of explanatory models for scientific concepts. We found evidence that, in addition to previously documented dialogical strategies that…

The Dirac delta function is a standard mathematical tool that appears repeatedly in the undergraduate physics curriculum in multiple topical areas including electrostatics, and quantum mechanics. While Dirac delta functions are often introduced in order to simplify a problem mathematically, students still struggle to manipulate and interpret them.…