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…

Researchers have argued teachers and students are not developing connected meanings for function inverse, thus calling for a closer examination of teachers' and students' inverse function meanings. Responding to this call, we characterize 25 pre-service teachers' inverse function meanings as inferred from our analysis of clinical interviews. After…

Background and purpose: To date, there has been little research on the Teacher Professional Development (TPD) for delivering a mobile technology-supported science curriculum. To address this, a TPD model for a science curriculum supported by mobile technology was developed and evaluated in this paper. The study reported focuses on the…

Evidence suggests that some students have learned procedures with little or no underpinning understanding while others have a much more connected and conceptual levels of understanding. In this article, the work of four primary students is discussed in terms of their contextual understanding of multiplicative concepts. The difference between…

Place-value is an essential concept that is foundational for understanding our number system and for developing procedures for multidigit operations, but there has been limited research into the place-value understanding of students with learning disabilities. This research is a two-part mixed-methods study that links basic research to…

As widespread as Science, Technology, Engineering, and Math (STEM) initiatives and reforms are today in education, a rudimentary problem with these endeavors is being overlooked. In general, education programs and school districts are failing to ensure that elementary teachers who provide children's early academic experiences have the appropriate…

This chapter describes a multidisciplinary faculty self-study about reciprocity in service-learning. The study began with each coauthor participating in a Decoding interview. We describe how Decoding combined with collaborative self-study had a positive impact on our teaching practice.

This report on the second year of data collection in the Understanding Consequential Assessment Systems of Teaching (UCAST) study describes administrators' learning during the first year that Los Angeles Unified School District's (LAUSD) observations were part of a consequential teacher evaluation system for teachers. Drawing on mixed methods, the…

Many chemistry laboratory exercises follow a given protocol with known results. Such traditional laboratories rarely give students an accurate representation of how research is conducted, the scientific practices involved in research, and the ownership that accompanies developing and carrying out an independent project. Several laboratory reforms…

Instructional strategies that support meaningful student learning of complex chemical topics are an important aspect of improving chemistry education. Adequately assessing the success of these approaches can be supported with the use of aligned instruments with established psychometrics. Here, we report the implementation and assessment of one…

We report our research of seven pairs of students enrolled in the second semester of sophomore-level organic chemistry as they attempted to describe (in their own words) and draw, respectively, three electron-pushing diagrams of three-step reaction mechanisms. The tasks' objective was to accurately reproduce the diagrams based solely on the…

Visual and analytic strategies are features of students' schemes for spatial tasks. The strategies used by six students to anticipate the folding of nets were investigated. Evidence suggested that visual and analytic strategies were strongly connected in competent performance.

The memorial costs and benefits of trial-and-error learning have clear pedagogical implications for students, and increasing evidence shows that generating errors during episodic learning can improve memory among younger adults. Conversely, the aging literature has found that errors impair memory among healthy older adults and has advocated for…

Mathematicians use example generation to test and verify mathematical ideas; however, the processes through which undergraduates learn to productively generate examples are not well understood. We engaged calculus students in a teaching experiment designed to develop skills in productively generating examples to learn novel concepts. This article…

The aim of this study was to investigate how reciprocal peer assessment in modeling-based learning can serve as a learning tool for secondary school learners in a physics course. The participants were 22 upper secondary school students from a gymnasium in Switzerland. They were asked to model additive and subtractive color mixing in groups of two,…