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…

Action-Process-Object-Schema (APOS) theory and tools resulting from dialogue with the Anthropological Theory of the Didactic (ATD) were used to analyse data from semi-structured interviews and teaching materials to study students' understanding of the relationship between tangent planes and the total differential. Results of the study show…

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…

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…

One of the tools that indicate the relationship between concepts is the volume of concept. Volume of concept is displayed that the relations between the concepts of the subject are exhibited in a meaningful harmonious and circular manner in a certain order. The purpose of this research; to be able to determine the usefulness volume of concept,…

Mathematics education practitioners and researchers have long debated best pedagogical practices for introducing new concepts. Our design-based research project evaluated a heuristic framework, whereby students first develop acontextual sensorimotor schemes and only then extend these schemes to incorporate both concrete narratives (grounding) and…

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.

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.

Teaching responsive to the needs of students with learning disabilities (LD) can be provided through understanding students' conceptions and their ways of learning. The current research, as a case study based on qualitative design, aimed to investigate the conceptions of students with learning disabilities with regard to the different…

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…

There are ongoing calls for research that identifies students' conceptions about geographical phenomena. In response, this study investigates junior secondary school students' (N = 95) conceptions about plate tectonics. Student response data was generated from semi-structured interviews-about-instances and a two-tiered multiple-choice test…

Philosophical debates about chemistry have clarified that the issue of emergence plays a critical role in the epistemology and ontology of chemistry. In this article, it is argued that the issue of emergence has also significant implications for understanding learning difficulties and finding ways of addressing them in chemistry. Particularly, it…

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,…