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…

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…

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.

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,…

This study is a quasi-experimental research with pretest-posttest control group design, which aims to determine (1) the tendency of students in using various media scaffolding based on gender, and (2) effect of media scaffolding on increasing understanding of students' geometry concepts. Media scaffolding used this study is chart, props, and…

Basic multiplication fact fluency is an expected outcome of most third grade classrooms throughout the United States. Students need to know their multiplication facts. This statement does not seem to be under question; it is more about how will students learn their multiplication facts. The purpose of this study was to investigate the use of…

Researchers examined how an inquiry-based instructional treatment emphasizing interrelated plant processes influenced 210 elementary pre-service teachers' (PTs) conceptions of three plant processes, photosynthesis, cellular respiration, and transpiration, and the interrelated nature of these processes. The instructional treatment required PTs to…

Background: A teaching method to improve students' ability to communicate ideas in genetics across the macro-micro levels of organisation was investigated in this study. Purpose: It is designed to help students deconstruct the level of organisation of each tier of a genetic diagram, as the symbols used in such diagrams (i.e. lines and letters) can…

This study with 79 students in Montreal, Quebec, compared the educational use of a National Aeronautics and Space Administration (NASA) global climate model (GCM) to climate education technologies developed for classroom use that included simpler interfaces and processes. The goal was to show how differing climate education technologies succeed…

Multiplicative thinking has been widely accepted as a critically important "big idea" of mathematics and one which underpins much mathematical understanding beyond the primary years of schooling. It is therefore of importance to consider the capacity of children to think multiplicatively but also to consider the capacity of their…