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…

Inspiration is the primary element of good design. Designers, however, also risk not being able to find inspiration. Novice designers commonly find themselves to be depressed during the conceptual design phase when they fail to find inspiration and the information to be creative. Accordingly, under the graphic design parameter, we have developed…

Concerns persist regarding high school students' chemistry learning. Learning chemistry is challenging because of chemistry's innate complexity and the need for students to construct associations between different, yet related representations of matter and its changes. Students should be taught to reason about and consider chemical phenomena using…

The effects of prior encodings of manipulatives (red and blue plastic chips) on children's ability to use them as representations of quantity were tested. First graders (N = 73) were assigned to four conditions in which the encoding of plastic chips was experimentally manipulated. All children then participated in an addition activity that relied…

The current study considered young students' (7 and 8 years old) experiences and perceptions of mathematics lessons involving challenging (i.e. cognitively demanding) tasks. We used the Constant Comparative Method to analyse the interview responses (n = 73) regarding what work artefacts students were most proud of creating and why. Five themes…

Stimulating thinking related to mathematical content is the focus of many tasks in the mathematics classroom. Beyond such content-related thinking, promoting forms of higher order thinking is among the goals of mathematics instruction as well. So-called hybrid tasks focus on combining both goals: they aim at fostering mathematical thinking and…

Effective feedback is an essential tool for making learning explicit and an essential feature of classroom practice that promotes learner autonomy. Yet, it remains a pressing challenge for teachers to scaffold the active involvement of students as critical, reflective and autonomous learners who use feedback constructively. This paper seeks to…

Video games offer an exciting opportunity for learners to engage in computational thinking in informal contexts. This paper describes a genre of learning environments called constructionist video games that are especially well suited for developing learners' computational thinking skills. These games blend features of conventional video games with…

In this paper, we analyze efforts to encourage teachers' attention to student thinking through a professional development (PD) program. We describe three groups of teachers within the same program who completed different types of assignments, either conducting interviews, planning classroom activities, or both. In both types of assignments,…

A variety of practices and specialised representational systems are required to understand, communicate and construct molecular genetics knowledge. This study describes teachers' use of multimodal representations of molecular genetics concepts and how their strategies and choice of resources were interpreted, understood and used by students to…

The concept of Knowledge Triangle (KT) links together research, education and innovation and replaces the traditional "one way" flow of knowledge, essentially from research to education, by a "both ways" circular motion between all the corners of a triangle that, besides research and education, also includes innovation, the…

We conducted an intervention-based study in secondary classrooms to explore whether the use of geometric transformations can help improve students' ability in constructing auxiliary lines to solve geometric proof problems, especially high-level cognitive problems. A pre- and post-test quasi-experimental design was employed. The participants were…

Assessments with features of games propose to address student motivation deficits common in traditional assessments. This study examines the impact of two "gameful assessment" prototypes on student engagement and teacher perceptions among 391 Grades 3-7 students and 14 teachers in one Midwestern and one Northwestern school. Using mixed…

In this article, we describe a model for reading engagement that emerged from interviews with high school students who participated in a yearlong supplemental intervention course. The course focused on motivation, strategies, content learning, and communication within the context of themed instruction. We sought to ascertain instructional factors,…

This interpretive case study explored the effectiveness of listening strategy instruction that promoted self-regulated learning and gained insights into students' and instructors' perceptions of strategy-integrated listening instruction among second semester learners of Chinese as a second language at a military college in Northern California.…