Teaching linear algebra at university

Linear algebra represents, with calculus, the two main mathematical subjects taught in science universities. However this teaching has always been difficult. In the last two decades, it became an active area for research works in mathematics education in several countries. Our goal is to give a synthetic overview of the main results of these works focusing on the most recent developments. The main issues we will address concern: the epistemological specificity of linear algebra and the interaction with research in history of mathematics; the cognitive flexibility at stake in learning linear algebra; three principles for the teaching of linear algebra as postulated by G. Harel; the relation between geometry and linear algebra; an original teaching design experimented by M. Rogalsk

Beyond deficit-based models of learners' cognition: Interpreting engineering students' difficulties with sense-making in terms of fine-grained epistemological and conceptual dynamics

Researchers have argued against deficit-based explanations of students' troubles with mathematical sense-making, pointing instead to factors such as epistemology: students' beliefs about knowledge and learning can hinder them from activating and integrating productive knowledge they have. In this case study of an engineering major solving problems (about content from his introductory physics course) during a clinical interview, we show that "Jim" has all the mathematical and conceptual knowledge he would need to solve a hydrostatic pressure problem that we posed to him. But he reaches and sticks with an incorrect answer that violates common sense. We argue that his lack of mathematical sense-making-specifically, translating and reconciling between mathematical and everyday/common-sense reasoning-stems in part from his epistemological views, i.e., his views about the nature of knowledge and learning. He regards mathematical equations as much more trustworthy than everyday reasoning, and he does not view mathematical equations as expressing meaning that tractably connects to common sense. For these reasons, he does not view reconciling between common sense and mathematical formalism as either necessary or plausible to accomplish. We, however, avoid a potential "deficit trap"-substituting an epistemological deficit for a concepts/skills deficit-by incorporating multiple, context-dependent epistemological stances into Jim's cognitive dynamics. We argue that Jim's epistemological stance contains productive seeds that instructors could build upon to support Jim's mathematical sense-making: He does see common-sense as connected to formalism (though not always tractably so) and in some circumstances this connection is both salient and valued.Comment: Submitted to the Journal of Engineering Educatio

Shifting the Focus: The Role of Presence in Reconceptualising the Design Process

In this paper the relationship between presence and imaging is examined with the view to establish how our understanding of imaging, and subsequently the design process, may be reconceptualised to give greater focus to its experiential potential. First, the paper outlines the research project contributing to the discussion. Then, it provides brief overviews of research on both imaging and presence in the process highlighting the narrow conceptions of imaging (and the recognition of the need for further research) compared to the more holistic and experiential understandings of presence. The paper concludes with an argument and proposed study for exploring the role of digital technology and presence in extending the potential of imaging and its role in the design process. As indicated in the DRS Conference Theme, this paper focuses “…on what people experience and the systems and actions that create those experiences.” Interface designers, information architects and interactive media artists understand the powerful influence of experience in design. ‘Experience design’ is a community of practice driven by individuals within digital based disciplines where the belief is that understanding people is essential to any successful design in any medium and that “…experience is the personal connection with the moment and… every aspect of living is an experience, whether we are the creators or simply chance participants” (Shedroff, 2001, p. 5). Keywords: Design, Design Process, Presence, Imaging, Grounded Theory</p

Learning dispositif and emotional attachment:a preliminary international investigation

This research investigated the significance of learning dispositif (LD) and emotional attachment (EA) on perceived learning success (LS) across a diaspora of Western, Russian, Asian, Middle Eastern and Chinese student cohorts. Foucault&rsquo;s LD captures the disparate socio-cultural contexts, institutional milieus and more or less didactic teaching styles that moderate learning. EA is a multi-dimensional notion involving affective bonds that emerged in child psychology and spread to marketing and other fields. The sequential explanatory research reviewed the learning and EA literatures and generated an LD&ndash;EA framework to structure the quantitative phase of its mixed investigations. In 2017 and 2018, the research collected 150 responses and used a range of statistical techniques for quantitative analysis. It found that LS varied significantly across cohorts, intimating that dispositifs influence learning. Nonparametric analysis suggested that EA also influenced learning, but regressions were inconclusive. Exploratory techniques hint at a dynamic mix of emotional or cognitive motivations during the student learning journey, involving structural breaks in student/instructor relationships. Cluster analysis identified distinct student groupings, linked to years of learning. Separately, qualitative analysis of open-ended survey questions and expert interviews intimates that frequent teacher interactions can increase EA. The synthesis of quantitative with qualitative results and pedagogical reflection suggests that LD and EA both influence learning in a complex, dynamic system. The key constituents for EA are Affection, Connection, Social Presence (SP), Teaching Presence (TP) and Flow but student emotional engagement is conditioned by the socio-cultural milieu (LD) and associated factors like relationships and trust. Unlike in the Community of Learning framework, in the EA framework Cognitive Presence (CP) is an outcome of the interaction between these EA constituents, associated factors and the socio-cultural milieu. Finally, whilst awareness of culture and emotions is a useful pedagogical consideration, learning mainstays remain inclusive educational systems that identify student needs and support well-designed programmes. Within these, scaffolded modules should include a variety of engaging learning activities with non-threatening formative and trustworthy summative feedback. We acknowledge some statistical study limitations, but its tentative findings make a useful preliminary contribution

Dalcroze meets technology : integrating music, movement and visuals with the Music Paint Machine

peer reviewedNew interactive music educational technologies are often seen as a ‘force of change’, introducing new approaches that address the shortcomings (e.g. score-based, teacher-centred and disembodied) of the so-called traditional teaching approaches. And yet, despite the growing belief in their educational potential, these new technologies have been problematised with regard to their design, reception, implementation and evaluation. A possible way to optimise the realisation of the educational potential of interactive music educational technologies is to connect their use to music educational approaches that stood the test of time and as such may inspire technologies to become a bridge between tradition and innovation. This article describes an educational technology (the Music Paint Machine) that integrates the creative use of movement and visualisation to support instrumental music teaching and learning. Next, it connects this application to such an established music educational method, the Dalcroze approach. Through the lens of a set of interconnected aspects, it is shown how the Music Paint Machine’s conceptual design aligns to the underlying principles of this approach. In this way, it is argued that integrating Dalcroze-inspired practices is a plausible way of realising the didactic potential of the system. An appendix with example exercises is provided

‘Do not block the way of inquiry’: cultivating collective doubt through sustained deep reflective thinking.

We provide a Camusian/Peircean notion of inquiry that emphasises an attitude of fallibilism and sustained epistemic dissonance as a conceptual framework for a theory of classroom practice founded on Deep Reflective Thinking (DTR), in which the cultivation of collective doubt, reflective evaluation and how these relate to the phenomenological aspects of inquiry are central to communities of inquiry. In a study by Fynes-Clinton, preliminary evidence demonstrates that if students engage in DRT, they more frequently experience cognitive dissonance and as a result improve their ability to engage in further and more frequent DRT. Sustained intellectual progress occurs when the inquiry reaches a point whereby students can thoughtfully move between the position of disequilibrium (doubt) and equilibrium (belief) whilst understanding the impermanency of any fixed belief, which, in turn, enables reconstruction of thinking and appropriation of learning in the context of collaborative philosophical inquiry

What do faculties specializing in brain and neural sciences think about, and how do they approach, brain-friendly teaching-learning in Iran?

Objective: to investigate the perspectives and experiences of the faculties specializing in brain and neural sciences regarding brain-friendly teaching-learning in Iran. Methods: 17 faculties from 5 universities were selected by purposive sampling (2018). In-depth semi-structured interviews with directed content analysis were used. Results: 31 sub-subcategories, 10 subcategories, and 4 categories were formed according to the “General teaching model”. “Mentorship” was a newly added category. Conclusions: A neuro-educational approach that consider the roles of the learner’s brain uniqueness, executive function facilitation, and the valence system are important to learning. Such learning can be facilitated through cognitive load considerations, repetition, deep questioning, visualization, feedback, and reflection. The contextualized, problem-oriented, social, multi-sensory, experiential, spaced learning, and brain-friendly evaluation must be considered. Mentorship is important for coaching and emotional facilitation

Advances in Teaching & Learning Day Abstracts 2004

Proceedings of the Advances in Teaching & Learning Day Regional Conference held at The University of Texas Health Science Center at Houston in 2004