Supporting students with learning disabilities to explore linear relationships using online learning objects

The study of linear relationships is foundational for mathematics teaching and learning. However, students’ abilities connect different representations of linear relationships have proven to be challenging. In response, a computer-based instructional sequence was designed to support students’ understanding of the connections among representations. In this paper we report on the affordances of this dynamic mode of representation specifically for students with learning disabilities. We outline four results identified by teachers as they implemented the online lessons

Multi-Media As a Cognitive Tool

Two of the modalities used to present information to students, namely, animation and verbal representation are in a constant competition in effectiveness, without any persistent winner, except when it comes to conceptual versus procedural knowledge. Here, we present an architecture that combines the two into a multi-media tutoring system. This system is tested and results indicate that combining the two media leads to a cognitive interaction that promotes student learning with no less than 40% from their post classical-classroom session levels. A test for individual differences indicates that this group is almost equally divided between those described as “spatially oriented” and those described as “verbally oriented”. Learning across the two types of learners does not show any significant differences, except with respect to one question. This implies that perhaps, the two media may have ambiguous internal factors that support each other. Additionally, individual learning styles does not seem to be a clear-cut division, and is instead a “preference” of one modality as a primary source of learning, not an only one

Cross-cultural representations of musical shape

In cross-cultural research involving performers from distinct cultural backgrounds (U.K., Japan, Papua New Guinea), we examined 75 musicians' associations between musical sound and shape, and saw pronounced differences between groups. Participants heard short stimuli varying in pitch contour and were asked to represent these visually on paper, with the instruction that if another community member saw the marks they should be able to connect them with the sounds. Participants from the U.K. group produced consistent symbolic representations, which involved depicting the passage of time from left-to-right. Japanese participants unfamiliar with English language and western standard notation provided responses comparable to the U.K. group's. The majority opted to use a horizontal timeline, whilst a minority of traditional Japanese musicians produced unique responses with time represented vertically. The last group, a non-literate Papua New Guinean tribe known as BenaBena, produced a majority of iconic responses which did not follow the time versus pitch contour model, but highlighted musical qualities other than the parameters intentionally varied in the investigation, focusing on hue and loudness. The participants' responses point to profoundly different 'norms' of musical shape association, which may be linked to literacy and to the functional role of music in a community

A theoretical view on concept mapping

Auto‐monitoring is the pivotal concept in understanding the operation of concept maps, which have been used to help learners make sense of their study and plan learning activities. Central to auto‐monitoring is the idea of a ‘learning arena’ where individuals can manipulate concept representations and engage in the processes of checking, resolving and confirming understandings. The learner is assisted by familiar metaphors (for example, networks) and the possibility of thinking ‘on action’ while ‘in action’. This paper discusses these concepts, and concludes by arguing that maps are part of the process of learning rather than a manifestation of learning itself. Auto‐monitoring is suggested as an appropriate term to describe the process of engaging in the learning arena

The Use of Multiple Representations in Undergraduate Physics Education: What Do we Know and Where Do we Go from Here?

Using multiple representations (MR) such as graphs, symbols, diagrams, and text, is central to teaching and learning in physics classrooms. While different studies have provided evidence of the positive impact of the use of MR on physics learning, a comprehensive overview of existing literature on the use of MR in physics education, especially at the undergraduate level, is missing. This manuscript addresses this gap in the literature by reporting on the outcomes of a systematic review study that aimed to provide an overview of the existing knowledge base, to identify gaps in the knowledge base, and to propose future research about the use of MR in the context of undergraduate physics education. For the purpose of this study, we reviewed 24 empirical studies published between 2002 and 2019 in scientific, peer-reviewed journals in the context of undergraduate physics education. The outcomes of this review study are discussed under these themes (a) In what ways does the use of MR in instruction support student learning? (b) What kinds of representations do students use? (c) What difficulties do students face in using MR? (d) What is the relation between students’ use of MR and students’ problem-solving skills? and, (e) What is the added value of technology integration in teaching with MR? We identify gaps in the existing knowledge base, and we propose future research directions in these three areas: (a) Exploring the use of MR in university physics textbooks; (b) Blending of different kinds of MR; and, (c) The use of virtual reality applications

Improving and assessing students’ line graph interpretations: the case of the graph-as-picture interpretation

The “graph-as-picture misconception” (GAPM) occurs when an abstract representation (e.g., a line graph) is interpreted as a picture of an object (e.g., a mountain). Previous research on students’ line graph interpretations has focused on secondary school level and above, thus this research extends the investigation of the GAPM to primary school level. Particularly, it investigates: which type of environment is more effective for improving young students’ line graph interpretations; and how can be assessed their interpretations. A pilot study involved an improved version of Janvier’s (1978) paper-and-pencil tasks (to create an interactive learning environment) and it investigated how to incorporate a card-sort task (to assess students’ interpretations). Different touch-screen technologies were considered too. Two experiments were conducted. In experiment one, 37 participants (third to sixth year) were assessed in their graphical knowledge through a picture/diagram card-sort task and a “pictorial group” was formed using participants’ interpretations. During the intervention, students performed an active or passive mode of a Racing Car activity in which they moved or watched a car along a track while its speed/distance graph was plotted concurrently alongside. The results suggested that a wide variety of pictorial interpretations exist and students seemed to benefit from the active modality. In experiment two, 38 fifth-year students performed different assessment tests. Extending experiment one, a “drawing the graph” mode and its passive modality were included. In that mode, students modified a plotted line of a speed/distance graph, which was used by the system to race a car along a track. Previous results were not confirmed: only students under the “drawing the graph” modality (including the “pictorial group”) significantly improved their interpretations; and different assessment tests seemed better to observe students’ various interpretations. In conclusion, a learning environment that allows interaction with the representation could potentially improve students’ interpretations, which might be better assessed through a rich set of tests

Towards a framework for investigating tangible environments for learning

External representations have been shown to play a key role in mediating cognition. Tangible environments offer the opportunity for novel representational formats and combinations, potentially increasing representational power for supporting learning. However, we currently know little about the specific learning benefits of tangible environments, and have no established framework within which to analyse the ways that external representations work in tangible environments to support learning. Taking external representation as the central focus, this paper proposes a framework for investigating the effect of tangible technologies on interaction and cognition. Key artefact-action-representation relationships are identified, and classified to form a structure for investigating the differential cognitive effects of these features. An example scenario from our current research is presented to illustrate how the framework can be used as a method for investigating the effectiveness of differential designs for supporting science learning