Exploring the mathematics of motion through construction and collaboration

In this paper we give a detailed account of the design principles and construction of activities designed for learning about the relationships between position, velocity and acceleration, and corresponding kinematics graphs. Our approach is model-based, that is, it focuses attention on the idea that students constructed their own models – in the form of programs – to formalise and thus extend their existing knowledge. In these activities, students controlled the movement of objects in a programming environment, recording the motion data and plotting corresponding position-time and velocity-time graphs. They shared their findings on a specially-designed web-based collaboration system, and posted cross-site challenges to which others could react. We present learning episodes that provide evidence of students making discoveries about the relationships between different representations of motion. We conjecture that these discoveries arose from their activity in building models of motion and their participation in classroom and online communities

A Study of Educational Simulations Part I - Engagement and Learning

Interactive computer simulations with complex representations and sophisticated graphics are a relatively new addition to the classroom, and research in this area is limited. We have conducted over 200 individual student interviews during which the students described what they were thinking as they interacted with simulations. These interviews were conducted as part of the research and design of simulations for the Physics Education Technology (PhET) project. PhET is an ongoing project that has developed over 60 simulations for use in teaching physics, chemistry, and physical science. These interviews are a rich source of information about how students interact with computer simulations and what makes an educationally effective simulation. We have observed that simulations can be highly engaging and educationally effective, but only if the student's interaction with the simulation is directed by the student's own questioning. Here we describe our design process, what features are effective for engaging students in educationally productive interactions and the underlying principles which support our empirically developed guidelines. In a companion paper we describe in detail the design features used to create an intuitive simulation for students to use

Learning interaction patterns using diagrams varying in level and type of interactivity

An experiment was conducted to investigate the differences between learners when using computer based learning environments (CBLEs) that incorporated different levels of interactivity in diagrams. Four CBLEs were created with combinations of the following two interactivity properties: (a) the possibility to rotate the whole diagram (b) the possibility to move individual elements of the diagram in order to apprehend the relationships between them. We present and discuss the qualitative findings from the study in terms of the learners’ interaction patterns and their relevance for the understanding of performance scores. This supports our previous quantitative analysis showing an interaction between cognitive abilities and interactivity. Based on our findings we reflect on the possibilities to inform CBLEs with relevant information regarding learners’ cognitive abilities and representational preferences

Developing and Researching PhET simulations for Teaching Quantum Mechanics

Quantum mechanics is difficult to learn because it is counterintuitive, hard to visualize, mathematically challenging, and abstract. The Physics Education Technology (PhET) Project, known for its interactive computer simulations for teaching and learning physics, now includes 18 simulations on quantum mechanics designed to improve learning of this difficult subject. Our simulations include several key features to help students build mental models and intuitions about quantum mechanics: visual representations of abstract concepts and microscopic processes that cannot be directly observed, interactive environments that directly couple students' actions to animations, connections to everyday life, and efficient calculations so students can focus on the concepts rather than the math. Like all PhET simulations, these are developed using the results of education research and feedback from educators, and are tested in student interviews and classroom studies. This article provides an overview of the PhET quantum simulations and their development. We also describe research demonstrating their effectiveness and share some insights about student thinking that we have gained from our research on quantum simulations.Comment: accepted by American Journal of Physics; v2 includes an additional study, more explanation of research behind claims, clearer wording, and more reference

Experiential Role of Artefacts in Cooperative Design

The role of material artefacts in supporting distributed and co-located work practices has been well acknowledged within the HCI and CSCW research. In this paper, we show that in addition to their ecological, coordinative and organizational support, artefacts also play an ‘experiential’ role. In this case, artefacts not only improve efficiency or have a purely functional role (e.g. allowing people to complete tasks quickly), but the presence and manifestations of these artefacts bring quality and richness to people’s performance and help in making better sense of their everyday lives. In a domain like industrial design, such artefacts play an important role for supporting creativity and innovation. Based on our prolonged ethnographic fieldwork on understanding cooperative design practices of industrial design students and researchers, we describe several experiential practices that are supported by mundane artefacts like sketches, drawings, physical models and explorative prototypes – used and developed in designers’ everyday work. Our main intention to carry out this kind of research is to develop technologies to support designers’ everyday practices. We believe that with the emergence of ubiquitous computing, there is a growing need to focus on personal, emotional and social side of people’s everyday experiences. By focusing on the experiential practices of designers, we can provide a holistic view in the design of new interactive technologies

Processing mathematics through digital technologies: A reorganisation of student thinking?

This article reports on aspects of an ongoing study examining the use of digital media in mathematics education. In particular, it is concerned with how understanding evolves when mathematical tasks are engaged through digital pedagogical media in primary school settings. While there has been a growing body of research into software and other digital media that enhances geometric, algebraic, and statistical thinking in secondary schools, research of these aspects in primary school mathematics is still limited, and emerging intermittently. The affordances of digital technology that allow dynamic, visual interaction with mathematical tasks, the rapid manipulation of large amounts of data, and instant feedback to input, have already been identified as ways mathematical ideas can be engaged in alternative ways. How might these, and other opportunities digital media afford, transform the learning experience and the ways mathematical ideas are understood? Using an interpretive methodology, the researcher examined how mathematical thinking can be seen as a function of the pedagogical media through which the mathematics is encountered. The article gives an account of how working in a spreadsheet environment framed learners' patterns of social interaction, and how this interaction, in conjunction with other influences, mediated the understanding of mathematical ideas, through framing the students' learning pathways and facilitating risk taking

Exploring the Relationship between K-8 Prospective Teachers’ Algebraic Thinking Proficiency and the Questions They Pose during Diagnostic Algebraic Thinking Interviews

In this study, we explored the relationship between prospective teachers’ algebraic thinking and the questions they posed during one-on-one diagnostic interviews that focused on investigating the algebraic thinking of middle school students. To do so, we evaluated prospective teachers’ algebraic thinking proficiency across 125 algebra-based tasks and we analyzed the characteristics of questions they posed during the interviews. We found that prospective teachers with lower algebraic thinking proficiency did not ask any probing questions. Instead, they either posed questions that simply accepted and affirmed student responses or posed questions that guided the students toward an answer without probing student thinking. In contrast, prospective teachers with higher algebraic thinking proficiency were able to pose probing questions to investigate student thinking or help students clarify their thinking. However, less than half of their questions were of this probing type. These results suggest that prospective teachers’ algebraic thinking proficiency is related to the types of questions they ask to explore the algebraic thinking of students. Implications for mathematics teacher education are discussed

Alcohol representations are socially situated: an investigation of beverage representations by using a property generation task

Previous research suggests that people's representations of alcoholic beverages play an important role in drinking behavior. However, relatively little is known about the contents of these representations. Here, we introduce the property generation task as a tool to explore these representations in detail. In a laboratory study (N = 110), and a bar field-study (N = 56), participants listed typical properties of alcoholic beverages, sugary beverages, and water. Each of these properties was then categorized using a previously developed, hierarchical coding scheme. For example, the property “sweet” was categorized as referring to “taste”, which falls under “sensory experience”, which falls under “consumption situation”. Afterwards, participants completed measures of drinking behavior and alcohol craving. Results showed that alcoholic beverages were strongly represented in terms of consumption situations, with 57% and 69% of properties relating to consumption in the laboratory and the bar study, respectively. Specifically, alcoholic beverages were more strongly represented in terms of the social context of consumption (e.g., “with friends”) than the other beverages. In addition, alcoholic beverages were strongly represented in terms of sensory experiences (e.g. “sweet”) and positive outcomes (e.g. “creates fun”), as were the sugary beverages and water. In Study 1, the extent to which alcoholic beverages were represented in terms of social context was positively associated with craving and regularly consuming alcohol. The property generation task provides a useful tool to access people's idiosyncratic representations of alcoholic beverages. This may further our understanding of drinking behavior, and help to tailor research and interventions to reduce drinking of alcoholic and other high-calorie beverages

Exploring Student Check-In Behavior for Improved Point-of-Interest Prediction

With the availability of vast amounts of user visitation history on location-based social networks (LBSN), the problem of Point-of-Interest (POI) prediction has been extensively studied. However, much of the research has been conducted solely on voluntary checkin datasets collected from social apps such as Foursquare or Yelp. While these data contain rich information about recreational activities (e.g., restaurants, nightlife, and entertainment), information about more prosaic aspects of people's lives is sparse. This not only limits our understanding of users' daily routines, but more importantly the modeling assumptions developed based on characteristics of recreation-based data may not be suitable for richer check-in data. In this work, we present an analysis of education "check-in" data using WiFi access logs collected at Purdue University. We propose a heterogeneous graph-based method to encode the correlations between users, POIs, and activities, and then jointly learn embeddings for the vertices. We evaluate our method compared to previous state-of-the-art POI prediction methods, and show that the assumptions made by previous methods significantly degrade performance on our data with dense(r) activity signals. We also show how our learned embeddings could be used to identify similar students (e.g., for friend suggestions).Comment: published in KDD'1