We have developed an activity using simulation hardware called the Quantum Teleportation & Superdense Coding toolkit. The toolkit contains classical electronic components, such as circuit boards and cables, that mimic the behaviour of quantum gates. The activity was designed to be accessible to upper-secondary school students who are not familiar with the mathematical formalism often used for teaching quantum mechanics. Groups of upper-secondary school students that have visited our university during outreach initiatives have participated in the activities, and we report on our experiences of introducing the toolkit for this group of students. 

Teacher students need a solid foundation in their subject matter, a clear understanding of teaching and learning, and the ability to integrate technology into their teaching. The TPACK framework assesses this comprehensive knowledge. This study explored how physics teacher students utilize educational technology for visualizing physical phenomena during lesson planning. The research involved ten first-semester physics teacher students and included two lectures, an online support session, and a one-hour workshop, with data collection focused on the workshop. The lectures introduced digital tools, emphasizing GeoGebra. Prior to the workshop, students evaluated GeoGebra simulations for teaching motion on an inclined plane. During the workshop, students were video filmed as they worked in pairs to discuss and modify simulations. The analysis was based on the TPACK framework, focusing on technology integration domains. The study found that most pairs collaborated effectively, demonstrating advanced TCK and a nuanced understanding of TPK. They evaluated the usability and motivational aspects of the simulations, highlighting their ability to leverage technology for engagement and understanding. The findings highlight the developmental process of integrating technology, pedagogy, and content, as outlined in the TPACK framework. By the end of the workshop, students exhibited some TPACK skills when using GeoGebra features to scaffold learning while maintaining scientific accuracy and pedagogical clarity. However, the results indicate room for further development of the participants’ TPACK. The TPACK framework, complemented by models for operationalizing physics teachers’ TPACK skills, provided a valuable structure to evaluate the students’ competencies in using GeoGebra for physics lessons.

The GTG Mathematics in Physics Education follows the philosophy of supporting physics understanding by the conscious use of mathematical structures in physics teaching. We discuss the possible roles of digital tools in promoting physics understanding by fostering sense making of computational models, using geometrical visualizations or interpreting app-generated diagrams in a physics context. We look into three types of digital tools: (a) Smartphone apps that allow data collection from the phone’s internal sensors to effortlessly produce graphical representations of the data. (b) GeoGebra, that combines different mathematical representations and allows their visualization and manipulation. (c) Computational modeling via Vpython where students can build or manipulate a computational model and compare it to experimental results. We will describe the potential of these tools to improve understanding of different mathematical features in physics, as well as obstacles that educators should take into account. In addition we present some empirical findings concerning graphs from smartphone apps and experiences from teacher professional development.

För att kunna fostra nästa generation av fysiklärare bör lärarutbildningen ge studenterna nödvändiga ämnesspecifika, ämnesdidaktiska kunskaper och kunskaper som krävs för att hantera teknologiska utmaningar. Det komplexa förhållandet mellan ämnesinnehåll, pedagogik och teknik och hur kunskaper inom dessa områden samverkar och påverka varandra för att god undervisning ska ske kan beskrivas med hjälp av ramverket TPACK (Technological Pedagogical Content Knowledge).

För att förbättra kunskaper kring utveckling av teknikstödda lektioner erbjuds ämneslärarstudenterna i fysik vid Karlstads universitet möjligheten att jobba med flera olika verktyg, exempelvis PASCO Capstone för automatisk insamling och bearbetning av data i realtid, PhET för datorsimuleringar och Excel för modellering. I tillägg har vi sedan förra året ett projekt där studenterna ges möjligheten att lära sig använda GeoGebra. Verktyget har under senaste decenniet fått mer och mer uppmärksamhet inom fysikundervisningen eftersom det erbjuder en miljö där lärare (med eller utan programmeringskunskap), utifrån lektionens syfte kan modifiera eller skapa sina egna matematiska modeller av fysiska fenomen som simuleringar.

Fysiklärarstudenterna får information i form av en föreläsning och en workshop om hur GeoGebra kan användas i fysikundervisningen. För vår studie har vi samlat in videodata av studenter som förbereder en datorstödd lektion om rörelse på ett lutande plan. För att analysera data har vi använt oss av ramverket TPACK. I vår presentation kommer vi att redogöra för några preliminära resultat av vår studie, exempelvis hur studenter tolkar och värderar GeoGebra-simuleringar och vad studenter gör när de upptäcker detaljer de är missnöjda med. 

This chapter synthesizes the physics education research work related to the interplay of visualization and mathematization in physics teaching and learning, specifically as mediated by dynamic, interactive digital visualization tools. In structuring our synthesis, we build on existing theories of visualization and mathematization to propose two “functions” that visualizations tools exhibit in facilitating mathematization: (1) bridging between physical phenomena and formalisms, and (2) bridging between idealized models of physical phenomena and formalisms. We populate these two broad categories with illustrative examples of visualization tools and conclude with a summary of the developmental history of those tools in physics education research. 

Med avsikt att bidra med ett kapitel till den planerade International Handbook of Physics Education Research har vi sammanställt en översikt av fysikdidaktisk forskning om hur digitala verktyg kan användas för visualisering av matematisk formalism i fysikundervisningen. Översikten är strukturerad utifrån att de digitala verktygen fyller två olika funktioner. Genom Funktion I utgör digitala verktyg en brygga mellan fysikaliska fenomen och matematisk formalism, medan de genom Funktion II utgör en brygga mellan idealiserade modeller av fysikaliska fenomen och matematisk formalism. Exempel på digitala verktyg som används för Funktion I inkluderar probeware, där elever kan visualisera mätdata genom grafer i realtid, videoanalys och augmented reality, där matematiska representationer, t.ex. vektorer, överlagras på bilder av fysiska föremål. Med Funktion II distanseras de digitala verktygen från den fysikaliska verkligheten. Här finner vi simuleringsmiljöer, som PhET och Algodoo, och pedagogiska spel. Det är en didaktisk utmaning att finna en lämplig nivå av elevers och studenters insyn i den programmering och matematik som ligger till grund för ett digitalt verktyg, för att kunna bidra till deras förståelse av den fysikaliska modelleringen.

The present study contributes to the understanding of physics students' representational competence by examining specific bodily practices (e.g. gestures, enactment) of students' interaction and constructions of representations in relation to a digital learning environment. We present and analyse video data of upper-secondary school students' interaction with a GeoGebra simulation of friction. Our analysis is based on the assumption that, in a collaborative learning environment, students use their bodies as means of dealing with interpretational problems, and that exploring students' gestures and enactment can be used to analyse their sensemaking processes. This study shows that specific features of the simulation-features connected with microscopic aspects of friction-triggered students to ask what-if and why questions and consequently, to learn about the representation. During this sense-making process, students improvised their own representations to make their ideas more explicit. The findings extend current research on students' representational competence by bringing attention to the role of students' generation of improvised representations in the processes of learning with and about representations.

The present study provides a new model that can be used to characterize students’ representational competence. By using this model, we explore upper secondary school students’ interaction with a GeoGebra simulation of friction by analyzing in which ways students express different aspects of their representational competence. The results show that by using the provided simulation in conjunction with provided set of instructions, students were able to express four of five aspects of representational competence.

In order to contribute to our understanding of how technologies can be used to visualise physical phenomena in order to support teaching and learning of the phenomena at hand, this licentiate thesis explores the ways in which visual representations created with GeoGebra can be used in upper-secondary physics education. In addition, this thesis provides a new model that can be used to characterise students’ representational competence.

This thesis is a compilation of two journal articles. The first article is a systematic review of the current literature on how GeoGebra can be used to support physics education in upper-secondary schools. The second article explores students’ use and interpretation of a provided representation, a GeoGebra simulation of friction, and generation of their own representations. 

The systematic literature review identifies three major ways in which teachers and researchers report using GeoGebra in physics education—namely, (1) to design custom-made computer simulations, (2) to augment real experiments with virtual objects, and (3) to engage students in constructing GeoGebra simulations. 

The second study shows how students used improvised representations, in the form of gestures, enactments, and drawings,  in their interpretation of links between microscopic aspects of friction and the provided GeoGebra simulation. The study also reveals how, during engagement with provided representations, students spontaneously move across modalities, shifting between provided and self-constructed representations, between physical and digital representations, and between modes of communication (including gestures, spoken language, and enactment).  In addition, a reanalysis of selected examples of data shows that GeoGebra can facilitate transformations of mathematical representations, supporting the structural role and technical role of mathematics, whereby students are enabled to focus on the physical phenomena at hand and the parameters that influence it.

This thesis explores the ways in which visual representations created with GeoGebra can be used in upper-secondary physics education. In addition, this thesis provides a new model that can be used to characterise students’ representational competence. The thesis is a compilation of two journal articles. The first article identifies three major ways in which teachers and researchers report using GeoGebra in physics education. The second article explores students’ use and interpretation of a provided GeoGebra simulation of friction. The study shows how students used improvised representations in their interpretation of links between microscopic aspects of friction and the provided representation. The study also reveals how students spontaneously move across modalities, shifting between provided and self-constructed representations, between physical and digital representations, and between modes of communication (including gestures, spoken language, and enactment). The reanalysis of selected examples of data shows that GeoGebra can facilitate transformations of mathematical representations, supporting the structural and the technical role of mathematics, whereby students are enabled to focus on the physical phenomena at hand.