A Taxonomy as a Vehicle for Learning

In this article, we describe the development of a classification system providing a framework for analysis of, and communication about, a subgroup of learning objects. The objects we consider are highly visual, animated, interactive, and mathematics-related, and we call them VaniMaps. Secondly, we discuss the use of the system. In the first phase, the development was based on literature studies and discussions on examples of VaniMaps. In the second phase, the classification system was tested by students and their responses were analyzed to identify possible improvements. Now, the system is developed further based on experience gained while using it for different purposes. We see several possible uses of the classification system, or selected parts of it: (a) to facilitate communication between the orderer and the developer, (b) to initiate discussions on VaniMaps in teacher education, (c) to analyze and choose between VaniMaps for teaching and learning activities, and (d) to establish a database for VaniMaps labeled using classification statements. We will discuss all these uses and especially emphasize the use in teacher education, illustrated with a case study. Keywords: classification, discussion, evaluation, learning object, mathematics, mathematics education,statements, taxonomy, teacher education, VaniMaps

Collaborative writing with web 2.0 technologies: education students' perceptions

Executive Summary Web 2.0 technologies are becoming popular in teaching and learning environments. Among them several online collaborative writing tools, like wikis and blogs, have been integrated into educational settings. Research has been carried out on a wide range of subjects related to wikis, while other, comparable tools like Google Docs and EtherPad remain largely unexplored in the literature. This work presents a case study investigating education students' perceptions of collaborative writing using Google Docs and EtherPad. Both tools provide opportunity for multiple users to work on the same document simultaneously, have a separate space for written metacommunication, and are promoted by software designers to be fairly intuitive to adopt without prior training. The work investigates if perceptions depend on factors such as gender, age, digital competence, interest in digital tools, educational settings, and choice of writing tool, and examines if the tools are easy to use and effective in group work. This paper focuses on quantitative results of survey questionnaires. Further qualitative analysis will be presented in a later paper. The theoretical framework is drawn from two learning theories, the social-constructivist learning theory and the community of practice, and their relationships to collaborative tools. Related re-search literature is characterized by a number of issues: positive elements of use, advantages of using Web 2.0 technologies, critical issues regarding the pedagogical value of Web 2.0, and the role of the teacher in using these technologies. The case study participants were 201 education students who just began their four-year initial teacher education at two study programs with a total of six classes at the university Teacher Education Unit. They were assigned a collaborative writing task and asked to take an on-line survey on completion. When the survey closed, a total of 166 students (83.6%) had participated. The results were analyzed based on frequency distributions. The hypothesis that students with high digital competence and a positive attitude towards digital tools are more positive than average seems to be confirmed. Also gender does not play any particular role. As for younger students being more positive than older, the population of older students was so low that no conclusion can be drawn. The work does not validate that EtherPad users are more positive than Google Docs users, but this may be explained by EtherPad being unavailable for some time during the students' collaborative writing period. Furthermore only 13.9% of the students were motivated to use the tools for collaboration, and only a minority of the students (15.7%) reported that the quality of collaboration in the group increased with use of the tools. Likewise, the tools did not work as expected for a majority of the students (70.5%). Forty-seven percent of the students liked to comment and edit others contributions to group work. Although the results cannot be generalized to a larger group of students, and no definite conclusions can be drawn from the questionnaires about the usefulness and effectiveness of Google Docs and EtherPad for collaborative writing, the results cannot be underestimated since some results are consistent with the research literature. Future research consists of the qualitative evaluation of the students' comments to open ended-questions in the questionnaire, the students' collaborative essay papers, and their contributions to group work. It may also be important to examine the extent and quality of utilization of the tools for collaborative writing. Triangulation of the data collected may shed light on how they really perceived the effectiveness of Google Docs and EtherPad to support collaborative writing among student

Imaginary Dialogues – In-service Teachers’ Steps Towards Mathematical Argumentation in Classroom Discourse

The purpose of this qualitative study was to explore in-service teachers’ first experiences with imaginary dialogues – a form of mathematical writing where students are introduced to a written and unfinished dialogue between two imaginary persons discussing a mathematical problem. Students are supposed to continue working with the problem and to complete the initial dialogue between these persons. In-service teachers were enrolled in a continuing university education mathematics course. They were given the task to try out imaginary dialogues in their classes from grades 4 to 10. Based on in-service teachers’ responses in open-ended self-evaluation forms, the study examined how the in-service teachers perceived imaginary dialogues as a tool to approach students’ mathematical argumentation. The study also sought to investigate how they identified levels of argumentation in their students’ written dialogues based on the background of Balacheff’s levels of proofs in school mathematics practices.publishedVersionNivå

In-Service Teachers’ Perceptions of the Design and Quality of Mathematics Videos in their On-Line Learning

This investigation is part of a continuing education program in mathematics, directed at in-service teachers in lower secondary schools holding teacher certificates. Online mathematics lessons, offered through a distant education course, consisted of a combination of text and video podcasts. University educators’ podcast development was guided by research-based design principles related to e-learning and multimedia instruction. The question arose as to whether in-service teachers enrolled in the course would perceive the podcast design as supportive for their learning. Using questionnaires, this study monitored how in-service teachers perceived podcast quality based on design dimensions. It sought to identify participants’ preferences and their recommendations for video development improvement. Key factors for quality included podcast length and the speaker’s narration. Inservice teachers perceived the podcasts as being useful for their learning processes and indicated efficiency, enjoyment, and concentration as critical learning conditions

Mathematics Video Podcasts as Integrated Elements of Online Lessons in Further University Education: In-Service Teachers’ Flow Experiences

This case-study examined in-service teachers’ perceptions of learning by means of online mathematic lessons consisting of a mix of text and video podcasts. The investigation is part of further university education directed at practicing teachers in lower secondary schools. The course was a distant education course, with in-service teachers learning online only. The research, based on a series of questionnaires and follow-up interviews, examined whether in-service teachers perceived that video podcasts embedded in online lessons fostered their learning compared to reading similar material. The study focused on efficiency, enjoyment, and concentration as perceived conditions for learning in conjunction with flow theoryMathematics Video Podcasts as Integrated Elements of Online Lessons in Further University Education: In-Service Teachers’ Flow ExperiencespublishedVersionNivå

Engaging Mathematical Reasoning-and-Proving: A Task, a Method, and a Taxonomy

This article is the second paper in a series of papers on studies focusing on teaching mathematical reasoning-and-proving in elementary mathematics classroom. Participants are in-service teachers enrolled in a continuing university education program in mathematics. Results from the first paper suggested the method of imaginary dialogues to have the potential to support in-service teachers in engaging their students in mathematical reasoning-and-proving, and Balacheff’s taxonomy of proofs to support in-service teachers in identifying students’ argumentation. This study is on the following years’ in-service teachers in the program. It examines their perceptions of the usefulness of two constituent parts of this approach, and what insights students’ written dialogues might provide. The study draws on G. J. Stylianides’ analytic framework for reasoning-and-proving. Main data were obtained from a questionnaire taken by 32 in-service teachers and follow-up interviews with four of them. The study reveals engaging students to reason, argue, and prove, while making students’ argumentation visible for teachers was perceived the most useful with imaginary dialogues. The teachers’ increasing awareness of levels of argumentation, was perceived to be the most useful with getting exposed to Balacheff’s distinctions. Keywords: Balacheff’s four levels of proofs, mathematical reasoning-and-proving, written imaginary dialoguesNivå

Developing further support for in-service teachers’ implementation of a reasoning-and-proving activity and their identification of students’ level of mathematical argumentation

This is the third in a series of papers focusing reasoning-and-proving. Participants were in-service teachers enrolled in a continuing university education programme in teaching mathematics for grades 5–10. Data were collected from a course assignment in 2018 and 2019, where the in-service teachers reported about their students’ work with a reasoning-and-proving task. Their reports included an identification of the levels the students’ written argumentation reached, based on Balacheff’s taxonomy of proofs. The course assignment’s instructions were expanded for the 2019-cohort. Comparing in-service teachers’ proof level identifications to the researchers’ by statistical analyses, indicated an improvement of the general quality from 2018 to 2019. A higher consensus in 2019 included identifying generic arguments and an understanding that there might be examples falling outside of the taxonomy levels. Qualitative content analysis of the two cohorts’ justifications of their identifications revealed an improved understanding of what is considered generic argumentation. The results encourage and contribute to further developments of the concept.publishedVersio

Education students' use of collaborative writing tools in collectively reflective essay papers

Published version of an article in the journal: Journal of Information Technology Education: Research. Also available from the publisher at: http://www.jite.org/documents/Vol13/JITEv13ResearchP091-120Brodahl0463.pdf Open AccessGoogle Docs and EtherPad are Web 2.0 tools providing opportunity for multiple users to work online on the same document consecutively or simultaneously. Over the last few years a number of research papers on the use of these collaborative tools in a teaching and learning environment have been published. This work builds on that of Brodahl, Hadjerrouit, and Hansen (2011) expanding its case study. The theoretical framework is the same as the one underlying Brodahl et al. (2011), drawing on two learning theories, the social-constructivist learning theory and the community of practice, and their relationships to collaborative tools. The literature review is extended to cover the recent research work in the field, related to Web 2.0 technologies in higher education. The case study of Brodahl et al. (2011) involved 201 education students who had just begun their four-year initial teacher education. However, 24 students are omitted in the current work, and the result tables from Brodahl et al. (2011) accordantly updated. Disregarding particular groups of students was due to their specific local dispersion, as they conducted their entire assignment and collectively reflective essay paper at the same physical location and, with respect to this, reported the use of collaborative tools as superfluous and unwanted in their setting. Partly based on the same survey, this work presents a case study investigating education students' perceptions of collaborative writing reflective essay papers. However, where Brodahl et al. (2011) presented a solely quantitative study derived from closed-ended questions, this work incorporates the survey's open-ended questions in a qualitative analysis. The analysis also draws on the students' written reflections on their experiences. The qualitative analysis supports the conclusion of Brodahl et al. (2011) that technical problems were a major issue, mostly related to EtherPad. All but one complaint about technical difficulties stemmed from EtherPad users during a limited period of time. Other major negative feedback concerned group size; several groups pointed out difficulties with organizing the work, problems ofkeeping track when editing simultaneously, and failure to produce a unified document. Positive issues frequently mentioned are the ability to work asynchronously and from different places. Furthermore, a majority of the reports on commenting on and editing each other's work were positive, mentioning that it is an advantage to be able to correct spelling errors and bad formulations, that it is educational, that one may contribute with ideas that the others do not have, and that it improves the final text. Larger issues on the negative side were fear of insulting or misunderstanding, and difficulties because of various work modes. Also qualitative results indicate that females are more concerned with group size than males, but less preoccupied with technical difficulties. Furthermore, younger students appear more concerned about the importance of preparation and planning than older ones. The major conclusions are that EtherPad and Google Docs facilitate new ways of approaching communication, for different collaborative writing work modes as well as in different settings. However, the setting in which the tool is used exerts an influence on the way students perceive its usefulness. Recommendations derived from students' perception of factors of success for using the collaborative writing tool include the following: group size should preferably not exceed three persons; the students ought to be prepared for technical difficulties and have a contingency plan; and they should have time in advance to discuss their work mode and agree on rules for commenting on and editing each other's work

Serving of free school lunch to secondary-school pupils - a pilot study with health implications

Published version of an article from the journal Public Health Nutrition, Copyright Cambridge University Press. Article also available from publisher: http://dx.doi.org/10.1017/S1368980009990772Objective: To study whether service of a free school lunch has an impact on weight development and food intake among pupils at a lower secondary school, and to assess the association between self-perceived school behaviour and food intake. Design: A controlled intervention study involving service of a free healthy school lunch to 9th grade pupils took place over 4 months, from January to May 2007. Weight and height were measured before and after the intervention. The pupils also completed a short FFQ and a questionnaire concerning self-perceived school behaviour and the classroom environment before and after the intervention. A healthy food score was calculated using the FFQ data. Setting: All 9th graders at three different lower secondary schools in southern Norway were invited to participate. One school was randomly selected as the intervention school. Subjects: Fifty-eight pupils (91 %) from the intervention school and ninety-two pupils (77 %) from the control schools participated. Results: BMI did not increase among the girls at the intervention school, but increased significantly among the boys at the intervention school and among the control school groups. The healthy food score correlated positively with the trait ‘satisfied with schoolwork’ (P,0?001). Fifteen per cent of the variance in food score could be explained by gender and the trait ‘satisfied with schoolwork’. Conclusions: Serving of a healthy free school lunch to secondary-school pupils may result in restricted weight gain. Further studies are needed to clarify the impact of school meals on overweight and academic performance