0000000000709150
AUTHOR
Martin Carlsen
Mathematics Education Research Group Agder
Emergent tech in teaching and learning, math in non-mathematical practices, teaching and learning math in kindergarten, mathematical thinking processes in school, math in teacher education, teaching and learning math in higher education.
The Effects of a Structured Curriculum on Preschool Effectiveness: A Field Experiment
Abstract: This study tests an intervention that introduces a structured curriculum for five-year-olds into the universal preschool context of Norway, where the business as usual is an unstructured curriculum. We conduct a field experiment with 691 five-year-olds in 71 preschools and measure treatment impacts on children’s development in mathematics, language, and executive functioning. The nine-month intervention has effects on child development at post-intervention and the effects persist one year following the end of the treatment. The effects are mainly driven by the preschools identified as low-quality at baseline, indicating that a structured curriculum can reduce inequality in early c…
Using assessment for learning mathematics with mobile tablet based solutions
Published version of an article in the journal: International Journal of Emerging Technologies in Learning (iJET). Also available from the publisher: http://dx.doi.org/10.3991/ijet.v9i2.3219 This article discusses assessment for learning in mathematics subjects. Teachers of large classes face the challenge of regularly assessing students’ ongoing mathematical learning achievements. Taking the complexity of assessment and feedback for learning as a background, we have developed a new approach to the assessment for learning mathematics at university level. We devised mobile tablet technology supported assessment processes, and we carried out user studies in both Rwanda and Norway. Results of …
Third grade students’ multimodal mathematical reasoning when collaboratively solving combinatorial problems in small groups
The aim of this study is to investigate Norwegian primary school students’ multimodal mathematical reasoning when solving combinatorial problems. The data collection took place in four small groups of altogether thirteen 8–9 years old third-graders. Our study shows a variety of approaches used to solve the given combinatorial problems, such as count-all and grouping. These approaches were characterized by the students’ use of inscriptions that displayed all combinations and inscriptions that did not display all combinations. Moreover, the students used gestures such as pointing and sliding. The students’ multimodal reasoning was characterized by the ways their utterances, inscriptions, and …
Situational Perception in Mathematics (SPiM)—Results of a Cross-Country Study in Austria and Norway
Situation-specific skills, as situational perception, are a central part of educators’ competence. This is especially true for kindergarten teachers (KTs) as most of their teaching is based on natural learning situations. The aim of this study is to contribute to the discussion on KTs’ situational perception by identifying aspects of early childhood education students’ situational perception in mathematics. Therefore, we conducted a qualitative study with N = 5 students from Austria and N = 5 students from Norway. Data was collected through a video-based questionnaire: The students watched seven video vignettes and wrote down their observations and reflections immediately upon watching. Dat…
Reasoning with paper and pencil: The role of inscriptions in student learning of geometric series
The purpose of this article is to analyse how students use inscriptions as tools for thinking and learning in mathematical problem-solving activities. The empirical context is that of learning about geometric series in a small group setting. What has been analysed is how students made use of inscriptions, self-made as well as those provided by text books and teachers, and the role these inscriptions played in the coordination of students’ learning/communication. Through the use of inscriptions (made on the chalkboard and with paper and pencil), the students externalised their thinking while engaging in mathematical reasoning on the topic of geometric series. The inscriptions were significan…
Capturing learning in classroom interaction in mathematics: Methodological considerations
International audience; This paper discusses issues of how to transcribe and analyze video-recordings when studying learning in small group work in mathematics. Since bodily features of interaction and the use of artefacts play important roles in mathematical reasoning, a multimodal approach to transcribing is necessary. Thus, the theoretical grounding for transcriptions has to be in accord with the perspective on learning adopted in the analysis. In the paper, the principles for studying what Radford (2000) refers to as knowledge objectification processes when learning mathematics will be discussed.
Designing Playful Inquiry-Based Mathematical Learning Activities for Kindergarten
This study addresses issues related to the process of designing mathematical activities for kindergarten based on the constructs of playful learning and inquiry. The mathematical activities were designed for 5-year-old children in a Norwegian kindergarten setting. In order to address this design process, we focus at issues of mediating design principles and ideas to kindergarten teachers, who are the ones to orchestrate and implement the mathematical activities with children. The study is situated within a design research methodology in which observations, written and personal communication have been used as sources of data. Our analysis shows that the kindergarten teacher closely followed …
Promoting Child Development in a Universal Preschool System: A Field Experiment
This study tests an intervention that introduces a structured curriculum for five-year olds into the universal preschool context of Norway. We conduct a field experiment with 691 five-year-olds in 71 preschools and measure treatment impacts on children's development in mathematics, language and executive functioning. Compared to business as usual, the nine-month curriculum intervention has effects on child development at post-intervention and the effects persist one year following the end of the treatment. The effects are entirely driven by the preschool centers identified as low-quality at baseline, suggesting that a structured curriculum can reduce inequality in early childhood learning e…
Engaging with mathematics in the kindergarten. Orchestrating a fairy tale through questioning and use of tools
ABSTRACTThe aim of this study is to analyse how a kindergarten teacher orchestrated a mathematical activity involving a fairy tale. Taking a sociocultural perspective on learning and development, naturally occurring talk-in-interaction has been analysed in order to scrutinise the subtleties of the orchestration. The fairy tale Goldilocks and the Three Bears was used both as context for the activity, but also as a means through which mathematical concepts were engaged with. The analysis shows that the orchestration bears characteristics of questioning and use of tools such as voice, facial expressions, and concrete materials. The orchestration is also characterised by sincere planning in adv…
Qualities of mathematical discourses in kindergartens
AbstractIn this study we investigated qualities of the mathematical discourse in four kindergarten classes in which kindergarten teachers and 5-year-old children engaged in mathematical learning activities. We analysed differences in the mathematical discourses in two experimental kindergarten classes and two control kindergarten classes, in a research and development project. The overarching research question guiding our study was as follows: what characterises the mathematical discourse unfolding in kindergarten classes? In our study we drew on the theoretical framework Mathematical Discourse in Instruction coined by Adler and Ronda, as we quantified the collected qualitative data. Our an…
Mathematical Learning Opportunities in Kindergarten through the Use of Digital Tools: Affordances and Constraints
Accepted version of an article in the journal: Nordic Journal of Digital Literacy. Also available from the publisher at: http://www.idunn.no/ts/dk/2013/03/mathematical_learning_opportunities_in_kindergarten_through This study aims at scrutinising the mathematical learning opportunities of children engaging with digital tools and the emerging affordances and constraints faced in such settings. By adopting a sociocultural perspective on learning and development, the multimodal analysis of the adult-child interaction shows that the children are participants in processes of appropriating the mathematical concepts of sorting and counting. Affordances are taken advantage of by the adults and cons…
Kindergarten teachers’ orchestration of mathematical activities afforded by technology: agency and mediation
This paper focuses on kindergarten teachers’ interactions with young children during mathematical learning activities involving the use of digital tools. We aim to characterise the teachers’ roles and actions in these activities and extend considerations of teachers’ orchestrations current in the research literature with regard to agency and mediation. Our analysis of teacher-children-digital tool interaction reveals that the kindergarten teachers took three roles in their work with young children, which we call Assistant, Mediator and Teacher roles. These roles were used interchangeably and purposefully by the kindergarten teachers. With regard to agency and mediation, we argue that agency…
Grunnskolelærerstudenters erfaring med eBok-basert undervisning i matematikk
I denne artikkelen analyserer vi grunnskolelærerstudenters respons på en eBok-basert undervisningsform i matematikk. Denne eBoka besto av oppgaver med både skriftlige og videobaserte løsningsforslag. Oppgavene ble hentet fra tidligere gitte eksamensoppgaver knyttet til nasjonal deleksamen i matematikk. Formålet var å undersøke: a) hvordan studentene benyttet de ulike læringsressursene i eBoka, og b) på hvilke måter studentens bruk av læringsressursene hadde pragmatisk og epistemisk verdi (Artigue, 2002). Analysene bygger på kvantitative og kvalitative data fra en spørreundersøkelse (N = 60) om bruk av eBoka og viser at nesten alle studentene benyttet de videobaserte løsningsforslagene, mens…
Children’s Engagement with Mathematics in Kindergarten Mediated by the Use of Digital Tools
The purpose of this chapter is to study children’s engagement with mathematics in kindergarten mediated by digital tools within the context of interactive whiteboard (IWB). Our study reports from a research project aiming at analysing in what ways digital tools may nurture children’s appropriation processes relative to mathematics. In adopting a sociocultural perspective on learning and development, observations together with video recordings have been analysed. Our study shows that the children make sense of the digital tools and are able to apply the tools purposefully due to the interaction with an adult within the zone of proximal development (ZPD). The children externalise their reason…
Rethinking practices of assessment for learning: Tablet technology supported assessment for learning mathematics
This article discusses assessment for learning in mathematics subjects. It is challenging for teachers of large classes to regularly assess students' mathematics in order to help them improve their learning achievement. Given the complexity of assessing and providing feedback for learning, a new approach to assessment for learning was suggested. Media tablet technology supported assessment processes were devised and user studies were conducted in Norway and Rwanda. There are indications that students like to be involved in assessing each other's mathematics work. Students expect to get learning gains by providing and obtaining feedback to/from their peers using technology supported tools.
Kindergarten teachers’ accounts of their developing mathematical practice
Published version of an article in the journal: ZDM. Also available from the publisher at: http://dx.doi.org/10.1007/s11858-012-0422-1 This study explores kindergarten teachers’ accounts of their developing mathematical practice in the context of their participation in a developmental research project. Observations and interviews were analysed to elaborate the accounts as regards orchestrating mathematical activities in the kindergarten. A co-learning agreement was established as collaboration between the kindergarten teachers and researchers. The study reveals that the kindergarten teachers argue that they have been empowered in developing an inquiry stance towards mathematics and mathemat…