Browsing by Subject "Mathematics education"

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  • Van Steenbrugge, Hendrik; Krzywacki, Heidi; Remillard, Janine; Koljonen, Tuula; Machalow, Rowan; Hemmi, Kirsti (Freudenthal Group & Freudenthal Institute, Utrecht University and ERME, 2019)
    This paper relates to the mathematics curriculum systems of the United States, Finland, Sweden, and Flanders (Belgium). These four regions are in the midst of curriculum reform, which provides interesting grounds for cross-cultural comparison. Our analysis builds on a framework that focuseson curriculum policy, design and enactment in each of these regions and draws on interview data with teachers in all four regions, sample cases of curriculum use, context descriptions, and available descriptions of mathematics education in these four regions. This leads to a more nuanced understanding of the particular curriculum systems through which reform manifests, and sheds light on a challenging balance concerning a curriculum reform that is both coherent across a region and supported by teachers.
  • Garcia Moreno-Esteva, Enrique; White, Sonia L. J.; Wood, Joanne M.; Black, Alex A. (2018)
    In this research, we aimed to investigate the visual-cognitive behaviours of a sample of 106 children in Year 3 (8.8 ± 0.3 years) while completing a mathematics bar-graph task. Eye movements were recorded while children completed the task and the patterns of eye movements were explored using machine learning approaches. Two different techniques of machine-learning were used (Bayesian and K-Means) to obtain separate model sequences or average scanpaths for those children who responded either correctly or incorrectly to the graph task. Application of these machine-learning approaches indicated distinct differences in the resulting scanpaths for children who completed the graph task correctly or incorrectly: children who responded correctly accessed information that was mostly categorised as critical, whereas children responding incorrectly did not. There was also evidence that the children who were correct accessed the graph information in a different, more logical order, compared to the children who were incorrect. The visual behaviours aligned with different aspects of graph comprehension, such as initial understanding and orienting to the graph, and later interpretation and use of relevant information on the graph. The findings are discussed in terms of the implications for early mathematics teaching and learning, particularly in the development of graph comprehension, as well as the application of machine learning techniques to investigations of other visual-cognitive behaviours.
  • Haataja, Eeva; Chan, Man Ching Esther; Salonen, Visajaani; Clarke, David (2022)
    In student collaboration, purposeful peer interaction crucial for success on the task. Such collaboration requires adequate and purposeful student agency. Theoretically, the between-individual complementarity of agency be-haviors enhances purposeful interaction. However, the level of agency of group members can disrupt the collaborative interactions. We conducted a case study of collaborative mathematical problem solving, where one student's behaviors of noncomplementary agency characterized the group interaction. We examined the video recording of the group by continuous quantitative coding of students' agency behaviors and segmented the interaction process into four phases. We analyzed qualitatively these phases based on the verbal transcript. We found that the target student's agency grew in relation to the other students despite her lack of mathematical competence. The findings provide us with a new perspective to understand the role of the situational individual agency in collaborative learning that underlines the tolerance of noncomplementarity of agency in student collaboration.
  • Rämö, Johanna; Reinholz, Daniel; Häsä, Jokke; Lahdenperä, Juulia (2019)
    In this article we describe a long-term departmental change effort in one mathematics department. The change began with one instructor adopting the Extreme Apprenticeship instructional model. This modest shift served as the catalyst for a series of subsequent, systemic improvements. We believe that this innovation and the resultant change demonstrate how instructional change can serve as a catalyst for broader change, rather than a change that focuses solely on instruction. We use four frames from the literature on organizational development to characterize the changes that have occurred in this department. This in-depth case study describes the department's current culture and how it developed, and we suggest that this explanation could serve as a guide for other departments seeking change.
  • Hannula, Markku S.; Laine, Anu; Pehkonen, Erkki; Kaasila, Raimo (Háskólaútgáfan, University of Iceland Press, 2012)
    Infinity is an important concept in mathematics, which students find difficult to learn. This paper will report Finnish elementary teacher students’ understanding of density at the beginning of their studies and the development of that understanding during a mathematics methods course. The results show that even quite limited teaching can initiate significant improvement. Moreover, students can make progress even if their initial level of performance is low. Yet, only 60 % of elementary education students reach satisfactory content knowledge and pedagogical content knowledge by the end of the course.
  • Haataja, Eeva; Salonen, Visajaani; Laine, Anu; Toivanen, Miika; Hannula, Markku S. (2021)
    Reciprocal eye contact is a significant part of human interaction, but its role in classroom interaction has remained unexplored, mostly due to methodological issues. A novel approach in educational science, multiple-person mobile gaze-tracking, allows us to gather data on these momentary processes of nonverbal interaction. The current mixed-method case study investigates the role of teacher-student eye contact in interpersonal classroom interaction using this methodological approach from three mathematics lessons. We combined gaze-tracking data with classroom videos, which we analyzed with continuous coding of teachers’ interpersonal behavior. Our results show that teacher communion and agency affect the frequency and durations of teachers and students’ gazes at each other. Students tend to gaze their teachers more during high teacher communion and low agency, but qualitative and quantitative differences between the teachers and their classes emerged as well. To conclude, the formation of eye contacts is situational and affected by momentary interpersonal changes as well as the qualities of teacher-student interactions.
  • Koponen, Mika; Asikainen, Mervi A.; Viholainen, Antti; Hirvonen, Pekka E. (2019)
    In this article we present a new approach to investigating teacher knowledge. The essay data related to Finnish future teachers' (N = 18) perceptions of the "knowledge required for teaching mathematics" were transformed into a network. We classified the knowledge topics using the Mathematical Knowledge for Teaching (MKT) framework and examined the relationships between the issues raised with the aid of network analysis. According to the results, the future teachers see the six MKT domains in a hierarchical sequence. As it is not subject specific, this approach is also applicable in the investigation of teacher knowledge of other subjects. (C) 2018 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (
  • Hannula, Markku S. (2019)
    This article is a commentary for the special issue on affect and mathematics in young children, written from the perspective of research on affect in mathematics education. The studies in this special issue focus on the individual learners' affective traits and use primarily surveys as the method. The most common type of affect is emotions, but some studies do examine student beliefs and motivation. The analysis of concept definitions and operationalizations identified some inconsistencies between the different articles, especially with how they operationalize anxiety either as sadness, worry, or fear. The results of the studies provide evidence that young learners' affect can be reliably measured and that there is a correlation between affect and achievement. This correlation is weaker than for older students and longitudinal data suggests that the causal direction is more likely from achievement to affect.