Educational policy to improve mathematics instruction at scale: conceptualizing contextual factors

Theories for conceptualizing educational policies aimed at improving classroom instruction at scale are under development in the educational sciences. In using such theories, it is essential to note the specific educational context. In this article, we conceptualize the role of contextual factors when operationalizing Cobb and Jackson (2012) [Journal of the Learning Sciences] in the Swedish context. Drawing on data and results from a large-scale project carried out during 2012–2017 and studies of Swedish educational contexts, we conceptualize contextual factors for large-scale projects. Besides rather obvious explicit contextual factors such as ongoing policies and practices, we elaborate on how the underlying, more implicit contextual factors of (1) the positioning of teachers within the educational system, (2) the positioning of teachers within the classroom, and (3) traditions of visible and invisible pedagogy affected the establishment of policy in the Swedish context. Insight into these factors deepens earlier frameworks of context, and helps not only to operationalize the policy within the context but also to make explicit hidden features of a cultural context that are important to influence if the aim of the educational policy is to reorganize school practices.publishedVersio

Construction of teachers’ roles in collegial discussions

This paper investigates how teachers portray their teaching role in a professional-development community. By analyzing data from five groups, the goal of the study is to understand how teachers portrayed within these practices. In the majority of interactions, teachers position themselves within a traditional teacher discourse, an official Swedish discourse, or a reform-oriented discourse. The analysis provides examples of different teacher roles both within and between groups. Teachers who advocate a reform-oriented teacher role indicate that, in this type of role, they face challenges, and they stress that they need more specialized content knowledge.publishedVersio

Teachers’ framing of students’ difficulties in mathematics learning in collegial discussions

This study investigates the diagnostic and prognostic framings of Swedish mathematics teachers regarding the difficulties experienced by students in mathematics learning. Collegial discussions among 65 mathematics teachers in nine collegial groups were videotaped during a professional development (PD) program entitled Boost for Mathematics for analysis. The results show that the diagnostic framings of the teachers were mainly attributed to the cognitive abilities of students, whereas the prognostic framings were mainly related to lesson organization such that students should collaborate. While the teachers emphasize collaborate group work, they put little emphasis on how they could act in these learning situations. These results contribute to the understanding of Swedish mathematics teachers’ framing of students’ difficulties in mathematics learning and to the role of collegial discussions in PD initiatives.publishedVersio

Using TIMSS items to evaluate the effectiveness of different instructional practices

Can instructional quality be measured using TIMSS items on how often certain instructional practices are used in the mathematics classroom? We focused on three instructional practices that have been the topics of longstanding debates in the educational literature: memorizing formulas, listening to the teacher, and relating mathematics to daily life. In a multi-level multiple regression analysis, we examined how class-level responses to these items predicted mathematics achievement. In Sweden, across four waves of TIMSS, relating to daily life was a negative predictor of achievement, whereas memorizing formulas and listening to the teacher were positive predictors. This was also the typical pattern of results across all countries participating in two waves of the international TIMSS. Our fndings are in line with certain positions on the abovementioned debates. Although conclusions are limited by the correlational nature of the data, we argue that TIMSS is a promising tool for evaluating the efectiveness of diferent instructional practices. We also suggest several improvements.publishedVersio

Analysing the nature of potentially constructed mathematics classrooms in Finnish teacher guides – the case of Finland

Given that curriculum materials serve as cultural artefacts, this study addresses the need for more research on curriculum materials in different contexts. Most studies concerning curriculum materials have been conducted in US and, therefore little is known about the nature of materials in other cultural-educational contexts. The aim of this paper is to identify the underlying cultural norms of potentially constructed classrooms, by analysing recurrent activities in the most commonly used Finnish teacher guides at primary-school level. We identified three norms embedded in them: (1) creating opportunities for learning through a variety of activities and communication; (2) keeping the class gathered around a specific mathematical topic; and (3) concurrent active involvement of teachers and students. The results add to knowledge about both teacher guides and the Finnish educational context. Moreover, it adds to the growing body of methodologies, as our analytical approach is novel in the context of textual analysis.publishedVersio

Towards an organizing frame for mapping teachers' learning in professional development

In their claim that teachers’ learning is treated as a “black box” in research on professional development programs for mathematics teachers, Goldsmith, Doerr, & Lewis (2014) call for “an organizing framework that clearly distinguishes dimensions of teachers’ learning and identifies catalysts of teachers’ learning…” (p. 23). The aim of this study is to present initial efforts to construct a framework for categorizing descriptions of activities designed to support teachers’ learning as presented in research articles within mathematics education. Based on existing literature on professional development and examination of research articles, an organizing frame is constructed

Approaching Mathematical Discourse : Two analytical frameworks and their relation to problem solving interactions

The driving force of conducting the two studies presented in this thesis is to examine ways that conceptual understanding and problem solving could be part of mathematics teaching, and through that, part of students' mathematical knowledge. The specific aims of the thesis are: 1) to characterize the classroom discourse of two, apparently similar, problem solving courses in teacher education and 2) to discuss the possibilities of developing two analytical approaches - the communicational approach to cognition and the dialogical approach - used for studying mathematical discourse. The two aims are elaborated on by means of data collected through audiotaped recordings and field notes from observations of problem-solving activities in engineering and teacher education. In relation to the first aim, the analysis of the classroom discourse within the two courses makes it clear that both courses displayed different kinds of discourse that could be broadly categorized in terms of: subject-oriented, didactically oriented, and problem solving oriented discourses. However, the comparisons between the two courses reveal a marked difference in the distribution of these categories of discourse. It is suggested that the introduction of explicit conceptual frameworks in teaching is of crucial importance for the topical focus of the classroom discourse, and for prospective teachers' opportunity to engage in mathematical productive discourse. The analyses of the two approaches for studying mathematical discourse reveal that the two frameworks can be further developed and the study also indicates ways in which such development can be achieved using a theory of contextualization and theories of mathematical learning. Finally, the thesis discusses theoretical and practical implications of the results, foregrounding issues of importance for the research on mathematical discourse, and for teachers and teacher educators involved in designing instructions for mathematical problem solving

EFFECTIVE TEACHING THROUGH PROBLEM-SOLVING BY SEQUENCING AND CONNECTING STUDENT SOLUTIONS

How can researchers support teachers in the complexity of orchestrating productive mathematical whole-class discussions based on students’ solutions to challenging problems? This study has two aims: Firstly, to study how the teacher can select, sequence and connect different student solutions in order to effectively orchestrate mathematical whole-class discussions. Secondly, to critically reflect on the role of the researchers in this intervention project. Analyses of audio recorded interviews and video recorded whole-class discussions result in suggestions for how student solutions can be sequenced in this particular case to set the scene for connecting them with each other and with key mathematical ideas. We further critically reflect on how we as researchers can improve our work in supporting practicing teachers

EFFECTIVE TEACHING THROUGH PROBLEM-SOLVING BY SEQUENCING AND CONNECTING STUDENT SOLUTIONS

How can researchers support teachers in the complexity of orchestrating productive mathematical whole-class discussions based on students’ solutions to challenging problems? This study has two aims: Firstly, to study how the teacher can select, sequence and connect different student solutions in order to effectively orchestrate mathematical whole-class discussions. Secondly, to critically reflect on the role of the researchers in this intervention project. Analyses of audio recorded interviews and video recorded whole-class discussions result in suggestions for how student solutions can be sequenced in this particular case to set the scene for connecting them with each other and with key mathematical ideas. We further critically reflect on how we as researchers can improve our work in supporting practicing teachers