Developing a reform mathematics curriculum program in Sweden: relating international research and the local context

This paper reports on a research-based mathematics curriculum program development project in Sweden, whose educational context is currently characterized by multiple reform initiatives. Current reforms include a repositioning of the teacher as central for students’ learning, but also a trend toward initiatives and teacher resources that are more directive than has been the case in the past 30 years. Collecting data from multiple sources, such as teacher log books, lesson observations and feedback meetings, we build on input from 11 elementary school teachers trying out our materials, including student texts and a teachers’ guide, during four trial rounds. We analyze how international research about curriculum programs and teachers’ use of these programs are interpreted and operationalized within the Swedish context. In particular, the two research questions guiding the study are: (1) “How do Swedish teachers interact with and reason about the reform-based classroom practices promoted by the curriculum program?” and (2) “How do Swedish teachers interact with and reason about their use of a teachers’ guide?” From our experiences in the Swedish educational context, we suggest the following contextual aspects to take into account when designing a curriculum program whose design is grounded in international research literature: characteristics of current classroom practices, teachers’ role in classrooms, the level of explicit/implicit support teachers are used to receiving, and teachers’ experiences using a teachers’ guide.     

A Comparison of TIMSS Items Using Cognitive Domains

The results of international assessments such as the Trends in International Mathematics and Science Study (TIMSS) are often reported as rankings of nations. Focusing solely on national rank can result in invalid inferences about the relative quality of educational systems that can, in turn, lead to negative consequences for teachers and students. This study seeks an alternative data analysis method that allows for improved inferences about international performance on the TIMSS. In this study, four classroom teachers categorized a sample of TIMSS items by the cognitive domains of knowing and applying using the definitions provided by the TIMSS 2011 Assessment Frameworks. Items of different cognitive domains were analyzed separately. This disaggregation allowed for more valid inferences to be made about student performance. Results showed almost no significant difference between the performance of U.S. students and the students of five other nations. Additionally, no differences were observed in U.S. students' performance on knowing items and applying items, although students from some sample nations performed significantly better on knowing items. These results suggest that policy makers, educators, and citizens should be cautious when interpreting the results of TIMSS rank tables.     

Mathematics capital in the educational field: Bourdieu and beyond

Mathematics education needs a better appreciation of the dominant power structures in the educational field: Bourdieu's theory of capital provides a good starting point. We argue from Bourdieu's perspective that school mathematics provides capital that is finely tuned to generationally reproduce the social structures that serve to keep the powerful in power, while ensuring that less powerful groups are led to accept their own failure in mathematics. Bourdieu's perspective thereby highlights theoretical inadequacies in much mathematics education research, insofar as it presumes a consensus about a ‘what works agenda’ for improving achievement for all. Drawing on one case where we manufactured awkward facts, we illustrate a Bourdieusian interpretation of mathematics capital as reproductive, and the crucial role of its cultural arbitrary. We then criticise the Bourdieusian concept of ‘mathematical capital’ as the value of mathematical competence in practice and propose to extend his tools to include the contradictory ‘use’ and ‘exchange’ values of mathematics instead: we will show how this conceptualisation goes ‘beyond Bourdieu’ and helps explain how teaching-learning might (ideally) produce ‘cultural use value’ in mathematical competence, while still recognising the contradictions teachers and learners face. Finally, we suggest how critical education research generally can benefit from this theoretical framework: (1) in exposing the interest of the dominant classes; but also (2) in researching critical pedagogic alternatives that challenge orthodoxy in educational policy and practice both in mathematics education and more generally.     

Relationships between emotional dispositions and mathematics achievement moderated by instructional practices: analysis of TIMSS 2015

ABSTRACT

This research is a secondary analysis with Korean students’ data collected in the TIMSS 2015 to describe the moderation effects of instructional practices on the relationships between students’ emotional dispositions toward mathematics and mathematics achievement. From the TIMSS 2015 database, we collected mathematics achievement scores, a student-level contextual scale for students’ emotional disposition, and teacher-level contextual scales representing teachers’ instructional practices. We applied hierarchical linear modelling to construct multilevel models. The findings showed that the achievement gap between emotional dispositions – like and dislike – became smaller when teachers more frequently implemented certain instructional practices like asking students to complete challenging exercises, decide their own problem-solving procedures, and express their ideas in class. Students who disliked mathematics were likely to have higher scores as their teachers implemented each of those practices more frequently. Findings provide important implications to teachers regarding: It is important to encourage students to reason through instructional practices like asking them to decide their own problem-solving procedures and to solve challenging problems.     

Teachers’ beliefs towards teaching calculus

This paper focuses on the belief systems towards teaching calculus of 29 upper secondary mathematics teachers. Firstly, we discuss different educational trends in teaching calculus, and the theoretical approach based on the construct of belief systems. Afterwards we describe the method of our study used to analyse the belief systems of the calculus teachers. Referring to findings of our research, we firstly focus on central and peripheral beliefs and thus discuss the structure of the teachers’ belief systems. Further, we compare the teachers’ belief systems to established educational trends of teaching calculus. Finally, we conclude the paper by reflecting on our main findings and by discussing possible directions of further research.     

Cognitive level in problem segments and theory segments

Problems play an important role in mathematics instruction and are therefore frequently seen as central points of application for measures of instructional development. The research project “Quality of instruction and mathematical understanding in different cultures” examines the cognitive level of practice problems and theory problems in a three-lesson unit on the Introduction to Pythagorean theorem¹: Analogously to the TIMSS 1999 video study, a differentiation was made between the cognitive level of problem statement and the cognitive level of problem implementation. Additionally, the lesson time was also divided into practice and theory segments. The results show that teachers with a high proportion of connection activities in practice segments do not necessarily also spend a greater proportion of time on an analogous level for theory.     

The Impact of a Multiyear Systemic Reform Effort on Rural Elementary School Students' Science Achievement

This paper is a report of the impact of an externally funded, multiyear systemic reform project on students' science achievement on a modified version of the Third International Mathematics and Science Study (TIMSS) test in 33 small, rural school districts in two Midwest states. The systemic reform effort utilized a cascading leadership strategy of professional development delivered at summer workshops and through distance technologies and local leadership groups that focused on helping teachers work in communities of practice to adapt science inquiry lessons to teach and reinforce strategies and skills in language arts in the lessons. Science achievement scores of Grade 3 and Grade 6 student cohorts on the two forms of the TIMSS administered at the beginning, middle, and end of the professional development effort revealed a V‐shaped pattern of scores, suggesting that teachers struggled with the newly adapted science inquiries at first but then became more effective in their use. The impact of the adaptation strategy on the students' achievement, questions about the time needed for new instructional strategies to be embraced by teachers, and the wisdom of using “low stakes” achievement tests in studies are discussed.     

New roles for mathematics in multi-disciplinary, upper secondary school projects

A new concept, compulsory multi-disciplinary courses, was introduced in upper secondary school curriculum as a central part of a recent reform. This paper reports from a case study of such a triple/four-disciplinary project in mathematics, physics, chemistry and ‘general study preparation’ performed under the reform by a team of experienced teachers. The aim of the case study was to inquire how the teachers met the demands of the introduction of this new concept and, to look for signs of new relations established by the students between mathematics and other subjects, as a result of the multi-disciplinary teaching. The study revealed examples of good practice in planning and teaching. In addition, it served to illuminate interesting aspects of how students perceived the school subject mathematics and its relations to other subjects and to common sense.     

Ethnomathematics and political struggles

The paper analyzes and discusses a research study in an ethnomathematics approach, which was developed in a Movimento Sem-Terra (Landless People Movement) settlement in Brazil. The research study is organized as a pedagogical project with peasants, students, teachers and technicians experiencing the construction of an educational process in which local and more global knowledge interacts and where native and technical knowledge are confronted and incorporated. The project allowed the production of a double movement of making community life penetrate the school at the same time as knowledge produced during the pedagogical process pours out from the school space. The approach used in the pedagogical work developed in the Itapui settlement focused on problems of practical and material needs. They were not transmuted into symbolic control problems, indicating other possibilities in the field of ethnomathematics, especially in mathematics education which is carried out with social movements such as the Landless People Movement. Based on her research, the author emphasizes that ethnomathematics finds its most relevant expression when it exposes its social engagement, when it does not treat cultural questions as exotic and unrooted elements, with no commitment to political struggles widespread throughout the world.     

How Common Is the Common Core? A Global Analysis of Math Teaching and Learning

The U.S. educational system is undergoing rapid and substantial changes with many states grappling with the adoption of the Common Core State Standards in Mathematics (CCSSM). Important research questions remain unanswered regarding the potential efficacy of the CCSSM to improve student math performance compared with students around the globe. This article utilized TIMSS 2007 8th‐grade math assessment results and curricular frameworks to (1) measure the degree of overlap between the CCSSM and TIMSS standards, and (2) use this finding to create a predictive model to determine the potential efficacy of the CCSSM in improving the U.S. 8th‐grade student math performance compared with six culturally matched, TIMSS‐assessed countries, provinces, and states. Comparisons of CCSSM and TIMSS‐assessed jurisdictions show that the CCSSM holds many items in common with TIMSS‐assessed jurisdictions, but lacks rigor in some key areas. The CCSSM deficiencies include algebraic knowledge and problem solving at the 8th‐grade level, and are a significant detractor from the CCSSM when compared with TIMSS.     

Gender perspectives in mathematics education: intentions of research in Denmark and Norway

A framework is presented for analyzing gender perspectives in mathematics education (structural, symbolic, personal and interactional gender), and the Danish and Norwegian researchers’/teachers’ work within the field of gender and mathematics is presented with reference to these four perspectives. Furthermore, the gender issue in TIMSS and PISA is briefly discussed. The main thread through the article is the researchers’ willingness and intentions of investigating the gender perspectives in mathematics education. However, so far, these research intentions have not been realized in Denmark and Norway.     

A model of professional competences in mathematics to update mathematical and didactic knowledge of teachers

This paper describes part of a research and development project carried out in public elementary schools. Its objective was to update the mathematical and didactic knowledge of teachers in two consecutive levels in urban and rural public schools of Region de Los Lagos and Region de Los Rios of southern Chile. To that effect, and by means of an advanced training project based on a professional competences model, didactic interventions based on types of problems and types of mathematical competences with analysis of contents and learning assessment were designed. The teachers’ competence regarding the didactic strategy used and its results, as well as the students’ learning achievements are specified. The project made possible to validate a strategy of lifelong improvement in mathematics, based on the professional competences of teachers and their didactic transposition in the classroom, as an alternative to consolidate learning in areas considered vulnerable in two regions of the country.     

Addressing prospective elementary teachers’ mathematics subject matter knowledge through action research

There is international dissatisfaction regarding the standard of mathematics subject matter knowledge (MSMK) evident among both qualified and prospective elementary teachers. Ireland is no exception. Following increasing anecdotal evidence of prospective elementary teachers in one Irish College of Education (provider of initial teacher education programme) demonstrating weaknesses in this regard, this study sought to examine and address the issue through two cycles of action research. The examination of the nature of prospective teachers’ MSMK (as well as related beliefs in the main study) informed the design and implementation of an intervention to address the issue. A mixed method approach was taken throughout. In both cycles, Shapiro's criteria were used as a conceptual framework for the evaluation of the initiative. This paper focuses on the perceived and actual effects of the intervention on participants’ MSMK. As well as its contribution at a local and national level, the study provides an Irish perspective on approaches taken to address the phenomenon internationally.     

Using video as a tool for promoting inquiry among preschool teachers and didacticians of mathematics

This paper explores the use of video as a tool for promoting inquiry among preschool teachers and didacticians. In this case, the didacticians are teacher educators who are also mathematics education researchers. Preschool teachers recorded themselves with video implementing number and geometry tasks with children and shared these recordings with other teachers and didacticians. The session where the teachers and didacticians viewed and discussed these recordings was recorded and viewed later by a group of didacticians. The multiple uses of video led to inquiry on several levels. Teachers inquired into the practice of implementing tasks with children, evaluating children’s knowledge, and the practice of using video as a tool. Didacticians inquired into their practice of research with children, their practice as teacher educators, the use of video as a tool in professional development, and the use of video in their inquiry process. Teachers’ and didacticians’ inquiries led to increased appreciation for the practice of inquiry, belonging to a community of practice, and its role in promoting both teachers’ and didacticians’ knowledge for teaching.     

Communicative characteristics of teachers’ mathematical talk with children: from knowledge transfer to knowledge investigation

In-service teachers actively collaborated in a developmental research project. The main aim of the research project was the advancement of one central aspect of teacher professionalism: teachers’ diagnostic competencies. Conditions of understanding and possibilities of enriching teachers’ talk are of special interest because mathematics teaching is particularly affected by speech and communication (Söbbeke and Steinbring in Mathematik für Kinder—Mathematik von Kindern, pp. 26–38, 2004). One research focus was on the support of a productive enhancement of the teachers’ talk with one child. Is the teacher’s talk mainly a kind of knowledge transfer similar to traditional instruction or can it be seen as an investigation of the child’s own views and ideas of elementary mathematical knowledge? These teachers’ talks with one child should offer more reflective communication between teacher and child and result in a changed view of the child’s mathematical understanding. Using an elaborate interpretation based on a theoretical instrument of analysis, called “Forms of teachers’ mathematical Interaction (Formal-In)”, we describe the development from the first diagnostic talk with one child, at the beginning to the last talk at the end of the research project. Using an elaborate analysis of short episodes of teachers’ talk distinguishing the interactive and the epistemological dimensions, we can describe how both dimensions influence each other. The theoretically identified characteristics of teachers’ talk together with compatible video cases can be used in theory-based (in-service) teacher training aimed at enhancing professionalism.     

Mathematics teacher educators’/researchers’ collaboration with teachers as a context for professional learning

This paper describes our joint activity as mathematics teacher educators and academic researchers in collaborating with both experienced and novice teachers in two contexts: an emergent community of inquiry into mathematics teaching and its development; and a research methods course, offered as part of a mathematics education Master’s program, aspiring to initiate participating teachers into research practice through inquiry. Adopting an Activity Theory (AT) perspective, we analyse our activity, identifying its nature and transformations that frame our professional learning. The results indicate that our professional learning is the outcome of a continuous process of becoming aware of our own activity and its transformation in relation to that of the teachers.     

Assessing Beginning Secondary Science Teachers' PCK: Pilot Year Results

While it is generally accepted that pedagogical content knowledge (PCK) is an essential knowledge base for science teachers, educational researchers are not clear on how it develops. Previous researchers have suggested that classroom practice may play a significant role. Therefore, it is important to look at beginning teachers' PCK and its development during the first years in the classroom. Using the pilot year data from a larger study, we developed and employed a rubric to help understand 24 beginning secondary science teachers ‘PCK, focusing on two categories: Knowledge of Student Learning and Knowledge of Instructional Strategies. The results of analysis did not show a statistically significant change between the groups, but when comparisons were made with all of the teachers, the category of Knowledge of Students Learning did significantly change. In this paper we report the results of the pilot year data, provide examples of how we employed the rubric to assess teachers’ PCK, and discuss how this study benefits understanding beginning teachers' PCK.     

Technical efficiency,managerial efficiency and objective-setting in the educational system: an international comparison

This study uses data envelopment analysis to analyse the efficiency of educational systems in 31 countries. This type of evaluation is of interest both when formulating a model for analysis and when applying such a model empirically. The efficiency of an educational system must take into account the students' economic and social background, as this is an environmental factor that decisively influences their performance. This is a highly important aspect and so we propose a specific evaluative process for it. Secondly, we evaluate the efficiency of educational systems in different countries, an analysis that has few forerunners since the majority of previous research has focused on analysing a single country. The results suggest that, in general, the most efficient management of educational systems can be found in those countries with a Communist past. They also suggest that there is a series of developed countries, which, judging by the results obtained, could increase their students' performance with even fewer resources than those currently allocated to their educational systems.     

Researching the enacted mathematics curriculum: learning from various perspectives on enactment

This issue of ZDM focuses on research related to the enacted curriculum from various perspectives within the context of the US educational system. In this editorial, we describe the broad view of curriculum enactment taken in this issue, highlighting that we mean more than just how instruction plays out within a classroom. For instance, enactment can occur at a national level as educational goals are enacted into a set of national objectives or standards. Enactment can occur as goals or standards are embedded into written curriculum materials or textbooks, both in terms of teacher guides and materials for students. Enactment can occur as teachers make decisions about how to use their written curriculum materials. Finally, enactment can occur as teachers and students engage and interact with written materials during classroom instruction. We elaborate briefly on these views and then outline the structure of this ZDM issue.