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Mathematical writing in school is difficult to teach. Reasons include that it is a domain in which there are rules for some parts of the writing like for example mathematical notation while others must be negotiated locally in the classroom. Writing is also seldom separated from the process of solving mathematical problems, creating a situation where students’ texts rarely are assessed based on their communicational merits alone. Writing done in connection with problem solving also often fails to distinguish between writing as a cognitive tool and writing to communicate with others. In this article we present and discuss a teaching design that addresses these problems by creating a separation between problem solving and the production of formal written mathematical communication. This separation creates an opportunity for the communicational merits of the texts that students produce to be discussed in class using a framework that suggests qualities to be considered.

Professional Learning Communities (PLC) have been used increasingly in designing and discussing teachers' professional development, but how PLC are organised and framed differ between contexts. There is a lack of meta-level studies that aim to define and compare different ways of organising PLC. In this literature review of 32 studies, Cultural-historical Activity Theory (CHAT) is used as an analytical lens to examine different models for PLC in mathematics. By examining and comparing PLC in mathematics, the review aims to expand understanding of how PLC in mathematics can be organised and framed. The result revealed three distinctive activity systems with different objects: developing norms for collaboration, developing teachers’ understanding about mathematics and its teaching, and developing teachers’ repertoire of teaching actions. The activity systems vary concerning the use of mediating artifacts and the norms that regulate each activity system, but are similar regarding participants, context, and division of labor. The review indicates that the teachers participating in PLC in mathematics change their norms of collaboration, enhance their understanding of mathematics and its teaching, and/or enhance their ability to design and carry out mathematics teaching. Our findings can assist designers, organisers, participants, and researchers in making informed decisions about PLC in mathematics.

Kollegialt lärande för skol- och undervisningsförbättring bygger på flera års praktiknära forskning och annan forskning inom skolutveckling, professionsutveckling och pedagogiskt ledarskap. Den erbjuder pedagogiska teorier, modeller och metoder för kollegialt lärande i ett helhetsperspektiv som stärker alla elever. I boken framträder kollegialt lärande både som ett arbetssätt och ett förhållningssätt, och du som läsare rustas med verktyg för att hantera det kollegiala lärandets möjligheter och utmaningar. Dessa verktyg är vetenskapligt förankrade. Kollegialt lärande för skol- och undervisningsförbättring vänder sig till lärarstudenter, lärare rektorer, kvalitetsutvecklare och skolchefer inom alla skolformer. Boken är lämplig som litteratur på rektorsprogrammet och för lärarutbildningens utbildningsvetenskapliga kärna, framför allt inom områdena utvärdering, utvecklingsarbete och pedagogiskt ledarskap.

We present three closely related projects concerned with supporting students’ mathe-matical problem solving. The projects build on the assumption that problem solving activities are beneficial to students’ learning but challenging for teachers to organise. Teachers must find ways to support students’ progress in problem solving without removing necessary challenges. The projects deal with this support in different ways, something we intend to use to illustrate the risk that mathematics education research becomes fragmented, making it more difficult for teachers to access and use research results in their professional development. We welcome participants to discuss how closely related research projects like ours can collaborate and complement each other to contribute to a knowledge base that is accessible and useful to teachers. 

Projektet KLÖS har undersökt hur lärares kollegiala lärprocesser kan stödjas i syfte att skapa hållbara strukturer för utvecklingsarbete. Målet var att skapa en Örebromodell för kollegialt lärande. En avslutande reflektion kring resultatet är att etableringen av denna modell kräver ett omfattande engagemang och tar tid att få på plats. Det är vår uppfattning att ett flertal aspekter återstår att undersöka. Bland annat är det intressant att undersöka hur arbetet med det kollegiala lärandet fortskrider på pilotskolan. Frågor som är intressanta är: Vilka faktorer har betydelse för att arbetet med kollegialt lärande ska bli permanent och fungera som ett naturligt sätt att arbeta med utveckling av praktiken? Vad blir resultatet av de utvecklingsomgångar som genomförts? Hur följs detta resultat upp och leder det till bestående gynnsamma förändringar? Frågorna handlar om hållbarhet och därmed om hur projektet går från att vara ett projekt som avslutas och glöms bort till att bli ett levande verktyg för utvecklingsarbete som kan göra en verklig skillnad i och för praktiken över tid. Eftersom mycket tid och resurser används till utvecklingsarbete i skolan är det viktigt att det arbete som görs verkligen leder till en konkret och för verksamheten gynnsam förändring. Det innebär att frågan om utvecklings- arbetets hållbarhet är en av de viktigaste frågorna. Det verktyg som utvecklats i projektet och som kommit att symbolisera det kollegiala arbetet på pilotskolan är KLÖS-hjulet. Frågan om hur KLÖS-hjulet 2.0 kan utvecklas och anpassas så att det verkligen blir ett flexibelt och användbart verktyg för att stötta det kollegiala lärandet är kanske den alla viktigaste konkreta frågan. Frågor som är besläktade med frågan om hållbarhet är de som syftar till att undersöka hur det kollegiala lärandet kan bli mer robust. Till dessa hör frågor om hur lärledarens roll kan förstärkas, hur verktyg som stöttar lärares observation och analys av den egna verksamheten kan designas, hur ansvar och engagemang på alla nivåer kan förstärkas och bli synligt samt hur arbetet med kollegialt lärande kan utvärderas. Vi har under projektets gång sett hur lärare behöver stöd i arbetet med att systematiskt identifiera behov i verksamheten för att sedan utforska möjligheter att utveckla och förändra praktiken. Medverkan från forskare som ställt frågor, problematiserat och belyst olika perspektiv har i flera fall varit avgörande för hur ett utvecklingsbehov har identifierats, avgränsats och formulerats som en undersökningsbar fråga. Det är av avgörande betydelse att utvecklingsarbetet inte står och faller med denna medverkan. Verksamheten måste själv ta fram strukturer för hur lärare och lärledare får ett tillfredsställande stöd i sitt utvecklingsarbete så att de har möjlighet att göra kollegialt lärande till en naturlig del av sitt arbete där de känner sig så bekanta med KLÖS-hjulet att de själva kan ställa de frågor som krävs. Således behöver många funktioner, både centralt och lokalt samverka för att vidareutveckla och stötta kollegialt lärande för att utveckla undervisningen i Örebro skolor. 

Papper och penna används ofta på matematiklektioner. Författaren diskuterar hur elevers matematiktexter kan och bör bli en egen väl definierad textgenre, vilket kan bidra till att förbättra elevers förmåga att uttrycka sig i skrift både för sitt eget lärandes skull och för att andra ska förstå dem bättre.

Vocational education and training (VET) is an important part of the EU aim to have 75% of its working-age population in work by 2020.  VET research which is focused on developing effective teaching is getting increased attention from the educational research community. A special area of interest for VET research is the integration of traditional theoretical subjects such as mathematics and English in vocational courses. Integration of subjects, if successfully organized, has proven to generate improved learning outcomes. What, then, are the factors that render such projects successful?

Previous research on integration projects has highlighted the importance of organizational framing such as time allotted for planning, scheduling, infrastructure and management support. Soft values such as relations, cooperation, pedagogical values, and perspectives, have however, not received as much attention in research. The aim of this study is therefor to contribute with knowledge about how teachers, who have been successful in integrating subjects, relate to each other We have chosen to examine how teachers talk about their cooperation and their understanding of the subject content, which in this case is mathematics. The study has taken place at a Swedish upper secondary school which offers only vocational education, and where they have had an active integration project, for several years. The teachers and the school management have identified the project as successful based on improved learning outcomes as well as an increased interest in pursuing more advanced mathematics courses. The Swedish National Agency for Education have also highlighted the project as an example of productive integration.

Theoretically we have chosen to focus on teachers’ room for maneuver or freedom to act professionally in relation to each other (Annerberg, 2007). To deal with relations and room for maneuver we use theories that derives from the power perspectives of Foucault (Foucault 1997, 2011). The professional relations between teachers are examined with theories of “professional identity” (Gustafson, 2010) and the room for maneuver is closely related to Parding´s “discretionary power” (2007). We consider power discourses (professional identities and relations) as mediated by language (Fairclough, 2010). 

The study has a qualitative approach and focuses on the discourses that emerge in the teachers’ talk. There are two groups of respondents; eight vocational teachers who each have been interviewed, and six math teachers who have each been interviewed but also engaged in six group interviews during one year. The interviews were semi-structured and they were transcribed and analysed using a thematic content analysis (Vaismoradi, et al, 2013). The group interviews focused on a particular theme and different data, provided by the researchers, were used as a base for the discussions. Examples of such data include interviews with students, curricular documents and statements regarding mathematics.  Discussions during group interviews were recorded and transcribed in the same manner as the individual interviews. 

The results show that the relations between vocational teachers and mathematics teachers are described differently. The feature that they have in common however is a mutual respect and a recognition of the other groups’ competence as teachers. Most of the vocational teachers talk about themselves as teachers with very good relations to students, they meet the students often and the students value their expertise. They also talk about mathematics in very positive terms and as something that is valuable and useful in their vocation. All vocational teachers do not talk about the integration project as quite as successful as the mathematics teachers do. It seems that one of the most important elements to the way the project is described as successful is the way the mathematics teachers have approached their vocational counterparts with modesty and a genuine interest in identifying the various ways in which mathematics is part of the different professions. This identification has also involved finding ways to incorporate this “workers’ mathematics” into the mathematics teaching. The school has also tried to develop similar integration projects in other subjects. These projects have however been less successful and the vocational teachers argue that identifying these subjects in their vocations is more challenging, hence the cooperation is also less fruitful. 

One important aspect of the relations between the vocational teachers and the mathematics teachers is the fact that the school offers only vocational programmes. There are no theoretical programmes. The school has an ambition to act as a model of a workplace where teachers act as managers rather than teachers and this creates an environment in which power and status does not come from having theoretical knowledge but rather in having being able to develop and sustain good relationships to the students and in being an expert in the various vocations.

Annerberg, A. (2016). Gymnasielärares skrivpraktiker: skrivande som professionell handling i en digitaliserad skola. Diss. Örebro: Örebro universitet, 2016. Örebro.

Fairclough, N. (2010). Critical discourse analysis: the critical study of language (2nd ed.). Harlow: Longman.

Foucault, M., Bjurström, C. G., & Torhell, S.-E. (2011). Vetandets arkeologi. Lund: Arkiv.

Foucault, M., & Ewald, F. (1997). ”Il faut défendre la société”: cours au Collège de France (1975-1976). Paris: Gallimard.

Frelin, A. (2010). Teachers’ relational practices and professionality. Uppsala: Institutionen för didaktik, Uppsala University.

Gustafson, N. (2010). Lärare i en ny tid: om grundskollärares förhandlingar av professionella identiteter. Diss. Umeå : Umeå universitet, 2010. Umeå.

Parding, K. (2007). Upper secondary teachers’ creation of discretionary power : the tension between profession and organisation. Luleå: Division of Industrial Processes, Department of Human Work Sciences, Luleå University of Technology.

Vaismoradi, M., Turunen, H. & Bondas, T. (2013). Content analysis and thematic analysis: Implications for conducting a qualitative descriptive study. Nurs Health Sci. 2013 Sep; 15(3):398-405. 

This study investigates young students’ writing in connection to mathematical problem solving. Students’ written communication has traditionally been used by mathematics teachers in the assessment of students’ mathematical knowledge. This study rests on the notion that this writing represents a particular activity which requires a complex set of resources. In order to help students develop their writing, teachers need to have a thorough knowledge of mathematical writing and its distinctive features. The study aims to add to the body of knowledge about writing in school mathematics by investigating young students’ mathematical writing from a communicational, rather than mathematical, perspective. A basic inventory of the communicational choices, that are identifiable across a sample of 519 mathematical texts, produced by 9–12 year old students, is created. The texts have been analysed with multimodal discourse analysis, and the findings suggest diversity in students’ use of images, words, numerals, symbols and layout to organize their texts and to represent their problem-solving process along with an answer to the problem. The inventory and the indication that students have different ideas on how, what, for whom and why they should be writing, can be used by teachers to initiate discussions of what may constitute good communication. 

This thesis is about young students’ writing in school mathematics and the ways in which this writing is designed, interpreted and understood. Students’ communication can act as a source from which teachers can make inferences regarding students’ mathematical knowledge and understanding. In mathematics education previous research indicates that teachers assume that the process of interpreting and judging students’ writing is unproblematic. The relationship between what students’ write, and what they know or understand, is theoretical as well as empirical. In an era of increased focus on assessment and measurement in education it is necessary for teachers to know more about the relationship between communication and achievement. To add to this knowledge, the thesis has adopted a broad approach, and the thesis consists of four studies. The aim of these studies is to reach a deep understanding of writing in school mathematics. Such an understanding is dependent on examining different aspects of writing. The four studies together examine how the concept of communication is described in authoritative texts, how students’ writing is viewed by teachers and how students make use of different communicational resources in their writing. The results of the four studies indicate that students’ writing is more complex than is acknowledged by teachers and authoritative texts in mathematics education. Results point to a sophistication in students’ approach to the merging of the two functions of writing, writing for oneself and writing for others. Results also suggest that students attend, to various extents, to questions regarding how, what and for whom they are writing in school mathematics. The relationship between writing and achievement is dependent on students’ ability to have their writing reflect their knowledge and on teachers’ thorough knowledge of the different features of writing and their awareness of its complexity. From a communicational perspective the ability to communicate [in writing] in mathematics can and should be distinguished from other mathematical abilities. By acknowledging that mathematical communication integrates mathematical language and natural language, teachers have an opportunity to turn writing in mathematics into an object of learning. This offers teachers the potential to add to their assessment literacy and offers students the potential to develop their communicational ability in order to write in a way that better reflects their mathematical knowledge.

The study aims to examine elementary school mathematics teachers' ways of discussing students' mathematical texts. Nineteen teachers were interviewed in groups and asked to discuss 15 texts. The object of study is the teachers' collective discussions, analyzed using a discourse analytic approach. Findings indicate that two different modes are visible in the discussions: a pedagogical mode, connected to the teachers' position as pedagogues and where identification of students' strategies is foregrounded, and an assessment mode, connected to the teachers' position as examiners, in which a deficiency perspective is adopted that views particular features as 'missing' from the texts.

The aim of this study is to increase general understanding of the factors influencing teachers’ choices of assessment tasks in distance courses in university mathematics and mathematics education. Six interviews were conducted in which teachers elaborated on their reasoning concerning choices of assessment tasks. The results show that the forms of assessment tasks used in distance education, along with the reasoning preceding the choice of these tasks, differ little from those used in campus based education. One possible explanation for this can be that nearly all assessment tasks described in the interviews were conducted in face-to-face situations. The technical aspects of modern distance education seem to have a minor influence on the choice of form ofassessment.