To Örebro University

Mathematical communication, encompassing writing in, about, and for mathematics, is a critical competency. Defining excellent mathematical writing standards, however, remains challenging. To address this, we conducted a systematic review of 48 scholarly works on quality in mathematical writing. Our findings reveal mathematical writing for different purposes under scrutiny, including general mathematical writing, proof writing, reflective writing, expository writing, and descriptive writing during problem solving. To assess quality, researchers explore a variety of facets, such as syntax and semantics. Progression pathways vary, with both quantitative and qualitative evaluations—analysing text structure, writing style, and the use of different semiotic elements. It seems that in mathematics education, a consensus on quality measurement remains elusive. Proof writing is a notable exception. Among reviewed articles examining proof writing, a common set of standards emerges and provides valuable guidance. We propose that mathematical writing, perhaps especially in the context of reporting solutions in problem solving, can draw from proof writing standards. ‘Good’ mathematical writing would then require students to focus on (1) defining assumptions and assigning variables; (2) producing a coherent narrative, including relevant calculations (semantic issues); (3) using correct language, representations, and mathematical symbols (syntax issues); and (4) attending to what is appropriate in the context.

In the past two decades, scholarly discourse has consistently emphasised the efficacy of collective efforts in professional development and school improvement. Collaborative endeavours among teachers, where they systematically explore their teaching practices and collaboratively address relevant improvement issues, have proven more effective than individual pursuits in educational change. However, research also underscores the inherent challenges of such collective initiatives, particularly in collegial learning. In a longitudinal study, we adopted a pragmatic perspective to delve into the collective habits of teacher teams working towards establishing collegial learning. The identified collective habits, which revolve around collective participation, the improvement process, and scientific activities, play a pivotal role in either facilitating or hindering the establishment of collegial learning to achieve professional development and school improvement. We posit that a critical exploration of collective habits is imperative for teacher teams aiming to nurture novel and impactful practices. Strategies conducive to teachers' collegial learning encompass fostering pedagogical leadership, cultivating continuity, and embracing scientific rigour in the analysis of classroom data.

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.

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. 

This study maps key features of effective Teacher Professional Development (TPD) and the framework of Communities of Inquiry (CoI), in an effort to gain an understanding of how these features contribute to teachers’ collegial learning. Activity system, as described by Engeström (1987)/(1999), is used as a theoretical lens which allows for the visualization of TPD as a complex system. The result indicates that, apart from differences in the level of detail in the description of various features, there are differences in the demands the two models place on teachers. Establishing norms that promote collegial learning, in which critical inquiry is expected, emerged as a critical issue. This highlights the importance of viewing any variant of TPD as a process, in which the functions of features shift. Awareness of this process may prove important in designing and implementing future TPD initiatives.

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.