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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.

Students are, to various degrees, expected to present a context or explain what problem they are working on when they report on their problem-solving work. This expectation rarely comes with instructions on the best way to do this, and, as with most writing in mathematics, research on the issue or curricular standards is limited. This study uses multimodal analysis to investigate students’ strategies for presenting the problem, premises, and facts. The students are part of a research project focused on developing their ability to design written accounts of problem solving by addressing the efficiency and clarity of their writing. Findings suggest students use one of two strategies: integrating the problem and its premises with the calculations or separating the information from the rest of the account. Within these strategies, students approach demands for effective and clear communication in different ways using different semiotic resources. 

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.