In mixed-ability classrooms that are common in Swedish upper-secondary school, as well as in other Nordic countries, particularly gifted learners (Skolverket, 2015) are taught alongside all other students (Mellroth et al., 2021) leaving individual teachers with limited time to create enrichment. In what way can enrichment offered online, parallel to regular classes, be used to support the learning development of these learners? In a small-scale project, upper-secondary school students were offered an asynchronous online enrichment program. The program was led by a specialist lecturer at the school (second author) who started by a short meeting individually with each student (self-nominated or identified by their regular teacher). Then, a task aiming to challenge the specific student was uploaded to the student’s individual OneNote. For some tasks, students could choose to reveal guiding questions further, the chat function could be used to pose questions. Once completed, the student uploaded the solution and notified the lecturer who then uploaded a new task and afterwards provided feedback on the solution. The students were allowed to work with the tasks during regular mathematics classes but decided themselves on the pace and timing. The flexibility of the program offered the students an opportunity to adjust to their own needs and desire (Mellroth & Szabo, 2022). Some students worked on a regular basis with the tasks; others only occasionally. Thus, the daily challenge (Rogers, 2007) was offered continuously and consistently and the autonomy of the students (e.g., Leikin & Sriraman, 2017; Szabo, 2017) was accounted for. The students could either write their solutions directly in OneNote, or upload pictures of handwritten solutions. For the lecturer it gave the opportunity to give detailed and personalized feedback. Consistent with research stating that these students gain specifically from straightforward feedback (Leikin & Sriraman, 2017; Szabo, 2017). The online environment also enabled to effectively offer instructional differentiation as suggested by Szabo (2017) as the lecturer easily could adapt comments or offer alternative solutions despite the students going through the program at a different pace. In-depth interviews with the participating students are planned, to investigate their perceptions of stimuli and support through the online enrichment program. Leikin, R., & Sriraman, B. (Eds.) (2017). Creativity and giftedness – Interdisciplinary perspectives from mathematics and beyond. SpringerMellroth, E., Bergwall, A., & Nilsson, P. (2021). Task design for differentiated instruction in mixed-ability mathematics classrooms: Manifestations of contradictions in a professional learning community. Mathematics Teacher Education and Development, 23(3), 78–96. Mellroth, E. & Szabo. A. (2022). Talented upper secondary student’s perception of online mathematical challenges. In S. A. Chamberlin (Ed.) On the Road to Mathematical Expertise and Innovation. Proceedings MCG 12. (pp. 311 – 313). VTM-Verlag.Rogers K. B. (2007). Lessons learned about education the gifted and talented: A synthesis of the research on educational practice. Gifted Child Quarterly, 51, 382-396.Skolverket (2015). Särskilt begåvade elever – stödmaterial.Szabo, A. (2017). Matematikundervisning för begåvade elever – en forskningsöversikt. Nordic Studies in Mathematics Education, 22(1), 21–44. 

KLiMaT-projektet är en del av Örebro kommuns skolutvecklingssatsning Topp 25 2025 och har haft som syfte att producera kunskap om hur effektivt och ändamålsenligt kollegialt lärande kan organiseras och genomföras i matematikämnet. Det specifika ändamålet har varit att lärare ska kunna möta elevers olika behov. Åtta matematiklärare på Tullängsgymnasiets teknikprogram har utvecklat en problembank med utmanande introduktions- och fördjupningsuppgifter i matematik. Två forskare från Örebro universitet har varit knutna till projektet.

Projektet har organiserats i samråd mellan lärarna, forskarna och skolledningen och har under projekttiden anpassats efter de lokala förutsättningarna. Viktiga utgångspunkter har varit lärdomar från KLÖS-projektet och från Matematiklyftet. Allt arbete har dokumenterats och kompletterats med intervjuer med deltagande lärare. Nedan sammanfattas de viktigaste lärdomarna.

Att ge lärare möjlighet att tillsammans utveckla uppgifter med det uttalade syftet att de ska utmana alla elever, har potential att utveckla lärares beredskap att möta elevernas olika behov. Men för att det kollegiala lärandet ska bli effektivt, ändamålsenligt och hållbart över tid, så är ett antal förutsättningar avgörande:

• Dedikerad tid: Lärarna behöver stöd i form av tid. Den ska finnas på schemat och aldrig konkurrera med andra arbetsuppgifter.

• Relevans: Lärarna behöver få fokusera på sådant som är relevant i närtid för deras egen undervisningspraktik. Detta kan möjliggöras genom att de får arbeta tillsammans med kollegor med liknande undervisningsuppgifter och genom att de själva får välja inriktning på utvecklingsarbetet.

• Ämneslag: Det är en stor fördel om lärarna är organiserade i ämneslag. Då har de ämnesdidaktiska samtalen en reell möjlighet att leva vidare även i dagliga informella möten lärare emellan.

• Deltagande: Alla lärare på skolan bör alltid vara delaktiga i kollegialt lärande.

• Långsiktighet: Innehåll, mål och genomförande i/för/av kollegialt lärande bör diskuteras/beslutas/organiseras med god framförhållning och åtminstone i ett läsårsperspektiv.

• Ledare: För att arbetet ska bli fokuserat och systematiskt behöver någon ha en uttalad ledarroll. Det är en fördel om den personen finns utanför lärargruppen.

Dessa förutsättningar är troligen viktiga oavsett undervisningsämne och ändamål. Det de har gemensamt är att de inte kan uppfyllas av lärarna själva. Det är rektor/skolledning som aktivt och kontinuerligt måste se till att de realiseras. Med utgångspunkt från lärarnas egna tankar ger vi förslag på en modell för genomförande av kollegialt lärande med potential att uppfylla dessa förutsättningar.

När det gäller det specifika ändamålet att möta alla elevers olika behov i matematikundervisningen så visar det här projektet att arbetet stödjs av att lärarna gemensamt utarbetar verktyg, uppgiftsanalysverktyg och observationsprotokoll i KLiMaT, som

• sätter fokus på, karaktäriserar och kan användas för att analysera centrala egenskaper hos de aktiviteter som ska utvecklas,

• synliggör dilemman och motsättningar mellan de olika mål man vill uppnå.

I KLiMaT har det kollegiala lärandet kring matematikundervisning resulterat i en problembank med 13 utmanande uppgifter, kopplade till kurserna Matematik 1c, 2c, 3c, 4 och 5, som på sikt kommer att bli tillgänglig för andra lärare via en webplattform.

Developing tasks for use in mixed-ability classrooms presents teachers with several dilemmas. By making one such dilemma an explicit object of inquiry, this study aims to capture characteristics for challenging tasks suitable for introduction or enrichment. It is based on eight teachers’ collaborative and retrospective analysis of challenging tasks developed in a combined research and school development project. Among the results are the observation that introductory tasks should have an easy entry level and not require pre-knowledge of the upcoming concept, while an enrichment task should require relatively deep conceptual pre-knowledge. It is suggested that attention to seemingly contradictory features of introductory and enrichment tasks can fuel collaborative learning processes so that they include several important aspects of tasks aimed at challenging all students. Teachers’ verbalization of task characteristics is one outcome of such a process.

Detta kapitel kommer mest handla om de vanligaste av de ovanliga, det vill säga de 5-10 procent av eleverna som är särskilt begåvade och befinner sig i det vanliga klassrummet. Det kan vara svårt att som lärare planera undervisningen så att även dessa elever ges möjlighet att utvecklas i sin kunskap. I kapitlet kommer jag att presentera differentierad undervisning som en lämplig strategi att använda för att inkludera elever med särskild begåvning. Jag kommer att omsätta teori i praktik och ge exempel från olika ämnen och årskurser på vad det kan innebära att differentiera undervisningens innehåll, process, resultat och lärmiljö. Kollegialt samarbete och lärande är centralt för möjligheterna att implementera och utveckla en differentierad undervisning där alla elever inkluderas.

The aim of this study is to investigate task design for differentiated instruction in mathematics inprofessional learning communities. Based on the cultural-historical activity theory, we conceptualizea professional learning community as an activity system and use the analytical construct ofcontradictions to give an account of structures that bring forward the teachers’ work. Eight Swedishupper secondary teachers, engaged in designing tasks for differentiated instruction in mixed-abilitymathematics classrooms, are studied. The analysis outlines three contradictions, manifested as threedilemmas, and shows how the teachers, by noticing a dilemma and making it an explicit object ofinquiry, came to address a diversity of issues related to differentiated instruction in mathematics. Forexample, the teachers addressed students’ different learning needs, problem-solving activities for amixed-ability classroom, and design of tasks that are challenging for all students. With input fromour findings on the three dilemmas, we then discuss the design of a task analysis guide as a meansfor facilitating the development of a professional learning community that is inquiry-oriented with astrong content focus on designing tasks for differentiated instruction in mixed-ability mathematicsclassrooms.

Challenging mathematical tasks are important for all students’ learning processes, and the demanding job of finding and developing such tasks is preferably done through teacher collaboration. Using cultural-historical activity theory, we analyze three upper secondary teachers’ collaborative learning process in choosing and rejecting tasks for a collection of challenging tasks they have agreed to develop. They collaboratively chose one task to fulfil the criteria of challenging tasks; one task was rejected as it did not fulfil the criteria, and another was temporarily rejected as not all the teachers knew how to solve it themselves. The analysis revealed a positive and open atmosphere among the teachers, with content-focused discussion highlighting mathematical content and teaching related to the tasks discussed. While their discussion showed several signs of collaborative learning, whether their work will result in changes to teaching practice remains to be explored.

Aiming to bring teachers' perspectives to research, teachers' (N = 12) discussions are explored in the context of a professional development program on teaching highly able pupils (HAPs) mathematics. The findings show that the teachers perceive they have the competence to recognize HAPs, for example through continuous assessment. However, they express that collaboration with colleagues is necessary and that they would like their principals' acknowledgement for their competence. They connect and verbalize their practical expertise with theories of teaching HAPs and demonstrate several criteria for teaching that successfully meet pupils' learning needs in heterogeneous classrooms. Thus, they feel confident in how to orchestrate teaching that is inclusive of HAPs in heterogeneous mathematics classrooms.

Mathematics meets industry day (MiMMR©Day) offers an orga-nized setup where companies pose challenges to applied mathemati-cians. The tasks are supposed to be tackled within one day. We brieflypresent the concept of the MiMMR©day and list the three mathematicalchallenges that were proposed during the 4th MiMMR©day organizedin Karlstad, Sweden, on December 15, 2020. This note should be seenas an invitation addressed to the industrial and applied mathematicscommunity to get actively involved in events of this type.

Inclusion of gifted education in teacher education is not common in Sweden or in many other European countries. As a result, many teachers lack knowledge of teaching highly able students. Most teachers do want to learn and develop this area of their teaching but, when teaching schedules are full, little time is available for ongoing professional development. A process in which professional development is intertwined with teachers’ daily work is needed, to ensure sustainable changes of practice. Teachers’ collaborative learning is an activity in which teachers collaboratively and systematically analyze their teaching, with the aim of developing their practice. This paper is based on an ongoing study, which explores how a group of mathematics teachers use principles of such collaborative learning to develop their own knowledge of educating and supporting students highly able in mathematics. This study indicates that collaborative learning provides a promising process for sustainable changes in teaching practice that can in turn provide highly able students with learning opportunities.

Design research och Cultural-Historical Activity Theory kommer i denna studie användas för att studera kollegialt lärande i matematik. Studien utförs med lärare som deltar i ett skolutvecklingsprojekt med ett delsyfte att utveckla undervisningen för elever med särskild begåvning. Forskningen syftar till att bidra med kunskap om kollegialt lärande som en hållbar utvecklingsprocess i en kommun.