Mathematics teaching

The group collaborates with a number of the department’s other research environments, such as STOLP and the group for the history and sociology of education. The department offers several cross-boundary seminars.

The group's intention is to expand its activities with new issues, materials and methods that complement current research. This means, among other things, a continued exchange with other universities both nationally and internationally in the form of visiting researchers and guest lecturers.

Several members of the group are also involved in various development projects such as the development of educational materials and improving teacher competencies.

The group is part of the Teaching and learning of algebra network which was started in spring 2016 on the initiative of researchers in algebra teaching in both Sweden and Finland. The aim is to share ideas, exchange experiences and cooperate on various research projects. The network's members come from several universities in Sweden and Finland, with the majority from Uppsala University and Åbo Akademi University in Vaasa.

Held on certain Tuesdays between 10 am and midday.
Mini conference in teaching and learning of algebra
November 7-8 2016, Blåsenhus, Uppsala University
The mini conference is organised by the Teaching and learning of algebra network

More information and programme

Införande av programmering i skolans matematik - när algebraiskt tänkande interagerar med datalogiskt tänkande

Under de senaste fem åren har flera länder infört programmering och datalogiskt tänkande i skolundervisningen. I debatten framhålls att det inte längre bara är datavetare och ingenjörer som behöver kunna programmera utan programmering ses numera som en nödvändig kompetens för alla medborgare. Utöver denna grundläggande kunskap brukar programmering även lyftas fram som ett pedagogiskt verktyg för utveckling av elevers datalogiska tänkande. Begreppet datalogiskt tänkande kan förklaras som en problemlösningsprocess för att beskriva, analysera och lösa problem på ett sätt så att datorer kan hjälpa till, eller något förenklat, ett sätt att tänka som påminner om en dator. Exempelvis kan det handla om att hitta återkommande mönster, organisera data samt att generalisera, abstrahera och skapa algoritmer för att lösa problem. Termen datalogiskt tänkande introducerades redan under 1980-talet av Seymour Papert som utvecklade ”Logo”, det första programmeringsspråket anpassat för barn. Paperts arbete fick inget större genomslag, vilket förmodligen berodde på att digital teknik inte var lika vanligt förekommande som idag på samhällets alla nivåer. I dagens samhällsdebatt kan man läsa hur forskare, ingenjörer och datavetare anser datalogiskt tänkande vara en lika grundläggande kompetens som att kunna läsa, skriva och räkna.

Det övergripande syftet med det här projektet är att bidra till den internationella forskningen kring den pågående implementeringen av programmering och datalogiskt tänkande i grundskolans matematik genom att undersöka det svenska fallet. Mera specifikt vill vi ta reda på hur datalogiskt tänkande relaterar till algebraiskt tänkande samt hur denna kombination kan skapa nya möjligheter för grundskoleelever att lära sig matematik. Implementeringen av programmering i skolans läroplaner har gjorts på olika sätt i olika länder. I England har programmering blivit en del av ett helt nytt ämne, ”Computing”, medan Finland och Sverige har fört in programmering både som ett ämnesövergripande inslag och som en del av redan befintliga ämnen, med tonvikt på matematik. Till skillnad från andra länder har Sverige inkluderat programmering tillsammans med algebra i kursplanen i matematik, vilket gör Sverige unikt i ett internationellt perspektiv. Hittills har datalogiskt tänkande respektive algebraiskt tänkande utgjorts av två separata forskningsfält. Med det svenska fallet erbjuds en möjlighet att studera vad som uppstår då algebra och programmering undervisas tillsammans.

Genom att integrera programmering med algebra öppnas nya möjligheter för skolans algebraundervisning men det medför också utmaningar och potentiella fallgropar. Ett problem är att de syntaktiska reglerna i algebra och programmering inte alltid är desamma. Exempelvis har likhetstecknet, variabler och funktioner olika betydelser i algebra jämfört med programmering. Vidare har algebra under en längre tid varit ett område inom den svenska skolmatematiken som elever har haft stora problem med. I internationella mätningar som TIMSS och PISA har svenska elevers resultat legat under det internationella genomsnittet ända sedan 1960-talet. Flera nyligen genomförda svenska studier visar att nybörjarstudenter har stora svårigheter med universitetsmatematiken just på̊ grund av bristande kunskaper i algebra.

Baserat på Chevallards teoretiska ramverk om hur kunskap transponeras planeras två delstudier i projektet. I en första studie analyserar vi innehållet av programmering i aktuella svenska styrdokument, statligt producerade läromaterial (lärarlyftet) och läroböcker inklusive lärarhandledningar för årskurs 1-9. Speciellt fokuserar vi på likheter och skillnader i syntaxen hos algebra och programmering samt eventuella progressionslinjer inom algebraiskt respektive datalogiskt tänkande. I en andra studie intervjuar vi verksamma lärare kring deras användning av de olika läromaterialen i undervisningen samt vilka möjligheter, utmaningar och eventuella problem som de identifierar i relation till algebra. Data kommer att samlas in genom ljudinspelade fokusgruppsintervjuer samt individuella intervjuer. Förutom att projektet bidrar till en bättre förståelse för relationen mellan algebraiskt och datalogiskt tänkande kommer det dessutom att bidra till den framtida utvecklingen av datalogiskt tänkande i skolmatematikens samtliga stadier.

TOWARDS RESEARCH-BASED TEACHING IN ALGEBRA – DIACHRONIC AND SYNCHRONIC ANALYSES OF POLICY DOCUMENTS, TEACHING MATERIALS AND TEACHER INTERACTION WITH THEM.

A good knowledge of algebra is important to study mathematics after compulsory school level. Previously it was common for students to start learning algebra at the age of 12-13 because it was felt that students were insufficiently mature to handle algebraic generalisations at an earlier age. However, mathematics teaching research has shown that children can advantageously develop algebraic thinking from an early age, and many countries, including Sweden, have reformed their mathematics curriculum so that algebra is integrated into maths teaching at an early stage. However, research shows that it is difficult to implement new ways of teaching without taking into account the prevailing educational culture. For example, the international comparison surveys TIMSS and PISA show no improvement among Swedish students' algebra skills despite the introduction of new curricula.

Swedish students' algebra skills have been below average in international surveys since the 1960s, and since the early 2000s they have deteriorated significantly. Several recent Swedish studies show that new students have great difficulty with university mathematics precisely because of their lack of knowledge of algebra. The project's overall aim is to contribute to the international research debate around the issue of implementing algebra in school mathematics by examining the Swedish case from different perspectives. More specifically, we are trying to find possible reasons for the failure to raise the quality of Swedish algebra teaching by investigating how algebra was traditionally treated in the Swedish curricula and by examining textbooks for Years 1 to 9 (a diachronic perspective).

We are also studying the current situation (a synchronous perspective) by analysing how algebra is treated in current policy documents, textbooks and teachers' guides. Special focus is placed on objectives, tasks, methods and progression routes. Through interviews with focus groups of teachers, we will also investigate teachers' interpretations of the intentions of the curriculum and areas in the teaching materials that relate to the development of algebraic thinking. Here we want to get an overview of different ways to understand and use the textbook materials in teaching. Teacher groups will be selected from various school levels and schools and – to get as much variety as possible in the interview material – schools will be selected according to the students' socio-economic background and academic success.

The analysis is based on a traditional curriculum theory perspective where the school system is seen as made up of different arenas with a number of different traditions. Policy documents and textbooks are considered as formulation arenas and teacher practice as realisation arenas because teachers must interpret and implement the intentions of policy documents in their teaching. Teaching materials are an important resource for both teachers and students, and we believe that they also maintain their own traditions regardless of policy document intentions. With the help of both diachronic and synchronous studies, we intend to identify and describe these traditions and, if possible, to find any aspects that may limit optimal teaching which can develop students' algebraic thinking from the beginning.

There are also invisible traditions in teacher practice which can hinder new approaches. Through our study, we also have the opportunity to discover these. We believe that an in-depth investigation of Swedish algebra teaching is extremely important from both a national and international perspective. Swedish students' poor performance in algebra has long been documented and the marked deterioration of Swedish results in the international surveys in the first decades of the twenty-first century is unique.

By studying the traditions in the various arenas from a diachronic and synchronous perspective, we can detect contradictory perceptions about the intended progression in school algebra. Furthermore, we should be able to determine what is not functioning optimally in today's algebra teaching in Sweden, and even suggest possibilities for concrete change. Internationally there is no lack of research on how to teach algebra and achieve good results. The problem is more about what can be implemented in schools on a larger scale so that the intentions are not misunderstood or met with resistance because of the prevailing educational culture. The results of our project will be important for curriculum developers, textbook authors and teacher trainers.

The development of School mathematics and reforms of the Swedish school system in the 20th century. A comparative and historical study of changes of contents, methods and institutional conditions

The project aims to investigate how the content and methods of school mathematics changed in compulsory schools during the period 1910-2010, and to identify mechanisms that governed the choice of content and methods. The project examines where changes in school mathematics are initiated in the school system and how proposed changes have had an impact. The focus is on the production of educational texts. Both the content of the texts and the social conditions for the production of educational texts are being studied.

The primary source materials are policy documents, textbooks, teachers' journals, method books and exams. The analysis of the texts is based on curriculum theory and the concepts of objective, content and method. A sociological study of the actors who produced these educational texts is also being carried out. The sociological analysis employs a prosopographic approach and is based on Bourdieu's theory of field and capital. To determine what is typical of the Swedish reform process, comparisons are being made between Sweden and Germany during the period 1910-2010.

School mathematics and its language

The overall aim of the project was to study and describe the subject-specific linguistic register within school mathematics used in student assignments such as those in TIMSS (Trends in International Mathematics and Science Study). The focus was on the topics of algebra, statistics and probability, geometry and arithmetic.

An important issue within the project was how different linguistic dimensions act as barriers or have a supporting function for different groups of students. In three sub-studies, various aspects of the academic language in school mathematics was analysed, such as grammatical functions, visualisations and mathematical symbols. The empirical material comprised information from the international study TIMSS. The study was based on systemic functional linguistics and built primarily on quantitative analyses.

The project was a PhD project and was part of the National Graduate School of Subject Language in mathematics and science practices. Professor Caroline Liberg was the scientific director of the graduate school.