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1.	Holmström, Simon, et al. (författare) Gymnasiets laborationsundervisning i fysik : mellan tradition och ändrade styrdokument 2018 Ingår i: LUMAT. - 2323-7104 .- 2323-7112. ; 6:1, s. 1-19 Tidskriftsartikel (refereegranskat)abstract Laborationer har lång tradition i fysikundervisningen och det finns många klassiska skolexperiment. Samtidigt påverkas laborationsundervisningen av reformer och teknikutveckling. I denna studie fick lärare på tre gymnasieskolor diskutera sin laborationsundervisning. Analysen baseras på händelselogik, där handling ses som intentionell och styrs av determinanterna: målsättning, förmåga, plikt och möjligheter. Studien ger insikt i hur olika faktorer påverkar lärares laborationsundervisning, och hur klassiska laborationer i fysikundervisningen både kan ha en given plats och utmanas av nya förutsättningar. Resultaten antyder att praxis och tradition är starkare påverkansfaktorer än styrdokument i lärares utformning av laborationsundervisningen, vilket delvis kan relateras till en avsaknad av fortbildning.
2.	Holmström, Simon, et al. (författare) Gymnasiets laborationsundervisning i fysik : vad påverkar lärares val av laborationer? 2019 Ingår i: LUMAT. - 2323-7104 .- 2323-7112. ; 7:1, s. 27-58 Tidskriftsartikel (refereegranskat)abstract Vilka faktorer påverkar svenska gymnasielärares laborationsundervisning i fysik? Frågan aktualiseras av den svenska läroplansrevisionen från 2011. I denna studie fick 17 lärare på fyra gymnasieskolor diskutera sin laborationsundervisning i fokusgruppsintervjuer. Baserat på en analys av dessa intervjuer genomfördes en kompletterande enkätundersökning med 66 lärare. Händelselogik användes som analysverktyg för att förstå hur lärarnas laborationsundervisning påverkas av olika faktorer. Resultaten från fokusgrupperna tyder på att lärare uppskattar laborationer som 1) bygger på enkel utrustning, 2) ger ett bra resultat avseende värdet på konstanter, samt 3) laborationer som eleverna tycker om. I enkätundersökningen framstod styrdokumenten som en starkare påverkansfaktor än i fokusgrupperna – men resultaten från båda delarna av undersökningen tyder på att styrdokumenten inte är den viktigaste faktorn i lärares val och upplägg av laborationer.
3.	Holmström, Simon, et al. (författare) Gymnasiets laborationsundervisning i fysik – Vad påverkar lärares val av laborationer? 2019 Ingår i: LUMAT: International Journal on Math, Science and Technology Education. - 2323-7112. ; 7:1, s. 27-58 Tidskriftsartikel (refereegranskat)abstract What factors influence Swedish upper secondary teachers' laboratory teaching in physics? This is an issue raised by the curriculum reform of 2011 in Sweden. In this study, 17 teachers at four different upper secondary schools discussed their laboratory teaching in focus group interviews. Based on an analysis of these interviews, a supplementary survey of 66 teachers was conducted. Logic of events was used as an analytical tool to understand how different factors influence teachers' teaching. The results from the focus groups indicate that teachers appreciate laboratory work that 1) are based on simple equipment, 2) provide good values of constants, 3) laboratory exercises that the students like. In the survey, the syllabus emerged as a stronger factor of influence than in the focus groups – but, the results from both parts indicate that other factors than the syllabus play a larger role for teachers' choice and layout of laboratory work.
4.	Andersson, Charlotta, et al. (författare) En modell som stöd för att utforska ekvationer : [A model to support exploring equations] 2022 Ingår i: LUMAT. - 2323-7112. ; 10:1, s. 182-209 Tidskriftsartikel (refereegranskat)abstract Syftet med artikeln är att lyfta fram om, och i sådant fall på vilka sätt, en specifik strukturell modell kan utgöra stöd när elever utforskar matematiska strukturer i ekvationer. Artikeln bygger på en empirisk forskningsstudie där elever utforskade matematiska strukturer med stöd av modellen, vilken är avsedd att visualisera strukturer. Lärare och forskare arbetade i en kollaborativ och intervenerande studie i iterativa processer. Sammantaget 149 elever från grundskolans årskurser 3, 8 och 9 deltog i filmade forskningslektioner utifrån forskningsansatsen learning study. Lektionerna designades med inspiration från ramverket lärandeverksamhet och eleverna utmanades i ett teoretiskt arbete. Analysen utfördes utifrån tematisk ansats och två kvalitativt skilda kärnteman identifierades: Formulär respektive Lärandemodell. I analysen framträdde att undervisningen behöver vara tillräckligt utmanande för att eleverna ska finna modellen meningsfull. Undervisningen behöver möjliggöra för eleverna att urskilja relationer mellan alla tal i en ekvation, där relationerna kan beskrivas som en del-helhetsstruktur.
5.	Björklund, Camilla, 1977, et al. (författare) Preschoolers’ ways of experiencing numbers 2022 Ingår i: LUMAT. - : University of Helsinki. - 2323-7112. ; 10:2, s. 84-110 Tidskriftsartikel (refereegranskat)abstract In this paper we direct attention to 5–6-year-olds’ learning of arithmetic skills through a thorough analysis of changes in the children’s ways of encountering and experiencing numbers. The foundation for our approach is phenomenographic, in that our object of analysis is differences in children’s ways of completing an arithmetic task, which are considered to be expressions of their ways of experiencing numbers and what is possible to do with numbers. A qualitative analysis of 103 children’s ways of encountering the task gives an outcome space of varying ways of experiencing numbers. This is further analyzed through the lens of variation theory of learning, explaining why differences occur and how observed changes over a prolonged period of time can shed light on how children learn the meaning of numbers, allowing them to solve arithmetic problems. The results show how observed changes are liberating new and powerful problem-solving strategies. Emanating from empirical research, the results of our study contribute to the theoretical understanding of young children’s learning of arithmetic skills, taking the starting point in the child’s lived experiences rather than cognitive processes. This approach to interpreting learning, we suggest, has pedagogical implications concerning what is fundamental to teach children for their further development in mathematics.
6.	Borke, Mikael, 1965 (författare) Student teachers’ knowledge of students’ difficulties with the concept of function 2021 Ingår i: LUMAT. - 2323-7112. ; 9:1, s. 670-695 Tidskriftsartikel (refereegranskat)abstract An important part of the mathematics syllabuses at the secondary school level in most countries is the concept of function. However, secondary school students often experience difficulties with this concept. These difficulties are well-known in the research literature. The study applies the mathematical knowledge for teaching (MKT) framework, including the category knowledge of content and students (KCS). Teachers’ ability to anticipate students’ difficulties is one aspect of KCS. The aim of this study is to investigate secondary mathematics student teachers’ KCS regarding the concept of function. Ten mathematics student teachers participating in a Supplementary Teacher Education Program answered a questionnaire about fictive secondary school students’ various difficulties with the concept of function. Followup interviews were conducted with four of the respondents. Compared to the findings of previous research on students’ difficulties with the concept of function, the respondents in the study sometimes provide reasonable suggestions about the sources of students’ difficulties. Some of the respondents demonstrate an aspect of KCS when they suggest that students can reason that a function must be defined by one algebraic expression only, and that students only know about continuous functions. However, no respondent suggests that one source of students’ difficulties with a constant function with an implicit domain is the missing domain. In addition, some respondents take for granted that students can interpret the algebraic representation of a piecewise-defined function and translate it into a graph. © 2021 University of Helsinki. All rights reserved.
7.	Dessen Jankell, Lotta, 1970- (författare) Elevers uppfattningar av systemmodellering i arbete med hållbarhetsfrågor 2023 Ingår i: LUMAT. - 2323-7112. ; 11:1, s. 25-51 Tidskriftsartikel (refereegranskat)abstract The article explores students’ experiences while using system models to analyze sustainability issues in geography teaching. Students at upper secondary school level in Sweden participated in a long-term teaching design study where system models were introduced and used to analyze complex issues. After the teaching segment, the students were interviewed about their experiences. The data, consisting of 32 interviews and 138 written reflections, was analyzed using phenomenography. The results show three qualitatively different ways of experiencing what it means to work with system models to deal with sustainability issues. The students perceived these as: a) a tool for modelling complex content, b) a representation of complex issues, and c) a way to explore reality in terms of systems. The results were quantified to compare if students’ experiences differed in relation to the teaching that they participated in. The conclusions show that during the first time that the students used the models they experienced the system models as a tool and there was a gap between the models and the real issues. Only few aspects of systems thinking developed. The second time, when the students used the models during a longer period of time they experienced the model work as a way to explore real problems as systems and developed more aspects of systems thinking. The article contributes with knowledge about what students need to discern to be able to develop systems thinking in geography and what learning teaching need to enable.
8.	Dyrvold, Anneli, 1970-, et al. (författare) Computer-based assessment in mathematics : Issues about validity 2023 Ingår i: LUMAT. - : University of Helsinki; LUMA Centre Finland. - 2323-7112. ; 11:3, s. 49-76 Tidskriftsartikel (refereegranskat)abstract Computer-based assessments is becoming more and more common in mathematics education, and because the digital media entails other demands than paper-based tests, potential threats against validity must be considered. In this study we investigate how preparatory instructions and digital familiarity, may be of importance for test validity. 77 lower secondary students participated in the study and were divided into two groups that received different instructions about five different types of dynamic and/or interactive functions in digital mathematics items. One group received a verbal and visual instruction, whereas the other group also got the opportunity to try using the functions themselves. The students were monitored using eye-tracking equipment during their work with mathematics items with the five types of functions. The result revealed differences in how the students undertook the dynamic functions due to the students’ preparatory instructions. One conclusion is that students need to be very familiar with dynamic and interactive functions in tests, if validity is to be ensured. The validity also depends on the type of dynamic function used.
9.	Dyrvold, Anneli, 1970-, et al. (författare) Static, dynamic and interactive elements in digital teaching materials in mathematics : how do they foster interaction, exploration and persistence? 2023 Ingår i: LUMAT. - : University of Helsinki. - 2323-7112. ; 11:3, s. 103-131 Tidskriftsartikel (refereegranskat)abstract Contemporary comprehensive mathematics teaching material covering whole courses has developed substantially from the early versions that roughly were ‘books as pdf’ with some complementary online material. In teaching materials that are offered in online web portals (digital teaching platforms) a variety of dynamic and interactive elements can be utilised, offering new ways to engage with mathematics. Despite this recent development, the variety of affordances of the digital environment are utilised to a surprisingly small extent. The pros and cons with digital teaching materials in mathematics are debated, and publishers advertise with arguments about algorithms that lay out an ideal learning path and about joyful content. Critical for students’ learning while working with teaching materials is however that they find it meaningful to use the materials, a persistence in the interaction with the materials, and furthermore that the willingness to explore mathematics remains. In this study students’ interaction with digital teaching material with various kinds of dynamic and interactive elements supplementing the static parts in the presentation of new content is explored. Differences in students’ attention to mathematical facts, essential in the problem solving, is captured using an eye-tracker. Analyses of differences in attentive behaviour depending on the kind of digital element that are used for presentation reveal that the type of digital element that students attend the least to is static elements. Differences in what is offered to and what is demanded from a reader when mathematical facts are presented using various digital elements is discussed and potential implications from the results are suggested.
10.	Ebbelind, Andreas, Dr, 1975-, et al. (författare) Examining interpersonal aspects of a mathematics teacher education lecture 2024 Ingår i: LUMAT. - : University of Helsinki. - 2323-7112. ; 12:1, s. 113-125 Tidskriftsartikel (refereegranskat)abstract In this paper we present findings from an initial phase of a more extensive study focussed on ways in which prospective mathematics teachers negotiate meaning from mathematics teacher education situations. The focus of this paper is on the language of one mathematics teacher educator and specifically the interpersonal aspects from one mathematics teacher education lecture in Sweden for prospective upper-primary school teachers. We draw on the enactivist view of cognition as a theoretical basis for a methodology we develop that utilises Systemic Functional Linguistics as an analytical tool for studying language-in-use. We exemplify our interpretations through a series of extracts from the mathematics education lecture. This initial phase of our study has exposed several important questions about how participating in an initial teacher education situation may contribute to the development of teacher identities, questions we raise throughout our analyses to provoke further investigation as part of our future research.
11.	Ebbelind, Andreas, Dr, 1975-, et al. (författare) How is students’ participation in a problem-solving project reflected in their drawings of a mathematics classroom? 2024 Ingår i: LUMAT. - : University of Helsinki. - 2323-7112. Tidskriftsartikel (refereegranskat)abstract The mathematics teaching young students encounter not only affects the mathematics they are given the opportunity to learn but also their view of what mathematics is, how mathematics is taught and how they view their ability to learn mathematics. In this paper, an Educational Design Research study on problem solving and problem posing with Swedish six-year-olds will serve as an example. We elaborate on how students’ participation in education may affect their views of what it means to be taught and to learn mathematics. We do so by comparing drawings of mathematics classrooms made by students from eight classes, of which four attended the project. The results indicate a reform-oriented and more diverse view of content and form reflected in the drawings by the students participating in the intervention.
12.	Ebbelind, Andreas, Dr, 1975-, et al. (författare) The lack of discursive opportunities when becoming a mathematics teacher 2024 Ingår i: LUMAT. - : University of Helsinki. - 2323-7112. Tidskriftsartikel (refereegranskat)abstract In this paper, we attempt to open a discussion about mathematics teacher education settings constraining prospective teachers’ discursive opportunities, a phenomenon noted in our respective doctoral dissertations. These two doctoral dissertations represent two different types of prospective teachers from three countries. Prospective primary school teachers who had positive experiences and interest in mathematics on the one hand, and prospective teachers who struggled with mathematics and were insecure about their future mathematics teaching on the other. In the discussion, we speculate about the implications of discursive opportunities for prospective teachers' process of becoming a mathematics teacher and highlight the need to place effort to offer sufficient discursive opportunities to prospective teachers.
13.	Ebbelind, Andreas, Dr, 1975-, et al. (författare) This is not how it should end : The role of mathematics teacher education in preparing teachers for sustainable careers 2024 Ingår i: LUMAT. - : University of Helsinki. - 2323-7112. ; 12:04 Tidskriftsartikel (refereegranskat)abstract In this paper, we reflect on the role of teacher education in preparing prospective teachers of mathematics for sustainable and rewarding careers as teachers. The basis of this reflection is the case of Alva, a teacher who, after a promising start, decided to leave the profession. Through a process of analysing Alva’s final interview before leaving teaching, we identify a set of interpretive repertoires relating to the notion of dissonance. These interpretive repertoires reveal several sources of tension for Alva some of which relate directly to the ‘ideal mathematics classroom’ promoted during Alva’s teacher education. By asking the question, what could have been different for Alva? We consider the potential implications for mathematics teacher education and for us as mathematics teacher educators.
14.	Elicer, Raimundo, et al. (författare) Comparing the integration of programming and computational thinking into Danish and Swedish elementary mathematics curriculum resources 2023 Ingår i: LUMAT. - : LUMA Centre Finland. - 2323-7112. ; 11:3, s. 77-102 Tidskriftsartikel (refereegranskat)abstract Computational thinking has become part of the mathematics curriculum in several countries. This has led recently available teaching resources to explicitly integrate computational thinking (CT). In this paper, we investigate and compare how curriculum resources developed in Denmark — digital teaching modules — and Sweden — printed mathematics textbooks — have incorporated CT in mathematics for grades 1–6 (age 7–12). Specifically, we identify and compare the CT and mathematical concepts, actions, and combinations in tasks within these resources. Our analysis reveals that Danish tasks are oriented toward CT concepts related to data, actions related to programming, and mathematical concepts within statistics. This is different from Swedish tasks, which are oriented toward CT concepts related to instructions and commands, actions related to following stepwise procedures, and mathematical concepts related to patterns. Moreover, what is most dominant in one country is almost or completely absent in the other. We conclude the paper by contrasting these two approaches with existing knowledge on computational thinking in school mathematics.
15.	Eriksson, Inger, 1952-, et al. (författare) “Learning models” : Utilising young students’ algebraic thinking about equations 2022 Ingår i: LUMAT. - : LUMA Centre Finland. - 2323-7112. ; 10:2, s. 215-238 Tidskriftsartikel (refereegranskat)abstract The overarching aim of this article is to exemplify and analyse how some algebraic aspects of equations can be theoretically explored and reflected upon by young students in collaboration with their teacher. The article is based upon an empirical example from a case study in a grade 1 in a primary school. The chosen lesson is framed by the El’konin-Davydov curriculum (ED Curriculum) and learning activity theory in which the concept of a learning model is crucial. Of the 23 participating students, 12 were girls and 11 boys, approximately seven to eight years old. The analysis of data focuses on the use of learning models and reflective elaboration and discussions exploring algebraic structures of whole and parts. The findings indicate that it is possible to promote the youngest students’ algebraic understanding of equations through the collective and reflective use of learning models, and we conclude that the students had opportunity to develop algebraic thinking about equations as a result of their participation in the learning activity.
16.	Grundén, Helena, 1968- (författare) Planning in mathematics teaching : a varied, emotional process influenced by others 2020 Ingår i: LUMAT. - Helsinki : University of Helsinki. - 2323-7112. ; 8:1, s. 67-88 Tidskriftsartikel (refereegranskat)abstract Planning is an essential part of teachers’ work that has consequences for students’ learning. However, previous research shows that what it means to plan vary. To explore the meaning of planning from teachers’ point of view, and to open up for planning as a situated and emotional process, an interview study with Swedish mathematics teachers was conducted. In the analysis, the theoretical concepts,meaning, and emotions were used as analytical tools to fill the gap identified in the review of previous research about planning. Findings reveal planning as a varied process in which teachers draw on different resources. Actors other than teachers influence both how planning is done and the mathematics teaching that is planned for. Findings also reveal that feelings, such as joy, shame, and insufficiency, are present in the process of planning. These feelings sometimes have consequences for decisions teachers make about their mathematics teaching.
17.	Holmström, Simon Johan Erland, et al. (författare) Gymnasiets laboratorionsundervisning i fysik–mellan tradition och ändrade styrdokument: Laboratory work in upper secondary physics teaching–between tradition and curriculum reform 2018 Ingår i: LUMAT: International Journal on Math, Science and Technology Education. - 2323-7112. ; 6:1, s. 1-21 Tidskriftsartikel (refereegranskat)abstract Laborationer har lång tradition i fysikundervisningen och det finns många klassiska skolexperiment. Samtidigt påverkas laborationsundervisningen av reformer och teknikutveckling. I denna studie fick lärare på tre gymnasieskolor diskutera sin laborationsundervisning. Analysen baseras på händelselogik, där handling ses som intentionell och styrs av determinanterna: målsättning, förmåga, plikt och möjligheter. Studien ger insikt i hur olika faktorer påverkar lärares laborationsundervisning, och hur klassiska laborationer i fysikundervisningen både kan ha en given plats och utmanas av nya förutsättningar. Resultaten antyder att praxis och tradition är starkare påverkansfaktorer än styrdokument i lärares utformning av laborationsundervisningen, vilket delvis kan relateras till en avsaknad av fortbildning.
18.	Kilhamn, Cecilia, et al. (författare) Programmering i svensk skolmatematik 2021 Ingår i: LUMAT. - 2323-7112. ; 9:1, s. 283-312 Tidskriftsartikel (refereegranskat)abstract När programmering skulle inkorporeras i skolans arbete valde Sverige i sin läroplansrevidering 2017 att skriva in det i matematikämnet, med stark koppling till algebra. Samtliga matematiklärare ställdes då inför utmaningen att undervisa i programmering. Vi undersöker här resultatet av 32 lärargruppers gemensamma arbete med att planera och genomföra lektioner i programmering i matematik i grundskolan. För att få insikt i hur lärare tolkar uppdraget och transponerar läroplananes beskrivning av programmering till klassrumspraktiken analyserar vi det matematiska innehållet i dessa lektioner samt vilken syn på relationen mellan matematik och programmering som framträder i lärarnas beskrivning av syfte, lärandemål, aktivitet och reflektion. Vi finner att programmeringsaktiviteter i 1/3 av lektionerna inte kopplas till något traditionellt matematiskt innehåll. I övriga lektioner är det främst aritmetik eller geometri som utgör det matematiska innehållet. Få explicita kopplingar görs till algebra förutom till begreppet variabler, men då är det främst variabler inom programmering som avses. I materialet framträder fyra olika relationer mellan matematik och programmering: 1) enbart programmering; 2) matematik som en kontext för programmering; 3) programmering som ett verktyg för att effektivisera beräkningar; 4) programmering som ett verktyg för att utforska matematik. Resultaten diskuteras i relation till matematikämnets syfte och innehåll i den svenska läroplanen.
19.	Kilhamn, Cecilia, 1963, et al. (författare) Programmering i svensk skolmatematik : Programming in Swedish school mathematics 2021 Ingår i: LUMAT. - 2323-7112. ; 9:1, s. 283-312 Tidskriftsartikel (refereegranskat)abstract When incorporating programming in the school curricula, Sweden decided to integrate it with mathematics, and specifically within the core content of algebra. As a result, all mathematics teachers at all levels were faced with the challenge of teaching programming. In this study we analyse documentation from 32 lesson studies where groups of teachers have planned, conducted, and revised lessons on programming within the school subject mathematics. To gain insight into how the teachers interpret the new task and thus contribute to the transposition of knowledge from the curriculum level to the classroom level, we analyse the mathematical content in these lessons and the relations between mathematics and programming that emerge in the way the teachers describe the aim, the activites and the learning outcomes of the lessons. We find that 1/3 of the lessons do not connect to any traditional mathematics content, and the rest of the lessons mostly focus on arithmetic or geometry. Few explicit connections are made to algebra, except for the variable concept, but when variables are treated the focus is on variables in the programming sense rather than algebra. Four different relationships between mathematics and programming emerge in the data: 1) programming without connecting to mathematics; 2) mathematics as a context for programming, 3)programming as a tool for efficient calculations; 4) programming as a tool for exploring mathematics.The results are discussed in relation to the transposition of knowledge of mathematics as a school subject. © 2021 University of Helsinki. All rights reserved.
20.	Norberg, Malin, 1975- (författare) Communicating mathematics through images : a multimodal study of year one students’ meaning-making when working with mathematics textbooks 2021 Ingår i: LUMAT. - : University of Helsinki. - 2323-7112. ; 9:1, s. 945-970 Tidskriftsartikel (refereegranskat)abstract This article focuses on how Swedish Year One students (age 7–8) make meaning when working with images in mathematics textbooks. Images include textbook images, but also students’ self-drawn images used as support for calculation. The focus was (1) what the images in the exercises were designed to offer (the designed affordance), and (2) what the students discovered when working with them. The data material consisted of video transcripts of 18 students working with subtraction exercises from mathematics textbooks. The results showed that the students sometimes discovered the designed affordance and sometimes did not. The students who discovered the designed affordance sometimes used the image when performing the calculations, while others did not. Some students expressed that images in mathematics textbooks are for those who find mathematics difficult, and that completing exercises without using the images was desired. The students’ approaches to images were discussed in two specific cases: First, the students’ desire to use mathematical symbols rather than images may lead to students not discovering the mathematics content that the exercise is designed to offer. Second, the use of mathematical symbols rather than images may lead to students not discovering themselves as mathematical individuals.
21.	Nyman, Martin, et al. (författare) The issue of ‘proudliness’ : Primary students’ motivation towards mathematics 2019 Ingår i: LUMAT. - 2323-7112. ; 7:2, s. 80-96 Tidskriftsartikel (refereegranskat)abstract In this paper, we study year 2 and year 5 students’ expressed motivations for doing mathematics. The responses were analysed using thematic analysis; first with a deductive approach using themes from previous research, and then an additional inductive analysis searching for new themes. The results show that the children express both intrinsic motivation (cognitive-oriented and emotional-oriented), as well as extrinsic motivation (including outward and compensation). Two new categories of cognitive intrinsic motivation were found—normative and personal. The results also indicated an interplay not only between the different categories but also within categories, signalling that expressed motivation is double-layered. Some implications are discussed.
22.	Planting-Bergloo, Sara, 1978-, et al. (författare) Att utveckla elevers förmåga att formulera undersökningsbara frågor i naturvetenskap : Mangling av en didaktisk modell 2021 Ingår i: LUMAT. - : LUMA Centre Finland. - 2323-7112. ; 9:1, s. 774-803 Tidskriftsartikel (refereegranskat)abstract En viktig målsättning för naturvetenskaplig undervisning är att utveckla förmågan att formulera undersökningsbara frågor. Syftet med den här studien är att undersöka hur undervisning som utformats med hjälp av metoden Question Formulation Technique (QFT) kan stödja utveckling av elevers förmåga att formulera naturvetenskapligt undersökningsbara frågor. QFT är en modell för att utveckla elevers förmåga att formulera och värdera sina egna frågor i allmänhet. I studien prövas QFT i en svensk skolkontext och inom ramen för naturvetenskaplig undervisning. Studien genomfördes som en interventionsstudie i gymnasieskolan och inom ramen för kursen Gymnasiearbete. I kursen ska eleverna genomföra en egen naturvetenskaplig undersökning. QFT användes för att utforma undervisning som del av introduktionen till kursen. Data består av videoinspelningar av elevsamtal från undervisning som har analyserats utifrån ett pragmatiskt ramverk med organiserande syften och praktisk epistemologisk analys. Resultaten visar vilka närliggande syften som etableras i elevernas samtal om undersökningsbara frågor i undervisningen: (A) att producera så många frågor som möjligt, (B) att bedöma vilka frågor som är mest relevanta, (C) att kategorisera frågor, (D) att hitta och specificera ett undersökningsobjekt och (E) att planera för att genomföra en undersökning. Slutsatsen är att QFT kan fungera som stöd för lärares planering av undervisning om naturvetenskapligt undersökningsbara frågor under förutsättning att läraren aktivt stödjer eleverna i att uppmärksamma centrala kvaliteter avseende undersökningsbarhet och genom att binda samman närliggande syften med det övergripande syftet.
23.	Sterner, Helén (författare) Teachers as actors in an educational design research : what is behind the generalized formula? 2019 Ingår i: LUMAT. - : University of Helsinki. - 2323-7112. ; 7:3, s. 6-27 Tidskriftsartikel (refereegranskat)abstract Educational design research provides opportunities for both the theoretical understanding and practical explanations of teaching. In educational design research, mathematics teachers’ learning is essential. However, research shows that little consideration is given to teachers and the participation of teachers throughout the entire design process as well as in continued learning. With this in mind, educational teacher-focused design research was used to explore the challenges teachers face, and the opportunities teachers are given when they participate as actors in all the phases of educational design research - designing, teaching, and refining theoretical concepts within the teaching. In this study, the mathematics focus of the design research was generalizations in patterns with Design Principles as the theoretical frame. The results show that the participation of teachers in all the phases of a design process is central for the teachers’ learning. Moreover, challenges that the teachers encounter in the classroom provide opportunities and consequences for the continued design process and lead to changes in the teachers’ understanding of generalizations. The results also indicate that functional thinking and linear equations contributed to both the teachers’ and students’ learning about generalizations in patterns. © 2019 University of Helsinki. All rights reserved.
24.	Sundqvist, Pernilla, et al. (författare) Svensk förskolepersonals beskrivningar av teknik 2015 Ingår i: LUMAT. - LUMA Centre Finland. - 2323-7112. ; 3:2, s. 237-257 Tidskriftsartikel (refereegranskat)abstract With regards to previous research results on how the teacher’s/preschool teacher’s understanding of a subject effects children’s learning and apprehending of the subject combined with the difficulties for the technology subject to take place in preschool this study aims at investigating how preschool staff (including preschool teachers and day care attendants) describe technology. A qualitatively designed questionnaire was sent out to 139 preschool teachers and day care attendants in a Swedish municipality, whereof 102 answered. The open question about what technology is thought to be was analyzed using a conventional content analysis resulting in nine categories, of which six interrelated hierarchically and one contained answers witch could not be categorized. Thus the result shows eight different ways in which technology is described, from a simple and naive description to a more complex description that implicates a deeper understanding of technology. A majority describes technology according to the latter. The result also shows that it is mainly the preschool teachers who describe technology in a more complex way. Many of the respondents have trouble separating technology from science, and quite a few describes technology as technique, which is another meaning for the word in the Swedish language.
25.	Tossavainen, Anne (författare) Student teachers’ common content knowledge for solving routine fraction tasks 2022 Ingår i: LUMAT. - : University of Helsinki. - 2323-7112. ; 10:2, s. 256-280 Tidskriftsartikel (refereegranskat)abstract This study focuses on the knowledge base that Swedish elementary student teachers demonstrate in their solutions for six routine fraction tasks. The paper investigates the student teachers’ common content knowledge of fractions and discusses the implications of the findings. Fraction knowledge that student teachers bring to teacher education has been rarely investigated in the Swedish context. Thus, this study broadens the international view in the field and gives an opportunity to see some worldwide similarities as well as national challenges in student teachers’ fraction knowledge. The findings in this study reveal uncertainty and wide differences between the student teachers when solving fraction tasks that they were already familiar with; two of the 59 participants solved correctly all tasks, whereas some of them gave only one or not any correct answer. Moreover, the data indicate general limitations in the participants’ basic knowledge in mathematics. For example, many of them make errors in using mathematical symbol writing and different representation forms, and they do not recognize unreasonable answers and incorrect statements. Some participants also seemed to guess at an algorithm to use when they did not remember or understand the correct solution method.
26.	Tossavainen, Timo, et al. (författare) Programming as a mediator of mathematical thinking : Examples from upper secondary students exploring the definite integral 2024 Ingår i: LUMAT. - : LUMA Centre Finland. - 2323-7112. ; 12:3, s. 78-99 Tidskriftsartikel (refereegranskat)abstract We report on three episodes from a case study where upper secondary students numerically explore the definite integral in a Python environment. Our research questions concern how code can mediate and support students' mathematical thinking and what kind of sociomathematical norms emerge as students work together to reach a mutual understanding of a correct solution. The main findings of our investigation are as follows. 1) Students can actively use code as a mediator of their mathematical thinking, and code can even serve as a bridge that helps students to develop their mathematical thinking collaboratively. Further, code can help students to perceive mathematical notions as objects with various properties and to communicate about these properties, even in other semiotic systems than the mathematical language. 2) For the participating students, a common norm was that an acceptable solution is a sufficient condition for the correctness of the solution method although students were aware of a problem in their code, yet also other norms emerged. This demonstrates that learning mathematics with programming can have an effect on what kind of sociomathematical norms emerge in classroom.
27.	Walla, Maria, et al. (författare) Discourses on mathematics education in the context of early assessment 2024 Ingår i: LUMAT. - 2323-7112. ; 12:4 Tidskriftsartikel (refereegranskat)abstract This paper is about the meanings Swedish preschool class teachers ascribe to early mathematics education when talking about assessment. The assessment material is new national, mandatory assessment material for six-year-old students. Based on a discourse analysis of four focus groups, five discourses were construed: preschool class mathematics is unique; the role of preschool class mathematics is changing; to assess is to categorize; assessment contributes to equity; and individualization implies grouping by level. The results illustrate how teachers hope that the status of and equity in preschool class mathematics education will increase by means of the assessment. However, the teachers’ talk about categorizing and grouping students may have implications for equity.
28.	Wang Wei, Sönnerhed, 1968 (författare) Quadratic equations in Swedish textbooks for upper-secondary school 2021 Ingår i: LUMAT. - 2323-7112. ; 9:1, s. 518-545 Tidskriftsartikel (refereegranskat)abstract This paper analyzes the content and tasks involving quadratic equations in eight mathematics textbooks published during the period 2000-2012 at the uppersecondary level in Sweden. The study applies the theoretical hypothetical learning trajectory (HLT) framework combining conceptual and procedural knowledge. The analysis includes horizontal and vertical dimensions within an HLT. The aim is to explore embedded HLTs and learning opportunities from both dimensions in these textbooks. A total of 250 examples and 1,068 tasks have been examined. Results show that all the textbooks contain algebra identities and four different methods for solving quadratic equations as well as their applications as a core hypothetical learning trajectory but differ in how an HLT starts and ends. Geometrical representations for some algebra identities and completing the square are widely used in both theoretical presentations and tasks, which implies that conceptual learning is encouraged among the Swedish textbooks. At the same time, procedural knowledge is still emphasized as a basic but important learning process. © 2021 University of Helsinki. All rights reserved.
29.	Wettergren, Sanna, et al. (författare) Yngre elevers uppfattningar av det matematiska i algebraiska uttryck 2021 Ingår i: LUMAT: International Journal on Math, Science and Technology Education. - 2323-7112. ; 9:1, s. 1-28 Tidskriftsartikel (refereegranskat)abstract Det övergripande syftet med denna artikel är att analysera och beskriva yngre elevers uppfattningar av det matematiska i ett algebraiskt uttryck och utifrån det diskutera vad som kan utgöra kritiska aspekter för utvecklandet av mera kvalificerade uppfattningar. Artikeln bygger på data från ett forskningsprojekt där elever i förskoleklass, årskurs 1 och årskurs 4 intervjuades med syfte att analysera de aktuella elevernas kvalitativt skilda sätt att uppfatta det matematiska i algebraiska uttryck. Intervjuerna analyserades fenomenografiskt. Studiens resultat visar tre kvalitativt skilda kategorier av yngre elevers uppfattningar av det matematiska i algebraiska uttryck. Det matematiska i ett algebraiskt uttryck erfars som ”något som kan och bör räknas ut”, ”något som beskriver en relation mellan komponenter” och ”något som representerar en situation”. Vidare identifierades tre kritiska aspekter i relation till kategorierna. De kritiska aspekter som ger eleverna möjlighet att kvalificera sina uppfattningar för att utveckla ett mer komplext kunnande av algebraiska uttryck är att kunna urskilja att 1) ett uttryck består av olika komponenter som har olika funktioner, 2) en och samma variabel i ett uttryck har samma värde och 3) värdet på en variabel i ett uttryck bestäms relationellt. Att urskilja sådana kritiska aspekter kan hjälpa eleverna att kvalificera sitt kunnande. Således måste de kritiska aspekterna beaktas vid utformningen av undervisningen.
30.	Åhman, Niclas, et al. (författare) Learning Study och kollegial CoRe stimulerar lärares professionella utveckling inom naturvetenskaplig undervisning 2020 Ingår i: LUMAT. - Helsngfors : University of Helsinki. - 2323-7112. ; 8:1, s. 200-228 Tidskriftsartikel (refereegranskat)abstract Syftet med studien är att klargöra hur lärares professionella utveckling stimuleras då de planerar och genomför en Learning Study (LS) kombinerad med verktyget Content Representation (CoRe). Data består av sex erfarna lärares inspelade diskussioner under åtta träffar då de planerar och analyserar en LS bestående av två lektioner i årkurs 6 inom kemi, samt tre CoRe som lärarna skriver. I början av studien talar lärarna mest om undervisning som att fakta ska förmedlas till eleverna. När de sedan planerar första lektionen övergår deras diskussioner till hur de kan stimulera eleverna till diskussion och reflektion. Lärarna planerar både lektion 1 och 2 utifrån ett variationsteoretiskt perspektiv, men lektion 1 genomförs inte i enlighet med vad de planerat. Det är först i lektion 2 som läraren behåller fokus på lärandeobjektet och dess kritiska aspekter. Resultatet av studien visar även att en Learning Study kombinerad med CoRe stimulerar lärares professionella utveckling och ämnesdidaktiska kompetens i form av lärande nätverk enligt Clarkes och Hollingsworths (2002) modell ”interconnected model of professional growth”.

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