| 1. |
- Holmström, Simon, et al.
(author)
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Gymnasiets laborationsundervisning i fysik – Vad påverkar lärares val av laborationer?
- 2019
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In: LUMAT: International Journal on Math, Science and Technology Education. - 2323-7112. ; 7:1, s. 27-58
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Journal article (peer-reviewed)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.
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| 2. |
- Andersson, Charlotta, et al.
(author)
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En modell som stöd för att utforska ekvationer : [A model to support exploring equations]
- 2022
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In: LUMAT. - 2323-7112. ; 10:1, s. 182-209
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Journal article (peer-reviewed)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.
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| 3. |
- Björklund, Camilla, 1977, et al.
(author)
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Preschoolers’ ways of experiencing numbers
- 2022
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In: LUMAT. - : University of Helsinki. - 2323-7112. ; 10:2, s. 84-110
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Journal article (peer-reviewed)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.
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| 4. |
- Borke, Mikael, 1965
(author)
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Student teachers’ knowledge of students’ difficulties with the concept of function
- 2021
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In: LUMAT. - 2323-7112. ; 9:1, s. 670-695
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Journal article (peer-reviewed)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.
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| 5. |
- Dessen Jankell, Lotta, 1970-
(author)
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Elevers uppfattningar av systemmodellering i arbete med hållbarhetsfrågor
- 2023
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In: LUMAT. - 2323-7112. ; 11:1, s. 25-51
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Journal article (peer-reviewed)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.
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| 6. |
- Dyrvold, Anneli, 1970-, et al.
(author)
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Computer-based assessment in mathematics : Issues about validity
- 2023
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In: LUMAT. - : University of Helsinki; LUMA Centre Finland. - 2323-7112. ; 11:3, s. 49-76
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Journal article (peer-reviewed)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.
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| 7. |
- Dyrvold, Anneli, 1970-, et al.
(author)
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Static, dynamic and interactive elements in digital teaching materials in mathematics : how do they foster interaction, exploration and persistence?
- 2023
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In: LUMAT. - : University of Helsinki. - 2323-7112. ; 11:3, s. 103-131
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Journal article (peer-reviewed)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.
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| 8. |
- Ebbelind, Andreas, Dr, 1975-, et al.
(author)
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Examining interpersonal aspects of a mathematics teacher education lecture
- 2024
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In: LUMAT. - : University of Helsinki. - 2323-7112. ; 12:1, s. 113-125
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Journal article (peer-reviewed)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.
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| 9. |
- Ebbelind, Andreas, Dr, 1975-, et al.
(author)
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This is not how it should end : The role of mathematics teacher education in preparing teachers for sustainable careers
- 2024
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In: LUMAT. - : University of Helsinki. - 2323-7112. ; 9:2
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Journal article (peer-reviewed)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.
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| 10. |
- Elicer, Raimundo, et al.
(author)
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Comparing the integration of programming and computational thinking into Danish and Swedish elementary mathematics curriculum resources
- 2023
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In: LUMAT. - : LUMA Centre Finland. - 2323-7112. ; 11:3, s. 77-102
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Journal article (peer-reviewed)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.
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