Kaikki aineistot
Lisää
In this article, we focused on sustainable development in mathematics education from the point of view of academic literacy in mathematics (ALM). ALM was understood here through three integrated components: mathematical proficiency, mathematical practices, and mathematical discourse (languaging). ALM skills support 21st Century competences which are important for citizen skills. Both ALM skills and 21st Century competences support lifelong learning and sustainable education. Citizens of future society need both ALM and 21st Century competences to model and solve the issues of sustainable development. We want to develop prospective teachers’ content knowledge and pedagogical content knowledge of school mathematics in the spirit of sustainable education. As the case, we chose the mathematical symbol “2/3” and how collaborative mean-ing making for “2/3” influences prospective class teachers’ interpretations. Col-laborative meaning making is part of ALM. Collaborative working as a tool for meaning making supports the other parts of ALM. By languaging different meanings for “2/3” in pairs, prospective class teachers deepened their under-standing about fractions. By supporting ALM skills in teacher education, future class teachers can have a more sustainable basis to teach mathematics for children. As a conclusion, based on the results of our case study, we summarized objectives for sustainable development for teacher education, teachers, and stu-dents in mathematics education.
The concept “mathematical thinking” can be found in several studies of mathematics education, in national curricula or in media during the decades all over the world. We searched words “mathematical thinking” from the database of international scientific articles, and we found 456 707 mentions at first time. These are the main reasons why we have chosen “mathematical thinking” as the central concept of the Special Issue. The other interesting question from our point of view is how a student can express his/her mathematical thinking? By answering this question, we have made simple model for the teacher education purposes, and we call it “languaging” (of mathematical thinking). The articles of the Special Issue gives some answers to the questions: “What is mathematical thinking and how we can express it?” and “What are the relationships between conceptual understanding and mathematical thinking?”.
Kirjallisuuden ja aikaisempien tutkimusten mukaan perinteisesti koulumatematiikan opetuksessa painotettu proseduraalinen osaaminen ei yksinään riitä matematiikan oppimisen onnistumiseen. Vuoden 2014 perusopetuksen opetussuunnitelman perusteet painottavat oppilaiden matemaattisten käsitteiden ymmärryksen merkitystä. Tässä artikkelissa esitellään Lehtosen väitöstutkimus esimerkkinä, kuinka oppimisteknologian käyttö voi tukea alakoululaisten matemaattisten käsitteiden ymmärrystä. Väitöstutkimuksen aikana kehitettiin moniesitysmuotoinen oppimisväline alakoululaisten yhtälönratkaisun oppimista varten. Kehitetty oppimisväline yhdistää fyysisten ja digitaalisten välineiden vahvuudet: fyysisten osien liikkuminen saa oppilaat ajattelemaan omaa toimintaa, kun taas digitaaliset osat motivoivat oppilaita oppimaan sekä mahdollistavat reaaliaikaisen ohjauksen ja palautteen saamisen. Luokkakokeilussa osoitettiin, että kehitetyn oppimisvälineen käyttö yhdessä matemaattisen ajattelun kielentämisen mallin kanssa tuki neljäsluokkalaisten yhtälönratkaisun käsitteiden oppimista. Kehitetty toimintamateriaali toimi oppilaiden oppimisen, kommunikoinnin ja vuorovaikutuksen välineenä. Oppilaat pitivät kehitettyä välinettä oman oppimisen kannalta hyödyllisenä, helppokäyttöisenä ja miellyttävänä käyttää. Lisäksi he kokivat tekemällä oppimisen ja yhteisöllisen kielentämisen mielekkääksi työtavaksi tulevaisuudessa matematiikan oppimiseen.
In this article, our focus is on sustainable development in mathematics education from the point of view of teacher training. The aim was to develop prospective teachers’ content knowledge and pedagogical content knowledge of school mathematics. As a case study, we chose the mathematical symbol “a/b”, and examined how prospective class teachers in Finland connect it to the concepts of fraction, ratio, division, rational number or probability. Mathematics textbooks often have a central role in lessons, and they affect strongly how pupils understand concepts and the relationships between them. We chose languaging as a multi-semiotic approach to interpreting what kind of meanings the prospective class teachers gave the mathematical symbol “a/b”. The results show that some of these concepts are difficult to see at the same time from the given mathematical symbol. The concept of ratio is particularly difficult for prospective class teachers to interpret. Pictorial presentation supported the interpretations. Mathematics learning materials and teacher education should develop in accordance with the results of the study.
In project-based learning, pupils have two central learning objectives: to understand the content of the subject and to develop their twenty-first-century skills. This article concerns the use of project work in mathematics learning, considered here in the context of the Finnish national core curriculum, mathematical proficiency and pupils’ previous level of attainment. The research consisted of two case studies in which a coordinate system project and a statistics project were tested with secondary school pupils (N=59+58). The main findings show it is possible to study the mathematics of the curriculum and to develop all types of mathematical proficiency using project work. Additionally, the pupils’ grades on the project work correlate positively with their overall grades in mathematics.
Artikkelin tarkoitus on tutkia miten luokanopettajaopiskelijat tulkitsevat koulumatematiikan käsitteitä murtoluku ja suhde heille annetussa tehtävässä, jossa on matematiikan symbolikielen merkintöjä ja niihin liittyviä kuvia. Tutkimukseen osallistui yhteensä 92 opiskelijaa kahdesta yliopistosta. Tuloksista näkyi useimpien opiskelijoiden proseduraalinen lähestymistapa annetun ratkaisun tulkinnassa käsitteellisen näkökulman jäädessä vain harvojen opiskelijoiden valinnaksi. Tulos on opetussuunnitelman ja oppimateriaalien näkökulmasta odotettu. Murtolukujen monipuolinen ymmärtäminen on haasteellista. Tämä tuo haasteita opettajankoulutuksen ja täydennyskoulutuksen kehittämiselle.
This article concerns mathematical project work in the context of Finnish StarT project competition. The focus is on how well pupils achieve the learning objective of their project work: learning mathematics and practicing 21st century skills. Development of the learning objectives is considered from the viewpoint of Finnish national core curriculum and evaluated using the framework of academic literacy. The research material consists of teams’ project reports, observation, and questionnaires. Project work in the StarT competition seems to develop the learning objectives of project-based learning: pupils practice 21st century skills while studying mathematical contents.
Beliefs have been conceived as a hidden variable in mathematics education. It is important to know teachers’ beliefs as they can inform the way that teachers teach mathematics, make decisions in the classroom, and form opinions about the abilities of students. In Costa Rica, studies about beliefs have been conducted with in-service teachers, but there is no research on pre-service teachers and the beliefs they bring to the classroom from their teacher education programs (TEPs). This research aims to describe the beliefs held by 76 pre-service teachers and 19 teacher educators from four Costa Rican public universities, using the Teacher Education and Development Study in Mathematics (TEDS-M) questionnaire. The results suggest that both pre-service teachers and teacher educators believe in a constructivist orientation focused on the learner. Both groups support the view of mathematics as a process of inquiry and active learning and agree that mathematical skills are not fixed or associated with gender or culture. In the literature, the beliefs manifested by the participants are associated with positive results regarding student outcomes and teaching practices. Therefore, policymakers should be concerned with providing environments that allow and encourage teachers to continue with these belief orientations when they start teaching
Despite the increasing use of technologies in the classroom, there are concerns that technology-enhanced learning environments may hinder students’ communication and interaction. In this study, we investigated how tangible technologies can enhance students’ multimodal communication and interaction during equation-solving pair work compared to working without such technologies. A tangible app for learning equation solving was developed and tested in fourth- and fifth-grade classrooms with two class teachers and 24 students. Video data of the interventions were analysed using deductive and inductive content analysis. Coded data were also quantified for quantitative analysis. Additionally, teacher interview data were used to compare and contrast the findings. The findings showed that the tangible app better promoted students’ multimodal communication and peer interaction than working only with paper and pencil. When working in pairs, tangible-app students interacted with one another much more often and in more ways than their paper-and-pencil peers. The implications of this study are discussed in terms of its contributions to research on tangible technologies for learning, educational technology development, and the use of tangibles in classrooms to support students’ multimodal communication and peer interaction.
The current study aimed (1) to analyse teachers’ view profiles from positive to negative based on the analysis of influencing factors and (2) to investigate the most studied concepts and methods in this context. According to the Preferred Reporting Items for Systematic Reviews and Meta-Analyses 2020 guidelines, we conducted a comprehensive review of 25 peer-reviewed articles published between January 2010 and December 2022. Our findings show a landscape in which concepts related to mathematics teaching and learning often intersect with other domains. Nevertheless, a distinction exists in the definition of the fundamental concept, with limited attention given to mathematics learning and the role of students in contrast to the focus on mathematics teaching and the role of teachers. Our research highlights the necessity of thorough exploration of the dynamic factors that influence these views and their associated outcomes, categorised as (A) mutual consistency, (B) weak consistency, and (C) inconsistency, each providing distinct implications for support needs. Additionally, from an ontological perspective on affect, many studies overlook the notion of 'view' as a state or trait characteristic, potentially leading to inappropriate method selection. Therefore, we propose recommendations for future research, advocating for methodological precision, expanded object exploration, dynamic profiling, and the inclusion of diverse teacher categories.
Tässä artikkelissa kartoitamme sitä, miten murtoluvun käsitettä on opetettu eräissä 1800–2000-lukujen alaluokkien oppikirjoissa, ja millaisia murtoluvun käsitekuvia tarkasteluun valituista oppikirjoista välittyy. Osoittautuu, että murtolukua on käsitelty monipuolisesti ja eri tavoin jo 1800-luvun oppikirjoissa ja osa näistä käsittelytavoista on edelleen käytössä. Uuden matematiikan kirjoissa korostuu jonkin verran konseptuaalinen ajattelu, muuten murtolukujen käsittelyä hallitsee laskemisen näkökulma.
Despite the increasing use of technologies in the classroom, there are concerns that technology-enhanced learning environments may hinder students’ communication and interaction. In this study, we investigated how tangible technologies can enhance students’ multimodal communication and interaction during equation-solving pair work compared to working without such technologies. A tangible app for learning equation solving was developed and tested in fourth and fifth-grade classrooms with two class teachers and 24 students. Video data of the interventions were analysed using deductive and inductive content analysis. Coded data were also quantified for quantitative analysis. Additionally, teacher interview data were used to compare and contrast the findings. The findings showed that the tangible app better promoted students’ multimodal communication and peer interaction than working only with paper and pencil. When working in pairs, tangible-app students interacted with one another much more often and in more ways than their paper-and-pencil peers. The implications of this study are discussed in terms of its contributions to research on tangible technologies for learning, educational technology development, and the use of tangibles in classrooms to support students’ multimodal communication and peer interaction.
Artikkelissa tarkastellaan kuudennen luokan lopussa oppilaiden tuottamia ratkaisuja kahteen sanalliseen ongelmanratkaisutehtävään. Tutkimuksen toteutti matemaattiseen ajatteluun ja sen kielentämiseen perehtynyt opettaja. Tutkimukseen osallistui 35 kuudennen luokan oppilasta. Tutkimusaineistona olivat oppilaiden kirjalliset ratkaisut kahteen sanalliseen ongelmanratkaisutehtävään. Oppilaat kuvasivat kielentämisen keinoin omaa matemaattista ajatteluaan sekä tehtävien tuottamisessa että ratkaisuprossien avaamisessa. Tuloksista on nähtävissä, että oppilailla oli taitoja kielentää monipuolisesti matemaattista ajatteluaan. Matematiikan opetuksessa olisikin hyvä ohjata oppilaita ilmaisemaan matemaattista ajatteluaan monipuolisesti ja täsmällisesti kielentämisen keinoin.
Projektioppiminen on ongelmakeskeinen menetelmä, jossa tavoitteena on oppiaineen sisältöjen syvällisen ymmärryksen lisäksi työelämätaitojen harjoittelu. Opetus pyrkii yhdistämään opiskeltavan aineen oppilaiden jokapäiväiseen elämään tai tulevaan työelämään. Tässä tutkimuksessa tarkastelemme oppilaiden (N = 201) ja opettajien (N = 10) kokemuksia projektityöskentelystä yläkoulun matematiikan tunneilla. Projektit tukivat oppilaiden ymmärrystä siitä, missä matematiikkaa tarvitaan koulun ulkopuolella ja motivoivat erityisesti poikia matematiikan opiskeluun.
Artikkelissa tarkastellaan kuudennen luokan lopussa oppilaiden tuottamia ratkaisuja kahteen sanalliseen ongelmanratkaisutehtävään. Tutkimuksen toteutti matemaattiseen ajatteluun ja sen kielentämiseen perehtynyt opettaja. Tutkimukseen osallistui 35 kuudennen luokan oppilasta. Tutkimusaineistona olivat oppilaiden kirjalliset ratkaisut kahteen sanalliseen ongelmanratkaisutehtävään. Oppilaat kuvasivat kielentämisen keinoin omaa matemaattista ajatteluaan sekä tehtävien tuottamisessa että ratkaisuprossien avaamisessa. Tuloksista on nähtävissä, että oppilailla oli taitoja kielentää monipuolisesti matemaattista ajatteluaan. Matematiikan opetuksessa olisikin hyvä ohjata oppilaita ilmaisemaan matemaattista ajatteluaan monipuolisesti ja täsmällisesti kielentämisen keinoin.
angible technologies provide interactive links between the physical and digital worlds, thereby merging the benefits of physical and virtual manipulatives. To explore the potentials of tangible technologies for learning linear equations, a tangible manipulative (TM) was designed and developed. A prototype of the initial TM was implemented and evaluated using mixed methods (i.e., classroom interventions, paper-based tests, thinking aloud sessions, questionnaires, and interviews) in real classroom settings. Six teachers, 24 primary school students, and 65 lower secondary school students participated in the exploratory study. The quantitative and qualitative analysis revealed that the initial TM supported student learning at various levels and had a positive impact on their learning achievement. Moreover, its overall usability was also accepted. Some minor improvements with regard to its pedagogy and usability could be implemented. These findings indicate that the initial TM is likely to be beneficial for linear equation learning in pre-primary to lower secondary schools and be usable in mathematics classrooms. Theoretical and practical implications are discussed.
Tangible technologies provide interactive links between the physical and digital worlds, thereby merging the benefits of physical and virtual manipulatives. To explore the potentials of tangible technologies for learning linear equations, a tangible manipulative (TM) was designed and developed. A prototype of the initial TM was implemented and evaluated using mixed methods (i.e., classroom interventions, paper-based tests, thinking aloud sessions, questionnaires, and interviews) in real classroom settings. Six teachers, 24 primary school students, and 65 lower secondary school students participated in the exploratory study. The quantitative and qualitative analysis revealed that the initial TM supported student learning at various levels and had a positive impact on their learning achievement. Moreover, its overall usability was also accepted. Some minor improvements with regard to its pedagogy and usability could be implemented. These findings indicate that the initial TM is likely to be beneficial for linear equation learning in pre-primary to lower secondary schools and be usable in mathematics classrooms. Theoretical and practical implications are discussed.