Browsing by Subject "matematiikka"
Now showing items 21-40 of 82
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(2015)Aims. All students, regardless of their capacity, should be offered impartial learning opportunities. Usually, it is well attended that each student will achieve learning goals. The gifted students are often unrecognized and ignored in school in everyday life. We must learn to recognize gifted students to provide them teaching that corresponds to their abilities. The reliable identification of giftedness is challenging. The mathematically gifted student brings both challenges and opportunities for teaching. There is a variety of differentiation methods to be used in teaching mathematics depending on pupils' needs and on the resources of the schools. The purpose of this study was to find out how the class teachers define mathematically gifted students, to find out the differentiation ways of teaching mathematics and to find out the class teachers' experiences of differentiation in mathematics. Methods. The study was a qualitative case study. The survey was conducted by interviewing the three class teachers, who had been selected for the research because of their interest of differentiation in mathematics. The direction based content analysis was used for the analysis of the research material. Results and conclusions. The teachers recognized the features of mathematical giftedness in their pupils. However, it was challenging for them to identify whether the students are really gifted or only a very successful at school work. The teachers used many ways to differentiate teaching of mathematics. Especially functional teaching was used as a mean to differentiate teaching. The teachers' experiences of differentiation in mathematics were very positive. The results of the study can be used by class teachers when they plan their differentiation in mathematics.
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(2023)Tässä työssä vertaillaan kolmea oppikirjaa (SanomaPron Moodi, Otavan Juuri sekä Editan Kaari) MAA11 moduulille (LOPS 2019). Työssä esitellään lukion opetussuunnitelman mukaiset tärkeät sisällöt moduulille ja tutkitaan voiko opiskelija oppia moduulin aiheet oppikirjojen avulla. Oppikirjojen teoriaosuuksia ja tehtäviä sekä digikirjojen erilaisia ominaisuuksia vertaillaan. Teoriaosuuksien tarkastelussa kiinnitetään huomiota siihen, että millaisia eroja esimerkkien välillä on ja kuinka paljon oppikirjat käyvät läpi opetussuunnitelmaan kuulumattomia aiheita, mutta jotka kuuluvat samoihin aihepiireihin kuten esimerkiksi Diofantoksen yhtälö. Näiden lisäksi tutkitaan, kuinka paljon todistamista kirjoissa on erilaisille lauseille ja määritelmille, sekä oppikirjojen tekijöiden laatimia aikatauluehdotuksia. Tehtävien tarkasteluun ja vertailuun on hyödynnetty Bloomin taksonomiaa, jonka teoriaosuus esitellään työssä. Ohjelmointitehtävissä Kaaren ja Juuren digikirjoihin on upotettu tehtäviin Python-ohjelmointiympäristö, jota ei Moodista löydy ollenkaan. Työssä ei huomattu suuria eroja oppikirjojen välillä. Tehtävät, aiheet ja esimerkit muistuttivat kovasti toisiaan tai olivat suoraan samoja, mutta vain eri kirjoitusasulla. Suurin ero kirjojen välillä oli aikatauluehdotuksissa ja siinä, kuinka monta kappaletta eri aihealueisiin on varattu. Moodi painotti kolmesta oppikirjasta eniten algoritmeja ja ohjelmointia ja Juuri painotti eniten lukuteoriaa. Lukion opetussuunnitelmaa ajatellen Kaari oli ainoa kirjoista, joka sisälsi tehtäviä, joissa aritmetiikan peruslausetta täytyi käyttää. Kahdessa muussa tällaista tehtävää ei ollut.
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(2016)The number of immigrant students has risen extremely during the last two decades in Finnish schools, but there still are not many studies about their competence. In my thesis I examine based on earlier studies how well immigrant students know mathematics in primary school and introduce factors which affect their competence. Additionally, I examine affective and cognitive factors and their effect on learning mathematics. I also introduce Wilson's (1970) taxonomy and Kilpatrick et al.'s (2001) intertwined strands of profiency for measuring competence in mathematics. I look for answers to my research questions by reading studies and articles and also by exploring other literature related to the topic. I found my sources by using well-known search engines, for example Nelli-portal, Google scholar and the University of Helsinki library's search engine. The earlier studies found out that immigrant students have lower mathematical competence than native population. It is socially concerning that one student group has lower competence than others. Mathematics is easily seen as a subject in which it is not important to know the language. However, the studies show that one of the most important factors in mathematical competence is knowing the language. Socio-economic background also affects competence in mathematics. Gender does not have a direct effect on mathematical competence but affective factors can indirectly affect mathematical competence in favor of the boys. It is interesting that immigrant students have a slighty more positive attitude towards mathematics than the native population in spite of lower mathematical competence.
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(2018)Tiivistelmä - Referat - Abstract Objectives. The purpose of this Bachelor's Thesis is to describe and highlight the perceptions and experiences that kindergarten teachers have of observing children’s need for support in their mathematical skills development in early childhood education. I want to find out which factors work as a prerequisite for observing the need to support the development of mathematical skills and which factors make it difficult to identify the needs for the support. Secondly, I would like to explore the practices of providing mathematical support in early childhood education before the preschool age. Methods. I carried out my research with qualitative research approach. In my research, I interviewed four university-educated kindergarten teachers who had work experience of 4-30 years. The material I gathered was analysed with thematic material-based content analysis. Based on the themes emerged from the analysis, I was able to create patterns that depicted the results graphically. Results and conclusions. In my research three factors were found to be affecting the observation of mathematical support: education, observation and cooperation. The kindergarten teachers were educated to have sufficient knowledge of the child's mathematical development. In addition, education was thought to have given the skills to sensitively observe the child's mathematical support needs. The detection for the need for mathematical support was hampered by the lack of time spent in observing it. Third, the cooperation with other professionals or parents affected the observation for mathematical support needs. The kindergarten teachers experienced that collaboration gave support for their own observations and experiences.Following the observations for need for mathematical support it was offered alongside the group's activities, paying particular attention to the practice of mathematical skills. The conclusion of the study is that mathematical support is based on teacher's mathematical awareness: understanding of the development of mathematical skills in interaction and understanding of mathematics as part of everyday life. Upon this base the planning, implementation and evaluation of the group's needs are built on. In early childhood education the planning and implementation of activities must take into account the use of everyday situations, explaining mathematical concepts, developing mathematical learning environments and also to observe and monitor numeracy of the environment in order to support child’s development of mathematical skills.
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(2019)Aims. The purpose of this thesis is to identify and analyze the mathematical difficulties faced by pupils entering school. Special consideration was given to pre- and initial training, but younger children were also examined. The hypothesis was that mathematical difficulties produce difficulties for the pupil in the start-up phase of the school, appear in other learning, and make it more difficult to learn and to live in everyday life. The research question was refined several times and the interest in the subject was born when I met Hannele Ikäheimo, the special teacher of mathematics. The aim of the thesis is to examine the material widely and to deepen to particular questions through the descriptive literature review. Methods. The thesis was made using the descriptive literature review method. The data was collected from several databases. Some of the data was limited by the age of the participants and the year of publication of the study. Studies were found both in English and in Finnish. Most of the studies found were in English Results and conclusions. The studies were statistical surveys. On the basis of the results, mathematical difficulties complicate in catching school, causing anxiety at the emotional level, guiding the school path and affecting everyday life performance. The studies described mathematical difficulties in an unrelenting way, but at the same time they discussed ways to support mathematical competence. The mathematical difficulties are tough and long lasting. In addition, difficulties cause anxiety and fear of studying mathematics. Teaching should consider ways of supporting mathematical learning difficulties without causing bullying and anxiety in the pupil. Research and case studies of qualitative analysis would be needed. In addition, it would be interesting to study the subject using discourse analysis.
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(2019)Aims. The purpose of this thesis is to identify and analyze the mathematical difficulties faced by pupils entering school. Special consideration was given to pre- and initial training, but younger children were also examined. The hypothesis was that mathematical difficulties produce difficulties for the pupil in the start-up phase of the school, appear in other learning, and make it more difficult to learn and to live in everyday life. The research question was refined several times and the interest in the subject was born when I met Hannele Ikäheimo, the special teacher of mathematics. The aim of the thesis is to examine the material widely and to deepen to particular questions through the descriptive literature review. Methods. The thesis was made using the descriptive literature review method. The data was collected from several databases. Some of the data was limited by the age of the participants and the year of publication of the study. Studies were found both in English and in Finnish. Most of the studies found were in English Results and conclusions. The studies were statistical surveys. On the basis of the results, mathematical difficulties complicate in catching school, causing anxiety at the emotional level, guiding the school path and affecting everyday life performance. The studies described mathematical difficulties in an unrelenting way, but at the same time they discussed ways to support mathematical competence. The mathematical difficulties are tough and long lasting. In addition, difficulties cause anxiety and fear of studying mathematics. Teaching should consider ways of supporting mathematical learning difficulties without causing bullying and anxiety in the pupil. Research and case studies of qualitative analysis would be needed. In addition, it would be interesting to study the subject using discourse analysis.
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(2019)Tiivistelmä - Referat – Abstract The purpose of this research was to find out how mathematics can be found if the working of early childhood teacher and in the physical learning environment of the day care center. In addition, the purpose was to understand the teacher’s pedagogical thinking concerning the teaching of mathematics. In the obligatory curriculum Varhaiskasvatussuunnitelma (2016) is dictated which parts of mathematics must be taught in early childhood education in Finland. This reseach tried to find out, which of these parts can be found in teaching and in the physical learning environtment. The second purpose was to find out how the teacher justifys their decisions in the teaching process and in which levels of thinking are they operating (Kansanen 2004). The reseach is qualitative case study and one teacher participated. The method usead was stimulated recall, which combined video and interview. Also photograph was used to document the environtment. The analysis was theory based. This reseach showed that allmost all the parts of mathematics dictated in the curriculum could be found in the learning environtment and the teaching, along with the pedagogical thinking of the teacher. Measuring, concept of time, problem solving and spatial thinking were shown less than other parts. Numeracy was shown the most. The teacher was operating in levels of operation and 1st level on thinking, but not on the meta level.
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(2023)Tavoitteet. Lasten, joilla on heikot matemaattiset taidot jo alle kouluiässä, on todennäköisesti vaikea oppia koulumatematiikkaa. Lisäksi ero matematiikkaa hyvin osaavien ja heikosti osaavien lasten välillä kasvaa koululuokilta ylemmälle siirryttäessä. Tämän tutkielman tavoitteena oli selvittää, miten jo varhaiskasvatuksessa voidaan tukea lapsen matemaattisia taitoja ja onko matematiikan harjoitusohjelmista hyötyä matemaattisten taitojen tukemisessa. Tutkielman keskeisimmät käsitteet ovat matematiikka varhaiskasvatuksessa, spontaani huomionkiinnittäminen lukumääriin (SFON, spontaneous focusing on numerosity) ja lukukäsite. Menetelmät. Tämä kanditutkielma on laadullinen tutkimus, jossa perehdyin sisällönanalyysin ja kirjallisuuskatsauksen keinoin lapsen varhaisiin matemaattisiin taitoihin, erityisesti huomionkiinnittämiseen lukumääriin ja lukukäsitteen kehittymiseen. Tutkin sisällönanalyysiä käyttäen kahta varhaiskasvatusikäisille suunnattua matematiikan harjoitusohjelmaa. Nämä ovat Nallematikka ─ Varhaisten matemaattisten oppimisvalmiuksien kehittämisohjelma ja Minäkin lasken! Lasten lukukäsitteen harjoitusohjelma. Lisäksi analysoin kirjallisuuskatsauksen keinoin kahta näiden harjoitusohjelmien vaikuttavuustutkimuksia käsittelevää artikkelia. Tulokset ja johtopäätökset. Tutkielman tuloksista ilmeni, että varhaiskasvatuksessa on mahdollista tukea lasten matemaattisia taitoja ja, että varhaiskasvatukseen suunnatut harjoitusohjelmat voivat toimia hyvänä työvälineenä matematiikan oppimisen tukemisessa. Molemmat tutkimukseni harjoitusohjelmat tukevat erityisesti lasten lukukäsitteen kehitystä. Varhaiskasvatuksessa työskentelevien rooli on kuitenkin suuri ─ heidän tulee tunnistaa, missä matemaattisen kehityksen vaiheessa lapsi on, ohjata lasta hänen lähikehityksen vyöhykkeellään sekä luoda matemaattisten ilmiöiden tutkimiseen ja oppimiseen innostava oppimisympäristö.
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(2017)The demand and supply of foreign language teaching is growing with internationalization and multiculturalism. The spectrum of foreign-language teaching is extensive and is defined different ways in different situations - often it is up to the user to decide, which one includes as foreign-language teaching. The thesis treats such foreign language teaching in which language is taught and learned concurrently with content. In my thesis I use the term content and language integrated learning of this kind of teaching model. The immersion is the best-known type for this kind of teaching model. The aim of this thesis was to introduce teaching in foreign languages, teaching mathematics, and what special requirements are imposed when combining these two into simultaneous action. My second research task was to find out what kind of learning outcomes are to be achieved in a mathematics subject when it is taught in a foreign language. The thesis is limited to pupils who have voluntarily participated in non-native language teaching. The context of the study is mainly in the first six grades of the elementary school, but it also presents some results of matriculation examination to get a wider picture. I am looking for answers to my research questions by reading the essentially related literature on the theory, first of mathematics and foreign-language teaching, and subsequent studies related to my research questions. I used a variety of sources from current news to fundamental research from both Finland and abroad. In searching for the material I used the Google Scholar –search service and the University of Helsinki library search engine. According to previous studies, foreign-language teaching itself does not hinder learning mathematics, and some of the studies even show that students participating in foreign-language instruction are better at math or math competence tests. Studying in a foreign language seems to affect only the language in which the student registers the concept of learning in their brains but not the quality of the data they have registered. The research does not take into account the impact of social factors such as motivation or family background. Considering the results, it must be taken into account that pupils applying for foreign language teaching may be more motivated, which affects the quality of the study and hence affects positively to the learning outcomes.
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(2019)Objective. There are indications in prior studies showing that STEM education (Science, Technology, Engineering, Mathematics) has a positive effect on learning. This bachelor’s thesis took account of adding art component to STEM and found out how often STEAM education (Science, Technology, Engineering, Art, Mathematics) in elementary school’s mathematics appears in present studies. Method. In this thesis the material was collected by using the systematic review. After that, four peer reviewed English studies were filtered to the examination. They all connected with STEAM education somehow. Two of the studies related to the teachers, one to the pupils and one to the teacher students. The studies were American and Korean. Results and conclusions. Studies related to STEAM education in elementary school’s mathematics was found only few. There could have been more results, if defining was wider. However the results were interesting: Especially male teacher’s attitudes towards STEAM education were positive. Furthermore the know-how of the pupils was improved when the art component was added to the STEM education.
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Matematiikan tunteiden mittarin teoreettinen tarkastelu edustavassa suomalaisten nuorten aineistossa (2020)Tässä tutkimuksessa oppilaiden tunnekokemuksia matematiikassa mitattiin kansainvälisesti käytössä olevalla matematiikan tunnekyselyllä (The Achievement Emotions Questionnaire-Mathematics, AEQ-M; Pekrun, Goetz & Frenzel, 2005). Tämä mittari on oppilaan itsearviointiin perustuva mittari, joka selvittää oppilaiden tunteita matematiikan luokassa, oppimisessa ja testissä. Tämän tutkimuksen tavoitteena on testata mittariin liittyviä teoreettisia malleja, faktorien luotettavuutta, erotteluvaliditeettia ja faktorien erillisyyttä. Lisäksi käsitellään tutkimusotantaa ja puuttuvan tiedon käsittelyä. Tutkimusotos (n = 1413) on maantieteellisesti edustava otos 8. luokan oppilaista (14- ja 15-vuotiaat). Tutkimusotos saatiin monivaiheisesti käyttämällä useita otantamenetelmiä kuten kouluihin pohjautuvaa ryväsotantaa, systemaattista otantaa ja implisiittistä osittamista. Konfirmatorista faktorianalyysia käytettiin tutkimaan teoreettisia AEQ-M-malleja edustavassa tutkimusotoksessa. Tulokset osoittivat, että teoreettinen tunne x tilanne -malli, jossa sekä tunteet että niihin liittyvät tilanteet huomioitiin, kuvasi dataa hyvin. Tässä mallissa kuusi matematiikkaan liittyvää tunnetta (nautinto, ylpeys, viha, ahdistus, häpeä ja tylsyys) mallinnettiin erillisinä latentteina faktoreina, ja eri tilanteiden (luokka, oppiminen ja testi) vaikutus huomioitiin antamalla samassa tilanteessa olevien tunnemuuttujien residuaalien korreloida keskenään. Vaikka tässä mallissa faktoreita vastaavien latenttimuuttujien reliabiliteetit olivat suhteellisen hyviä, tämä tutkimus kuitenkin kyseenalaistaa tunnefaktorien erotteluvaliditeetin ja samaan tilanteeseen liittyvien tunteiden residuaalien väliset korrelaatiot. Nämä tulokset osoittavat, että mittari on varsin toimiva mittaamaan suomalaisten nuorten tunteita matematiikassa. Lisäksi tutkimustulokset tukevat teoriaa siitä, että akateemisten tunteiden mittaamisessa olisi huomioitava sekä erilliset tunteet että niiden erilaisuus luokka-, oppimis- ja testitilanteessa. Tutkimustulokset herättävät kuitenkin kysymyksen siitä, onko tarkoituksenmukaista yhdistää korkeasti korreloivat tunteet samoiksi faktoreiksi vai käyttää teoreettista mallia korkeista korrelaatioista huolimatta. Vaikka teoria määrittää tunteiden vahvan yhteyden eri tilanteisiin, tämä tutkimus herättää kysymyksen, ovatko kaikki tunteet samassa tilanteessa kuitenkaan merkittävästi yhteydessä. Tulevaisuudessa olisi esitettävä laajempaa analyysia faktorien erillisyydestä ja tunteiden tilannesidonnaisuudesta.
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Matematiikan tunteiden mittarin teoreettinen tarkastelu edustavassa suomalaisten nuorten aineistossa (2020)Tässä tutkimuksessa oppilaiden tunnekokemuksia matematiikassa mitattiin kansainvälisesti käytössä olevalla matematiikan tunnekyselyllä (The Achievement Emotions Questionnaire-Mathematics, AEQ-M; Pekrun, Goetz & Frenzel, 2005). Tämä mittari on oppilaan itsearviointiin perustuva mittari, joka selvittää oppilaiden tunteita matematiikan luokassa, oppimisessa ja testissä. Tämän tutkimuksen tavoitteena on testata mittariin liittyviä teoreettisia malleja, faktorien luotettavuutta, erotteluvaliditeettia ja faktorien erillisyyttä. Lisäksi käsitellään tutkimusotantaa ja puuttuvan tiedon käsittelyä. Tutkimusotos (n = 1413) on maantieteellisesti edustava otos 8. luokan oppilaista (14- ja 15-vuotiaat). Tutkimusotos saatiin monivaiheisesti käyttämällä useita otantamenetelmiä kuten kouluihin pohjautuvaa ryväsotantaa, systemaattista otantaa ja implisiittistä osittamista. Konfirmatorista faktorianalyysia käytettiin tutkimaan teoreettisia AEQ-M-malleja edustavassa tutkimusotoksessa. Tulokset osoittivat, että teoreettinen tunne x tilanne -malli, jossa sekä tunteet että niihin liittyvät tilanteet huomioitiin, kuvasi dataa hyvin. Tässä mallissa kuusi matematiikkaan liittyvää tunnetta (nautinto, ylpeys, viha, ahdistus, häpeä ja tylsyys) mallinnettiin erillisinä latentteina faktoreina, ja eri tilanteiden (luokka, oppiminen ja testi) vaikutus huomioitiin antamalla samassa tilanteessa olevien tunnemuuttujien residuaalien korreloida keskenään. Vaikka tässä mallissa faktoreita vastaavien latenttimuuttujien reliabiliteetit olivat suhteellisen hyviä, tämä tutkimus kuitenkin kyseenalaistaa tunnefaktorien erotteluvaliditeetin ja samaan tilanteeseen liittyvien tunteiden residuaalien väliset korrelaatiot. Nämä tulokset osoittavat, että mittari on varsin toimiva mittaamaan suomalaisten nuorten tunteita matematiikassa. Lisäksi tutkimustulokset tukevat teoriaa siitä, että akateemisten tunteiden mittaamisessa olisi huomioitava sekä erilliset tunteet että niiden erilaisuus luokka-, oppimis- ja testitilanteessa. Tutkimustulokset herättävät kuitenkin kysymyksen siitä, onko tarkoituksenmukaista yhdistää korkeasti korreloivat tunteet samoiksi faktoreiksi vai käyttää teoreettista mallia korkeista korrelaatioista huolimatta. Vaikka teoria määrittää tunteiden vahvan yhteyden eri tilanteisiin, tämä tutkimus herättää kysymyksen, ovatko kaikki tunteet samassa tilanteessa kuitenkaan merkittävästi yhteydessä. Tulevaisuudessa olisi esitettävä laajempaa analyysia faktorien erillisyydestä ja tunteiden tilannesidonnaisuudesta.
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(2023)Tavoitteet Tutkimuksen tarkoituksena on selvittää mitä ovat oppimiseen liittyvät tunteet ja millaisia tunteita 6-8-vuotiaat alakoulun ensimmäisillä vuosiluokilla opiskelevat oppilaat kokevat matematiikan parissa opiskellessaan. Lisäksi tarkoituksena on selvittää millä tavoin nautinnon -,ahdistuksen - ja tylsistymisen tunteet ovat yhteydessä matematiikassa suoriutumisen kanssa samalla ikäluokalla. Menetelmät. Tutkimus toteutettiin kuvailevana kirjallisuuskatsauksena, jossa oli systemaattisen kirjallisuuskatsauksen piirteitä. Suurin osa aineistosta kerättiin systemaattisen kirjallisuuskatsauksen menetelmin. Tämän lisäksi aineistoon hyväksyttiin viisi julkaisua, jotka noudattivat vain osittain aineistolle annettuja kriteerejä. Aineisto kerättiin Helkasta, Eric-tietokannasta ja Google Scholarista. Laadullisen seulonnan jälkeen tutkimukseen päätyi 12 julkaisua. Tulokset ja johtopäätökset. 6-8-vuotiaat oppilaat kokevat matematiikan parissa sekä positiivisia että negatiivisa tunteita. Suurin osa oppilaista raportoi positiivisista tunteista. Nautinnon tunteella oli positiivinen yhteys matematiikassa suoriutumisen kanssa, ahdistuksella oli sekä positiivinen että negatiivinen yhteys matematiikassa suoriutumisen kanssa, mutta tylsistymisen ja matematiikassa suoriutumisen väliltä ei löydetty yhteyttä.
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(2020)The aim of this study was to find out how much enjoyment, boredom and anxiety students experience in mathematics-related situations: during lessons, homework and tests. The study investigates the relations of these emotions with achievement in mathematics. Moreover, gender, school and classroom differences in these relationships are examined. In spring 2017, 215 third-graders from four Helsinki schools responded to the AEQ-ES (Achievement Emotions Questionnaire-Elementary School) survey and participated in three tests measuring mathematics achievement as part of the MathMot study. The fit of the data for the AEQ-ES structural model was analysed using confirmatory factor analysis. The connections between emotions and achievement as well as differences in these connections were studied by non-parametric methods: the Mann-Whitney U and Kruskal-Wallis H tests, as well as Spearman’s rank correlation coefficient. The study revealed that students experienced much more mathematics-related enjoyment than boredom or anxiety, which were experienced very little. Consistent with findings from previous research, it was found that emotions are related to achievement, positively to enjoyment and negatively to boredom and anxiety. This connection was strongest in emotions associated with lessons. Few statistically significant differences were observed between genders. In terms of achievement, there was a statistically significant difference between schools in all mathematics tests. Differences were also found between classrooms, albeit not in all tests. Furthermore, between a school receiving positive discrimination funding and a school providing weighted-curriculum education, there was a statistically significant difference in achievement and some emotions.
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(2022)Tässä tutkimuksessa esitellään matematiikan sähköisten ylioppilaskirjoitusten käyttöönottoa ja niiden vaikutusta matematiikan opetukseen lukiossa. Tutkimuksen aineisto muodostuu tekijän omakohtaisista kokemuksista sähköisten ylioppilaskirjoitusten käyttöönotosta vastanneena lukio-opettajana vuosina 2015 - 2020, oppilaiden koevastauksista sähköisiin kurssikokeisiin sekä havainnoinnista todellisilla matematiikan lukiotunneilla. Havainnoidut oppitunnit jaoteltiin kolmeen kategoriaan: Perinteiset tunnit ilman sähköisten menetelmien käyttöä, hybridimenetelmän tunnit joissa vastaukset koostettiin osin perinteisin ja osin sähköisin menetelmin sekä kokonaan sähköisiä menetelmiä käyttävät tunnit. Oppilaiden koevastauksista havaittiin, että opettajan käyttämä opetustekniikka vaikuttaa oppilaiden tapaan tuottaa matemaattista tekstiä. Opetettaviksi valitut ohjelmistot vaikuttavat suuresti oppilaiden koevastausten ulkoasuun ja osin myös vastauksen matemaattiseen sisältöön. Myös oppilaiden tekniset taidot asettavat rajoitteita vastausten tuottamiselle. Lukion matematiikan opetus on kokenut suuren murroksen sähköisten ylioppilaskokeiden käyttöönoton myötä. Sähköinen matematiikan tuottaminen on heterogenisoinut opetusta ja aiheuttanut eroja eri opettajien opetustapojen välille. Tämä tutkimus tarjoaa kvalitatiivisia, pedagogis-sosiologiseen havainnointiin perustuvia näkökulmia aiheeseen.
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(2016)The meaning of this study is to research the development process of self-efficacy in learning mathematics, and to distinguish factors that affect this process. Because of the strong affects regarding it, mathematics is in a disparate position as a school subject. In this study, self-efficacy is conceptualized as a part of the affective area. The interaction between affect and learning outcomes in mathematics has not been researched enough to understand it thoroughly. The research method in this study was literature review, performed by studying literature and articles regarding the topic. Finna search services and Nelli-portaali were used as resources inter alia. The impacts on self-efficacy were divided into physical, psychological and social factors in the learning environment, and to the impacts of individual differences. Self-efficacy is a complex, dynamic belief, which is easily influenced from the outside and the inside. The interaction between self-efficacy and learning outcomes can not be determined unequivocally.
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(2019)Aims. In Finland all pupils in preparatory education study mathematics. This study focuses on the multilingual process of concept formation and meaning making in the context of math-ematics classroom of newly arrived pupils. In addition of new language of introduction, they face the specific language of mathematics. Previous studies have shown the close connection between mathematics and language. Studying mathematics also requires language skills. The purpose of this study is to find out how and in what ways newly arrived pupils use multilingual concept learning in mathematics. The purpose is to analyze how pupils use their language resources in mathematical meaning making process. Methods. The study was carried out as part of the project Meeting in the middle at the Uni-versity of Helsinki. The study was a qualitative case study and the research material con-sisted of four videos recorded in the secondary school preparatory class. During the videos, the pupils did mathematical tasks in pairs. Four pupils were chosen as participants, and they worked in two pairs. One pair was speaking Arabic together, and the other one chose to speak English instead of Arabic. The pupils’ use of multilingual concept learning was ana-lyzed with discourse analytical microethnography. Results and conclusions. My study showed that pupils use their different languages abun-dantly during the mathematical verbal tasks. Use of multilingual content learning became ap-parent when pupils shifted between languages. They did this to create meanings or to solve the content of task. Shifts between languages were connected to the way pupils created meanings of concepts and tasks that were in Finnish. The pupils also discussed the seman-tics of the concepts and the interpretations of the tasks. Possibility to use all their languages gave pupils the space where they could use their languages the way they thought was use-ful. Results of this study gave new knowledge about multilingual content learning in mathe-matics, especially since this has not been studied extensively in Finland yet.
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(2019)Aims. In Finland all pupils in preparatory education study mathematics. This study focuses on the multilingual process of concept formation and meaning making in the context of math-ematics classroom of newly arrived pupils. In addition of new language of introduction, they face the specific language of mathematics. Previous studies have shown the close connection between mathematics and language. Studying mathematics also requires language skills. The purpose of this study is to find out how and in what ways newly arrived pupils use multilingual concept learning in mathematics. The purpose is to analyze how pupils use their language resources in mathematical meaning making process. Methods. The study was carried out as part of the project Meeting in the middle at the Uni-versity of Helsinki. The study was a qualitative case study and the research material con-sisted of four videos recorded in the secondary school preparatory class. During the videos, the pupils did mathematical tasks in pairs. Four pupils were chosen as participants, and they worked in two pairs. One pair was speaking Arabic together, and the other one chose to speak English instead of Arabic. The pupils’ use of multilingual concept learning was ana-lyzed with discourse analytical microethnography. Results and conclusions. My study showed that pupils use their different languages abun-dantly during the mathematical verbal tasks. Use of multilingual content learning became ap-parent when pupils shifted between languages. They did this to create meanings or to solve the content of task. Shifts between languages were connected to the way pupils created meanings of concepts and tasks that were in Finnish. The pupils also discussed the seman-tics of the concepts and the interpretations of the tasks. Possibility to use all their languages gave pupils the space where they could use their languages the way they thought was use-ful. Results of this study gave new knowledge about multilingual content learning in mathe-matics, especially since this has not been studied extensively in Finland yet.
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(2021)Most of the world’s population is either bilingual or multilingual. Schools also face multilingualism, and Finland has not escaped the challenges of multilingualism either. Various programs have been developed around the world for the teaching of multilingual students. Mathematics is one of the most important subjects in school, and success in it facilitates access to postgraduate studies, and contributes to employment placement. Language skills also affect the study of mathematics. The aim of this dissertation was to investigate the effects of different bilingual programs on the achievement and development of mathematics among students of different ages. Data were collected from scientific studies. The study included CLIL programs and various immersion programs. The studies were divided into three parts: cohort studies, interventions, and studies on cognition, language exchange costs, and the use of different methods in bilingual curricula. In this dissertation, the material has been compiled by means of a systematic literature review. The research material has been collected from various databases (Eric, EBSCO, PsycINFo, Springer). 31 previous international and 2 Finnish studies were selected as research material, which dealt with the use of different bilingual programs and their effects on mathematics competence. The research material was analysed based on data. The use of CLIL and immersion programs in almost all studies had a positive effect on students ’academic achievement in mathematics. The most positive results were obtained through interventions. The results contributed to confirming the contribution of the Cummins Threshold Hypothesis to the use of bilingual curricula, i.e., learning a second language requires reaching a certain minimum level of language before a learner can benefit from language use while also studying mathematics. Teaching through a foreign language seemed to support and promote students ’mathematical thinking and learning processes. Once thought processes have evolved, the use of a foreign language as a tool for learning appears to be an advantage in cognitive development.
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(2019)The earlier studies have shown that the intrinsic motivation has a strong connection with the learning results of the mathematics. Objective of this pro gradu was firstly to analyse the connection of the sixth grade girls and boys' of the school success, to study mathematics at school and at informal learning environment, which in this case was Math & Art exhibition based on STEAM-model. Secondly the connection of the relative autonomy experience of the girls' and boys' was studied in connection to interest in mathematics at school and at mathematics exhibition. Thirdly and last it was studied how autonomy experience was connected to plans to continue education at the upper secondary school or at the vocational educational institution. The target group of the pro gradu thesis was the 256 sixth grade pupils of the comprehensive school (134 girls and 122 boys) from a medium size Finnish municipality. A questionnaire was applied. The differences between the groups were examined with a one-way analysis of variance. The connections between the variables were tested with a correlation coefficient. In the analysis IBM SPSS Statistics 25 -software was used. The main results were that the interest to study mathematics at school was higher among the higher achievers but at the mathematics exhibition there were no differences between the lower and higher achievers. The exhibition seemed to succeed in levelling down differences which are related to the school success. The experience of the relative autonomy (RAI) correlates with interest in studying mathematics at school, especially among girls. The boys were more interested than girls in continuing at the vocational school, and girls at the upper secondary school. The connection of school success and going to the upper secondary school was stronger than going to the vocational school. The success of the boys at school was more tied up with the plans than that of the girls. The more the pupil regarded himself as autonomous furthermore the more they wanted to go on after the comprehensive school to the upper secondary school. This connection was stronger on the boys.
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