Browsing by Subject "matematiikka"

The aim of the study: The preschool education of mathematics has been studied fairly little. However, the earlier studies have showed that mathematical education in preschool has failed to compensate the differences in mathematical skills of the pre-schoolers. The aim of this study was to find out how the Varga Neményi teaching method effects in the Finnish preschool education and especially for children with problems in their learning or development. The effectiveness of the teaching method was studied from the view of children's mathematical abilities and their involvement to activity. Also children's opinions of mathematics and themselves as learners of mathematic were studied. Research method: Multiple research methods have been used in this study. The study has features of the action research. The intervention of mathematic, based on Varga Neményi-teaching method, was carried out in preschool group with children of special needs. All ten pre-schoolers participated in the research. Some of the children had need for intensified or special support. Children's skills in mathematics were studied using MAVALKA 1 – survey in the beginning and in the end of the intervention. Children's involvement to activity was observed and assessed using LIS-YC Scale also in the beginning and in the end of intervention. Children's opinions of mathematics and themselves as learners of mathematics were studied with interviews and drawings. Findings and conclusions: The engagement of children was statistically significantly higher during the mathematic lessons based on Varga Neményi- method than during the other type of preschool action. The engagement of children strengthened during the intervention both in mathematics and in other preschool activities. Children's skills in mathematics improved during the intervention. The skills in mathematics of the children with lower performance in the beginning of the intervention improved the most. The children experienced mathematics to be something functional, interactive and mainly pleasant. In the light of these findings, the Varga Neményi teaching method seems to suit well to the Finnish pre-school education, and for children with special needs.

The challenge of teaching mathematics is to make the student’s mathematical thinking heard and visible. To find out how students mathematical thinking can be supported I familiarized concept of mathematical languaging. Mathematical languaging allows student to express their thinking through the language, orally and in writing. Theoretical background of this study is Joutsenlahti’s and Rättyä’s model of four languages of mathematics, which allows students to express their mathematical thinking. The purpose of this study is to find out which mathematics languages teachers emphasize in their teaching and how teachers guide students to languaging in mathematics lessons. In addition, I also explore which mathematic languages the textbooks tend to use, and how the textbooks support the teacher’s role in guiding students languaging mathematics. The material of my study was based on video material: Oppimaan oppimisen avaimet, which was filmed in fall 2012. It included eight sixth grade math lessons. The videos featured a total of seven teachers, one of whom taught a lesson to two different classes. Mathematics textbooks, which were used in the lessons, from four different book series were also used as research material. The data were analyzed using quantification and sosiosemiotics analysis. The videos showed that the lessons were quite teacher-regulated. Teachers asked questions that students answered briefly and accurately. Teachers guided students to use mainly natural language and symbolic language, and to switch between these languages. The textbooks guided to interpret the text in natural language as well as in symbolic language and to produce only symbolic language. Teachers and textbooks also guided to use pictorial language mainly in connection with the contents of geometry. The content of the subject of mathematics influences the language used by the student to express mathematical thinking. Teachers guided oral languaging in the classroom, while textbooks supported written languaging.

Objectives. The aim of this study was to investigate how flipped learning could be utilized in teaching mathematics in primary school from fourth to sixth grade. Another aim of this study was to examine the benefits and challenges of utilizing flipped learning in teaching mathema-tics from the perspective of both the teacher and the pupil. Flipped learning is a pupil-oriented learning culture which involves supporting the development of autonomy and self-determination of the pupil. Flipped learning enables individual learning pace and also utilizes collaborative learning. Flipped learning investigated in this study has been marginally studied as the majority of flipped learning studies focus on examining flipped classroom method. Methods. This study is a qualitative case study. The participants in this study were class teachers who had utilized flipped learning for the past five years as well as one pupil who had been in flipped learning utilizing class for the past three years. The research material was collected by conducting theme interviews and the results were analyzed with theory-based content analysis. Results and conclusions. The mathematics class investigated in this study utilized flipped learning by means of digital games and weekly achievement plan. The pupils made progress at their own pace and studied in small groups. From the point of view of both the teachers and the pupil, the benefits of flipped learning in this study turned out to be well-being and school satisfaction, the development of studying skills, collaborative learning, clarity of lear-ning objectives and increased motivation. From the point of view of the teachers, the challen-ges presented themselves in maintaining a peaceful working environment as well as concern for the proactivity of the pupils when in need of assistance. From the point of view of the pu-pil, the challenge of flipped learning method appeared as stress involved with scheduling the studies and matching the weekly achievement plan. It can be concluded from these results that in the class investigated in this study, flipped learning resulted in more benefits than chal-lenges although some of the pupils experienced the responsibility involved in flipped learning as burdensome.

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.

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.

The Finnish school system has long been credited for consistently achieving equality in learning outcomes. However, recent research revealed an emerging segregation, especially within the Helsinki metropolitan area. There has also been frequent discussions revolving around motivation and learning outcomes differences between genders. The connections between motivation factors and mathematical skills have been vastly researched, but disportionately, due to limited research on those in lower primary school. The purpose of this study is to investigate the differences in motivation and mathematical skills between genders and schools. This study also investigates how motivation factors correlates to mathematical skills on primary schools third grade pupils. The motivation factors used in this study are mathematical self-concept and expectancy-value theory fields: intrinsic value, utility value and costs. The data used in this study was collected for the international MathMot investigation project. 215 third grade pupils from four different schools within Helsinki participated in the research. The participants filled out a questionnaire that measured their mathematical motivation, followed by three different test to measure their mathematical skills. In the analysis non-parametric methods where used: Mann-Whitney U test, Kruskal-Wallis H test, and Spearman's rank correlation coefficient. Based on the results of this study it can be concluded that there were some differences between schools: intrinsic value, utility value, and costs. There were no differences in mathematical self-concept despite the significant differences in mathematical skills between the schools. Girls tended to show greater interest in mathematics, as well as a higher regard for its usefulness. In comparison, Girls outperformed slightly better in the non-verbal fluid intelligence measuring Ravens test. Self-concept had the strongest relation to mathematical skill.

Tavoitteet. Tutkimuksen tavoitteena on selvittää, millaisia käsityksiä opettajilla on ongelmanratkaisun opettamisesta ja kuinka paljon ongelmanratkaisua opetetaan. Ongelmanratkaisua pidetään julkisessa keskustelussa tärkeänä taitona tulevaisuuden työelämän kannalta. Kuitenkaan suomalaisessa peruskoulussa ongelmanratkaisu ei ole yleistynyt keskeiseksi osaksi matematiikan opetusta, vaikka ongelmanratkaisu onkin ollut opetussuunnitelmassa yli kolmekymmentä vuotta. Opettajan toimintatapoja ohjaa opetussuunnitelmaakin voimakkaammin opettajan käsitykset ja uskomukset. Tarkoituksena on selvittää, millaisia käsityksiä opettajilla on ongelmanratkaisun opettamisesta, mitkä tekijät vaikuttavat ongelmanratkaisun opettamisen määrään sekä miten opettajien käsitykset vaikuttavat ongelmanratkaisun opettamisessa koettuihin vaikeuksiin. Menetelmät. Tutkimus toteutettiin monimenetelmällisenä kyselytutkimuksena. Aineistona käytetiin 160 suomalaisen alakoulun opettajan vastauksia kyselyyn, joka toteutettiin osana suomalaissaksalaista tutkimusprojektia. Aineistoa analysoitiin sekä kvalitatiivisin että kvantitatiivisin menetelmin, tarkoituksena kuvata opettajien käsityksiä ongelmanratkaisun opettamisesta, ja toisaalta myös selittää eroja opettajien käsitysten välillä. Tulokset ja johtopäätökset. Puolet opettajista kertoi käsittelevänsä ongelmanratkaisua opetuksessaan ainakin kerran viikossa. Opettajan taustatekijöillä ei ollut vaikutusta ongelmanratkaisun opetuksen määrään. Tutkimuksen aineiston perusteella osa opettajista pitää sanallisia rutiinitehtäviä ongelmatehtävinä. Siksi tutkimuksen perusteella ei voida päätellä, kuinka paljon ongelmanratkaisua todellisuudessa opetetaan alakouluissa. Opettajat kokivat erityisesti ajan ja tehtävien puutteen vaikeuttavan ongelmanratkaisun opetusta. Noin viisi kuudesta opettajasta koki ongelmanratkaisun opetukseen liittyvän runsaasti erilaisia vaatimuksia niin oppilaiden kuin opettajan asenteeseen ja osaamiseen.

The purpose of this study was to find out students' views of themselves and others in the math class. Pupils' views were examined from the drawings they drew. The study also wanted to find out how girls and boys describe girls and boys in math class. The attitude of mathematics influences the success of the subject and in making future career choices. The attitude of mathematics can be viewed from the perspective of the individual or from the perspective of the atmosphere of the whole class. Previous research has shown that students’ attitudes toward math are declining during the school years. The subject of the study was the fourth, fifth and sixth graders of one primary school. Students who participated in the study drew drawings of a math lesson in their class. A total of 172 drawings were collected. The pupils' drawings were used to examine the affections marked on the drawn characters, i.e., the expressions and the texts of the thought and speech bubbles. The findings were collected in a spreadsheet program and the findings were quantified. The study revealed that among the students who participated in the study, fourth graders most often described their own attitude as positive. Older students were more likely to describe their attitudes as negative than fourth graders. In the fourth grade of the whole class, the atmosphere was mostly positive, in the fifth grade ambivalent, and in the sixth grade, the atmosphere was almost equally described as positive and ambivalent. Both girls and boys described boys more positively in math class. In addition, both girls and boys more often described same-sex students as negative in math lessons than the opposite sex.

Aims of the study. Achievement goal orientations refer to the individual tendencies of a student and describe how they act in learning situations. For example, the student may favor deep learning, minimal workload, or a good grade. Earlier experiences and situations, as well as assessment of one’s own abilities are guided by the individual’s goal orientation. This affects the way how the student is motivated and regulates their own actions. Learning situations are experienced through individual views and orientations. That is why the same learning situation may appear different for everyone. The aim of the study is to find out what kind of achievement goal orientations can be identified among primary school seventh graders in mathematics. Participants are divided into groups based on which achievement goal orientation they fit. Then the groups are compared with each other based on how they differ in gender, stress, interest, and math grade. Utilizing a person-oriented approach, this study examined the differences of achievement goal orientation groups in mathematics. Goal orientation theory and expectancy value theory were used as a frame of reference. Methods. The data (N = 874) was collected in autumn 2019 as a part of Growing Mind and Bridging the Gaps study. The project examined learning, motivation and well-being among children and adolescents. The participants were seventh graders from 28 different schools in Helsinki and 56.4 % of them were girls, 39.8 % were boys and 3.4 % identified as other. The study was made as a questionnaire which measured achievement goal orientations in mathematics, stress, and interest towards mathematics. The students were divided into groups based on achievement goal orientation profiles with K-Means Cluster Analysis. Gender differences were measured by cross-tabulation and Chi-square test of independence. The differences between the groups in interest in mathematics, stress and math grades were examined by using Analysis of Variance. Result and conclusions. Four achievement goal orientation groups were identified, of which 24.9 % were mastery-oriented, 29.1 % were success-oriented, 29.6 % were uncommitted and 16.4 % avoidance-oriented. The findings suggest that there was no significant difference between the groups in gender distribution. The mastery-oriented experienced the most interest and the least stress in studying math. The success-oriented were the second most interested in math and the group of uncommitted the third most interested. The avoidance-oriented were the least interested in mathematics. The uncommitted experienced the most stress, and the avoidance-oriented and success-oriented experienced the second most stress. The success-oriented had the best grades in math and the mastery-oriented had the second best grades. The avoidance-oriented and the uncommitted had slightly lower grades than the success and mastery-oriented.

In this study the researcher wanted to show the observed connection of mathematics and textile work. To carry this out the researcher designed a textbook by herself for the upper secondary school in Tietoteollisuuden Naiset - TiNA project at Helsinki University of Technology (URL:http://tina.tkk.fi/). The assignments were designed as additional teaching material to enhance and reinforce female students confidence in mathematics and in the management of their textile work. The research strategy applied action research, out of which two cycles two have been carried out. The first cycle consists of establishing the textbook and in the second cycle its usability is investigated. The third cycle is not included in this report. In the second cycle of the action research the data was collected from 15 teachers, five textile teachers, four mathematics teachers and six teachers of both subjects. They all got familiar with the textbook assignments and answered a questionnaire on the basis of their own teaching experience. The questionnaire was established by applying the theories of usability and teaching material assessment study. The data consisted of qualitative and quantitative information, which was analysed by content analysis with computer assisted table program to either qualitative or statistical description. According to the research results, the textbook assignments seamed to be applied better to mathematics lessons than textile work. The assignments pointed out, however, the clear interconnectedness of textile work and mathematics. Most of the assignments could be applied as such or as applications in the upper secondary school textile work and mathematics lessons. The textbook assignments were also applicable in different stages of the teaching process, e.g. as introduction, repetition or to support individual work or as group projects. In principle the textbook assignments were in well placed and designed in the correct level of difficulty. Negative findings concerned some too difficult assignments, lack of pupil motivation and unfamiliar form of task for the teacher. More clarity for some assignments was wished for and there was especially expressed a need for easy tasks and assignments in geometry. Assignments leading to the independent thinking of the pupil were additionally asked for. Two important improvements concerning the textbook attainability would be to get the assignments in html format over the Internet and to add a handicraft reference book.