12 resultados para Knowledge for mathematics teaching

em Doria (National Library of Finland DSpace Services) - National Library of Finland, Finland


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This thesis is about the educational purpose of foreign language teaching (FLT) in an increasingly internationalised world.The past 20-30 years have witnessed a fundamental rethinking of the aims of FLT, entailing a shift in emphasis from linguistic competence over communicative competence to intercultural competence. The growing emphasis on cultural issues, called for by research and international curricular documents, places new demandson language teachers. The overall aim of this study is to deepen the knowledge about the attitudes of teachers at the upper level of the Finland-Swedish comprehensive school towards the treatment of culture in English foreign language (EFL) teaching. The questions in focus are: 1) How do teachers interpret the concept"culture" in EFL-teaching?, 2) How do they specify the cultural objectives of their teaching? and 3) What do they do to attain these objectives? The thesis strives to reveal whether or not language teaching today can be describedas intercultural, in the sense that culture is taught with the aim of promotingintercultural understanding, tolerance and empathy. This abductive and largely exploratory study is placed within a constructivist and sociocultural framework,and is inspired by both phenomenography and hermeneutics. It takes its starting-point in language didactics, and can also be regarded as a contribution to teacher cognition research. The empirical data consists of verbatim transcribed interviews with 13 Finland-Swedish teachers of English at grades 7-9. The findings are presented according to three orientations and reviewed with reference to the 2004 Finnish National Framework Curriculum. Within the cognitive orientation, "culture" is perceived as factual knowledge, and the teaching of cultureis defined in terms of the transmission of knowledge, especially about Britain and the USA (Pedagogy of Information). Within the action-related orientation, "culture" is seen as skills of a social and socio-linguistic nature, andthe teaching aims at preparing the students for contacts with people from the target language areas (Pedagogy of Preparation). Within the affective orientation, which takes a more holistic approach, "culture" is seen as a bi-directional perspective. Students are encouraged to look at their own familiar culture from another perspective, and learn to empathise with and show respect for otherness in general, not just concerning representatives of English-speaking countries (Pedagogy of Encounter). Very few of the interviewed teachers represent the third approach, which is the one that can be characterised as truly intercultural. The study indicates that many teachers feel unsure about how to teach culture in an appropriate and up-to-date manner. This is attributed to, among other things, lack of teacher insights as well as lack of time and adequate material. The thesis ends with a set of recommendations as to how EFL could be developed ina more intercultural direction.

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The purpose of the thesis is to study how mathematics is experienced and used in preschool children’s activities and how preschool teachers frame their teaching of mathematical content. The studies include analyses of children’s actions in different activities from a mathematical perspective and preschool teachers’ intentions with and their teaching of mathematics. Preschool teachers’ understanding of the knowledge required in this area is also scrutinised. The theoretical points of departure are variation theory and sociocultural theory. With variation theory the focus is directed towards how mathematical content is dealt with in teaching situations where preschool teachers have chosen the learning objects. The sociocultural perspective has been chosen because children’s mathematical learning in play often takes place in interactions with others and in the encounter with culturally mediated concepts. The theoretical framework also includes didactical points of departure. The study is qualitative, with videography and phenomenography as metholological research approaches. In the study, video observations and interviews with preschool teachers have been used as data collection methods. The results show that in children’s play mathematics consists of volume, geometrical shapes, gravity, quantity and positioning. The situations also include size, patterns, proportions, counting and the creation of pairs. The preschool teachers’ intentions, planning and staging of their goal-oriented work are that all children should be given the opportunity to discern a mathematical content. This also includes making learning objects visible in here-and-now-situations. Variation and a clear focus on the mathematical content are important in this context. One of the study’s knowledge contributions concerns the didactics of mathematics in the preschool. This relates to the teaching of mathematics and includes the knowledge that preschool teachers regard as essential for their teaching. This includes theoretical and practical knowledge about children and children’s learning and didactical issues and strategies. The conclusion is that preschool teachers need to have a basic knowledge of mathematics and the didactics of mathematics.

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Tulevaisuusorientaatio on tullut entistä tärkeämmäksi myös koulumaailmassa johtuen yhteiskunnassa nopeasti eteen tulevista muutoksista. On myös esitetty epäilyjä, että tulevaisuuteen reagoimisessa heikoin tilanne olisikin juuri kuntatason päätöksenteossa. Ymmärrys ja tieto opettajan työstä nimenomaan opettajan omasta perspektiivistä tarkasteltuna mahdollistavat lähtökohdan ja edellytykset todelliselle koulun uudistamiselle. Peruskysymys, johon tässä tutkimuksessa etsittiin vastausta oli: Millaisia ovat lukion aineenopettajien käsitykset lukion muutosprosesseista ja miten he visioivat oman lukionsa ja yleensä lukioiden tulevaisuutta? Aineiston keruu osui ajankohtaan, joka oli hyvin otollinen tulevaisuuden tarkasteluun, sillä uusi opetussuunnitelma otettiin käyttöön kaikissa Suomen lukioissa viimeistään lukuvuonna 2005-2006. Tutkimuksessa oli mukana kaksi hyvin erilaista lukiota Länsi-Suomen läänistä eli pieni maaseudun lukio ja hyvin suuri kaupunkilukio. Tutkimusaineiston keruu eteni kaksivaiheisesti: informoitu kysely ja teemahaastattelu. Tutkimusjoukon suuruus oli yhteensä 20, joista puolet oli miehiä ja puolet naisia. Aineenopettajien käsityksiä muutoksista ja visioista tutkittiin fenomenografisen tutkimusotteen avulla. Fenomenografiassa kiinnostuksen kohteena ovat ihmisten erilaiset käsitykset todellisuudesta ja näin saatava ymmärrys tavoista, joilla ihmiset kokevat tilanteita ja maailmaa. Organisaation muutosprosesseja voidaan kutsua myös oppimiseksi. Tutkimuksen oppivan organisaation näkökulmat perustuivat juuri yhteistyössä tapahtuvaan yhteisen toiminnan kehittämiseen. Aineenopettajien käsityksiä työyhteisöstään tarkasteltiin seuraavista oppivan organisaatiomallin näkökulmista: vuorovaikutus, päätöksenteko sekä rehtorin ja aineenopettajan rooli ja asema työyhteisössä. Aineenopettajien keskeisimmät käsitykset muutoksista lukiossa viime vuosina kohdistuivat aineenopettajan ammattirooliin ja lukio-opiskelijaan sekä opiskelijalta vaadittaviin lukio-opintoihin. Muutokset ammattiroolissa korostavat tutkimustulosten perusteella aineenopettajilta vaadittavia muitakin kuin opetettavien aineiden hallintataitoja. Suoranaista ammattitaidon puutetta opettajat kokivat varsinkin ryhmänohjaustehtävien yhteydessä, osittain myös uusien oppimisympäristöjen, esimerkiksi verkkopedagogisten taitojen, yhteydessä. Opettajien lisäkoulutuksen tarve koetaan konkreettisena, mutta sekä koulutusten sisältöihin, järjestelyihin ja ajankohtiin että koulun sijais- ym. järjestelyihin kaivattaisiin parannuksia. Verrattuna aikaisempiin tutkimuksiin näyttäisi siltä, että luokaton lukio on saanut opettajat enenevässä määrin huolestumaan opiskelijoiden syrjäytymisriskistä ja hyvinvoinnista. Opiskelijoiden syrjäytymisriskin kasvu lukio-opintojen aikana nouseekin yhdeksi lukion pessimistiseksi skenaarioksi. Muista pessimistisistä skenaarioista lukiolle, jotka saattoi johtaa tutkimustuloksista, voidaan mainita työyhteisön demokratiavajeen syveneminen sekä opetussuunnitelmasisältöjen ja ylioppilastutkintovaatimusten välisen kuilun syveneminen. Aineenopettajien käsitykset oman lukionsa visioista olivat sisällöiltään pääosin välineellisiä ja ne kohdentuivat kaikki opiskelijoihin. Esimerkiksi työyhteisöllisiä kehittämisajatuksia ei visioissa ilmennyt. Myöskään visioinnin dynaamisuus ei aineistossa korostunut. Aineenopettajien käsitykset visioiden arvopohjasta heijastivat perinteistä suomalaista arvomaailmaa eli itsekuria, velvollisuudentuntoa, kuuliaisuutta esivaltaa kohtaan ja perinteisten arvojen kunnioittamista. Sen sijaan antiikista perityviä Sokrateen edustamia keskustelua ja auktoriteettien kyseenalaistamista ei arvoissa ilmennyt, eikä myöskään uusliberalistista individualismia. Käsitykset visioiden synnystä näyttävät parhaiten selittävän opettajan muita käsityksiä liittyen visioon, visiointiin ja työyhteisöllisiin vaikutusmahdollisuuksiin sekä opettajan tulevaisuusorientoitumiseen.. Käsitykset vision syntytaustasta voidaan jakaa seuraaviin pää- ja alakategorioihin: 1. auktoriteettikeskeinen visiointi: johdon linjaus tai valtakunnallinen linjaus, 2. yhteisökeskeinen visiointi: yhteisöllinen linjaus tai toiminnallinen linjaus ja 3. yksilökeskeinen visiointi. Pessimistisimmiksi eli vähiten tulevaisuusorientoituneiksi opettajiksi työyhteisössä osoittautuivat ne opettajat, jotka pitivät oman lukionsa visiota koulun johdon sanelemana. Monet teoriat oppivasta organisaatiosta korostavat johtajuuden merkitystä työyhteisöä kehitettäessä. Johtajuuden merkitys nousi tämänkin tutkimuksen aineistosta keskeisesti esiin. Pyrkimystä kohti oppivaa organisaatiota opettajien puheista löytyy paljonkin, esimerkkeinä viittaukset johtajuuden ja vuorovaikutustapojen kehittämistarpeisiin. Sen sijaan opettajien puheet omista työyhteisöllisistä kehittymistarpeistaan, ns. alaistaidot, jäivät vähäisiksi. Tutkimustuloksista on luotu sovellusmalli kouluyhteisöjen visioinnin ja muun kehittämistyön tueksi.

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Teaching the measurement of blood pressure for both nursing and public health nursing students The purpose of this two-phase study was to develop the teaching of blood pressure measurement within the nursing degree programmes of the Universities of Applied Sciences. The first survey phase described what and how blood pressure measurement was taught within nursing degree programmes. The second intervention phase (2004-2005) evaluated first academic year nursing and public health nursing students’ knowledge and skills results for blood pressure measurement. Additionally, the effect on the Taitoviikko experimental group students’ blood pressure measurement knowledge and skills level. A further objective was to construct models for an instrument (RRmittTest) to evaluate nursing students measurement of blood pressure (2003-2009). The research data for the survey phase were collected from teachers (total sampling, N=107, response rate 77%) using a specially developed RRmittopetus-questionnaire. Quasi-experimental study data on the RRmittTest-instrument was collected from students (purposive sampling, experimental group, n=29, control group, n=44). The RRmittTest consisted of a test of knowledge (Tietotesti) and simulation-based test (TaitoSimkäsi and Taitovideo) of skills. Measurements were made immediately after the teaching and in clinical practice. Statistical methods were used to analyse the results and responses to open-ended questions were organised and classified. Due to the small amount of materials involved and the results of distribution tests of the variables, non-parametric analytic methods were mainly used. Experimental group and control group similar knowledge and skills teaching was based on the results of the national survey phase (RRmittopetus) questionnaire results. Experimental group teaching includes the supervised Taitoviikko teaching method. During Taitoviikko students studied blood pressure measurement at the municipal hospital in a real nursing environment, guided by a teacher and a clinical nursing professional. In order to evaluate both learning and teaching the processes and components of blood pressure measurement were clearly defined as follows: the reliability of measurement instruments, activities preceding blood pressure measurement, technical execution of the measurement, recording, lifestyle guidance and measurement at home (self-monitoring). According to the survey study, blood pressure measurement is most often taught at Universities of Applied Sciences, separately, as knowledge (teaching of theory, 2 hours) and skills (classroom practice, 4 hours). The teaching was implemented largely in a classroom and was based mainly on a textbook. In the intervention phase the students had good knowledge of blood pressure measurement. However, their blood pressure measurement skills were deficient and the control group students, in particular, were highly deficient. Following in clinical practice the experimental group and control group students’ blood pressure measurement recording knowledge improve and experimental groups declined lifestyle guidance. Skills did not improve within any of the components analysed. The control groups` skills on the whole, declined statistically.There was a significant decline amongst the experimental group although only in one component measured. The results describe the learning results for first academic year students and no parallel conclusions should be drawn when considering any learning results for graduating students. The results support the use and further development of the Taitoviiko teaching method. The RRmittTest developed for the study should be assessed and the results seen from a negative perspective. This evaluation tool needs to be developed and retested.

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Programming and mathematics are core areas of computer science (CS) and consequently also important parts of CS education. Introductory instruction in these two topics is, however, not without problems. Studies show that CS students find programming difficult to learn and that teaching mathematical topics to CS novices is challenging. One reason for the latter is the disconnection between mathematics and programming found in many CS curricula, which results in students not seeing the relevance of the subject for their studies. In addition, reports indicate that students' mathematical capability and maturity levels are dropping. The challenges faced when teaching mathematics and programming at CS departments can also be traced back to gaps in students' prior education. In Finland the high school curriculum does not include CS as a subject; instead, focus is on learning to use the computer and its applications as tools. Similarly, many of the mathematics courses emphasize application of formulas, while logic, formalisms and proofs, which are important in CS, are avoided. Consequently, high school graduates are not well prepared for studies in CS. Motivated by these challenges, the goal of the present work is to describe new approaches to teaching mathematics and programming aimed at addressing these issues: Structured derivations is a logic-based approach to teaching mathematics, where formalisms and justifications are made explicit. The aim is to help students become better at communicating their reasoning using mathematical language and logical notation at the same time as they become more confident with formalisms. The Python programming language was originally designed with education in mind, and has a simple syntax compared to many other popular languages. The aim of using it in instruction is to address algorithms and their implementation in a way that allows focus to be put on learning algorithmic thinking and programming instead of on learning a complex syntax. Invariant based programming is a diagrammatic approach to developing programs that are correct by construction. The approach is based on elementary propositional and predicate logic, and makes explicit the underlying mathematical foundations of programming. The aim is also to show how mathematics in general, and logic in particular, can be used to create better programs.

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This study addresses the question of teacher educators’ conceptions of mathematics teacher education (MTE) in teacher colleges in Tanzania, and their thoughts on how to further develop it. The tension between exponents of content as opposed to pedagogy has continued to cause challenging conceptual differences, which also influences what teacher educators conceive as desirable in the development of this domain. This tension is connected to the dissatisfaction of parents and teachers with the failure of school mathematics. From this point of view, the overall aim was to identify and describe teacher educators’ various conceptions of MTE. Inspired by the debate among teacher educators about what the balance should be between subject matter and pedagogical knowledge, it was important to look at the theoretical faces of MTE. The theoretical background involved the review of what is visible in MTE, what is yet to be known and the challenges within the practice. This task revealed meanings, perspectives in MTE, professional development and assessment. To do this, two questions were asked, to which no clear solutions satisfactorily existed. The questions to guide the investigation were, firstly, what are teacher educators’ conceptions of MTE, and secondly, what are teacher educators’ thoughts on the development of MTE? The two questions led to the choice of phenomenography as the methodological approach. Against the guiding questions, 27 mathematics teacher educators were interviewed in relation to the first question, while 32 responded to an open-ended questionnaire regarding question two. The interview statements as well as the questionnaire responses were coded and analysed (classified). The process of classification generated patterns of qualitatively different ways of seeing MTE. The results indicate that MTE is conceived as a process of learning through investigation, fostering inspiration, an approach to learning with an emphasis on problem solving, and a focus on pedagogical knowledge and skills in the process of teaching and learning. In addition, the teaching and learning of mathematics is seen as subject didactics with a focus on subject matter and as an organized integration of subject matter, pedagogical knowledge and some school practice; and also as academic content knowledge in which assessment is inherent. The respondents also saw the need to build learner-educator relationships. Finally, they emphasized taking advantage of teacher educators’ neighbourhood learning groups, networking and collaboration as sustainable knowledge and skills sharing strategies in professional development. Regarding desirable development, teacher educators’ thoughts emphasised enhancing pedagogical knowledge and subject matter, and to be determined by them as opposed to conventional top-down seminars and workshops. This study has revealed various conceptions and thoughts about MTE based on teacher educators´ diverse history of professional development in mathematics. It has been reasonably substantiated that some teacher educators teach school mathematics in the name of MTE, hardly distinguishing between the role and purpose of the two in developing a mathematics teacher. What teacher educators conceive as MTE and what they do regarding the education of teachers of mathematics revealed variations in terms of seeing the phenomenon of interest. Within limits, desirable thoughts shed light on solutions to phobias, and in the same way low self-esteem and stigmatization call for the building of teacher educator-student teacher relationships.

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This thesis develops a method for identifying students struggling in their mathematical studies at an early stage. It helps in directing support to students needing and benefiting from it the most. Thus, frustration felt by weaker students may decrease and therefore, hopefully, also drop outs of potential engineering students. The research concentrates on a combination of personality and intelligence aspects. Personality aspects gave information on conation and motivation for learning. This part was studied from the perspective of motivation and self-regulation. Intelligence aspects gave information on declarative and procedural knowledge: what had been taught and what was actually mastered. Students answered surveys on motivation and self-regulation in 2010 and 2011. Based on their answers, background information, results in the proficiency test, and grades in the first mathematics course, profiles describing the students were formed. In the following years, the profiles were updated with new information obtained each year. The profiles used to identify struggling students combine personality (motivation, selfregulation, and self-efficacy) and intelligence (declarative and procedural knowledge) aspects at the beginning of their studies. Identifying students in need of extra support is a good start, but methods for providing support must be found. This thesis also studies how this support could be taken into account in course arrangements. The methods used include, for example, languaging and scaffolding, and continuous feedback. The analysis revealed that allocating resources based on the predicted progress does not increase costs or lower the results of better students. Instead, it will help weaker students obtain passing grades.

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The study focuses on primary school teachers’ perceptions of environmental education, its integration into primary school education and teachers’ teaching practices in Tanzania. The thesis is based on empirical research. The theoretical underpinnings of the study are based on Palmer’s (1998) model of environmental education. According to the model, meaningful environmental education should include education about, in or through and for the environment. The study is supported by national and international literature from research done on environmental education and education for sustainable development and policy statements. The study is qualitative in nature, adopting phenomenography and phenomenology as points of departure. The empirical data was collected from four primary schools in Morogoro region in Tanzania. The study sample consisted of 31 primary school teachers. Data was collected through interviews and lesson observations. According to the results of the study, primary school teachers expressed variations in their perceptions of environmental education and education for sustainable development. Most of the teachers focused on the aspect of knowledge acquisition. According to Tanzanian education and training policy, environmental education has to be integrated into all subjects. Although there is environmental education in the primary school curriculum, it is not integrated on an equal footing in all subjects. Some subjects like science, social studies and geography have more environmental content than other subjects. Teachers claim that the approach used to integrate environmental education into the school curriculum was not favoured because many claimed that what is to be taught as environmental education in the various subjects is not shown clearly. As a result, many teachers suggested that to ensure that it is taught properly it should be included in the curriculum as an independent subject or as specific topics. The study revealed that teachers’ teaching practices in integrating environmental education varied from one subject to another. Although most of the teachers said that they used participatory methods, lesson observations showed that they limited themselves to question and answer and group discussion. However, the teachers faced a number of barriers in the teaching of environmental education, some of which include lack of teaching and learning resources, time and large class size. The role of teachers in the implementation of environmental education in developing an environmentally literate citizenry is of great significance. The responsibility of the government in developing a curriculum with clear goals and content, developing teachers’ capacity in the teaching of environmental education and provision of teaching and learning materials needs to be taken seriously by the government in educational plans and programs.

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The aim of the study was to create and evaluate an intervention programme for Tanzanian children from a low-income area who are at risk of reading and writing difficulties. The learning difficulties, including reading and writing difficulties, are likely to be behind many of the common school problems in Tanzania, but they are not well understood, and research is needed. The design of the study included an identification and intervention phase with follow-up. A group based dynamic assessment approach was used in identifying children at risk of difficulties in reading and writing. The same approach was used in the intervention. The study was a randomized experiment with one experimental and two control groups. For the experimental and the control groups, a total of 96 (46 girls and 50 boys) children from grade one were screened out of 301 children from two schools in a low income urban area of Dar-es-Salaam. One third of the children, the experimental group, participated in an intensive training programme in literacy skills for five weeks, six hours per week, aimed at promoting reading and writing ability, while the children in the control groups had a mathematics and art programme. Follow-up was performed five months after the intervention. The intervention programme and the tests were based on the Zambian BASAT (Basic Skill Assessment Tool, Ketonen & Mulenga, 2003), but the content was drawn from the Kiswahili school curriculum in Tanzania. The main components of the training and testing programme were the same, only differing in content. The training process was different from traditional training in Tanzanian schools in that principles of teaching and training in dynamic assessment were followed. Feedback was the cornerstone of the training and the focus was on supporting the children in exploring knowledge and strategies in performing the tasks. The experimental group improved significantly more (p = .000) than the control groups during the intervention from pre-test to follow-up (repeated measures ANOVA). No differences between the control groups were noticed. The effect was significant on all the measures: phonological awareness, reading skills, writing skills and overall literacy skills. A transfer effect on school marks in Kiswahili and English was found. Following a discussion of the results, suggestions for further research and adaptation of the programme are presented.

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The focus of the present work was on 10- to 12-year-old elementary school students’ conceptual learning outcomes in science in two specific inquiry-learning environments, laboratory and simulation. The main aim was to examine if it would be more beneficial to combine than contrast simulation and laboratory activities in science teaching. It was argued that the status quo where laboratories and simulations are seen as alternative or competing methods in science teaching is hardly an optimal solution to promote students’ learning and understanding in various science domains. It was hypothesized that it would make more sense and be more productive to combine laboratories and simulations. Several explanations and examples were provided to back up the hypothesis. In order to test whether learning with the combination of laboratory and simulation activities can result in better conceptual understanding in science than learning with laboratory or simulation activities alone, two experiments were conducted in the domain of electricity. In these experiments students constructed and studied electrical circuits in three different learning environments: laboratory (real circuits), simulation (virtual circuits), and simulation-laboratory combination (real and virtual circuits were used simultaneously). In order to measure and compare how these environments affected students’ conceptual understanding of circuits, a subject knowledge assessment questionnaire was administered before and after the experimentation. The results of the experiments were presented in four empirical studies. Three of the studies focused on learning outcomes between the conditions and one on learning processes. Study I analyzed learning outcomes from experiment I. The aim of the study was to investigate if it would be more beneficial to combine simulation and laboratory activities than to use them separately in teaching the concepts of simple electricity. Matched-trios were created based on the pre-test results of 66 elementary school students and divided randomly into a laboratory (real circuits), simulation (virtual circuits) and simulation-laboratory combination (real and virtual circuits simultaneously) conditions. In each condition students had 90 minutes to construct and study various circuits. The results showed that studying electrical circuits in the simulation–laboratory combination environment improved students’ conceptual understanding more than studying circuits in simulation and laboratory environments alone. Although there were no statistical differences between simulation and laboratory environments, the learning effect was more pronounced in the simulation condition where the students made clear progress during the intervention, whereas in the laboratory condition students’ conceptual understanding remained at an elementary level after the intervention. Study II analyzed learning outcomes from experiment II. The aim of the study was to investigate if and how learning outcomes in simulation and simulation-laboratory combination environments are mediated by implicit (only procedural guidance) and explicit (more structure and guidance for the discovery process) instruction in the context of simple DC circuits. Matched-quartets were created based on the pre-test results of 50 elementary school students and divided randomly into a simulation implicit (SI), simulation explicit (SE), combination implicit (CI) and combination explicit (CE) conditions. The results showed that when the students were working with the simulation alone, they were able to gain significantly greater amount of subject knowledge when they received metacognitive support (explicit instruction; SE) for the discovery process than when they received only procedural guidance (implicit instruction: SI). However, this additional scaffolding was not enough to reach the level of the students in the combination environment (CI and CE). A surprising finding in Study II was that instructional support had a different effect in the combination environment than in the simulation environment. In the combination environment explicit instruction (CE) did not seem to elicit much additional gain for students’ understanding of electric circuits compared to implicit instruction (CI). Instead, explicit instruction slowed down the inquiry process substantially in the combination environment. Study III analyzed from video data learning processes of those 50 students that participated in experiment II (cf. Study II above). The focus was on three specific learning processes: cognitive conflicts, self-explanations, and analogical encodings. The aim of the study was to find out possible explanations for the success of the combination condition in Experiments I and II. The video data provided clear evidence about the benefits of studying with the real and virtual circuits simultaneously (the combination conditions). Mostly the representations complemented each other, that is, one representation helped students to interpret and understand the outcomes they received from the other representation. However, there were also instances in which analogical encoding took place, that is, situations in which the slightly discrepant results between the representations ‘forced’ students to focus on those features that could be generalised across the two representations. No statistical differences were found in the amount of experienced cognitive conflicts and self-explanations between simulation and combination conditions, though in self-explanations there was a nascent trend in favour of the combination. There was also a clear tendency suggesting that explicit guidance increased the amount of self-explanations. Overall, the amount of cognitive conflicts and self-explanations was very low. The aim of the Study IV was twofold: the main aim was to provide an aggregated overview of the learning outcomes of experiments I and II; the secondary aim was to explore the relationship between the learning environments and students’ prior domain knowledge (low and high) in the experiments. Aggregated results of experiments I & II showed that on average, 91% of the students in the combination environment scored above the average of the laboratory environment, and 76% of them scored also above the average of the simulation environment. Seventy percent of the students in the simulation environment scored above the average of the laboratory environment. The results further showed that overall students seemed to benefit from combining simulations and laboratories regardless of their level of prior knowledge, that is, students with either low or high prior knowledge who studied circuits in the combination environment outperformed their counterparts who studied in the laboratory or simulation environment alone. The effect seemed to be slightly bigger among the students with low prior knowledge. However, more detailed inspection of the results showed that there were considerable differences between the experiments regarding how students with low and high prior knowledge benefitted from the combination: in Experiment I, especially students with low prior knowledge benefitted from the combination as compared to those students that used only the simulation, whereas in Experiment II, only students with high prior knowledge seemed to benefit from the combination relative to the simulation group. Regarding the differences between simulation and laboratory groups, the benefits of using a simulation seemed to be slightly higher among students with high prior knowledge. The results of the four empirical studies support the hypothesis concerning the benefits of using simulation along with laboratory activities to promote students’ conceptual understanding of electricity. It can be concluded that when teaching students about electricity, the students can gain better understanding when they have an opportunity to use the simulation and the real circuits in parallel than if they have only the real circuits or only a computer simulation available, even when the use of the simulation is supported with the explicit instruction. The outcomes of the empirical studies can be considered as the first unambiguous evidence on the (additional) benefits of combining laboratory and simulation activities in science education as compared to learning with laboratories and simulations alone.

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The aim of the present set of studies was to explore primary school children’s Spontaneous Focusing On quantitative Relations (SFOR) and its role in the development of rational number conceptual knowledge. The specific goals were to determine if it was possible to identify a spontaneous quantitative focusing tendency that indexes children’s tendency to recognize and utilize quantitative relations in non-explicitly mathematical situations and to determine if this tendency has an impact on the development of rational number conceptual knowledge in late primary school. To this end, we report on six original empirical studies that measure SFOR in children ages five to thirteen years and the development of rational number conceptual knowledge in ten- to thirteen-year-olds. SFOR measures were developed to determine if there are substantial differences in SFOR that are not explained by the ability to use quantitative relations. A measure of children’s conceptual knowledge of the magnitude representations of rational numbers and the density of rational numbers is utilized to capture the process of conceptual change with rational numbers in late primary school students. Finally, SFOR tendency was examined in relation to the development of rational number conceptual knowledge in these students. Study I concerned the first attempts to measure individual differences in children’s spontaneous recognition and use of quantitative relations in 86 Finnish children from the ages of five to seven years. Results revealed that there were substantial inter-individual differences in the spontaneous recognition and use of quantitative relations in these tasks. This was particularly true for the oldest group of participants, who were in grade one (roughly seven years old). However, the study did not control for ability to solve the tasks using quantitative relations, so it was not clear if these differences were due to ability or SFOR. Study II more deeply investigated the nature of the two tasks reported in Study I, through the use of a stimulated-recall procedure examining children’s verbalizations of how they interpreted the tasks. Results reveal that participants were able to verbalize reasoning about their quantitative relational responses, but not their responses based on exact number. Furthermore, participants’ non-mathematical responses revealed a variety of other aspects, beyond quantitative relations and exact number, which participants focused on in completing the tasks. These results suggest that exact number may be more easily perceived than quantitative relations. As well, these tasks were revealed to contain both mathematical and non-mathematical aspects which were interpreted by the participants as relevant. Study III investigated individual differences in SFOR 84 children, ages five to nine, from the US and is the first to report on the connection between SFOR and other mathematical abilities. The cross-sectional data revealed that there were individual differences in SFOR. Importantly, these differences were not entirely explained by the ability to solve the tasks using quantitative relations, suggesting that SFOR is partially independent from the ability to use quantitative relations. In other words, the lack of use of quantitative relations on the SFOR tasks was not solely due to participants being unable to solve the tasks using quantitative relations, but due to a lack of the spontaneous attention to the quantitative relations in the tasks. Furthermore, SFOR tendency was found to be related to arithmetic fluency among these participants. This is the first evidence to suggest that SFOR may be a partially distinct aspect of children’s existing mathematical competences. Study IV presented a follow-up study of the first graders who participated in Studies I and II, examining SFOR tendency as a predictor of their conceptual knowledge of fraction magnitudes in fourth grade. Results revealed that first graders’ SFOR tendency was a unique predictor of fraction conceptual knowledge in fourth grade, even after controlling for general mathematical skills. These results are the first to suggest that SFOR tendency may play a role in the development of rational number conceptual knowledge. Study V presents a longitudinal study of the development of 263 Finnish students’ rational number conceptual knowledge over a one year period. During this time participants completed a measure of conceptual knowledge of the magnitude representations and the density of rational numbers at three time points. First, a Latent Profile Analysis indicated that a four-class model, differentiating between those participants with high magnitude comparison and density knowledge, was the most appropriate. A Latent Transition Analysis reveal that few students display sustained conceptual change with density concepts, though conceptual change with magnitude representations is present in this group. Overall, this study indicated that there were severe deficiencies in conceptual knowledge of rational numbers, especially concepts of density. The longitudinal Study VI presented a synthesis of the previous studies in order to specifically detail the role of SFOR tendency in the development of rational number conceptual knowledge. Thus, the same participants from Study V completed a measure of SFOR, along with the rational number test, including a fourth time point. Results reveal that SFOR tendency was a predictor of rational number conceptual knowledge after two school years, even after taking into consideration prior rational number knowledge (through the use of residualized SFOR scores), arithmetic fluency, and non-verbal intelligence. Furthermore, those participants with higher-than-expected SFOR scores improved significantly more on magnitude representation and density concepts over the four time points. These results indicate that SFOR tendency is a strong predictor of rational number conceptual development in late primary school children. The results of the six studies reveal that within children’s existing mathematical competences there can be identified a spontaneous quantitative focusing tendency named spontaneous focusing on quantitative relations. Furthermore, this tendency is found to play a role in the development of rational number conceptual knowledge in primary school children. Results suggest that conceptual change with the magnitude representations and density of rational numbers is rare among this group of students. However, those children who are more likely to notice and use quantitative relations in situations that are not explicitly mathematical seem to have an advantage in the development of rational number conceptual knowledge. It may be that these students gain quantitative more and qualitatively better self-initiated deliberate practice with quantitative relations in everyday situations due to an increased SFOR tendency. This suggests that it may be important to promote this type of mathematical activity in teaching rational numbers. Furthermore, these results suggest that there may be a series of spontaneous quantitative focusing tendencies that have an impact on mathematical development throughout the learning trajectory.

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Speed, uncertainty and complexity are increasing in the business world all the time. When knowledge and skills become quickly irrelevant, new challenges are set for information technology (IT) education. Meta-learning skills – learning how to learn rapidly - and innovation skills have become more essential than single technologies or other specific issues. The drastic changes in the information and communications technology (ICT) sector have caused a need to reconsider how IT Bachelor education in Universities of Applied Sciences should be organized and employed to cope with the change. The objective of the study was to evaluate how a new approach to IT Bachelor education, the ICT entrepreneurship study path (ICT-ESP) fits IT Bachelor education in a Finnish University of Applied Sciences. This kind of educational arrangement has not been employed elsewhere in the context of IT Bachelor education. The study presents the results of a four-year period during which IT Bachelor education was renewed in a Finnish University of Applied Sciences. The learning environment was organized into an ICT-ESP based on Nonaka’s knowledge theory and Kolb’s experiental learning. The IT students who studied in the ICT-ESP established a cooperative and learned ICT by running their cooperative at the University of Applied Sciences. The students (called team entrepreneurs) studied by reading theory in books and other sources of explicit information, doing projects for their customers, and reflecting in training sessions on what was learnt by doing and by studying the literature. Action research was used as the research strategy in this study. Empirical data was collected via theme-based interviews, direct observation, and participative observation. Grounded theory method was utilized in the data analysis and the theoretical sampling was used to guide the data collection. The context of the University of Applied Sciences provided a good basis for fostering team entrepreneurship. However, the results showed that the employment of the ICT-ESP did not fit into the IT Bachelor education well enough. The ICT-ESP was cognitively too tough for the team entrepreneurs because they had two different set of rules to follow in their studies. The conventional courses engaged lot of energy which should have been spent for professional development in the ICT-ESP. The amount of competencies needed in the ICT-ESP for professional development was greater than those needed for any other ways of studying. The team entrepreneurs needed to develop skills in ICT, leadership and self-leadership, team development and entrepreneurship skills. The entrepreneurship skills included skills on marketing and sales, brand development, productization, and business administration. Considering the three-year time the team entrepreneurs spent in the ICT-ESP, the challenges were remarkable. Changes to the organization of IT Bachelor education are also suggested in the study. At first, it should be admitted that the ICT-ESP produces IT Bachelors with a different set of competencies compared to the conventional way of educating IT Bachelors. Secondly, the number of courses on general topics in mathematics, physics, and languages for team entrepreneurs studying in the ICTESP should be reconsidered and the conventional course-based teaching of the topics should be reorganized to support the team coaching process of the team entrepreneurs with their practiceoriented projects. Third, the upcoming team entrepreneurs should be equipped with relevant information about the ICT-ESP and what it would require in practice to study as a team entrepreneur. Finally, the upcoming team entrepreneurs should be carefully selected before they start in the ICT-ESP to have a possibility to eliminate solo players and those who have a too romantic view of being a team entrepreneur. The results gained in the study provided answers to the original research questions and the objectives of the study were met. Even though the IT degree programme was terminated during the research process, the amount of qualitative data gathered made it possible to justify the interpretations done.