This study was designed to describe and understand how children perceive and explain mathematical situations. During our work based training we have met several students who have been insecure in the subject of mathematics and therefore come to think that it's difficult and boring. The questions we have asked ourselves are why and how this insecurity occurs. In preschools around the country teachers actively worked to create opportunities for children to meet and discover mathematics. The question is whether the teachers are aware of how children perceive mathematics and how children think in mathematical situations.  We chose to conduct a qualitative study using different methods of data collecting in order to approach the children's world. We have used interviews, observations, experimental circle times and drawings. This study assumes a child’s perspective, because we want to understand their thoughts and perceptions about mathematics. The starting point is the didactic questions what, how and why.  The result of our study indicates that children in preschool perceive mathematics in different ways and that they are unaware that they actually can use and understand athematical situations in the specific context that is preschool. / Studiens syfte var att beskriva och förstå hur barn uppfattar och beskriver matematiska situationer. Vi har under vår verksamhetsförlagda utbildning mött flera elever som har varit osäkra inom matematik och där med tyckt att ämnet är svårt och tråkigt. Vi ställer oss då frågan varför det är så och hur detta tänkesätt uppstår. I förskolan runt om i landet arbetas det aktivt för att skapa möjligheter för barnen att få möta och upptäcka matematik. Frågan är om lärarna är medvetna om hur barn uppfattar matematik och hur barnen tänker kring matematiska situationer.  Vi valde att göra en kvalitativ studie och med hjälp av olika datainsamlingsmetoder närma oss barnens värld. Vi har använt oss av intervjuer, observation, experimentella samlingar och teckningar. Studien utgår ifrån barns perspektiv, då vi vill få förståelse för deras uppfattningar och beskrivningar inom matematik. Utgångspunkten har varit de didaktiska frågeställningarna Vad, Hur och Varför.  Resultatet i vår studie visar att barn i förskolan dagligen använder matematik i verksamheten, men de är omedvetna om att de faktiskt kan, använder och förstår matematiska situationer i den specifika kontexten som är förskola.

När elever börjar i årskurs 1 på gymnasiet kan det förekomma att deras förkunskaper i matematik undersöks med någon form av diagnostiskt test. Syftet med min undersökning är att få veta i vilken utsträckning det förekommer diagnostiskt test, och om dessa test prövar kunskaper baserade på kursmålen i grundskolans årskurs 9. I samband med detta vill jag också försöka få svar på om tillvägagångssättet att inhämta information skiljer sig mellan lärare beroende på ålder, yrkeserfarenhet eller andra faktorer. För att få svar på mina frågor har jag valt att använda mig av kvantitativ metod i form av enkät, och en kvalitativ dokumentanalys på ett urval av diagnostiska test. Enkäten skickades ut till samtliga matematiklärare på kommunala gymnasieskolor i tre kommuner, totalt 76 stycken. Svaren visar att en majoritet av lärarna anser att det är viktigt att inhämta information om sina kommande elever och att detta vanligtvis sker vanligast med hjälp av skriftliga diagnostiska test. De diagnostiska tester som lärarna har utformat provar ett begränsat antal områden och delar av kunskapsmålen får årskurs 9. Min undersökning pekar inte på att något annat än att just detta prövas. / In many cases during the first year of upper secondary school the mathematical knowledge and skills of the students are investigated by using some form of diagnostic test. The purpose of this study is to find out to what extent the knowledge of the students is being tested diagnostically, if these tests are based on the aims of grade 9 of compulsory school and how the teachers gather that information. Along with this I am also trying to answer the question whether the ways of gathering information differ depending on the age of the teachers, their experience or other factors. To answer these questions I have chosen a quantitative method using a questionnaire and also a qualitative method to analyse a sample of tests. The questionnaire was sent to all teachers in mathematics at municipal sixth-form schools in three municipalities, in total 76 teachers. The answers show that a majority of the teachers think it is important to gather information about their students to be and that most commonly, the information is gathered using written diagnostically tests. The diagnostically tests analyzed in this essay tests certain parts and areas of the goals of year 9. This study does not indicate that anything but these goals are tested.

The purpose of this study was to investigate plane geometry problem solving strategies of pre-service elementary mathematics teachers in technology and paper-and-pencil environments after receiving an instruction with GeoGebra. Qualitative research strategies were used to investigate teacher candidates&lsquo / solution strategies. The data was collected and analyzed by means of a multiple case study design. The study was carried out with 7 pre-service elementary mathematics teachers. The main data sources were classroom observations and interviews. After receiving a three-week instructional period, the participants experienced data collection sessions during a week. The data was analyzed by using records of the interviews, answers to the instrument, and transcribing and examining observation records. Results revealed that the participants developed three solution strategies: algebraic, geometric and harmonic. They used mostly algebraic solutions in paper-and-pencil environment and v geometric ones in technology environment. It means that different environments contribute separately pre-service teachers&lsquo / mathematical problem solving abilities. Different from traditional environments, technology contributed students&lsquo / mathematical understanding by means of dynamic features. In addition, pre-service teachers saved time, developed alternative strategies, constructed the figures precisely, visualized them easily, and measured accurately and quickly. The participants faced some technical difficulties in using the software at the beginning of the study but they overcome most of them at the end of instructional period. The results of this study has useful implications for mathematics teachers to use technology during their problem solving activities as educational community encourages to use technology in teaching and learning of mathematics.

Elevers upplevelser av att befinna sig i stödåtgärder är antagligen av stort intresse för de lärare som undervisar elever med allmänna eller specifika matematiksvårigheter. Hur beskriver då några elever själva sina upplevelser av stödåtgärder? Syftet med denna studie är att få större kunskap om och ökad förståelse för hur stödåtgärder i matematik upplevs av de elever som fått särskilt stöd under en längre period. För att kunna ta del av några elevers upplevelser av stödåtgärder valde jag att utgå från en livsvärldsfenomenologisk forskningsansats. Denna ansats lämpar sig väl för att studera just upplevelsen i elevernas livsvärldar. Jag har fått möjlighet att ta del av elevers upplevelser och erfarenheter så som de själva beskriver dem och sedan hermeneutiskt tolkat dessa utifrån min egen förförståelse och erfarenhet. Det resultat som jag presenterar bygger på intervjuer jag genomfört med tre elever i årskurs 9. Resultatet berättar om dessa tre elevers upplevelser av stödåtgärder i matematik och jag finner här både likheter och skillnader. För de elever som jag intervjuat innebar stödåtgärder framförallt det som sker utanför den ordinarie undervisningen, det vill säga extra matematik lektioner, men efter reflektion och samtal nämner eleverna även annat material, extra böcker, lättare böcker och miniräknare som exempel på stödåtgärder. Elevernas berättelser om positiva upplevelser handlar om att få mer tid med läraren. Stödåtgärderna blir mer positivt mottagna då eleverna själva känner sig delaktiga i valet av stödåtgärder. Resultatet kan tolkas som att då eleven beskriver sig själv som bärare av problematiken blir eleven mer positiv till den hjälp han får. Resultatet tolkar jag som att läraren och relationen till läraren är av stor betydelse för elevens upplevelse av de stödåtgärder som sätts in. / The experiences of students receiving support measures are probably of great interest to teachers who teach students with general or specific difficulties in mathematics. How do students themselves describe their experiences of support measures? The purpose of this study is to gain greater knowledge and understanding of how support measures in mathematics is perceived by the students who have received special support for an extended period of time. In order to study and observe the experiences of students who receive support measures, I have chosen a phenomenological life-world approach. This approach is well suited for studying the experiences in students' life worlds. I have had the opportunity to share students’ experiences as they describe them themselves, and then hermeneutically interpreted them from my own understanding and experience. The results presented in this thesis are based on interviews which I conducted with three students in the grade 9. The findings tell us about the three students' own experiences of support measures in mathematics. I found both similarities and differences. For the students I have interviewed, support measures above all mean what occurs outside the regular curriculum, that is extra lessons in Mathematics, but after reflection and discussion the students also mention other material, extra books, easier books and calculators as examples of support measures.   Students' accounts of positive experiences are about spending more time with their teacher. The help was more positively received when the students themselves were made to feel a part of the selection of measures. The result can be interpreted as when the student describes himself as the bearer of the problem, the student becomes more positive to the help he gets. I interpret the result as that the teacher and the relationship to the teacher are of great importance to students' experiences of support measures.

Studien syftar till att beskriva hur lärare i matematik upplever att de praktiskt hanterar elevers olika förutsättningar i sin matematikundervisning. Undersökningen genomfördes som en fallstudie av två lärare i matematik i grundskolans senare år. Det empiriska materialet består av fyra klassrumsobservationer, som analyserades för att identifiera olika typer av individualisering, samt fyra intervjuer, för att belysa lärarnas upplevelser av och tankar kring individualisering. Det framkom att det förekommer flera olika typer av individualisering. En del individualisering var ett resultat av lärarens medvetna val, men det förekom även individualisering som lärarna delvis var omedvetna om. / The study aims to describe how teachers of mathematics feel that they practically handle student differences in their mathematics teaching. The survey was conducted as a case study of two teachers of mathematics in secondary school. The empirical material consists of four classroom observations, which were analyzed to identify types of individualization, and four interviews, to highlight the teachers' experiences of and thoughts about individualization. It was found that there are several different types of individualization. Some individualization was the result of the teacher's conscious choice, but there were also individualization as teachers in part, were unaware of.

This study analyzes the kinds of beliefs pre-service elementary mathematics teachers hold about mathematical problem solving, and investigates whether, or not, gender and university attended have any significant effect on their problem solving beliefs. The sample of the present study consisted of 244 senior undergraduate students studying in Elementary Mathematics Teacher Education programs at 5 different universities located in Ankara, Bolu, and Samsun. Data were collected in spring semester of 2005-2006 academic years. Participants completed a survey composed of three parts as demographic information sheet, questionnaire items, and non-routine mathematics problems. The results of the study showed that in general the pre-service elementary mathematics teachers indicated positive beliefs about mathematical problem solving. However, they still had several traditional beliefs related to the importance of computational skills in mathematics education, and following predetermined sequence of steps while solving problems. Moreover, a number of pre-service teachers appeared to highly value problems that are directly related to the mathematics curriculum, and do not require spending too much time. Also, it was found that although the pre-service teachers theoretically appreciated the importance and role of the technology while solving problems, this belief was not apparent in their comments about non-routine problems. In addition to these, the present study indicated that female and male pre-service teachers did not differ in terms of their beliefs about mathematical problem solving. However, the pre-service teachers&rsquo / beliefs showed significant difference when the universities attended was concerned.

<p>This study was designed to describe and understand how children perceive and explain mathematical situations. During our work based training we have met several students who have been insecure in the subject of mathematics and therefore come to think that it's difficult and boring. The questions we have asked ourselves are why and how this insecurity occurs. In preschools around the country teachers actively worked to create opportunities for children to meet and discover mathematics. The question is whether the teachers are aware of how children perceive mathematics and how children think in mathematical situations.</p><p> We chose to conduct a qualitative study using different methods of data collecting in order to approach the children's world. We have used interviews, observations, experimental circle times and drawings. This study assumes a child’s perspective, because we want to understand their thoughts and perceptions about mathematics. The starting point is the didactic questions what, how and why.</p><p> The result of our study indicates that children in preschool perceive mathematics in different ways and that they are unaware that they actually can use and understand athematical situations in the specific context that is preschool.</p> / <p>Studiens syfte var att beskriva och förstå hur barn uppfattar och beskriver matematiska situationer. Vi har under vår verksamhetsförlagda utbildning mött flera elever som har varit osäkra inom matematik och där med tyckt att ämnet är svårt och tråkigt. Vi ställer oss då frågan varför det är så och hur detta tänkesätt uppstår. I förskolan runt om i landet arbetas det aktivt för att skapa möjligheter för barnen att få möta och upptäcka matematik. Frågan är om lärarna är medvetna om hur barn uppfattar matematik och hur barnen tänker kring matematiska situationer.</p><p> Vi valde att göra en kvalitativ studie och med hjälp av olika datainsamlingsmetoder närma oss barnens värld. Vi har använt oss av intervjuer, observation, experimentella samlingar och teckningar. Studien utgår ifrån barns perspektiv, då vi vill få förståelse för deras uppfattningar och beskrivningar inom matematik. Utgångspunkten har varit de didaktiska frågeställningarna Vad, Hur och Varför.</p><p> Resultatet i vår studie visar att barn i förskolan dagligen använder matematik i verksamheten, men de är omedvetna om att de faktiskt kan, använder och förstår matematiska situationer i den specifika kontexten som är förskola.</p>

Στον Πατραϊκό κόλπο έχουν γίνει πλήθος ερευνητικών εργασιών με διαφορετικά αντικείμενα. Στη Φυσική Ωκεανογραφία φαίνεται να εμφανίζεται ένα ερευνητικό κενό, που αφορά την προσομοίωση της κυκλοφορίας του νερού στην περιοχή. Το κενό αυτό προσπαθεί να καλύψει η εργασία αυτή, με απώτερο σκοπό την κατανόηση του υδροδυναμικού καθεστώτος της περιοχής μελέτης. Στην εργασία χρησιμοποιούνται όλες οι υφιστάμενες βιβλιογραφικές πηγές και μετρήσεις. Επίσης χρησιμοποιείται το μαθηματικό μοντέλο ΜΙΚΕ21 για την δυσδιάστατη προσομοίωση της κυκλοφορίας του νερού αφού πρώτα προηγήθηκε η βαθμονόμηση του. Το αποτέλεσμα της εργασίας αυτής οδηγεί στην κατανόηση της δυσδιάστατης υδροδυναμικής κυκλοφορίας του νερού, κυρίως στον Πατραϊκό κόλπο αλλά και στο Στενό Ρίου – Αντιρρίου και σε ένα μικρό τμήμα του Κορινθιακού κόλπου. / In the Patras gulf they have become many of inquiring work with different objects. In the Natural Oceanography it appears that is presented an inquiring void that concerns the simulation of circulation of water in the region. This project tries to cover this void, with final aim the comprehension of hydrodynamic arrangement of region of study. In the work are used all the existing bibliographic sources and measurements. Also is used mathematic model MIKE21 for the 2-dimensions simulation of water circulation. The result of this work leads to the comprehension of 2-dimensions hydrodynamic circulation of water, mainly to the Patras gulf but also to the channel Rio-Antirio and to a small part of Corinthian gulf.

The aim of this study has been to survey what kind of view primary school teachers have on the dyscalculia diagnosis, and which learning methods they believe are important for pupils with mathematic difficulties and dyscalculia. The study will also clarify what they believe is important in the development of the pupils’ self-perception. The following questions have been covered What is the primary school teachers view on the diagnosis dyscalculia? Which learning methods do the teachers consider to be the best for pupils with mathematic difficulties and dyscalculia? How are teachers in primary school reasoning over the identity of pupils with mathematic difficulties and dyscalculia? The method used to answer these questions has been the qualitative research method. This method goes in-depth with the goal of producing coherence and entirety. It aims to convey understanding (Larsen, 2009). The empirical material has been analyzed and discussed based on various theories as starting point. The theoretical starting points have been the sociocultural perspective, the concept of integration, the special education perspective and the concept of identity. The study shows that the teachers have rich, but different reasonings regarding dyscalculia as a diagnosis. They have different perceptions of how the teaching should be organized for pu-pils with mathematic difficulties and dyscalculia. The teachers believe that the school is playing a role in the self-perception of the pupils, but they are divided in their opinions re-garding whether it is decisive or not. They consider that there are various factors in the pupils‘ school life that has great influence on the pupils’ self-perception.

Baigiamajame darbe nagrinėjamos visureigio automobilio dinaminės charakteristikos bei pagrindiniai jas lemiantys parametrai, ieškoma būdų šių parametrų pagerinimui. Taip pat darbe apžvelgiamos automobilį veikiančios jėgos, apžvelgiama automobilio masės bei įkrovos lygio įtaka automobilio dinamikai, priekabos įtaka automobilio stabilumui bei valdomumui. Atlikus eksperimentinius visureigio automobilio kėbulo svyravimų bandymus priklausomai nuo: priekabos įkrovos, kelio dangos, bei transporto priemonės ir transporto priemonių junginio greičio gauti rezultatai išanalizuoti ir palyginti tarpusavyje. Pateikiami skaitinius bandymų rezultatus atitinkantys grafikai. Išvadose apibendrinami tyrimo rezultatai. / This master thesis analysis dynamic characteristics of all – terrain vehicle, main parameters having impact on them, searches for ways to improve them. The paper also reviews the forces operating on the vehicle, reviews the impact of the vehicle’s weight and the level of load on the dynamics of the vehicle, the influence of a trailer on the stability and controllability of the vehicle. The results of the experimental tests of all – terrain vehicles body’s swinging were analyzed and compared. The charts depicting numeric results of tests are provided. The conclusions summarize the results of the research.