The diploma thesis deals with the topic of a didactic mathematical environment Biland. The theoretical part is concerned with the definition of two opposite educational styles, transmissive and constructivist, and their comparison. Within the constructivist educational style, it is also focused on The Hejný's method, and it defines the two basic pillars of this conception. The first pillar is the personality of the teacher and the other one is the mathematical content, which is provided by different mathematical environments. This diploma thesis introduces the environment Biland, describes on which mathematical basis it stands on and shows why should be Biland included into the teaching of mathematics. It answers the question of importancy of teaching also non-base ten systems and therefore it describes the history of place-value system. It also studies the tasks in contemporary textbooks of mathematics for primary schools by Hejný et al. published by publishing house FRAUS. The practical part includes the preparation and implementation of experiments in which the new environment Biland was introduced to the pupils. The experiments were recorded into protocols, followed by analysis. Another aim of the practical part was creation of worksheets for the pupils which were handed out after the...

I årskurserna 4–6 ska eleverna genomgå en progression att lära sig hur rationella tal och tal i decimalform är uppbyggda. Forskning har visat att det kan uppstå flera svårigheter och missuppfattningar kring området, bland annat veta siffrors olika platsvärde. Denna studie har inspirerats av en tidigare studie, genomförd av Jarl och Johansson (2014). Syftet med denna studie är att jämföra om samma kritiska aspekter som identifierats i Jarl och Johansson (2014) studie även visar sig i andra elevgrupper. Frågeställningen som studien ska besvara är: Vilka kritiska aspekter kan identifieras i en årskurs 4 och en årskurs 5 kring tal i decimalform? För att kunna besvara frågeställningen har eleverna i denna studie fått genomföra ett arbetsblad med uppgifter kopplade till tal i decimalform. Därefter har kvalitativa intervjuer genomförts för att få en breddad insikt kring vilka kritiska aspekter eleverna har eller inte har urskilt. Metodvalet i studien har inslag av variationsteorin där eleverna behöver få syn på nödvändiga detaljer (i studien benämnd som kritiska aspekter). Studiens resultat visar att samtliga kritiska aspekter som identifierades i Jarl och Johanssons (2014) studie, även var kritiska i denna studie. Däremot identifierades en ny kritisk aspekt: Elever behöver förstå att siffror på varsin sida om decimaltecknet tillsammans utgör ett tal. Kunskaper om kritiska aspekter kan ses som specialkunskaper för lärare att veta vad som kan missuppfattas kring det matematiska området. Dessa kunskaper kan inte generaliseras, men de kan vara överförbara att en kritisk aspekt kan identifieras i andra elevgrupper. / In grades 4–6, students must undergo a progression to learn how rational numbers and numbers in decimal form are structured. Research has shown that there can be several difficulties and misconceptions about the area, including knowing the different place value of numbers. This study has been inspired by a previous study, conducted by Jarl and Johansson (2014). The aim of this study is to compare whether the same critical aspects identified in Jarl and Johansson (2014) studies also show up in other student groups. The subject of interest in this study was: What critical aspects can be identified in a grade 4 and a grade 5 around numbers in decimal form? In order to be able to answer the question, the students in this study have had to complete a worksheet with tasks linked to numbers in decimal form. Thereafter, qualitative interviews were conducted to gain a broader insight into what critical aspects the students have or have not distinguished. The choice of method in the study has elements of the theory of variation where the students need to see the necessary details (in the study called critical aspects). The results of the study show that all critical aspects that were identified in Jarl and Johansson's (2014) study were also critical in this study. However, a new critical aspect was identified: Students need to understand that numbers on each side of the decimal point together must become a number. Knowledge of critical aspects can be seen as special knowledge for teachers to know what can be misunderstood about the mathematical field. This knowledge cannot generalize, but it can be transferable so that a critical aspect can be identified in other student groups.

Denna studie syftar till att undersöka värdet av en plats och hur det kan påverka lokalbefolkningens inställning till storskalig turismutveckling och nyetablering. För att besvara syftet har naturområdet Skutberget i Karlstad valts ut och etableringen av Muminvärlden utifrån frågeställningarna: Hur värderas naturområdet Skutberget som plats? samt Vad har invånarna för inställning till etableringen av en Muminvärld på Skutberget? I studien testades även fyra olika hypoteser där hypotes 1 och 2 ämnar besvara frågeställning 1 medan hypotes 3 och 4 kopplar an till frågeställning 2. Studien grundar sig på följande fyra teman: värdet av en plats, planeringsperspektiv, friluftsliv samt destinationsutveckling. Dessa teman utgör också studiens teoretiska ramverk. Studien har använt sig av en kvantitativ metod där en enkätstudie har varit det valda tillvägagångssättet för insamling av data och kritisk realism är studiens vetenskapsteoretiska förhållningssätt. Utifrån hypoteserna har enkäten strukturerats i verktyget Survey & Report och den insamlade data sedan har analyserats i SPSS för att komma fram till ett resultat. Resultatet visar tydligt på att Skutberget som plats har ett stort värde för Karlstads invånare och att det råder en skepticism mot etableringen av Muminvärlden. Detta diskuteras närmare i analyskapitlet som sedan övergår i en slutsats med förslag till framtida forskning. / The purpose of this essay is to study the value of a place and how it can affect the local residents’ attitudes towards a large-scale tourism development and a new establishment. To fulfill the purpose, the nature area Skutberget in Karlstad Sweden, has been selected and the establishment of the Moomin inspired theme park. The questions for this study to answer is: How is the nature area Skutberget valued as a place? and What are the local residents’ attitude towards establishing a Moomin inspired theme park at Skutberget? The study also tested four different hypotheses in which hypothesis 1 and 2 intend to answer question 1, while hypothesis 3 and 4 relate to question 2. The study is structured with topics as: the value of a place, the planning perspective, outdoor life and destination development. These themes also form this study’s theoretical framework. The study has used a quantitative method where a questionnaire was chosen as a method for data collection and the study is based on the notion of critical realism. The survey has been constructed in Survey & Report and the collected data has been analyzed in SPSS to compile the results. The results clearly show that Skutberget has a great value for the local residents’ and that there is a skepticism towards the establishment of the Moomin inspired theme park. This is discussed in more details in the analysis chapter, and to conclude the study discusses conclusions with suggestions for further research.

The purpose of this study was to examine my own practice of teaching place value and the influence virtual manipulatives had, in addition to physical manipulatives, on place value understanding of my second grade students. I wanted to see how adding a base-ten computer applet might better meet the needs of all learners while also meeting the needs of today’s technological classroom. Through this study, I found that both physical and virtual manipulatives helped students acquire place value concepts. I found that virtual manipulatives had features that engaged students in a way that increased their mathematical language, increased students’ ability to represent more conceptual understanding of composing and decomposing numbers, and express enthusiasm towards mathematics. A pretest and posttest revealed that students’ academic performance increased. While research on virtual manipulatives and mathematical achievement is fairly recent, this study offers insight to other classroom teachers and the research community.

Understanding base-ten numbers is one of the most important mathematics topics taught in the primary school, and yet also one of the most difficult to teach and to learn. Research shows that many children have inaccurate or faulty number conceptions, and use rote-learned procedures with little regard for quantities represented by mathematical symbols. Base-ten blocks are widely used to teach place-value concepts, but children often do not perceive the links between numbers, symbols, and models. Software has also been suggested as a means of improving children's development of these links but there is little research on its efficacy. Sixteen Queensland Year 3 students worked cooperatively with the researcher for 10 daily sessions, in 4 groups of 4 students of either high or low mathematical achievement level, on tasks introducing the hundreds place. Two groups used physical base-ten blocks and two used place-value software incorporating electronic base-ten blocks. Individual interviews assessed participants' place-value understanding before and after teaching sessions. Data sources were videotapes of interviews and teaching sessions, field notes, workbooks, and software audit trails, analysed using a grounded theory method. There was little difference evident in learning by students using either physical or electronic blocks. Many errors related to the "face-value" construct, counting and handling errors, and a lack of knowledge of base-ten rules were evident. Several students trusted the counting of blocks to reveal number relationships. The study failed to confirm several reported schemes describing children's conceptual structures for multidigit numbers. Many participants demonstrated a preference for grouping or counting approaches, but not stable mental models characterising their thinking about numbers generally. The independent-place construct is proposed to explain evidence in both the study and the literature that shows students making single-dimensional associations between a place, a set of number words, and a digit, rather than taking account of groups of 10. Feedback received in the two conditions differed greatly. Electronic feedback was more positive and accurate than feedback from blocks, and reduced the need for human-based feedback. Primary teachers are urged to monitor students' use of base-ten blocks closely, and to challenge faulty number conceptions by asking appropriate questions.