Identification of Genomic Regions Associated with Phenotypic Variation between Dog Breeds using Selection Mapping

Peer reviewe

Studying the views of preservice teachers on the concept of function

This thesis consists of an overview of the subject, where in particular five papers are put into a frame. The research conducted for the thesis concerns the views of preservice teachers on the concept of function. Preservice teachers’ conceptions of the function concept are in particular examined in relation to mathematical statements that can be related to different topics on a variety of levels in mathematics; in this research, concept mapping technique is a research tool of interest. Questions concerning preservice teachers’ conceptions of the significance of functions in mathematics, and the presence of functions in school mathematics, are also considered relevant aspects of their views of functions. The final part of the research study includes an intervention study regarding the concept of function, located to a calculus course as one of the concluding courses in mathematics on the educational programme. There is a range of findings from the study that is summarized and further discussed in the overview part of the thesis. One result, is that preservice teachers in their reasoning show signs of knowledge compartmentalization which is an issue of concern in their development of conceptual frameworks rich in meaningful connections. This might have consequences for their abilities to operate in a constructivist environment and reason with their students from different points of view. The function concepts’ large network of relations to other concepts is frequently omitted in the preservice teachers’ reasoning. One reason for this is that to preservice teachers, properties of functions seem to be results of isolated procedures, associated with operational conceptions rather than structural conceptions of functions. The findings imply that preservice teachers should encounter functions in a variety of context, to develop their views of the concept of function – including frameworks rich of meaningful relations – and realize that the concept of function is one of the underlying concepts of mathematics, and an important concept to introduce to their future students. The preservice teachers’ reflections concerning functions in school mathematics contribute to emphasize the significance of the process of transformation of subject matter knowledge to pedagogical content knowledge. Further results of the research study, and an outline of the implications, are included in the concluding discussion of the overview part of the thesis. The preservice teachers participating in the study are enrolled in a four and a half year teacher preparation program in mathematics and science, grades 4 to 9. The five papers included in the thesis, describe parts of a larger study essentially conducted until the sixth term during the concluding mathematics courses of the program

Preservice teachers' views of y=x+5 and y=πx2 expressed through the utilization of concept maps : a study of the concept of function

This paper considers a group of preservice teachers’ construction of concept maps derived from y=x+5 and y=x2 with emphasis on their conceptual understanding of function. The two statements are perceived to represent a number of different concepts with indications of compartmentalized knowledge structures that might prevent the preservice teachers from building rich conceptual structures. The preservice teachers’ view on the concept of function contrasts with a view where the function concept is a unifying concept in mathematics with a large network of relations to other concepts. Different properties and categorizations of functions are less frequently recognized. In the preservice teachers’ response of drawing concept maps there are signs of metacognitive activity

Matematiska modeller

Material till lärmodulen "Undervisa matematik utifrån förmågorna" på "Lärportalen för matematik" / Skolverket</p

En studie i lärarstuderandes begreppsuppfattning : "Vi skriver y=x+5. Vad betyder det?"

Under en termin följde jag en grupp studenter som utbildar sig till grundskollärare i matematik och naturvetenskap för årskurs 4-9. Studenterna fick i början och slutet av terminen skriftligen besvara frågan ?Vi skriver y=x+5. Vad betyder det??. Vidare fick de i uppgift att rita begreppskartor över utsagan y=x+5. Blomhøj och Grevholm har båda studerat en frågeställning där y=x+5 ingår. Blomhøjs undersökning omfattade grundskoleelever i årskurs 9. Grevholm ställde samma fråga som i föreliggande studie till lärarstudenter som gick sin tredje termin på lärarutbildningen i matematik och naturvetenskap. Vid en jämförelse med Grevholms studie har studenterna i början av terminen svarat på ett sätt som tyder på en mindre utvecklad begreppsbildning än tredjeterminsstudenterna. Däremot visar de en mer utvecklad begreppsbildning än Grevholms studenter i slutet av terminen. En progression i studenternas svar är tydlig men svaren innehåller endast gymnasiala matematikkunskaper. En osäkerhet kan skönjas när studenterna tolkar utsagan y=x+5 som både en funktion och en ekvation. Vidare, begreppskartorna visar att då studenterna anger begreppet funktion är det få som visar att funktioner kan ha olika egenskaper. Det tyder på att studenterna inte har ett fullt utvecklat funktionsbegrepp. Begreppskartor utgör ett värdefullt komplement till studenternas skriftliga svar (och intervjuer). De bidrar till att tydligare illustrera studenternas uppfattning om matematiska begrepp

Preservice teachers' views on the concept of function : a study including the utilization of concept maps

The thesis consists of an overview of the subject, where in particular three papers are put into a frame. The overview part consists of: an introduction, a short description of some related research and theoretical framework, a summary of papers I-III and the concluding discussion. The thesis considers preservice teachers' view of the concept of function. It is primarily conducted during the concluding courses in mathematics of a teacher preparation program in mathematics and science, grades 4 to 9. Some of the findings show that a more developed conceptual knowledge of functions, as an object with a set of properties and an understanding of the function concept's network of relations and significance in mathematics, is not prominent in the preservice teachers' view upon functions as it appears in the study. This could mean that they as inservice teachers do not sufficiently promote the concept of function, or functional thinking, in their teaching. Furthermore, the concept maps give the impression that the preservice teachers' knowledge structures tend to be compartmentalized, including the knowledge structures representing the concept of function, thus preventing preservice teachers from building a conceptual framework rich of meaningful connections. A consequence could be that the preservice teachers become less flexible in their way of reasoning about concepts, and are only able to offer a more limited range of teaching strategies regarding different concepts and their relations to functions, as inservice teachers.Godkänd; 2004; 20070131 (ysko