Conceptual development and conceptual change processes are described by a longitudinal study on preschool children’s conception of the earth. Conceptual change is often described as a causal process in which changes in an embraced system of beliefs result in a new system of beliefs. A normative line of research has been dominating the research field of conceptual change. There has been a search for specific conceptions that are missing in the learners’ reasoning or that prevent conceptual change from occur. Here, the learner’s capacity of reasoning is focused. The children’s reasoning is described in its own right (Driver &amp; Easley, 1978). It is argued that conceptual change is to be understood as an intentional activity with regard to the learner, that is, what the learner is doing when trying to understand something. Children were interviewed annually from four to six years of age. There were 37 children participating, of which 29 were followed during all three years. The children were interviewed about their conceptions of the earth. The results directs the focus of conceptual change from specific conceptions to structural changes. The children processed a lot of conflicting information. However, there does not appear to be any specific conflict that causes the process of conceptual change to occur. Rather, conceptual change is about the reorganization of the sum total of beliefs and to find adequate contexts to which they relate. Conceptual change involves a simultaneous processing of information and complex conception as well as revisions and changes at a model level, and all of this processing is related to contexts for description and explanation. The result also indicates some core stability in reasoning over the course of the investigation. / <p>At the time of the doctoral defence the folowing papers were unpublished and had a status as follows: Paper 1: Manuscript; Paper 2: Manuscript.</p>

Sweden is a multicultural country and because of this the Swedish school-system should be adapted so that all pupils can develop their linguistic skills so that they can participate andunderstand the education. By using scientific work from other researchers and my own experiences from a general point of view, I noticed that pupils with foreign origin perform less good in mathematics than pupils with Swedish origin, in the Swedish education system. The purpose of this research is to find out if communication and interplay between the pupils makes it easier for them to understand mathematics and its’ concepts. My research involves acertain school class were all pupils have another etnicity then the Swedish one. My aim was to find out if the pupils reached the knowledge-goals for mathematics in the third grade. Especially in the areas of solution solving and the understanding of mathematical texts. I wanted to find out if communication and interplay between the pupils lead to increasedprogress in the Swedish language and increased understanding of mathematical texts. I also examined what possibilities the pupils have to absorb and understand the education and how favourable the conditions are in their teaching process. My starting points were Vygotskijs’ sociocultural perspective. The main research questions were: Is the language a barrier for the pupils in my research group when they develop their mathematical knowledge? Which approach may enhance the pupils knowledge in mathematics? The research is based on interviews with the teacher and observations of the pupils during mathematic lessons. With the help of the empirical material I wanted to increase myunderstanding about the process of learning and development in the class and about how the teacher labours and reflects around the situation. She practiced silent and individual studies in the class. The result of this research showed that the pupils were not benefited by the teachersmethods and that they did not reach the main goals in Swedish and mathematics for the earlier years in Swedish compulsory school. The reason to this result is mainly that language and learning go hand in hand and that mathematics requires a good vocabulary and good reading comprehension.

The development of spatial thinking proficiency has been increasingly demanded in Geographic Information System (GIS) education. Despite this educational trend, there is little empirical research on college students' spatial concept knowledge, which critically affects the quality of spatial thinking. This study addressed the following three research questions: 1) What differences exist between students' understandings of spatial concepts at the beginning, middle, and end of an introductory-level GIS course?, 2) What spatial misconceptions students may possess while taking an introductory-level GIS course?, and 3) Which spatial concepts are easy or hard for undergraduate students to understand? The researcher asked twelve participants who were taking an introductory-level GIS course to create concept maps about space and revised their concept maps in three experiment sessions. For the first question, the researcher scored the sixty obtained concept maps and statistically analyzed those scores to examine if there is any significant difference among the scores of the three experiment sessions. For the second question, the researcher examined participants' misconceptions by analyzing the incorrect statements of distortion, map projection, and scale. For the third question, the researcher statistically analyzed concept-based scores to examine if there is any significant difference among the scores of three different complexity levels. A main finding for the first question was that there was a significant difference among the scores of the concept maps created in the first session and the scores of the concept maps revised in the second and third sessions. This implied that participants could successfully revise their own original concept maps in the middle of a semester. The result of the study of the second question indicated that a half of participants misunderstood the concepts of map projections and scale. This result suggested that some undergraduate students may have difficulty shifting from scientifically inappropriate spatial concept knowledge to appropriate knowledge. Analysis of the third question resulted that the concept-based scores of simple spatial concepts are significantly higher than the scores of complicated spatial concepts. This result inferred that participants' scores decreased as the complexity of the concepts increased.

This dissertation deals with the development of mathematical concepts from a historical and didactical perspective. In particular, the development of concepts in mathematical analysis during the 19th century is considered. The thesis consists of a summary and three papers. In the first paper we investigate the Swedish mathematician E.G. Björling's contribution to uniform convergence in connection with Cauchy's sum theorem from 1821. In connection to Björling's convergence theory we discuss some modern interpretations of Cauchy's expression x=1/n. We also consider Björling's convergence conditions in view of Grattan-Guinness distinction between history and heritage. In the second paper we study visualizations in mathematics from historical and didactical perspectives. We consider some historical debates regarding the role of intuition and visual thinking in mathematics. We also consider the problem of what a visualization in mathematics can achieve in learning situations. In an empirical study we investigate what mathematical conclusions university students made on the basis of a visualization. In the third paper we consider Cauchy's theorem on power series expansions of complex valued functions on the basis of a paper written by E.G. Björling in 1852. We discuss Björling's, Lamarle's and Cauchy's different conditions for expanding a complex valued function in a power seris. In the third paper we also discuss the problem of the ambiguites of fundamental concpets that existed during the mid-19th century. We argue that Cauchy's and Lamarle's proofs of Cauchy's theorem on power series expansions of complex valued functions are correct on the basis of their own definitions of the fundamental concepts involved.

Abstract Research into memory processes has progressed in recent years through the combined efforts of neuroscientists and cognitive scientists. This is especially aided by modern scientific research methods of the brain such as positron emission tomography and functional magnetic resonance imaging. The learner, through interaction with his environment, must actively create individual cognition; the brain is a dynamic adaptable organ. This research will limit the discussion of authentic learning and e-learning to an introductory chemistry laboratory course. The most popular, and yet the most heavily criticized style of laboratory instruction is the traditional (also termed verification or expository) style with a "cookbook" nature. On the basis of pilot action research, the goal of this study has been the use of e-learning for the purpose of placing more emphasis on the contemplation of chemistry's theoretical topics for effecting the quality of conceptual understanding. With systems thinking as a background, the qualitative research method was primarily used, but statistics of the external influences in the e-learning process were also improved. In an e-learning environment, the individually supported development of a learner's conceptual understanding was analyzed by SOLO-taxonomy by comparing the learner's own outcomes. The results show that e-learning with traditional laboratory activities has the effect of forming chemistry concepts, and results in meaningful learning. The SOLO-taxonomy would be a powerful tool for faculty for analyzing points of difficulty or confusion in students' understanding of chemistry concepts. To better understand the effectiveness of e-learning, studies have to be directed toward higher-order cognition by collaborative learning in addition to conceptual understanding of individuals.

No description available.

Este estudo teve como objetivo verificar como ocorre e se desenvolve a construção dos conceitos acerca da estrutura da matéria e quais as dificuldades envolvidas nesse processo de aprendizagem. Para esta finalidade foi realizado um estudo longitudinal com um grupo de alunos ao longo do ensino médio. O estudo apresenta a análise do desenvolvimento conceitual desses estudantes, ao manifestarem explicações sobre fenômenos do seu cotidiano, utilizando ideias sobre a estrutura da matéria. Foram empregadas três dimensões de análise: natureza corpuscular da matéria (1ª dimensão), natureza elétrica da matéria (2ª dimensão) e interações intra e interpartículas (3ª dimensão). O estudo foi dividido em duas etapas. Na primeira etapa, participaram 91 alunos de 1ª a 3ª séries de uma escola de Ensino Médio de São Paulo, cujo ensino esteve a cargo de uma mesma professora. A compreensão dos conceitos acerca da estrutura da matéria foi extraída de suas respostas a um questionário contendo questões abertas e fechadas. O conhecimento dos alunos foi avaliado considerando suas respostas em níveis de adequação e compreensão elaborados a partir de uma comparação com respostas de professores especialistas na área de química e de ensino ao mesmo questionário. Verificou-se que as respostas dos alunos se apresentaram entre os níveis de inadequação e parcial adequação com vaga à alguma compreensão na 1ª dimensão de análise para todas as séries. Na 2ª dimensão de análise as respostas foram inadequadas com insuficiente compreensão, entre os alunos da 1ª série, inadequadas com vaga compreensão entre os alunos da 2ª e 3ª séries. Na 3ª dimensão, as respostas foram inadequadas, com insuficiente compreensão entre os alunos das 1ª e 3ª séries, o que implica em avanços e retrocessos do conhecimento dos conceitos e, para a 2ª série, as respostas foram inadequadas com vaga compreensão. Na segunda etapa do estudo, foram acompanhados quatro alunos (A, B, C e D) durante os três anos do Ensino Médio. O conhecimento individual de cada aluno foi extraído de suas respostas a questionários, entrevistas e representações pictóricas. O desenvolvimento conceitual de cada aluno foi avaliado por meio da elaboração de mapas cognitivos a partir de suas manifestações verbais e escritas. Os resultados indicaram que dois dos estudantes desenvolveram uma compreensão gradual dos conceitos acerca da estrutura da matéria, um deles finalizou o ensino com vaga compreensão (A), outro com alguma compreensão (D) e dois deles alcançaram bom nível de compreensão (B e C), estes últimos parecem ter integrado de maneira mais coesa seus conhecimentos, o que indicou que reestruturaram e reorganizaram suas estruturas de conhecimento. O estudo sugere que é necessária uma retomada constante dos conceitos sobre estrutura da matéria, possibilitando ao aluno estabelecer inter-relações conceituais na explicação de fenômenos, de maneira a facilitar uma reestruturação das concepções dos estudantes, tornando a aprendizagem mais significativa. / This study aims to investigate how High School students understand and develop concepts related to structure of matter and how they apply these concepts to explain everyday phenomena related to Chemistry. For this purpose, we conducted a longitudinal study with 91 High School students from 2012 to 2014. The conceptual development of these students was investigated by analyzing their answers to a questionnaire applied in the beginning of the 1st and 2nd grades and in the end of the 3rd grade of High School. In addition, four students were chosen to answer to five interviews conducted over the three years of High School. The students had the same Chemistry teacher in these three years. Students\' answers were categorized in three dimensions of analysis elaborated by the researcher: particle model of matter (1st dimension), electrical nature of matter (2nd dimension) and intra- and inter-particle interactions (3rd dimension). The analyses were conducted in two steps. In the first step, the concepts expressed by the 91 students were analyzed according to the three dimensions. Adequacy and comprehension levels were created to categorize students\' responses. These levels were elaborated by comparing students\' answers to Chemistry experts\' answers. The second step consisted of analysis of each of four students (A, B, C, D) during learning process on 1st, 2nd and 3rd grades of High School. The concept development of each student was evaluated through cognitive maps elaborated by the researcher from student\'s verbal and written manifestations. On the first step, concerning to the 1st dimension of analysis, the students on the three grades showed answers classified in inadequacy and partial adequacy levels, and low comprehension level. For the 2nd dimension, 1st graders\' ideas were classified as inadequate with insufficient understanding, the students of 2nd and 3rd grades showed a low level of understanding. On the 3rd dimension, the answers given by students of the 1st and 3rd grades were classified as inadequate, with insufficient understanding. The responses of 2nd grade students were also inadequate but with a little better level of understanding. On the second step, results indicated that students A and D developed a gradual understanding of the concepts concerning the structure of matter. Although, student A has achieved a low level of comprehension, student D has achieved the level of some comprehension. Students B and C achieved good level of understanding and their concepts seem to be closely integrated, which indicates that they have restructured and reorganized their knowledge structures. In conclusion, this study suggests that concepts related to structure of matter should be frequently reviewed in order to enable the student to establish conceptual interrelationships to explain phenomena at sub-microscope level, promote students\' conceptions restructuration, and provide meaningful learning during the teaching-learning process.

This study, which was conducted among middle-school students in California, focused on the effectiveness of using innovative strategies for enhancing the classroom environment, students' attitudes, and conceptual development. Six hundred and sixty-one (661) students from 22 classrooms in four inner city schools completed the modified actual forms of the Constructivist Learning Environment Survey (CLES), the What Is Happening In this Class? (WIHIC) questionnaire, and the Test Of Mathematics Related Attitudes (TOMRA). The data were analyzed for the CLES, WIHIC, and TOMRA to check their factor structure, reliability, discriminant validity, and the ability to distinguish between different classes and groups. In terms of the validity of the CLES, WIHIC, and TOMRA when used with middle-school students in California, the factor analysis results attest to the sound factor structure of each questionnaire. The results for each CLES, WIHIC, and TOMRA scale for the alpha reliability and discriminant validity for two units of analysis (individual and class mean) compare favorably with the results for other well-established classroom environment instruments. A one-way analysis of variance (ANOVA) was also calculated for each scale of the CLES and WIHIC to investigate its ability to differentiate between the perceptions of students in different classrooms. The ANOVA results suggest that students perceived the learning environments of different mathematics classrooms differently on CLES and WIHIC scales. In general, the results provided evidence of the validity of these instruments in describing psychosocial factors in the learning environments of middle-school mathematics classrooms in California. The effectiveness of the innovative strategy was evaluated in terms of classroom environment and attitudes, as well as achievement, among a subgroup of 101 students. / Effect sizes and t-tests for paired sample were used to determine changes in classroom environment perceptions, attitudes, and achievement for experimental and control groups. Pretest-posttest differences were statistically significant (p<0.05) for: the CLES scale of Shared Control for the experimental group, the TOMRA scale of Normality of Mathematicians for both the control and the experimental groups, the TOMRA scale of Enjoyment of Mathematics for the experimental group, and the achievement measure for both groups. Also ANCOVA was calculated to determine if differential pretest-posttest changes were experienced by the experimental and control groups in classroom environment perceptions, attitudes, and achievement. The results suggest that there were a statistically significant differential changes for Task Orientation, Normality of Mathematicians, Enjoyment of Mathematics, and achievement between the experimental and control groups. In each case, the experimental group experienced larger pretest-posttest changes than the control group. Overall, a comparison of the pretest-posttest changes for an experimental group, which experienced the innovative strategy, with those for a control group, supported the efficacy of the innovative teaching methods in terms of learning environment perceptions, attitudes to mathematics, and mathematics concept development. The results of simple correlation and multiple correlation analyses of outcome-environment associations for two units of analysis clearly indicated that there is an association between the learning environment and students’ attitudes and mathematics achievement for this group of middle-school mathematics students. / In particular, there is a positive and statistically significant correlation between: Normality of Mathematicians and Student Negotiation, Involvement, and Task Orientation with the individual as the unit of analysis; Enjoyment of Mathematics and all three CLES and three WIHIC scales with the student as a unit of analysis, and for the four scales of Personal Relevance, Shared Control, Involvement, and Task Orientation with the class mean as the unit of analysis. The multiple correlations between the group of three CLES and three WIHIC scales and each of the two TOMRA scales are statistically significant for the individual as a unit of analysis. Overall, the study revealed positive and statistically significant associations between the classroom learning environment and students’ attitudes to mathematics. A two-way MANOVA with repeated measures on one factor was utilized to investigate gender differences in terms of students’ perceptions of classroom environment and attitudes to mathematics, as well as mathematics achievement. A statistically significant but small difference was found between the genders for Student Negotiation and Task Orientation. Female students perceived their mathematics classrooms somewhat more positively than did the male students. There was no statistically significant difference between the genders on achievement and students’ attitudes to mathematics. Qualitative information, gathered through audiotaped interviews, students’ journal, and analysis of students’ work, was used to clarify students’ opinions about the new approach, classroom environment perceptions, attitudes, and conceptual development. / These qualitative information-gathering tools were utilized to obtain a more in-depth understanding of the learning environments (Tobin, Kahle, & Fraser, 1990) and the results of my study (Punch, 1998), as well as insights into students’ perceptions (Spinner & Fraser, 2005). The responses from the students’ interviews and students’ reflective journals from the group that experienced the innovative methods generally suggested that introducing Cramer’s rule as a method for solving systems of linear equations in the middle school can be beneficial and therefore might be considered for inclusion in the middle-school Algebra 1 curriculum more widely in California. Using only quantitative data would not have provided the richness that was derived from using mixed methods (Johnson & Onwuegbuzie, 2004). Therefore, qualitative data obtained from students who experienced the innovative method generally supported the quantitative findings concerning the effectiveness of this method for teaching and learning systems of linear equations.

Este estudo teve como objetivo verificar como ocorre e se desenvolve a construção dos conceitos acerca da estrutura da matéria e quais as dificuldades envolvidas nesse processo de aprendizagem. Para esta finalidade foi realizado um estudo longitudinal com um grupo de alunos ao longo do ensino médio. O estudo apresenta a análise do desenvolvimento conceitual desses estudantes, ao manifestarem explicações sobre fenômenos do seu cotidiano, utilizando ideias sobre a estrutura da matéria. Foram empregadas três dimensões de análise: natureza corpuscular da matéria (1ª dimensão), natureza elétrica da matéria (2ª dimensão) e interações intra e interpartículas (3ª dimensão). O estudo foi dividido em duas etapas. Na primeira etapa, participaram 91 alunos de 1ª a 3ª séries de uma escola de Ensino Médio de São Paulo, cujo ensino esteve a cargo de uma mesma professora. A compreensão dos conceitos acerca da estrutura da matéria foi extraída de suas respostas a um questionário contendo questões abertas e fechadas. O conhecimento dos alunos foi avaliado considerando suas respostas em níveis de adequação e compreensão elaborados a partir de uma comparação com respostas de professores especialistas na área de química e de ensino ao mesmo questionário. Verificou-se que as respostas dos alunos se apresentaram entre os níveis de inadequação e parcial adequação com vaga à alguma compreensão na 1ª dimensão de análise para todas as séries. Na 2ª dimensão de análise as respostas foram inadequadas com insuficiente compreensão, entre os alunos da 1ª série, inadequadas com vaga compreensão entre os alunos da 2ª e 3ª séries. Na 3ª dimensão, as respostas foram inadequadas, com insuficiente compreensão entre os alunos das 1ª e 3ª séries, o que implica em avanços e retrocessos do conhecimento dos conceitos e, para a 2ª série, as respostas foram inadequadas com vaga compreensão. Na segunda etapa do estudo, foram acompanhados quatro alunos (A, B, C e D) durante os três anos do Ensino Médio. O conhecimento individual de cada aluno foi extraído de suas respostas a questionários, entrevistas e representações pictóricas. O desenvolvimento conceitual de cada aluno foi avaliado por meio da elaboração de mapas cognitivos a partir de suas manifestações verbais e escritas. Os resultados indicaram que dois dos estudantes desenvolveram uma compreensão gradual dos conceitos acerca da estrutura da matéria, um deles finalizou o ensino com vaga compreensão (A), outro com alguma compreensão (D) e dois deles alcançaram bom nível de compreensão (B e C), estes últimos parecem ter integrado de maneira mais coesa seus conhecimentos, o que indicou que reestruturaram e reorganizaram suas estruturas de conhecimento. O estudo sugere que é necessária uma retomada constante dos conceitos sobre estrutura da matéria, possibilitando ao aluno estabelecer inter-relações conceituais na explicação de fenômenos, de maneira a facilitar uma reestruturação das concepções dos estudantes, tornando a aprendizagem mais significativa. / This study aims to investigate how High School students understand and develop concepts related to structure of matter and how they apply these concepts to explain everyday phenomena related to Chemistry. For this purpose, we conducted a longitudinal study with 91 High School students from 2012 to 2014. The conceptual development of these students was investigated by analyzing their answers to a questionnaire applied in the beginning of the 1st and 2nd grades and in the end of the 3rd grade of High School. In addition, four students were chosen to answer to five interviews conducted over the three years of High School. The students had the same Chemistry teacher in these three years. Students\' answers were categorized in three dimensions of analysis elaborated by the researcher: particle model of matter (1st dimension), electrical nature of matter (2nd dimension) and intra- and inter-particle interactions (3rd dimension). The analyses were conducted in two steps. In the first step, the concepts expressed by the 91 students were analyzed according to the three dimensions. Adequacy and comprehension levels were created to categorize students\' responses. These levels were elaborated by comparing students\' answers to Chemistry experts\' answers. The second step consisted of analysis of each of four students (A, B, C, D) during learning process on 1st, 2nd and 3rd grades of High School. The concept development of each student was evaluated through cognitive maps elaborated by the researcher from student\'s verbal and written manifestations. On the first step, concerning to the 1st dimension of analysis, the students on the three grades showed answers classified in inadequacy and partial adequacy levels, and low comprehension level. For the 2nd dimension, 1st graders\' ideas were classified as inadequate with insufficient understanding, the students of 2nd and 3rd grades showed a low level of understanding. On the 3rd dimension, the answers given by students of the 1st and 3rd grades were classified as inadequate, with insufficient understanding. The responses of 2nd grade students were also inadequate but with a little better level of understanding. On the second step, results indicated that students A and D developed a gradual understanding of the concepts concerning the structure of matter. Although, student A has achieved a low level of comprehension, student D has achieved the level of some comprehension. Students B and C achieved good level of understanding and their concepts seem to be closely integrated, which indicates that they have restructured and reorganized their knowledge structures. In conclusion, this study suggests that concepts related to structure of matter should be frequently reviewed in order to enable the student to establish conceptual interrelationships to explain phenomena at sub-microscope level, promote students\' conceptions restructuration, and provide meaningful learning during the teaching-learning process.

Thesis (M. Ed.) -- University of Limpopo, 2017. / One of the effective ways of teaching science is by developing the thinking abilities of individuals by allowing them to engage in enquiry-based learning. Computer simulation (CS) can help improve understanding of scientific concepts and enhance conceptual development and performance. This study focused on exploring learners’ conceptual development using CS in Grade 10 science class. A pre- and post-test research designs were used. 105 Grade 10 learners participated: 53 from one whole class were assigned to an Experimental Group (EG) and 52 from another class to a Control Group (CG). The EG was taught using CS while the CG was taught using the traditional approach. Data on learners’ performance were collected using a performance test and interviews were employed to collect data on learners’ attitudes towards science. The results revealed that the EG performed better than the CG (t-test, p < 0.05), (ANCOVA, p < 0.01). Girls in the EG performed better than girls from the CG (t-test, p < 0.05), and independent sample t-test revealed that girls in the EG were in the same range with boys after intervention suggesting that CS did not discriminate against gender in this study. Furthermore, the results from interviews indicate that learners from EG exhibited positive attitudes towards science, unlike their counterparts from the CG. This suggests that learners from the EG may have been excited to observe phenomena on the screen of a computer that they would otherwise not do due to lack of laboratory equipment in their school.