Mathematics students and teachers are familiar with the difficulty of learning and teaching concepts of continuity and limits. Research has expanded our knowledge of how students think about these concepts, including different conceptions and metaphors students use to reason about continuity and limits at a point. From the literature I have identified four potentially problematic conceptions (PPCs) students may use when reasoning about limit and continuity at a point. Questionnaires were administered to 861 BYU students in various mathematics courses to determine how prevalent and persistent the PPCs are among the students in each course. Interviews were conducted with nine first semester calculus to get an idea of how students reason about continuity and limit at a point and how that influences whether they use the PPCs. Students showed evidence of holding the four PPCs with a decrease in these conceptions typically after they took a course in analysis. Participants also did not understand the Formal definition of a Limit until they took a course in Analysis. Students were able to reason appropriately using many different conceptions of continuity. Considering limit conceptions, students using a Dynamic conception of Limit tended to be better able to reason about continuity and limit at a point. Students who did not use a Dynamic conception of limit tended to use the PPCs in general and incorrectly more often.

This study investigated the effectiveness of commonly used instructional methods for teaching the phases of the Moon to fifth and sixth grade students. The instructional methods investigated were the use of diagrams, animations, and models. The effectiveness of each method was tested by measuring students' understanding of Moon phases with a pre and post-assessment after receiving instruction with a specific method or combination of methods. These methods were then evaluated for their ability to help students learn essential concepts, reinforce relevant vocabulary and discourage misconceptions. Results showed that students had better scores with less prevalence of misconception when they were taught using two methods instead of one. Students taught with only computer animations had significantly lower scores and a higher prevalence of misconceptions when compared to the other methods. This may be due to some design errors in the animation used in this study. Even though students taught with only computer animations had significantly lower scores, students taught with computer animations followed by instruction with diagrams had significantly higher scores. Why this combination of instruction was more effective for student learning is a question that requires further research.

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The purpose of this study was to examine the content knowledge of 64 elementary preservice teachers for the concepts of dissolving and density. Vygotsky’s (1987) theory of concept development was used as a framework to categorize concepts and misconceptions resulting from evidences of preservice teacher knowledge including pre/post concept maps, writing artifacts, pre/post face-to-face interviews, examination results, and drawings. Statistical significances were found for pre- and post-concept map scores for dissolving (t = -5.773, p < 0.001) and density (t = -2.948, p = 0.005). As measured using Cohen’s d values, increases in mean scores showed a medium-large effect size for (dissolving) and a small effect size for density. The triangulated results using all data types revealed that preservice teachers held several robust misconceptions about dissolving including the explanation that dissolving is a breakdown of substances, a formation of mixtures, and/or involves chemical change. Most preservice teachers relied on concrete concepts (such as rate or solubility) to explain dissolving. With regard to density, preservice teachers held two robust misconceptions including confusing density with buoyancy to explain the phenomena of floating and sinking, and confusing density with heaviness, mass, and weight. Most preservice teachers gained one concept for density, the density algorithm. Most preservice teachers who participated in this study demonstrated Vygotsky’s notion of complex thinking and were unable to transform their thinking to the scientific conceptual level. That is, they were unable to articulate an understanding of either the process of dissolving or density that included a unified system of knowledge characterized as abstract, generalizable, and hierarchical. Results suggest the need to instruct preservice elementary science teachers about the particulate nature of matter, intermolecular forces, and the Archimedes' principle.

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Student misconceptions in science are common and may be present even for students who are academically successful. Concept inventories, multiple-choice tests in which the distractors map onto common, previously identified misconceptions, are commonly used by researchers and educators to gauge the prevalence of student misconceptions in science. Distractor analysis of concept inventory responses could be used to create profiles of individual student misconceptions which could provide deeper insight into the phenomenon and provide useful information for instructional planning, but this is rarely done as the inventories are not designed to facilitate it. Researchers in educational measurement have suggested that diagnostic cognitive models (DCMs) could be used to diagnose misconceptions and to create such misconception profiles. DCMs are multidimensional, confirmatory latent class models which are designed to measure the mastery/presence of fine-grained skills/attributes. By replacing the skills/attributes in the model with common misconceptions, DCMs could be used to filter students into misconception profiles based on their responses to concept inventory-like questions. A few researchers have developed new DCMs that are specifically designed to do this and have retrofitted data from existing concept inventories to them. However, cognitive diagnostic assessments, which are likely to display better model fit with DCMs, have not been developed. This project developed a cognitive diagnostic assessment to measure knowledge and misconceptions about Newton's laws and fitted it with the deterministic input noisy-and-gate (DINA) model. Experienced physics instructors assessed content validity and Q-matrix alignment. A pilot test with 100 undergraduates was conducted to assess item quality within a classical test theory framework. The final version of the assessment was field tested with 349 undergraduates. Results showed that response data displayed acceptable fit to the DINA model at the item level, but more questionable fit at the overall model level; that responses to selected items were similar to those given to two items from the Force Concept Inventory; and that, although all students were likely to have misconceptions, those with lower knowledge scores were more likely to have misconceptions. / Doctor of Philosophy / Misconceptions about science are common even among well-educated adults. Misconceptions range from incorrect facts to personal explanations for natural phenomena that make intuitive sense but are incorrect. Frequently, they exist in people's minds alongside correct science knowledge. Because of this, misconceptions are often difficult to identify and to change. Students may be academically successful and still retain their misconceptions. Concept inventories, multiple-choice tests in which the incorrect answer choices appeal to students with common misconceptions, are frequently used by researchers and educators to gauge the prevalence of student misconceptions in science. Analysis of incorrect answer choices to concept inventory questions can be used to determine individual student's misconceptions, but it is rarely done because the inventories are not known to be valid measures for this purpose. One source of validity for tests is the statistical model that is used to calculate test scores. In valid tests, student's answers to the questions should follow similar patterns to those predicted by the model. For instance, students are likely to get questions about the same things either all correct or all incorrect. Researchers in educational measurement have proposed that certain types of innovative statistical models could be used to develop tests that identify student's misconceptions, but no one has done so. This project developed a test to measure knowledge and misconceptions about forces and assessed how well it predicted student's misconceptions compared to two statistical models. Results showed that the test predicted student's knowledge in good agreement and misconceptions in moderate agreement with the statistical models; that students tended to answer selected questions in the same way that they answered two similar questions from an existing test about forces; and that, although students with lower test scores were more likely to have misconceptions, students with high test scores also had misconceptions.

Cette thèse explore les ressources cognitives que mobilisent des élèves ingénieurs dans un APP (Apprentissage par problème) dans une tâche de conception d’un objet technique. La situation-problème à laquelle ces élèves sont confrontés est constituée par un système technique inédit de réfrigération sans apport extérieur d’énergie. Dans cet apprentissage, les élèves doivent concevoir l’objet technique et apprendre des concepts en thermodynamique. Deux groupes d’élèves sont comparés : le premier dispose d’un modèle analogique d’une situation connue pour aborder la situation nouvelle, le second ne dispose que du texte. Les questions de recherches : Que construisent ces élèves comme connaissances ?Qu’apportent ces deux types d’apprentissage (l’apprentissage par une situation connue et l’apprentissage par le texte) ? Quels sont les obstacles que rencontrent ces élèves ? Les hypothèses : un apprentissage par une situation connue conduit à la construction de connaissances opératives (des concepts outils). Un apprentissage par le texte conduit à la construction de connaissances décontextualisées (des concepts objets). Un apprentissage par les situations dans un dispositif didactique conduit ultérieurement à la construction de concepts catégoriels. Ces deux types d’apprentissage impliquent l’obstacle épistémologique dans la construction des concepts dans leurs deux fonctions : outil et objet. / This thesis investigates the cognitive resources that pupils engineers in a PBL (Problem based Learning) in a task of conception of a technical object mobilize. The situation-problem with which these pupils are confronted is constituted by an unpublished technical system of refrigeration without outside contribution of energy. In this learning, the pupils have to conceive the technical object and learn concepts in thermodynamics. Two groups of pupils are compared: the first one has an analogical model of a situation known to approach the new situation; the second has only the text. The questions of researches: what build these pupils as knowledge? What bring these two types of learning (the learning by a known situation and the learning by the text)? What are the obstacles which meet these pupils? The hypotheses: a learning by a known situation leads to the construction of operational knowledge (concepts tools). A learning by the text leads to the construction of knowledge out of context (concepts objects). A learning by the situations in a didactic device leads later to the construction of category-specific concepts. These two types of learning involve the epistemological obstacle in the construction of the concepts in them two functions: tool and object.

The purpose of this study was to field test a two-tiered instrument including multiple-choice and short answer tasks to assess college students’ ideas and level of understanding in genetics. The instrument was constructed from previously tested assessment tasks and findings from the current research literature. Ninety-seven freshmen enrolled in a biology lab course were surveyed. Test validity and reliability were measured using Chronbach coefficients. Multiple-choice and short answer responses were analyzed using descriptive statistics to identify frequencies of answer selections. Written responses were independently evaluated using a five-point scoring rubric by three researchers to identify common misconceptions revealed in students’ written responses. A purposeful stratified sample of 15 students was selected across low, middle, and high performance on the instrument for individual interviews. Findings revealed that undergraduates have a variety of ideas concerning gene concepts. While the instrument revealed student conceptual difficulties, there also were issues with previously tested survey items. The findings suggest students possess superficial understanding regarding transcription and translation. Students also hold hybrid conceptual models of gene structure and function. The paper presents a critique of the instrument and discusses the broader impacts to teaching and learning college biology. Recommendations for improving assessment techniques also are discussed.

This research reviewed the neglect of cities in the mission work of the Reformed Churches in Southern Africa with a special reference to churches of Synod Soutpansberg. The biblical passage, Jeremiah 29:1-14 was used, as a representative of other biblical passages, to shed light on the role of cities in mission work of the church while addressing misconceptions and false theology about the cities and the role they played and still play in the mission work of the church. The same biblical message is confirmed by many missiology literature, including, "Cities, Missions' New Frontier" by R.S. Greenway and T.M. Monsma (1989); "City of God - City of Satan" by R.C. Linthicum(1991) and "Discipling the City" by R.S. Greenway (1992). The biblical message and the missiology literature mentioned above were the basis from which the neglect of the role of the cities in the history of the mission work of the Reformed Churches in Southern Africa was studied. From these basis, the causes, implementations and effects of such neglect in the mission work of the Soutpansberg churches was studied in Chapter 3. The empirical research was conducted using the interview questionnaire in Chapter 4. The empirical results and findings, which were presented in this research, can direct churches towards a remedy of the neglect of the cities in their mission work as far as the strategies is concerned. The neglect of the cities in the history of the mission work of the Reformed Churches in Southern Africa was studied with an aim that churches learn from it and hence avoid the past neglect in their present and future mission plans, strategies and programs. In other words, the lesson is important for churches to view the role of the secular cities as important instruments used by God to speed up not only the planting and growing big holy churches from those secular cities outwards, but also the biblical reformation of the rural - orientated theories, strategies and practice! / Thesis (M.A. (Theology))--North-West University, Vaal Triangle Campus, 2008.