Immersive virtual reality (VR) technology has brought many new opportunities for training researchers and students. In the traditional training environment, trainees usually follow verbal instructions (lecture) or visual instructions (video tutorial, job manual) as certain training methods. For this research study, we not only tested how much procedural knowledge the trainees could learn from the VR training compared with traditional media training (video plus instruction manual), we also specifically focused on how well the knowledge could retain in a certain amount of time. The finding of this study shows that VR training can help trainees learn procedural knowledge, and also shows that VR training can help enhance procedural knowledge retention in terms of recall error. However, we did not find any significant difference in recall time between VR training group and traditional media training group.

The goal in mathematics has shifted towards an emphasis on both procedural knowledge and conceptual understanding. The importance of gaining procedural knowledge and conceptual understanding is aligned with Principles and Standards for School Mathematics (National Council of Teachers of Mathematics, 2000), which encourages fluency, reasoning skills, and ability to justify decisions. Possession of only procedural skills will not prove useful to students in many situations other than on tests (Boaler, 2000). Teachers and researchers can benefit from this study, which examined the effects of representations, constructivist approaches, and engagement on middle school students' algebraic understanding. Data from an algebra pretest and posttest, as well as 16 algebra video lessons from an NSF-IERI funded project, were examined to determine occurrences of indicators of representations, constructivist approaches, and engagement, as well as student understanding. A mixed methods design was utilized by implementing multilevel structural equation modeling and constant comparison within the analysis. Calculation of descriptive statistics and creation of bar graphs provided more detail to add to the findings from the components of the statistical test and qualitative comparison method. The results of the final structural equation model revealed a model that fit the data, with a non-significant model, p > .01. The new collectively named latent factor of constructivist approaches with the six indicators of enactive representations, encouragement of student independent thinking, creation of problem-centered lessons, facilitation of shared meanings, justification of ideas, and receiving feedback from the teacher was shown to be a significant predictor of procedural knowledge (p < .05) and conceptual understanding (p < .10). The indicators of the original latent factor of constructivist approaches were combined with one indicator for representations and two indicators for engagement. Constant comparison revealed similar findings concerning correlations among the indicators, as well as effects on student engagement and understanding. Constructivist approaches were found to have a positive effect on both types of student learning in middle school mathematics.

There are many researchers that emphasize the importance of how teachers’ knowledge will affect students’ learning. However, not much research is focused on an international comparison between preservice mathematics teachers’ procedural knowledge and conceptual knowledge. There were 91 preservice mathematics teachers involved in this study. A test on the operations on fractions, decimals, percentages, and integers knowledge showed a) the significant differences between the United States and Chinese preservice teachers’ (PTS) procedural knowledge, b) the significant differences between the United States and Chinese PTS’ conceptual knowledge, and c) the relationships between the United States and Chinese PTS’ procedural knowledge and conceptual knowledge. By comparing the results, the researcher determined the strengths and weaknesses of preservice mathematics teachers in the two countries. The researcher will provide PTS some information based on the results of the knowledge test.

Literature describes different stances with respect to conceptual and procedural mathematical knowledge. The concept-driven versus skills-orientated perspectives have led to “math wars” between researchers, while some mathematics education specialists advocate that the five strands of mathematical proficiency should be seen as interconnected. Conceptual knowledge is the knowledge of concepts or principles, and procedural knowledge the knowledge of procedures. Both types of knowledge are critical components of mathematical proficiency. This study used a mixed methods design to analyse the relationship between conceptual and procedural knowledge. The qualitative content analysis investigated relations between procedural and conceptual knowledge within the solutions of 33 calculus items. The analysis included the number of procedural and conceptual steps needed to answer the item, item label and item classification into one of four knowledge classes based on the type and quality of knowledge. The items were included in a data collection instrument used for quantitative analysis. Rasch analysis was performed to measure item difficulty and person proficiency, and describe the underlying cognitive construct between items. The Rasch person–item map confirmed that items were not clustered together per class and that item difficulty was not linked to the number of procedural and/or conceptual steps needed to do the mathematics. Confirmatory factor analysis showed over-correlation between classes and that defined classes cannot be separated, confirming integration of procedural and conceptual cognitive processes. The relationship between procedural and conceptual knowledge within and between items is complex. Findings indicated that item solutions drew on both procedural and conceptual components that cannot be separated. Solutions could follow more than one approach and analyses could differ, since what is conceptual for one student could be procedural for another. Therefore, teaching strategies should navigate between concepts and procedures, methods and representations. / Thesis (PhD)--University of Pretoria, 2020. / Science, Mathematics and Technology Education / PhD / Unrestricted

Learning of threshold concepts in engineering science courses such as statics has traditionally been a difficult and critical juncture for engineering students. Research and other systematic efforts to improve the teaching of statics in recent years range widely, from development of courseware and assessment tools to experiential and other "hands-on" learning techniques. This dissertation reports the findings from a multi-year, dual-institution study investigating possible links between short writing assignments and conceptual knowledge development in statics courses. The theoretical framework of the study draws on elements from cognitive learning theory: expertise, procedural and conceptual knowledge development, and conceptual change. The way that students approach learning in statics with regard to procedural and conceptual knowledge is explored qualitatively, and the relationship between the writing assignments and conceptual knowledge development is examined using a mixed-methods approach. The results show that students approach learning in statics with varying emphasis placed on procedural and conceptual knowledge development and that a student's learning approach influences their perception of the written problems and the ways that they utilize them in learning. Thus, they provide evidence that the learning approach of students may be an important factor in the success of interventions designed to improve conceptual knowledge in statics. Increases in conceptual knowledge as a result of completing the written problems are also empirically supported though limited by problems with data collection. Areas for future work in light of these findings are identified. / Ph. D.

The performance of mathematics and physical science students are very low in South Africa. These students lack algebraic knowledge and skills in physics education. They tend to treat mathematics and science as separate entities; to them the two subjects are not related. Even the teachers seem not to realise the interrelationship of the two subjects, because according to the research, they perpetuate this attitude. A possible reason could be that they are unfamiliar with common objectives and applications. Knowledge of science is enhanced by the application of mathematics, but the role of mathematical knowledge and skills in the understanding of physical science is uncertain. Even in the new National Curriculum Statement (NCS) of South Africa the relationship between mathematics and physical science is not clearly indicated. Algebraic language is a main tool used in physics, but students still display a lack of understanding of mathematical concepts and problem solving skills. The study was aimed at identifying the mathematical knowledge and skills that would enable students to solve physics problems in grades 11 and 12. The aim was also to identify the specific problems experienced by students in applying these skills and knowledge in physics at grades 11 and 12 level. The empirical study was conducted amongst a group of 120 students in four schools in the Rustenburg Region, North- West Province, South Africa and 28 teachers of which 10 were from these schools and 18 were teachers participating in the Sediba project of the North-West University. The investigation was done by means of a self constructed test and questionnaires. The results indicate that the biggest problem lies with a lack of conceptual knowledge, especially with a basic understanding of proportional reasoning. Other problems were identified and possible remedies proposed. / Thesis (M.Ed.)--North-West University, Potchefstroom Campus, 2006.

This study assessed the knowledge structure of undergraduate participants related to previously determined critical concepts of Analysis of Variance (ANOVA) by using Pathfinder networks. Three domain experts’ knowledge structures regarding the same concepts were also elicited and averaged to create a referent knowledge structure. The referent knowledge structure served as a basis for formative feedback. Then, each participant’s knowledge structure was compared with the referent structure to identify common, missing, and extraneous links between the two networks. Each participant was provided with individualized written and visual, and multi-media feedback through an online Concept Mapping tool based on the principals of formative assessment and feedback in an attempt to increase their conceptual knowledge of ANOVA. The study was conducted with 67 undergraduate participants from a mid-size university in the United States. Participants completed two data collection tools related to the critical concepts of ANOVA. Later, three different types of feedback around the critical concepts were given to participants in three stages. First, each participant was given visual feedback as a result of the comparison between their own knowledge structures and the referent knowledge structure to highlight similarities and differences between the two. Then, participants were provided with individualized written and multi-media feedback to emphasize conceptual understanding behind ANOVA procedures. This procedure was followed by the re-assessment of participants’ reasoning ability related to ANOVA and knowledge structures related to critical concepts to measure the effect of the intervention. Results suggest that participants both in control and intervention groups had the same level of statistics experience and anxiety before this study indicating that randomization of participants into two different groups was successful. Moreover, women participants reported a statistically significant higher level of statistics anxiety than men, however, it seems that this small difference did not limit their ability to perform required statistical tasks. Further, findings revealed that participants’ conceptual knowledge related to critical concepts of ANOVA increased significantly after the individualized feedback. However, the increase in the conceptual understanding did not help participants to transform this knowledge into more formal understanding related to procedures underlying ANOVA. Moreover, even though, previous similar studies suggest that participants are consistent in using a single strategy for making inferential reasoning across datasets, in the present study, qualitative data analysis revealed that statistics learners demonstrate diverse patterns of inferential reasoning strategies when they were provided with different size of datasets each with varying amount of variability. As a result, findings support the use of an extended framework for describing and measuring the development of participants’ reasoning ability regarding consideration of variation in statistics education.

This dissertation represents the research and development of new concepts and techniques for modeling the knowledge about the many concepts we as hydrologists must understand such that we can execute models that operate in terms of conceptual abstractions and have those abstractions translate to the data, tools, and models we use every day. This hydrologic knowledge includes conceptual (i.e. semantic) knowledge, such as the hydrologic cycle concepts and relationships, as well as functional (i.e. procedural) knowledge, such as how to compute the area of a watershed polygon, average basin slope or topographic wetness index. This dissertation is presented as three papers and a reference manual for the software created. Because hydrologic knowledge includes both semantic aspects as well as procedural aspects, we have developed, in the first paper, a new form of reasoning engine and knowledge base that extends the general-purpose analysis and problem-solving capability of reasoning engines by incorporating procedural knowledge, represented as computer source code, into the knowledge base. The reasoning engine is able to compile the code and then, if need be, execute the procedural code as part of a query. The potential advantage to this approach is that it simplifies the description of procedural knowledge in a form that can be readily utilized by the reasoning engine to answer a query. Further, since the form of representation of the procedural knowledge is source code, the procedural knowledge has the full capabilities of the underlying language. We use the term "functional ontology" to refer to the new semantic and procedural knowledge models. The first paper applies the new knowledge model to describing and analyzing polygons. The second and third papers address the application of the new functional ontology reasoning engine and knowledge model to hydrologic applications. The second paper models concepts and procedures, including running external software, related to watershed delineation. The third paper models a project scenario that includes integrating several models. A key advance demonstrated in this paper is the use of functional ontologies to apply metamodeling concepts in a manner that both abstracts and fully utilizes computational models and data sets as part of the project modeling process.

Ce travail, adossé au paradigme de la prise de décision en situation (Klein, Orasanu, Calderwood, & Zsambok, 1993) porte sur le processus de prise de décisions d‘entraîneurs de handball au cours du match. La situation de match, caractérisée par ses aspects dynamiques, coopératifs et compétitifs, donne une conception chaotique de ce processus (Bowes & Jones, 2006). C‘est pourquoi, son étude nécessite de mobiliser plusieurs approches et modèles théoriques (e.g., cognition collective, théorie du focus régulateur [Higgins, 1997], théorie du contrôle [Carver & Scheier, 1982], modèles de persuasion [Chaiken, 1980 ; Petty & Cacioppo, 1986], communication dialogique [Goffman, 1961], modèle de l‘activité coopérative [Hoc, 2001]). Les données, issues de situations réelles de matchs (protocoles verbaux, choix de système défensif) ou d‘entretiens (e.g., auto-confrontations avec technique de rappel stimulé) font l‘objet d‘analyses quantitatives ou qualitatives. Les résultats révèlent les connaissances procédurales des entraîneurs concernant : la gestion de l‘équipe, les informations permettant aux joueurs d‘acquérir ou de mettre à jour des structures de connaissances adaptées à la situation, et les tentatives d‘influence des arbitres. Ces connaissances procédurales sont fonction des conditions du match (notamment le rapport d‘opposition entre les deux équipes) et influencées par des connaissances sur le jeu et les caractéristiques des joueurs. Différents modes de contrôle cognitif et styles de coaching sont aussi mis en évidence. Ainsi, le processus de prise de décisions d‘entraîneurs experts possède des régularités et suit des règles génériques, des heuristiques ou patterns. / This work, based on naturalistic decision-making paradigm (Klein, Orasanu, Calderwood, & Zsambok, 1993) is focused on team sport (handball) coaches decision-making during match. The coaching activity is dynamic and chaotic (Bowes & Jones, 2006) and generated by on-going events, especially during match. Therefore, coaches decision-making studies require to use many theoretical approaches and models (e.g., team cognition, regulatory focus theory [Higgins, 1997], control theory [Carver & Scheier, 1982], persuasive models [Chaiken, 1980 ; Petty & Cacioppo, 1986], dialogic communication [Goffman, 1961], cooperative activity model [Hoc, 2001]). Data have been collected from official games (verbal protocols, defense system choices) or interviews (self-confrontation with stimulated technique recall) and analysed with quantitative and qualitative approach. Results highlight procedural knowledge concerning team management, information allowing players to acquire or update knowledge structures, and influence referee. This procedural knowledge varied depending on the game conditions and is influenced by the coach‘s deep knowledge of the game and player profiles. Results highlight also different cognitive control modes, and different coaching styles. There exist contextual factors effects on procedural knowledge and cognitive control modes. Among these factors, ratio of strength between the two teams appears especially salient. Therefore, our empirical studies show that expert coaches‘ decision-making process have some regularity and follow generic rules, heuristics or patterns

El concepto de procedimiento médico se refiere al conjunto de actividades seguidas por los profesionales de la salud para solucionar o mitigar el problema de salud que afecta a un paciente. La toma de decisiones dentro del procedimiento médico ha sido, por largo tiempo, uno de las áreas más interesantes de investigación en la informática médica y el contexto de investigación de esta tesis. La motivación para desarrollar este trabajo de investigación se basa en tres aspectos fundamentales: no hay modelos de conocimiento para todas las actividades médico-clínicas que puedan ser inducidas a partir de datos médicos, no hay soluciones de aprendizaje inductivo para todas las actividades de la asistencia médica y no hay un modelo integral que formalice el concepto de procedimiento médico. Por tanto, nuestro objetivo principal es desarrollar un modelo computable basado en conocimiento que integre todas las actividades de decisión y planificación para el diagnóstico, tratamiento y pronóstico médico-clínicos. Para alcanzar el objetivo principal, en primer lugar, explicamos el problema de investigación. En segundo lugar, describimos los antecedentes del problema de investigación desde los contextos médico e informático. En tercer lugar, explicamos el desarrollo de la propuesta de investigación, basada en cuatro contribuciones principales: un nuevo modelo, basado en datos y conocimiento, para la actividad de planificación en el diagnóstico y tratamiento médico-clínicos; una novedosa metodología de aprendizaje inductivo para la actividad de planificación en el diagnóstico y tratamiento médico-clínico; una novedosa metodología de aprendizaje inductivo para la actividad de decisión en el pronóstico médico-clínico, y finalmente, un nuevo modelo computable, basado en datos y conocimiento, que integra las actividades de decisión y planificación para el diagnóstico, tratamiento y pronóstico médico-clínicos. / The concept of medical procedure refers to the set of activities carried out by the health care professionals to solve or mitigate the health problems that affect a patient. Decisions making within a medical procedure has been, for a long time, one of the most interesting research areas in medical informatics and the research context of this thesis. The motivation to develop this research work is based on three main aspects: Nowadays there are not knowledge models for all the medical-clinical activities that can be induced from medical data, there are not inductive learning solutions for all the medical-clinical activities, and there is not an integral model that formalizes the concept of medical procedure. Therefore, our main objective is to develop a computable model based in knowledge that integrates all the decision and planning activities for the medical-clinical diagnosis, treatment and prognosis. To achieve this main objective: first, we explain the research problem. Second, we describe the background of the work from both the medical and the informatics contexts. Third, we explain the development of the research proposal based on four main contributions: a novel knowledge representation model, based in data, to the planning activity in medical-clinical diagnosis and treatment; a novel inductive learning methodology to the planning activity in diagnosis and medical-clinical treatment; a novel inductive learning methodology to the decision activity in medical-clinical prognosis, and finally, a novel computable model, based on data and knowledge, which integrates the decision and planning activities of medical-clinical diagnosis, treatment and prognosis.