Ο βασικός σκοπός της παρούσας εργασίας είναι η διερεύνηση του κατά πόσον: κατά τη διαδικασία επίλυσης μαθηματικού προβλήματος εντός ενός ευνοϊκού μαθησιακού περιβάλλοντος μιας τάξης πρωτοσχολικής ηλικίας, τα παιδιά, αλληλεπιδρώντας μεταξύ τους και με τη νηπιαγωγό, εμπλέκονται σε διεργασίες οι οποίες προάγουν την ανάπτυξη δεξιοτήτων. Ο πιο πάνω σκοπός διερευνάται μέσα από τρία βασικά ερευνητικά ερωτήματα καθένα από τα οποία αναλύεται σε επιμέρους ερωτήματα: 1. πώς λειτουργεί η εκτενής σε χρονική διάρκεια, τακτική (καθημερινή) και οργανωμένη από την νηπιαγωγό ενασχόληση παιδιών με διαδικασία επίλυσης μαθηματικού προβλήματος, μέσα σε ένα ευνοϊκό μαθησιακό περιβάλλον; 2. πώς επιδρά στα παιδιά η διαδικασία επίλυσης μαθηματικού προβλήματος στην ανάπτυξη των δεξιοτήτων (α) εμπλοκής στην επίλυση του μαθηματικού προβλήματος : (i) το παιδί χρησιμοποιεί το υλικό αναπαράστασης του προβλήματος και καταγραφής των λύσεών του με τρόπο που οδηγεί σε επίλυση του προβλήματος; (ii) το παιδί εργάζεται με τρόπο που δείχνει ότι έχει λάβει υπόψη τα δεδομένα του προβλήματος; (iii) το παιδί εργάζεται με τρόπο που οδηγεί σε επίλυση του προβλήματος; (β) ανάπτυξης στρατηγικών επίλυσης του μαθηματικού προβλήματος: (i) ποιες στρατηγικές αναπτύσσουν τα παιδιά κατά τη διαδικασία επίλυσης του κάθε μαθηματικού προβλήματος; (ii) τα παιδιά εφαρμόζουν την ίδια στρατηγική και σε επόμενες διαδικασίες επίλυσης του ίδιου μαθηματικού προβλήματος; (iii) παρατηρείται ανάπτυξη ή βελτίωση της στρατηγικής από τα παιδιά σε επόμενη εφαρμογή της διαδικασίας επίλυσης του ίδιου μαθηματικού προβλήματος; (γ) ανίχνευσης των λύσεων του μαθηματικού προβλήματος: (i) μπορούν τα παιδιά να ανιχνεύσουν όλες τις λύσεις του μαθηματικού προβλήματος (ii) με ποιους τρόπους καταφέρνουν τα παιδιά να ανιχνεύσουν όλες τις λύσεις του προβλήματος; (δ) γραφικής αναπαράστασης των λύσεων του μαθηματικού προβλήματος: (i) πώς επιλέγουν τα παιδιά να αναπαραστήσουν γραφικά τις λύσεις του κάθε προβλήματος; (ii) πώς χρησιμοποιούν τα παιδιά τις γραφικές αναπαραστάσεις των λύσεων του προβλήματος στη διαδικασία επίλυσής του; 3. μπορούν οι γλωσσικές αλληλεπιδράσεις που αναπτύσσονται σε μια τάξη πρωτοσχολικής εκπαίδευσης μεταξύ παιδιών αλλά και μεταξύ παιδιών και νηπιαγωγού να συνεισφέρουν στην επίλυση μαθηματικού προβλήματος; : (ι)σε ποια από τις κατηγορίες σωρευτικός λόγος, λόγος αμφισβήτησης, διερευνητικός λόγος εμπίπτει ο διάλογος μεταξύ παιδιών και πού οδηγεί; (ii) που οδηγεί ο διάλογος μεταξύ παιδιού/παιδιών και νηπιαγωγού; (iii) πού οδηγεί ο μονόλογος του παιδιού; Τα αποτελέσματα δείχνουν ότι (α) μέσα από την αλληλεπίδραση, τόσο μεταξύ τους όσο και με τη νηπιαγωγό, ακόμη και τετράχρονα παιδιά μπορούν να καταστούν ικανά να εφαρμόσουν διαδικασία επίλυσης μαθηματικού προβλήματος (β) η συστηματική, εκτενής και οργανωμένη ενασχόληση παιδιών με διαδικασία επίλυσης μαθηματικού προβλήματος προάγει την ανάπτυξη δεξιοτήτων (γ) βασικό ρόλο στην ανάπτυξη των δεξιοτήτων παίζει η νηπιαγωγός και ο τρόπος με τον οποίο η ίδια οργανώνει το μαθησιακό περιβάλλον της τάξης. Η παρούσα εργασία αποτελείται από τέσσερα Κεφάλαια. Στο πρώτο Κεφάλαιο μελετάται η διαδικασία επίλυσης μαθηματικού προβλήματος στο νηπιαγωγείο και ο όρος του ευνοϊκού μαθησιακού περιβάλλοντος. Ο καθορισμός των στοιχείων του ευνοϊκού μαθησιακού περιβάλλοντος γίνεται μέσα από βιβλιογραφική ανασκόπηση σχετικά με το ρόλο της εκπαιδευτικού στη δημιουργία του όλου περιβάλλοντος και της προαγωγής γλωσσικών αλληλεπιδράσεων μεταξύ της ίδιας και των παιδιών και μεταξύ των παιδιών. Στο δεύτερο Κεφάλαιο αναλύεται η μεθοδολογία της έρευνας. Στο τρίτο Κεφάλαιο παρουσιάζονται και αναλύονται τα δεδομένα της παρούσας έρευνας. Στο τέταρτο, και τελευταίο, Κεφάλαιο συνοψίζονται τα σημαντικότερα ευρήματα της παρούσας εργασίας και διατυπώνονται τα βασικά της συμπεράσματα, μέσα από την απάντηση των ερευνητικών της ερωτημάτων και παρουσιάζονται εισηγήσεις για μελλοντική διερεύνηση ερωτημάτων που προέκυψαν από την παρούσα εργασία. / The aim of this study is to investigate whether: during the process of mathematical problem solving within a favorable learning environment of a pre-school classroom setting, while child-child and child-teacher interaction takes place, children involve themselves in processes promoting skill development. The above hypothesis is studied through three basic research questions, each of which is analysed in further and more specific questions: 1. how does the extensive, frequent (daily) and organized by the teacher, occupation of children with mathematical problem solving process, within a favorable learning environment, function? 2. how does the mathematical problem solving process effect children’s skill development in (a)their involvement in the mathematical problem solving process : (i)can the child use the material created for the mathematical problem representation in a way that leads to the solution of the problem? (ii) does the child’s work show that he/she has considered the problem’s data, (iii) does the child’s work lead to the solution of the mathematical problem? (b)the development of strategies in order to solve the mathematical problem : (i)which strategies do the children develop during the mathematical problem solving process? (ii) do the children apply the same strategy every time they engage in the process of solving the same mathematical problem? (iii) is there a development or an improvement of the children’s strategy during future processes of solving the same mathematical problem? (c)the detection of all possible solutions of a mathematical problem : (i)can children detect all possible solutions of the mathematical problem? (ii) in which ways do the children manage to detect all possible solutions of the mathematical problem? (d)graphically representing the solutions of the mathematical problem : (i)how do children chose to graphically represent the solutions of the mathematical problem? (ii) how do children use graphical representations of problem solutions during the problem solving process? 3. can child-child and child-teacher language interactions, which develop within a pre-school classroom setting, contribute to the problem solving process (i)in which of the categories cumulative talk, investigative talk, exploratory talk does children’s dialogue fall and where does it lead? (ii) where does child-child and child-teacher dialogue lead? (iii) where does child monologue lead? The results show that (a) through child-child and child-teacher interaction children as young as four years old can become capable of applying the mathematical problem solving process, (b) extensive, frequent and organized occupation of young children with the mathematical problem solving process leads to skill development, (c) the teacher’s role is central to the development of skills in the way she organizes the classroom’s learning environment. The present study consists of four chapters. Chapter I studies the problem solving process in pre-school and the term “favorable learning environment”. The determination of the elements of such an environment is established through bibliographical research relative to the teacher’s role in the creation of the classroom environment and the promotion of language interaction between herself and children and between children. Chapter II analyses the methodology of the current study. Chapter III presents and studies the research findings. Chapter IV summarizes the basic findings of the study and presents its conclusions through answering its research questions and gives suggestions for future investigation of questions that have emerged from the present study.

Problem-solving ability is now the most sought-after trait in up-and-coming executives, according to a survey of 1 000 executives conducted by Caliper Associates, reported in the Wall Street Journal by Hal Lancaster (Hoenig, 2002:338). This trait would include the ability to solve human performance problems, something many people tend to steer clear of. According to Piskurich (2002:57-58) and Rothwell, Hohne and King (2000:67-71), the most common problem-solving tools that are used when solving human performance problems are brainstorming, cause-and-effect analysis, and the five why’s technique. Although techniques such as these have proven to be robust and useful, what is required to solve human performance problems is a logical and verifiable process that can establish a data point about which relevant information can be recognized and gathered, and against which the conclusion can be evaluated, to have confirmed knowledge of the root cause of the problems. Unfortunately, existing root cause analysis processes tend to focus on processes and systems, rather than on individual performance (Bowling, 2003). The main objective of this study was to develop a root cause analysis process that would uncover the root cause(s) of uncontrolled variation(s) in human performance and prevent the recurrence of events causing the variation. In addition to addressing individual human performance incidents, it is also necessary continually to manage people’s performance to detect and address any occurrences (or recurrences) of performance variations. Therefore, in addition to the main objective, the study also aimed to develop a Human Performance Management Model that incorporated the root cause analysis process as a problem-solving tool. Action research was used in this study, because of the cyclical iterative nature of this type of research, and because it is a rigorous, responsive and flexible process. The study consisted of three cycles. The end result was a structured root cause analysis process – the Human Performance Variation Analysis (HPVA) process – that enables the systematic collection of valid and reliable information, as is required to solve variation in human performance. The HPVA process is a three-part process that consists of 11 steps. The process is in turn a tool that forms part of a ten-step Human Performance Management Model. The study contributes to the body of knowledge on human performance management by presenting the following: • a systematic root cause analysis process that uncovers the root causes of human performance problems effectively and consistently and that controls these causes of problems in a way that prevents the problems from recurring; and • a Human Performance Management Model that will help to sustain the new, improved performance; prevent the same or similar performance problem(s) in other areas of the organisation; and ultimately, create an environment and culture of continuous human performance improvement. / Thesis (PhD)--University of Pretoria, 2009. / Human Resource Management / unrestricted

The aim of this study is to report findings of inquiry into the role that problem-based approach can play in the teaching and learning of Technology in Thabo-Mofutsanyana District in Qwaqwa. This study followed qualitative research methods and ethnographic design informed by the researcher’s desire for the study to be conducted from firsthand knowledge generated in the research setting. The researcher interviewed Grade 9 Technology teachers and experts, observed teaching and learning in two participating and two non-participating secondary schools in Murray & Roberts Technology Olympiad and analysed Technology teachers’ lesson plans and workschedules, portfolios and files of Grade 9 Technology learners. Key findings that this study produced include: PBL is a need in the teaching of Technology; learners function at a higher level of thinking; learners treat concepts at higher and deeper level; learners become more motivated and learners are able to discover theories and make inventions. / Educational Studies / M. Ed. (Didactics)

At some point during a creative action something clicks, suddenly the prospective problem solver just knows the solution to a problem, and a feeling of joy and relief arises. This phenomenon, called Eureka experience, insight, Aha moment, hunch, epiphany, illumination, or serendipity, has been part of human narrations for thousands of years. It is the moment of a subjective experience, a surprising, and sometimes a life-changing event. In this thesis, I narrow down this moment 1. conceptually, 2. experientially, and 3. temporally. The concept of emerging solutions has a multidisciplinary background in Cognitive Science, Arts, Design, and Engineering. Through the discussion of previous terminology and comparative reviews of historical literature, I identify sources of ambiguity surrounding this phenomenon and suggest unifying terms as the basis for interdisciplinary exploration. Tracking the experience based on qualitative data from 11 creative practitioners, I identify conflicting aspects of existing models of creative production. To bridge this theoretical and disciplinary divide between iterative design thinking and sequential models of creativity, I suggest a novel multi-layered model. Empirical support for this proposal comes from Dira, a computer-based open-ended experimental paradigm. As part of this thesis I developed the task and 40 unique sets of stimuli and response items to collect dynamic measures of the creative process and evade known problems of insightful tasks. Using Dira, I identify the moment when solutions emerge from the number and duration of mouse-interactions with the on-screen elements and the 124 participants' self-reports. I provide an argument for the multi-layered model to explain a discrepancy between the timing observed in Dira and existing sequential models. Furthermore, I suggest that Eureka moments can be assessed on more than a dichotomous scale, as the empirical data from interviews and Dira demonstrates for this rich human experience. I conclude that the research on insight benefits from an interdisciplinary approach and suggest Dira as an instrument for future studies.

The aim of this study is to report findings of inquiry into the role that problem-based approach can play in the teaching and learning of Technology in Thabo-Mofutsanyana District in Qwaqwa. This study followed qualitative research methods and ethnographic design informed by the researcher’s desire for the study to be conducted from firsthand knowledge generated in the research setting. The researcher interviewed Grade 9 Technology teachers and experts, observed teaching and learning in two participating and two non-participating secondary schools in Murray & Roberts Technology Olympiad and analysed Technology teachers’ lesson plans and workschedules, portfolios and files of Grade 9 Technology learners. Key findings that this study produced include: PBL is a need in the teaching of Technology; learners function at a higher level of thinking; learners treat concepts at higher and deeper level; learners become more motivated and learners are able to discover theories and make inventions. / Educational Studies / M. Ed. (Didactics)