Recent research has elucidated the sustained benefits of early mathematics instruction. With growing concern about the performance of South Africa’s senior learners in mathematics, it is imperative to look at long-term solutions within the education process. One such solution may be to focus on improved mathematics instruction as early as preprimary school. However, children at this young age are not typically suited to formal teaching. Alternative methods of mathematics instruction must be considered for maximum and effective impact. The study was conducted to test the notion that not all early methods of mathematics instruction are equal. During the empirical research approximately 200 preprimary school children in three different socio-economic environments (urban higher SES, township and rural) were tested after experiencing a teacher-guided play-based mathematics teaching intervention, or after experiencing a worksheet-based or free-flow play-based curriculum. The test performance of the participants was primarily compared to find relations between teaching methods and early mathematics performance. The study found that a teacher-guided play-based curriculum is superior to other curriculums in the instruction of mathematics in all educational settings, regardless of socioeconomic background. / Psychology of Education / M. Ed. (Psychology of Education)

Cette thèse considère l'apprentissage de motifs récurrents dans la perception multimodale. Elle s'attache à développer des modèles robotiques de ces facultés telles qu'observées chez l'enfant, et elle s'inscrit en cela dans le domaine de la robotique développementale.Elle s'articule plus précisément autour de deux thèmes principaux qui sont d'une part la capacité d'enfants ou de robots à imiter et à comprendre le comportement d'humains, et d'autre part l'acquisition du langage. A leur intersection, nous examinons la question de la découverte par un agent en développement d'un répertoire de motifs primitifs dans son flux perceptuel. Nous spécifions ce problème et établissons son lien avec ceux de l'indétermination de la traduction décrit par Quine et de la séparation aveugle de source tels qu'étudiés en acoustique.Nous en étudions successivement quatre sous-problèmes et formulons une définition expérimentale de chacun. Des modèles d'agents résolvant ces problèmes sont également décrits et testés. Ils s'appuient particulièrement sur des techniques dites de sacs de mots, de factorisation de matrices et d'apprentissage par renforcement inverse. Nous approfondissons séparément les trois problèmes de l'apprentissage de sons élémentaires tels les phonèmes ou les mots, de mouvements basiques de danse et d'objectifs primaires composant des tâches motrices complexes. Pour finir nous étudions le problème de l'apprentissage d'éléments primitifs multimodaux, ce qui revient à résoudre simultanément plusieurs des problèmes précédents. Nous expliquons notamment en quoi cela fournit un modèle de l'ancrage de mots acoustiques / This thesis focuses on learning recurring patterns in multimodal perception. For that purpose it develops cognitive systems that model the mechanisms providing such capabilities to infants; a methodology that fits into thefield of developmental robotics.More precisely, this thesis revolves around two main topics that are, on the one hand the ability of infants or robots to imitate and understand human behaviors, and on the other the acquisition of language. At the crossing of these topics, we study the question of the how a developmental cognitive agent can discover a dictionary of primitive patterns from its multimodal perceptual flow. We specify this problem and formulate its links with Quine's indetermination of translation and blind source separation, as studied in acoustics.We sequentially study four sub-problems and provide an experimental formulation of each of them. We then describe and test computational models of agents solving these problems. They are particularly based on bag-of-words techniques, matrix factorization algorithms, and inverse reinforcement learning approaches. We first go in depth into the three separate problems of learning primitive sounds, such as phonemes or words, learning primitive dance motions, and learning primitive objective that compose complex tasks. Finally we study the problem of learning multimodal primitive patterns, which corresponds to solve simultaneously several of the aforementioned problems. We also details how the last problems models acoustic words grounding.

University of Macau / Faculty of Education

Recent research has elucidated the sustained benefits of early mathematics instruction. With growing concern about the performance of South Africa’s senior learners in mathematics, it is imperative to look at long-term solutions within the education process. One such solution may be to focus on improved mathematics instruction as early as preprimary school. However, children at this young age are not typically suited to formal teaching. Alternative methods of mathematics instruction must be considered for maximum and effective impact. The study was conducted to test the notion that not all early methods of mathematics instruction are equal. During the empirical research approximately 200 preprimary school children in three different socio-economic environments (urban higher SES, township and rural) were tested after experiencing a teacher-guided play-based mathematics teaching intervention, or after experiencing a worksheet-based or free-flow play-based curriculum. The test performance of the participants was primarily compared to find relations between teaching methods and early mathematics performance. The study found that a teacher-guided play-based curriculum is superior to other curriculums in the instruction of mathematics in all educational settings, regardless of socioeconomic background. / Psychology of Education / M. Ed. (Psychology of Education)

The study aimed to explore misconceptions that Grade 9 learners at a school in Soweto had concerning the topic of fractions. The study was based on the ideas of constructivism in a bid to understand how learners build on existing knowledge as they venture deeper into the development of advanced constructions in the concept of fractions. A case study approach (qualitative) was employed to explore how Grade 9 learners describe the concept of fractions. The approach offered a platform to investigate how Grade 9 learners solve problems involving fractions, thereby enabling the researcher to discover the misconceptions that learners have/display when dealing with fractions. The research allowed the researcher to explore the root causes of the misconceptions held by learners concerning the concept of fractions. Forty Grade 9 participants from a township school were subjected to a written test from which eight were purposefully selected for an interview. The selection was based on learners’ responses to the written test. The researcher was looking for a learner script that showed application of similar but incorrect procedures under specific sections of operations of fractions, for example, multiplication of fractions. Both performance extremes were also considered, the good and the worst performers overall. The written test and the interviews were the primary sources of data in this study. The study revealed that learners have misconceptions about fractions. The learners’ definitions of what a fraction is were neither complete nor precise. For example, the equality of parts was not emphasised in their definitions. The gaps brought about by the learner conception of fractions were evident in the way problems on fractions were manipulated. The learners did not treat a fraction as signifying a specific point on the number system. Due to this, learners could not place fractions correctly on the number line. Components of the fraction were separated and manipulated as stand-alone whole numbers. Consequently, whole number knowledge was applied to work with fractions. A lack of conceptual understanding of equivalent fractions was evident as the common denominator principle was not applied. In the multiplication of fractions, procedural manipulations were evident. In mixed number operations, whole numbers were multiplied separately from the fractional parts of the mixed number. Fractional parts were also multiplied separately, and the two answers combined to yield the final solution. In the division of fractions, the learners displayed a lack of conceptual knowledge of division of fractions. Operations were made across the division sign numerators separate from the denominators. This reveals that a fraction was not taken as an outright number on its own by learners but viewed as one number put on top of the other which can be separated. Dividing across, learners rendered division commutative. A procedural attempt to apply the invert and multiply procedure was also evident in this study. Learners made procedural errors as they showed a lack of conceptual understanding of the keep-change-flip division algorithm. The study revealed that misconceptions in the concept of fraction were due to prior knowledge, over-generalisation and presentation of fractions during instruction. Constructivism values prior knowledge as the basis for the development of new knowledge. In this study, learners revealed that informal knowledge they possess may impact negatively on the development of the concept of fractions. For example, division by one-half was interpreted as dividing in half by learners. The prior elaboration on the part of a whole sub-construct also proved a barrier to finding solutions to problems that sought knowledge of fractions as other sub-constructs, namely, quotient, measure, ratio and fraction as an operator. Over generalisation by learners in this study led to misconceptions in which a procedure valid in a particular concept is used in another concept where it does not apply. Knowledge on whole numbers was used in manipulating fractions. For example, for whole numbers generally, multiplication makes bigger and division makes smaller. The presentation of fractions during instruction played a role in some misconceptions revealed by this study. Bias towards the part of a whole sub-construct might have limited conceptualisation in other sub-constructs. Preference for the procedural approach above the conceptual one by educators may limit the proper development of the fraction concept as it promotes the use of algorithms without understanding. The researcher recommends the use of manipulatives to promote the understanding of the fraction concept before inductively guiding learners to come up with the algorithm. Imposing the algorithm promotes the procedural approach, thereby depriving learners of an opportunity for conceptual understanding. Not all correct answers result from the correct line of thinking. Educators, therefore, should have a closer look at learners’ work, including those with correct solutions, as there may be concealed misconceptions. Educators should not take for granted what was covered before learners conceptualised fractions as it might be a source of misconceptions. It is therefore recommended to check prior knowledge before proceeding with new instruction. / Mathematics Education / M. Ed. (Mathematics Education)

L'obiettivo del presente lavoro è quello di esaminare criticamente le prospettive teoriche più note sul problema delle relazioni tra sviluppo concettuale del bambino ed acquisizione della prima lingua. Per quanto il lavoro si concentri in particolare sullo sviluppo della componente lessicale, ovvero sul legame tra concetti e apprendimento delle parole con cui gli stessi vengono codificati, verranno necessariamente trattati anche alcuni aspetti relativi alla competenza morfologica e sintattica. Dopo aver presentato sinteticamente le principali teorie proposte nell'ambito della linguistica acquisizionale e della psicologia dello sviluppo, procederemo ad una problematizzazione e discussione dei punti critici delle stesse alla luce dei risultati ottenuti in sede sperimentale negli ultimi anni. Partendo dalla consapevolezza che nell'ambito della linguistica, forse ancor più che in altre discipline, il contrasto tra impostazioni teoriche diverse si traduce spesso in discrepanze significative nell'interpretazione degli stessi dati empirici, abbiamo cercato di dare lo stesso spazio ai vari orientamenti teorici. L'obiettivo di questa tesi, infatti, non è quello di dare giudizi di merito sulla validità di una teoria in quanto tale rispetto ad un'altra, quanto di discutere in modo trasversale i nodi più problematici delle varie teorie e le implicazioni delle stesse. Questo intento è particolarmente evidente nelle conclusioni della tesi, strutturate intorno ad una serie di domande di ricerca. / This work provides a critical overview of the major theoretical perspectives on the relationships between conceptual development and first language acquisition. While our focus is on lexical development (ie. on the relation between learning a word and acquiring the relevant concept), we will also touch on some aspects which pertains more specifically to morphological and syntactical development. After briefly introducing the major theories developed in the field of first language acquisition and developmental psychology, we will discuss them in the light of experimental data collected in recent years. As the same empirical findings tend to be interpreted in completely different ways, in our work we tried to give voice to authors supporting different views. Our goal is not to assess the merits of these theores as such, but to take this comparison as an opportunity to discuss the implications and issues thereof. This will be particularly clear in the Conclusions of our work, which are structured as a series of research questions.