211 research outputs found
Using a lens of awareness in phenomenographic research: an example from early mathematics education research
No full textThis paper aims to contribute to the advancement of methodological practice for phenomenographic research by introducing the notion of a lens of awareness, as a device that can enable researchers to zoom into the detail of the research process (the parts of the whole) and out again to the related context of a phenomenographic study (the whole). The lens enables researchers to embrace a reflexive stance to bracket prior assumptions, allowing critical inspection of the whole research process and a thorough retrospective and transparent account of the approaches used. We use a lens of awareness to communicate the component parts of a study that examined preschool children’s understandings of the use of numerals in everyday environments. Through an analytical documentation of processes and decisions, we examine challenges, the powerful affordances and application of a phenomenographic approach to research with young children. We discuss four strands of researcher awareness that we argue are important in the application of phenomenography: the nature of the phenomenon; the operationalization of phenomenographic theoretical notions; the researcher’s versus the participant’s experience of the phenomenon and the applied research processes. The paper closes with explorative strategies that may enhance transparency and trustworthiness in phenomenographic research.</p
Preschool children’s conceptions of the meanings and use of written numerals in everyday life: a phenomenographic study of the nature and structure of qualitative variation
No full textSupporting children’s understanding of the everyday, cultural use of written numerals is highly significant, as it is this understanding that gives meaning to classroom conversations on the purposes of written numbers. This paper presents findings from a phenomenographic study of the qualitatively different ways in which 3–5-year-old children interpret the meanings and use of numerals in everyday contexts. The study involved a volunteer sample of 37 preschool children. With their family’s support, children played a Number Spotting game, taking photographs of numerals in their environments. These photographs were supplemented with other photographs selected by the researchers and used in individual photo-elicitation interviews with children. We collected data on children’s interpretations of a range of examples of numerals used to denote quantity, order and measurement, and numerals used as labels/identifiers. The findings document qualitatively different categories that capture the range of children’s expressed conceptions as well as the critical aspects of variation that underpin how qualitatively different categories of conceptions differ or relate to each other. The study provides original insights into the nature and structure of children’s awareness of the cultural uses of written numerals. The findings can support early mathematics teaching to make meaningful connections between the knowledge that children develop outside school and the new knowledge about written numbers that they develop in formal education
Preschool children’s notations for denoting ordinal position and quantity
No full textThe research is funded by The Leverhulme Trust (RPG-2019-330), in the UK
An investigation of a mathematics recovery programme for multiplicative reasoning to a group of learners in the South African context : a case study approach
No full textThis thesis describes an intervention using the Mathematics Recovery programme in a
South African context with a small sample of Grade 4 learners. The study uses a qualitative
case study approach. The data collection included video recorded one-to-one oral interviews
with the learners. I used the Learning Framework in Number (LFIN) developed by Wright,
Martland, Stafford and Stanger (2006) to profile the learners using pre and post intervention
interview data and to determine their levels of multiplicative reasoning. The analysis
showed the positive impact of the Mathematics Recovery programme on the improvement
of multiplicative reasoning. The study contributes to the use of Mathematics Recovery
programmes in South Africa from both a teacher and teacher educator perspective
Examining the nature of learning within an afterschool mathematics club : a case study of four learners
No full textThis study examined the nature of learning within an afterschool mathematics club established by the South African Numeracy Chair project. The study sought to establish what sort of progress in mathematical learning occurred in a grade 3 afterschool maths club, using assessment instruments associated with the Learning Framework in Number. The study also sought to understand the nature and effects of mentor mediation in the maths club, using Vygotsky’s notion of the Zone of Proximal Development (ZPD) together with the notion and practice of scaffolding. The study made use of a variety of data collection techniques, including one-to-one assessment interviews, task-based interviews and observations. In line with the case study approach adopted, four learners were selected for interviews. The assessment interview results revealed that, in terms of proficiency in early arithmetical learning, all four learners showed progress after spending four months in an afterschool maths club. Even though they were found to have advanced in their Strategies for Early Arithmetic Learning (SEAL), some of them were observed still using their fingers to support their counting. Such strategies were likely to mirror the teaching approaches used in their usual school mathematical lessons. The overall findings in terms of learners’ proficiency and progress give rise to concerns about current number teaching practices in their school, which emphasize the standard written algorithm in the lower primary grades. The study also made use of Vygotsky’s notion of the ZPD to analyse the nature of mentor-peer mediation. Witnessing the learners’ use of trial and error strategies during the task-based interview allowed both mentors to support learners through understanding their thinking, prompting them and encouraging them to reflect on their answers and develop more effective strategies. Learners progressed through the ZPD at different paces and in different ways, with ‘aha’ moments happening at different points for individual learners. Their progression in the ZPD seemed to depend on interaction among all participants, which varied according to what was contributed and what requested by each participant. The findings revealed that although there was evidence of learners achieving success at the tasks in task based interviews there were also there were also some learners who experienced difficulties. Additionally, in order to argue that learning was fully realised within the ZPD would have required follow up task based interviews to assess the extent to which learners were able to complete the tasks independently without the scaffolding of mentors. This was not possible within the scope of this research but would be useful in future research
Principles and methods in the homiletics of John R.W. Stott
No full textProefskrif (ThD (Diakoniologie-Homiletiek))--PU vir CHO, 19971. The purpose of this study. A closer specification of the aim of this study is threefold: * To undertake a closer investigation of and to describe his exegetical, hermeneutic and homiletic principles and methods. * To arrive at a descriptive analysis of his homiletic principles and especially, to examine his views concerning the application in a sermon, i.e., 'Bridge Building'.
* To interpret and evaluate his principles and methods of sermon in the context of the biblical and Reformed theology. 2. The method of this study It is imperative to undertake an intensive analytical study of his published works because all of his principles and methods concerning exegesis, as well as hermeneutic and homiletic questions are contained in his extensive number of sermons and the treatise on preaching (/believe in preaching). The method of this study is threefold: * To investigate John Stott's works in literature by means of analysis and interpretation. * To examine the recorded tapes of his sermons, have a personal interview with him and closely scrutinize of all materials published by him on the overall subject of preaching. * In our presentation it is sometimes inevitable that many quotations and examples have to be used in order to elucidate his principles and methods. 3. Stott's biographical background The influences that his home (parents), the various schools (high school and university) that he attended, and the other primary factors (Nash, Simeon, Ryle,
Morgan) had on John Stott molded the characteristics of the greatest preacher and evangelist of the late twentieth century.
4. Stott's exegesis 4.1. He stresses that without a proper basic understanding of the Bible, both the principles and methods of exegesis cannot help a preacher in attaining his goal: discovering the original meaning of the text. 4.2. His characteristic attitude to the study of the Bible is governed by at least three bases: * The exegete should study the whole Bible using the comprehensive method. * The preacher should face Scripture as far as possible with fairness and an open mind. * The pastor has to be expectant in his Bible study, i.e., God is going to speak to him through the text of the Bible. 4.3. We sum up all biblical exegesis as Stott's characteristic principles in three ways: * 'Scriptura sui ipsius interpres' - The Scripture is its own interpreter. This is not just a formal, technical rule. An obscure and doubtful passage of Scripture must be interpreted by another clear and certain passage. * The expositor must pray for the illumination of the Spirit of God before reading the Bible. Because without prayer we cannot understand the Word of
God. Therefore, the important key to the exegesis of Stott is the confession 'Spiritus Sanctus est Verus Interpres Scripturae' (the Holy Spirit is the true interpreter of Scripture). * The preacher has to discern what the original writers meant by discovering the original sense or the natural sense, which may be either literal or figurative. He must also represent the precise meaning of the text as intended by the biblical authors. These are respectively the principles of history and of simplicity. 4.4. We summarize Stott's characteristic method of all biblical exegesis by stating that he does not use new exegetical procedures, but he reminds one afresh of the time-honoured exegetical practices: * The preacher must derive the text for his sermon from the Holy Scripture. * The expositor has to meditate on the text for as long a time as possible. * The exegete should approach the Bible inductively. Stott calls it the art of discovering the original meaning of the text. 4.5. Ultimately, exegetical aids (e.g., semantic and syntactic analysis) help the
preacher to analyze a word's tense, case, and number so that its specific grammatical features can be identified or researched by a grammatical aid or lexicon. The exegetical tools will guide preachers to the original-language meanings and uses of the biblical words, and then they are available to help grant pastors confidence that they are preaching what the Holy Spirit wants
them to say. 5. Stott's hermeneutics and the process of hermeneusis 5.1. His hermeneutics' prominent elements is described as follows: * His principles and methods of hermeneutics persist in the traditional viewpoint of interpretation of the Reformers. In that regard Stott concentrates on grasping the meaning of the passage of the Bible in which He speaks to us. * His deepest concern is to consider the context as part of any text. The first task of hermeneutics is to interpret precisely what a biblical author's statement means in its context. * The principles of his hermeneutics are dominated by guidelines of three teachers, e.g., the Holy Spirit, the preachers and the Church. It is by receiving the illumination of the Holy Spirit, by using our own reason and by listening to the teaching of others in the Church that we grow in our understanding of Scripture. * Stott emphasizes that the principles can be dominated by the threefold rules of hermeneutics, that is, the natural meaning, the original meaning and the general meaning. Each of his characteristic principles of hermeneutics is not only common but also an immutable rule in biblical interpretation. * Stott does not neglect the basic methods of hermeneutics, but he sticks to them. With regard to the meaning of the text, he emphasizes the pre-eminence of the contextual, the grammatical and the verbal approaches. In the case of the significance of the text, he stresses the theological and cultural
understanding. * His principle of the salient features of hermeneutics is the Christ-centred approach. He consistently attempts to extract redemptive truths from all of Scripture. So his idea of a message from the text highlights the central theme
of the atonement as it relates to all the issues of faith and life. The Bible is indeed the cradle that brings Christ to us. * Stott uses the principle of the 'analogy of faith' to guide his hermeneutics, as the Protestant Reformers did. This standard requires preachers to use Scripture alone as the basis for their exhortation. Stott determines the biblical truths intended for the persons addressed by the text and then identifies similarities in our present condition that require the application of precisely the same truths. 5.2. We sum up Stott 's characteristics in the process of hermeneusis: * The purpose of his hermenuesis does not merely obligate preachers to explain what the Bible says; it requires them to explain what the Bible means in the lives of people today. Therefore, he always tries to apply the original meaning of the text to the modem situation. * According to Stott essential elements in the process of hermeneusis are the
indicative, the imperative and the promise in the text, because hermeneusis deals with the meaning of the text ' then' bridging the gap to 'today'. * The aim of Stott's hermeneusis not only inspires us by its example, but provides the principles and methods for the interpretation of the Bible by which the Church today can do what he has done during his life time, as the
Reformers of old did. * The central elements in the process of hermeneusis are the revelation of the Triune God that the author makes known about God, i.e. His will, His mercy, His wrath, etc. and about His grace in Christ and His Spirit within us.
6. Stott's homilesis 6.1. He stresses that an expository sermon must be established on a sound theological foundation. The principles of the theological foundation are the doctrines of God: the Holy Scripture, the Church, the pastorate, and the
preaching as the ground work. 6.2. The practice of preaching cannot be separated from the person of the preacher because the whole theology of a preacher lies beneath the practice of his
sermon and a whole lifestyle stands behind it. Therefore, the preacher's personality and competence are of such vital importance to the delivery of the sermon. 6.3. His characteristic form of preaching is governed by a few basic homiletic principles: * The sermon must arise out of a text the preacher has chosen. Within his sermon Stott is committed to the idea that the text should dominate. He emphasizes that the text should always furnish the message and the theme of the sermon, regardless of the length of the text. * The sermon needs to have a sound and functional structure, i.e., the
introduction, the body and the conclusion in a sermon. For Stott, formulating the sermon is of vital importance to creating a sound sermon structure. He states firmly that no sermon is really strong which is not strong in structure too. Just as bones without flesh make a skeleton, so flesh without bones makes
a jellyfish. * For Stott, the purpose of the formulation of the sermon is an essential process to convey the message of the text and to lead the audience to face God. For this purpose the preacher has to study and develop his sermon. And then he
has to be sure at all times that he must depend upon the Holy Spirit, and not rely only on his own skill. 6.4. Stott emphasizes that the preacher should interpret the Bible as Christ-centred,
as well as preach the kerygmatic message, because there are some unbelievers among his congregation. Moreover, Stott thinks that preaching not only tells us about Jesus Christ but also stresses the presence of Christ in Christian communities. This has been at the very heart of John Stott's life and message.
6.5. The core of Stott's methods on homilesis is bridge-building as the application in a sermon. He describes the deep rift between the biblical and the modern world. His particular concern of bridge-building can be summarized as follows:
* The preacher must understand the cultural background of the text in order to build a bridge. * The preacher also has to know the listener's contemporary situation (culture, politics, ethics) in order to make bridge-building comprehensible to him. * The model of bridge-building in a sermon is the incarnation of Jesus Christ. * The methods of bridge-building as an application in a sermon are governed by the direct and indirect way of application throughout the content of a sermon. * The final purpose of the bridge-building is to lead the people of God into
maturity. 6.6. The way to improve our expository preaching is not to emulate Stott's homiletical principles and methods directly, but to imitate his passion and tender heart for the people of God. Above all, the real secret of his sermon is not the mastering of certain homiletic principles and methods, but the fact that he is being controlled by a consuming pastoral love for the people to whom he is preaching. 6.7. Finally, we want to conclude this thesis by quoting Stott's prayer that he has been praying for the past number of years before mounting the pulpit (Stott, 1982a:340): Heavenly Father, we bow in your presence.
May your Word be our rule, our Spirit our teacher, and your greater glory our supreme concern, through Jesus Christ our Lord. Amen.Doctora
Faithful semigroup diagram representations of homeomorphism groups
No full textIn this thesis we investigate two different classes of objects. The first is the class of Dénes cycles of a tree; we show a ‘strong’ correspondence between such cycles and certain partial orders on the edges of the tree. This allows us to find a slick new proof of a classical result, as well as give an algorithm for computing the multiplicity of a Dénes cycle. The second class of objects we investigate, and the main focus of this thesis, is groups generated by geometrically fast sets of bumps. We show that the class of such groups on the interval coincides with a certain subclass of diagram groups, and then exploit this connection to answer a question of Matthew Brin. We then go on to consider groups generated by fast bumps in a general setting and, in so doing, find a necessary and sufficient condition for when groups generated by fast sets of bumps on the circle are isomorphic to certain annular diagram groups. To finish, we deduce a couple of properties of fast groups of the interval using their diagram group representations. In aid of this, we define a group structure on infinite tree diagrams."The author has been partially funded by the EPSRC through the University of St Andrews doctoral training program during the creation of this thesis."--Acknowledgement
Research tensions with the use of timed numeracy fluency assessments as a research tool
No full textIn this paper, we describe how we came to use timed fluency activities, along with personal learner reflections on those activities, in our after-school maths club as a complementary research and developmental tool for assessing the changing levels of learners’ mathematical proficiency over time. We use data from one case-study after-school maths club. Not only did the activities provide us as researchers, and mentors, with a quick way of tracking, evaluating, encouraging and valuing learner progress, but also with a mechanism for the learners to practise the fluency they were developing through other activities of the club. More importantly, the use of learner reflections assisted learner buy-in and reduced the stress related to such timed assessments. This alleviated, to some extent, our ethical unease with the use of such instruments. We have subsequently extended this research and development tool in all clubs that we run and continue to research their affect and effect in order to gain deeper understanding of the research and development opportunities enabled by such activities
- …
