No description available.

No description available.

No description available.

Changing teachers' practice through the CPD process is challenging. Programmes frequently based on centrally devised government interventions and produced on the of a 'one size fits all ' approach. This could be criticised for disempowering teachers they are seen a.5 passive recipients of a system. Programmes may also be ineffective because they ignore the vast range of abilities and backgrounds of the children they originally intended to help. I argue that CPD programmes should facilitate teachers' professional agency and report on how teachers develop and maintain their professional identities despite conflicts between their personal aspirations, programme ' ideals' and the context of perfomativity present within the UK education system. I discuss how a primary mathematics CPD programme applied the 'Discipline of Noticing' in order to facilitate teacher agency and enabled teachers to develop a deeper understanding of their own pedagogical subject knowledge primarily through researching their own practice and developing skills of critical reflexivity. 'Noticing' as a discipline involves practitioners recording salient, micro incidents within their teaching. Subsequent reflection aims to facilitate a drawing back from immediate practice and so enables teachers to see things they have previously overlooked, or have become habituated to see. I report on practitioners who by employing skills of noticing demonstrated an enhanced ability to reflect critically and an increased awareness of their own pedagogical practice. This led to changes in their practice and enabled them to articulate the choices they made within their teaching, thus gaining agency as professional decision-makers. furthermore, I discuss how the Discipline of Noticing facilitated a move into a 'third! space' (Gutierrez, Baquedano-Lopez and Tejeda 1999), characterised by the hybridisation of the roles of practitioner and researcher. I conclude that the potential for real change and teacher empowerment can come about through the dissolution of the boundary between practitioner and researcher.

No description available.

No description available.

This longitudinal study charts the development of counting skills in a group of children with Down syndrome and a group of typically developing children, matched for non-verbal mental age. The role of parent-child interaction in this development is explored. The children with Down syndrome (chronological age range: 3.5-7 years at the start of the study) were seen three times over a 2-year period. The typically developing children (chronological age range: 2 - 4 years at the start) were also seen three times but over 1 Y2 years. Non-verbal mental ages in each group ranged from 2 to 4 years at Phase 1. The difference in interval between test points meant the groups remained matched on non-verbal mental age. The children's count word production, procedural counting performance and understanding of cardinality was assessed at each test point. The Down syndrome group produced significantly shorter count word sequences and had significantly smaller count word vocabularies than the typically developing group at each test point. Despite this disadvantage there were no differences in object counting or cardinal understanding, and both groups made similar progress over the three test points. When provided with parental support during the object counting task, both groups significantly improved their performance, and to a similar degree. Countingspecific parental support and general parent-child interactional style were investigated. No differences were found between the two groups of parents in terms of: how they introduced count task to their children, feedback following sequence and correspondence errors, and feedback following successful counts. The parents of the children with Down syndrome were found to be significantly more directive, however. No relationships were found between parental support or general parent-child interactional style and children's later counting skills. However, there was some evidence that parental support was influenced by the child's earlier counting performance. The overall conclusions drawn were that for children with Down syndrome counting and understanding of cardinality, but not count word sequence production, develop in line with non-verbal mental age. Parental support for counting given to children with Down syndrome does not differ from that given to typically developing children. This support significantly improves counting performance for both groups of children equally, however no evidence was found that parental support effected children's counting development.

This thesis explores children’s conceptions of the equals sign from the vantage point of notating task design. The existing literature reports that young children tend to view the equals sign as meaning “write the result here”. Previous studies have demonstrated that teaching an “is the same as” meaning leads to more flexible thinking about mathematical notation. However, these studies are limited because they do not acknowledge or teach children that the equals sign also means “can be exchanged for”. The thesis explores the “sameness” and “exchanging” meanings for the equals sign by addressing four research questions. The first two questions establish the distinction, in terms of task design, between the two meanings. Does the “can be exchanged for” meaning for the equals sign promote attention to statement form? Are the “can be exchanged for” and “is the same as” meanings for the equals sign pedagogically distinct? The final two research questions seek to establish how children might coordinate the two meanings, and connect them with their existing implicit knowledge of arithmetic principles. Can children coordinate “can be exchanged for” and “is the same as” meanings for the equals sign? Can children connect their implicit arithmetical knowledge with explicit transformations of notation? The instrument used is a specially designed notational computer-microworld called Sum Puzzles. Qualitative data are generated from trials with pairs of Year 5 (9 and 10 years), and in one case Year 8 (12 and 13 years), pupils working collaboratively with the microworld toward specified task goals. It is discovered that the “sameness” meaning is useful for distinguishing equality statements by truthfulness, whereas the “exchanging” meaning is useful for distinguishing statements by form. Moreover, a duality of both meanings can help children connect their own mental calculation strategies with transformations of properly formed notation.

This study investigates the relationship between teacher’s presentation and children’s understanding of the number line within an English primary school that follows the curricular guidance presented within the National Numeracy Strategy (DfEE, 1999a). Following an exploratory study, which guided the development of a questionnaire, the preparation of a pilot study, and the initial investigation with the trainee teachers, the study was re-conceptualised to consider the way in which teachers within each year group of a primary school used the number line and the ways in which their children conceptualized and interpreted it. Using a mixed methodology, the theoretical framework of the study draws upon methods associated with case study, action research and ethnography and involved the use of questionnaires, teacher observations and interviews with selected children. Analysis of the questionnaire data is mainly through the use of descriptive statistics that lead to discussion on children’s embodiments of the number line, their interpretations of what it is and their accuracy in estimating magnitudes. The results of the study suggest that conceptualising the number line as a continuous rather than discrete representation of the number system that evolves for the notion of a repeated unit was less important than carrying out actions on the number line. It is suggested that this emphasis caused ambiguity in the way teachers referred to the number line and restricted understanding amongst the children that focused upon the ordering of numbers and the actions that could be associated with this ordering. The results also suggest that children’s conceptions of magnitude on a segmented 0 to 100 number line neither meet objectives specified within the National Numeracy Strategy nor confirm hypothesised models that suggest a linear or logarithmic pattern of accuracy. The number line is seen to be a tool but its use as a tool becomes limited because teachers, and consequently children, display little if any awareness of its underlying structure and its strength as a representation of the number system.

The fundamental purpose of this research is to establish whether mathematics can be taught effectively with the use of appropriate media and to further establish the possible effects of media in the teaching of mathematics. The research touched on the principles and guidelines of media selection and the various methods that could be utilized in conjunction with media in the teaching of mathematics in the pre-primary and primary schools. In media selection, the emphasis was that media must be chosen objectively rather than on the basis of personal preference and that the effectiveness of media is dependent on the suitability of the physical conditions surrounding it. The overall findings regarding media utilization is that most educators believe that media used in conjunction with a suitable or appropriate method should help to actualize what is expected from the learner. The research method in this study can be divided into a literature study and an empirical investigation. The literature study was done with a view to support the introductory orientation of this study. The focus was on learning as an active process, it also highlighted how the young learners acquire knowledge and how their interaction with their environment impacts on their cognitive development. The research also dealt with concept formation with special reference to the variety of concepts such as physical sensory concepts, action-function concepts, evaluative concepts and abstract concepts. The questionnaire was used to gather data from seventy (70) educators about media integration in the teaching of mathematics in the pre-primary and primary schools. An observation guide was also used during the observation of the presentation of twelve (12) lessons by eight (8) teachers from the pre-primary and primary schools. The lessons included the nature and characteristics of media employed in the lessons. The following factors were taken into account: (a) lesson plan layout (b) specific outcomes (c) contact accuracy and relevance (d) learner variables and interest (e) the learning environment and (ij the mediation capabilities of the educator (g) availability of media in schools The discussion of data collected was followed by the data analysis and interpretation. The statistical techniques were used to put the researcher in a position to either reject or accept the null hypothesis. The techniques used were the Wilcoxon Signed Ranks Test, the Pearson Correlation coefficient, the NPar Test and Friedman Test. On the basis of the findings the researcher has sufficient, concrete evidence to conclude that the results invalidate the null hypothesis tested. Therefore the researcher's conclusion is that: (a) there is a possible effect of media in the teaching of mathematics lessons in the preprimary and primary schools. (b) there is a possible effect of media selection and integration of media in mathematics lessons. / Psychology of Education / D. Ed. (Psychology of Education)