Details of Thesis

Title Like a Bridge: Scaffolding as a means of assisting low-attaining students in mathematics during cognitively challenging tasks
Author Ferguson, Sarah
Institution Australian Catholic University
Date 2012
Abstract The present study examined the case of two upper primary teachers and two low-attaining target students in each of their classes. This study was a component of a large study examining three specific types of mathematics tasks aimed at building conceptual understanding. The two classes observed and described in the present study were engaged in using these cognitively challenging types of mathematics tasks. The study aimed to explore the impact that particular scaffolding practices had on the cognitive and affective responses of the target students during their work on these challenging tasks. The three scaffolding practices focussed on during this study were the use of discussion; the use of manipulative materials and visual representations; and explicit attention paid to concepts. This study aimed to build a rich and detailed description of this case and data were gathered in three phases. The purpose of the initial phase of data collection was to examine the participants' beliefs about mathematics, about themselves as mathematics teachers or learners and, in the case of the teachers, about teaching mathematics to low-attaining students. During this phase, data on the target students' understanding of the mathematics concepts to be taught during the observed lessons were gathered through use of an assessment task. The second phase of data collection involved the observation of six mathematics lessons in each classroom. From these lessons, eight tasks from each classroom, aligned with the task types from the larger study, were selected for further analysis. The focus of lesson observations was the extent and use of the three scaffolding practices, the cognitive and affective responses of the target students, the choice of tasks used by the teachers, and the ways in which they were used. The third phase of data collection occurred one year after the lesson observation period concluded. These data were gathered using semi-structured interviews with all the participant teachers and students. During these interviews, emerging themes and patterns from the data were shared with the teachers, and their reactions sought. Data were analysed using a coding framework developed under the categories of the three scaffolding practices. There were also codes relating to different types of tasks and how tasks were implemented in the classroom. Codes were devised from the literature in each of these areas. Patterns and themes were explored using these predetermined codes but also those which emerged through interviews and observations. The teachers in this study represented differing approaches to teaching mathematics to low-attaining students. One teacher consistently maintained the high level of cognitive demand of all tasks with no variations for low-attaining students. The other teacher used less cognitively demanding tasks with the class most of the time with some shorter tasks maintaining a higher level, and occasionally varied the demands of the task for the target students. The responses of the target students also varied, with two of these low-attaining students struggling to cope with the higher level of cognitive demand for half of the tasks and therefore completing little mathematical activity. The other two target students demonstrated clear progress in their ability to carry out teacher devised procedures but did not appear to develop in their understanding of the concepts underlying such processes. The findings from this study have implications for teachers of low-attaining mathematics students. First, most whole class discussions were not effective in scaffolding the learning of low-attaining students, whereas individual "scaffolding conversations" with teachers were generally effective. The use of manipulative materials and visual representations was effective in providing scaffolding to the low-attaining students if the mathematical concept focussed on was illustrated through the use of the materials. However, manipulative materials or representations that were intended to trigger prior knowledge or link knowledge sets were less effective. Effective use of the third scaffolding practice, explicit attention to concepts, relied on the use of the more effective elements of the previous two scaffolding practices. That is, using scaffolding conversations and materials or representations that illustrated concepts, were most effective in drawing out the underlying concepts. This case study has the potential to offer classroom examples of scaffolding; a complex and little understood practice, which has been under researched in mathematics classrooms. There is also little research that has combined the study of conceptually challenging mathematics tasks and low-attaining students, creating the need and space for this study. This research also adds to the literature on effective teaching of low-attaining students in mathematics, and prompts further worthwhile research topics for investigation.
Thesis 01front.pdf 153 Kb
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