Faculty of Education - Theses
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ItemAn investigation of the implementation of a problem-solving intervention in two primary classrooms( 2020)Problem-solving in mathematics is an important component of curricula around the world and it has been identified as essential that students develop this capacity in order to achieve success in mathematics. Studies have found that more teachers need to teach their students strategies to problem-solve in mathematics. The aim of this case study was to investigate the implementation of a problem-solving intervention by two primary school teachers over two lessons each. It focussed on their perceptions of the effectiveness of the intervention and how it might improve their teaching of problem-solving in mathematics in the future. It also focussed on how they implemented the intervention and how their students responded to the intervention. The problem-solving intervention was designed based on features identified in problem-solving literature and in discussion with the two teachers. Particular features that were incorporated into the intervention included: enabling and extending prompts; the provision of periods of time in which students were left to ‘struggle’ with trying to solve the problems themselves; and the provision of periods in which students shared problem-solving strategies with peers. The teachers were interviewed separately before and after teaching the lessons. The researcher observed all four lessons and collected student work samples from each lesson. Data was analysed using a content analysis strategy. The results suggest that the two teachers perceived that the intervention had both positive and negative impacts on their students’ problem-solving abilities. They found that the enabling prompts supported and extended their students’ thinking in the lessons and commented that their students enjoyed being challenged in the lessons. The two teachers perceived that it was often not beneficial for some of their students to struggle with problems in the lessons due to perceived resilience and confidence issues. Both teachers deviated from the intervention in the lessons in order to reduce the amount of struggle their students experienced. However, where students were given time to struggle in the lessons, they were able to formulate and record a greater range of problem-solving strategies. There appeared to be a tension for the teachers between providing time for their students to struggle with problems and preserving some of their students’ confidence. One of the teachers facilitated student share time in the middle of one of her lessons which allowed students to experience both struggle and success. This approach could serve as a compromise between these two tensions. The two teachers perceived that the intervention had a positive impact on their teaching practice. One teacher commented that she intended to implement problem-solving lessons based on the intervention in the future and the other suggested that she would incorporate more manipulatives in her problem-solving lessons.
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ItemDesigning and implementing an intervention program to improve under-achieving Year 8 students’ understanding of multiplicative thinking and assess associated gains in motivation and engagement( 2016)A fifteen-week intervention was carried out in order to examine the efficacy of the Scaffolding Numeracy in the Middle Years (SNMY) (Education Victoria, 2013b) instructional resources in improving the multiplicative thinking of eight under-achieving Year 8 students. The eight students participating in the intervention were contrasted against a similarly profiled control group of ten students. Participants were drawn from a co-educational high school on the lands of the People of the Kulin Nation in Northern Metropolitan Melbourne. Changes in students’ multiplicative thinking, as well as associated changes in motivation and engagement, were measured in pre- and post-intervention assessments. Multiplicative thinking was measured with the SNMY Assessment Booklets 1 and 2, with motivation and engagement examined by use of the High School Motivation and Engagement Scale (MES-HS) (Martin, 2003), also prior-to and following the intervention. These quantitative data sources were complemented with qualitative sources in the form of researcher’s notes and student work samples. Whilst analysis of quantitative data did not indicate significant changes in multiplicative thinking for either the intervention or the control groups, qualitative data sources indicated that students within the intervention group demonstrated modest gains in multiplicative thinking. No statistically significant changes to motivation and engagement were recorded for students in the control group, whereas those in the intervention group showed a significant decrease in both failure avoidance and anxiety, and a significant increase in disengagement between pre- and post-testing. Findings point to several barriers to achievement for mathematically under- achieving students in the middle years, as well as directions for the improvement of similar interventions in future.
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ItemThe smart test system: teachers’ views about this formative assessment for mathematics( 2014)Given the continuous challenge of improving the quality of students’ learning of mathematics at the school level, and the consensus on the impact that teaching practices have on student learning, several countries have incorporated the development of assessments to directly influence teaching practices, known as formative assessments. However, this response has faced challenges, such as the need for more evidence about which particular formative assessment strategies may be beneficial for the learning of both students and teachers. Accordingly, this research is focused on providing evidence about teachers’ opinions from their experience as users of a particular formative assessment, the ‘Specific Mathematics Assessments that Reveal Thinking’ also known as the Smart Test System, developed at The University of Melbourne. The research aims to answer three fundamental questions. First, how do teachers perceive the quality of the Smart Tests items and the diagnosis provided from the Smart Test System? Second, to what extent, and how, do teachers utilize the information provided by the Smart Test System to change their teaching? Thirdly, to what extent, and how, do teachers report on their learning from their use of the Smart Test System? A mixed methodology approach was utilized according to the research questions, and an on-line self-administered survey was used as the method of data collection. The findings suggest that a majority of teachers who participated in this study have had a positive experience as users of the Smart Test System. Along with reporting that the Smart Tests items and the diagnosis provided are of high quality, many teachers mention formative uses of the Smart Test System. These uses mainly correspond to adjusting their planning and differentiation of their practices according to students’ needs. Almost all teachers in this study stated that they have learnt something from the Smart Test System. The findings of this study provide some understanding about how the Smart Test System fulfils its formative purposes. The results contribute to determining teachers’ opinions about the scope and the ways that they use the Smart Test System to adjust their practices. The results also identify some challenges that could be attended to in order to maximize the potential benefit from the use of the Smart Test System, and which can be considered to develop further formative assessment initiatives.
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ItemDiagnostic testing and changes to teaching practice in Year 9 mathematics classes( 2014)Teachers can use various means, including diagnostic tests, to determine their students’ knowledge. It is of interest to know the ways in which teachers interpret and act upon such diagnostic information. The aim of this study was to examine the use of a particular diagnostic testing system by six teachers in Year 9 mathematics classrooms. The focus diagnostic system was the SMART system (Specific Mathematics Assessment that Reveal Thinking), which provides teachers with an online diagnostic test, diagnostic analysis and teaching advice. This study focused on the use of the SMART system in two topics, linear equations and linear graphs. The participant teachers were interviewed before each topic to ascertain the ways in which they gathered knowledge about student understanding, current and intended teaching practices, and how they met individual student’s learning needs. On conclusion of each topic, participants completed a questionnaire and an interview to determine if any changes had been made. The teachers found the SMART system gave them some useful data on their students. The diagnostic analysis revealed gaps or misunderstandings in some students’ knowledge, the teachers realised that they could no longer assume that all students had the requisite prior knowledge. Through this discovery, teaching practice changed in a number of ways. First, the teachers were able to decide on a better starting point for the particular topic. For example, if many students did not have the expected prior knowledge the teachers began the topic with earlier concepts. Second, teachers could identify groups of students with similar learning needs and these students could be provided with activities that supported their learning. Furthermore, for some teachers it changed their view of students mathematical ability from, ‘some students do not have the ability to learn maths’ to, ‘these students have gaps in their knowledge and if these gaps or misconceptions are addressed they could progress to more complex concepts’. Most significantly, teachers reported becoming more prepared with appropriate materials for either individual students or groups of students. Hence the SMART system supported teachers to cater for individual student needs by highlighting the learning needs of students.
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ItemThe factors influencing secondary school girls' mathematics subject selections( 2014)In Australia, the number of enrolments of secondary school students in advanced Mathematics courses has been declining. This is at a time when mathematical abilities are considered to be a key component in the progressive and contemporary economy with the future prosperity of the nation depending on a significant proportion of the workforce to be educated disciplines including advanced mathematics. High technological skills and productivity are essential in a world that is becoming increasingly dependent on knowledge and innovation. Of particular concern is, while the gap between genders is closing (with the exception of the high performing students); the gender discrepancies in enrolments in some programs are substantial, particularly in the areas of mathematics and engineering. There continues to be an underrepresentation of females in mathematics courses and careers. With consideration of the previous literature, this research study explores the factors that influence girls’ mathematics subject selection in secondary school and discusses the findings and implications. The research was conducted at Hilltop Girls’ College, an all-female secondary school in Melbourne and employed qualitative methods to investigate the experiences and self-perceptions of the participants’ mathematics story together with their ability in mathematics. The data were collected via semi-structured interviews with 22 students from Year 9 to Year 12 and 3 teachers from Hilltop. The analysis of the language used by the girls and teachers in the study revealed the major influence on the students’ subject selection was the perception that mathematics is required as it is a prerequisite for many desirable university courses and it will contribute to increasing the students’ Australian Tertiary Admittance Rank. The students uncovered that studying mathematics is considered valuable primarily because of the understanding that it is important for university entrance, not because is it interesting or required for a career. One of the most interesting findings from this research was that the students had very little idea of how the mathematics they study at school is used in everyday life or in the workforce. The investigation of the culture of mathematics at Hilltop revealed the high status of mathematics at the College which can cause some students to experience anxiety about mathematics and the assessment of mathematics. The other factors that proved to be lesser influences on girls’ choice of mathematics subjects include, gender stereotype, pedagogy, parental influence, the value the girls’ placed on mathematics and the girls’ attitudes towards mathematics.
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ItemCreating the conditions for rich teacher-led whole-class discussions( 2013)Teacher-led whole class discussion is an important pedagogical tool that is still widely used in classrooms today. This research analysed video recordings of four actual mathematics classrooms to look for segments where rich discussions in mathematics were taking place in order to understand how the teachers created the conditions for those rich discussions. By providing an empirical foundation for the construct of a ‘rich’ discussion, this research hopes to contribute towards greater understanding of the nature, enabling conditions and possible outcomes of a rich discussion. The findings of this research project suggest that teachers play a critical role in creating conditions favourable to the occurrence of rich discussions by their actions or non-actions towards student responses. It is hoped that the results of this research will contribute towards informing both teaching practice and programmes of teacher education.
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ItemAn investigation of the impact of LEGO® robotics on the learning of scientific and mathematical concepts at primary level( 2013)This study analysed the way students at grade 3 and 4 learned to manipulate the design projects that are part of lessons from the LEGO® Mindstorms Robotics Invention system. Students worked in cooperative groups of three to four members. Within the hour allocated for each lesson the participants swapped roles, being either a programmer or LEGO® designer. The students were required to utilise many skills, including design, directional language, communication and evaluation. The research methods of the study are qualitative. To find out what the students were learning the research relied on observational notes, written records and photographs. The research aimed to compile evidence of how this style of learning affected the outcomes of student’s achievement and attitudes. Students were required to analyse something that was active. They had to write observational notes to show their understanding of what was occurring and they also had to document how they changed the program to effect the robot’s movements.