An exploratory investigation of the roles and development needs of teachers in promoting problem solving in the secondary school mathematics classroom

Description

Needed: Chapter 1-Introduction, Chapter 2 – Literature review, Chapter 3 – Methodology What this dissertation is about: Worldwide, linking mathematics education and workplace preparedness is a central policy theme. Recently, increased emphasis has been given to the importance of mathematical problem solving (MPS), as it permeates all aspects of life. In England, the national curriculum for mathematics for secondary schools was revised in 2013, giving more weight to MPS. The curriculum concentrates on the essential knowledge and skills students should have, such as the ability to apply mathematical facts and skills to a variety of routine and non-routine problems with increasing sophistication (DfE, 2014), giving teachers freedom in how they implement the curriculum. Research on MPS in education has spanned many decades, yielding pendulum-like swings in recommendations on various issues, such as numerous conceptual definitions of MPS, and the effectiveness of teaching general strategies and heuristics. Consensus has not been reached regarding what constitutes MPS in the classroom (English & Gainsburg, 2016; Schoenfeld, 1992; Schoenfeld, 2013). As teachers may be suspicious of educational reform, given its equivocal success over the past decades (OECD, 2014), they may rely more on their own beliefs than on current trends in pedagogy when implementing MPS in their classes (Ho & Hedberg, 2005). Therefore, the dissertation seeks to explore how teachers, guided by their beliefs, promote MPS in their classrooms, and to identify proficiencies needed to implement MPS effectively. Qualitative data has been collected through semi-structured interviews with ten teachers of mathematics from different schools in the north of England, and with different teaching experience, ranging from NQT to Head of Department.

The data is analysed, using Thematical Analysis, for any patterns, common issues, and differences among participants’ views. Also, further analysis will consider how these potential differences could be explained and  what their practical implications in the classroom might be. Social constructivism is used as a methodological source to support this analytic approach. The intention is to highlight issues most relevant to the development needs of teachers to fulfil the demands of the national curriculum. Findings may lead to increased direction for curricula and instructional decisions or future research in MPS to increase effective implementation in classrooms. What is needed: – It should be a coherent story / argument – More theory backup – Justification, “this is the way I did this, this is what the literature says about it”, showing the pros and cons. Chapter One: Introduction (words: ~800) 1.1 Background – Problem solving (PS) and teachers’ beliefs – Why is PS important? The demands of 21st century work and life National curriculum for mathematics – Fact s from research literature 1.2 Aims of the study / Research purpose Chapter Two: Review of the literature (words: ~4000) 2.1 Problem solving – The demands of 21st century work and life – National curriculum for mathematics – Research literature Definition of problem and PS PS strategies (brief) 2.2 Teachers’ beliefs – Theories about teachers’ beliefs Ways of teaching: – traditionally vs inquiry orientated – transmission- orientated vs discovery- and connectionist orientated (mention constructivism) – teaching PS vs teaching mathematics through PS – Impact of teacher’s belief on curriculum reform & student outcome – Teaching and learning practice influence teacher’s belief 2.3 Research questions Chapter Three: Methodology and Methods (words: ~3200) 3.1 Social constructivism as a philosophical approach