A study of Scottish teachers' beliefs about the interplay of problem solving and problem posing in mathematics education

LB Theory and practice of education

McDonald, Paul Argyle ; Fagan, Catherine

University:University of Glasgow

Department:School of Education

关键词: Mathematics education, teachers beliefs, mathematical problem solving, mathematical problem posing, Curriculum for Excellence.;   

Others  :  http://theses.gla.ac.uk/9030/7/2017McDonaldPhD.pdf

来源: University of Glasgow

【 摘 要 】

The Scottish Curriculum for Excellence (CfE) advocates that the learning and teaching of mathematical problem solving is no longer compartmentalised but is an overarching feature designed to improve higher order thinking skills at all levels by focusing on conceptual understanding. Comitantly, a growing body of literature acknowledges the interrelated educational benefits of mathematical problem posing within classrooms. Teachers’ beliefs are considered powerful indicators of professional practice and can articulate the positionality of teachers with regards to curricula reform. Despite their significance, research into the implementation of mathematical problem solving and mathematical problem posing is, as yet, under-researched particularly in Scotland. The main purpose of this study was to investigate Scottish teachers’ beliefs and espoused instructional practices of mathematical problem solving and mathematical problem posing. More prosaically, it explored beliefs regarding the nature of mathematics, the learning of mathematics and the teaching of mathematics. A mixed methods explanatory design consisting of an online questionnaire followed by semi-structured interviews was selected as the instruments to measure and capture espoused beliefs and reported practices. This study involved a representative sample of 478 participants (229 primary and 249 secondary mathematics practitioners respectively) generated from 21 local education authorities in Scotland. A supplementary feature of the online questionnaire, which harvested 87 volunteered comments, augmented the data collection process. Descriptive and inferential statistics were employed to analyse quantitative data with thematic coding used to organise and interrogate qualitative data. Factor analysis identified three distinct belief systems consistent with a dominant learner-centred approach (i.e. social constructivist, problem solving and collaborative orientation), mainly learner-centred approach (i.e. social constructivist, problem solving and static transmission orientation) and dominant teacher-centred approach (i.e. static and mechanistic transmission orientation). In other words, teachers’ deep-rooted beliefs do not align to one particular group of belief systems but are embedded mutually within a cluster. A mixture of positive, negative and inconsistent beliefs is reported. Significant dissonance exists between the sectors. Characteristics impacting on beliefs include grade and highest level of qualification in the field of education. This study suggests that the conceptualisation and operationalisation of mathematical problem solving and problem posing may be circumscribed in practice and that primary teachers hold stronger mathematical beliefs than secondary mathematics teachers. Several reasons help to illuminate these findings including a lack of pedagogical content knowledge, ineffective manifestations of mathematical creativity, low mathematics teaching self-efficacy and an over dominant national assessment culture. Implications and recommendations for policy and ITE are discussed.