Content Knowledge Development Needs of Pre-service Teachers in Bhutan Based on the Primary Mathematics Curriculum: An application of SOLO

Abstract

<p>The mathematics curriculum in Bhutan has undergone significant change over last 20 years, moving from behaviourist teaching and learning strategies towards a constructivist focus by teachers. In 2005, a new national mathematics curriculum in schools was implemented nationwide. When planning for the new curriculum to have a significant impact on the education system many factors were considered such as: teachers’ attitudes, teachers’ content knowledge and pedagogical knowledge, teachers’ perceptions, availability of teaching and learning materials, classroom settings, and preparation of pre-service teachers (PSTs). Teachers across the country were oriented through workshops to learn about the new curriculum, and new textbooks, guidebooks and workbooks were developed and made available to schools.</p> <p>Now there are concerns that these reforms, as significant and necessary as they were, are not delivering the student outcomes (BCSEA, 2011, 2013, 2017) that would best serve the country through the 21^st Century. Needed are studies that chose to identify important issues they may be impeding student learning and offer evidenced informed suggestions on possible ways to enhance the education system. This study was undertaken with this goal in mind.</p> <p>The purpose of the study was to investigate the mathematics content knowledge of PSTs in terms of the mathematics in the primary school mathematics curriculum. Such a study had not been undertaken previously in the Bhutanese context. The focus of the research was on (i) investigating the breadth and depth of primary mathematics curriculum content knowledge of PSTs with the purpose of seeking out their ‘development needs’; and (ii) how might the data collected be a basis for enhancing the quality of teacher education preparation in primary mathematics in Bhutan.</p> <p>There are two theoretical underpinnings of the study. The first is the Mathematical Knowledge for Teaching (MKT) model of Ball et al. (2008) based on Lee Shulman’s pedagogical content knowledge – mathematical knowledge needed to carry out the work of teaching mathematics. The second is the Structure of the Observed Learning Outcome (SOLO) model (Biggs and Collis, 1982) – a post-Piagetian analytical tool used to determine the quality of a student’s response to a task in any learned activity.</p> <p>The study data were collected using a survey and interviews. The survey instrument consisted of 40 multiple-choice items (MCIs) and six free response questions (FRQs), covering the first four strands (Numbers Strand, Operations Strand, Patterns Strand and Measurement Strand) of the primary mathematics curriculum. Using the explanatory sequential mixed-methods design, data were collected from 3^rd Year and 4^th Year PSTs from the two teacher training colleges in Bhutan (<i>n</i>=234). The quantitative data collected through MCIs were analysed using the Rasch model. The qualitative data collected through FRQs was analysed using the SOLO Model and was further interrogated through interviews undertaken with a sample of PSTs.</p> <p>The Rasch analysis of the survey instrument (MCIs) used both the binary model and partial credit model. For the binary model, PSTs’ responses were marked as either correct or incorrect. For the partial credit model, PSTs were given credit for partially correct answers to items. Both models demonstrated high reliability estimates for the survey instrument (MCIs).</p> <p>To facilitate discussion on PST developmental growth further, five broad bands were identified in the MCI difficulty estimates and PST ability estimates. Boundaries between bands were evident by clear separations in the item map. The approach identified groups of responses (items) upon which generalisations about the nature of the items and what PSTs could achieve.</p> <p>Band 5 (highest-level) characteristics comprised approximately 4% of the PST cohort. The next band, band 4, comprised approximately 12% of the PST cohort. Nearly 80% of PSTs were not able to answer correctly 16 items of the forty-item test. It was found that the inability to utilise all needed information in a question, inadequate conceptual understanding and unfamiliar context of the questions may have escalated the difficulty level of items.</p> <p>Some PSTs demonstrated abstract and high-level thinking in primary mathematics content. This was evident in the approaches used in solving abstract and non-routine questions. PSTs going beyond what was asked in the questions and using adequate and appropriate ways of solving the questions are some positive findings.</p> <p>PSTs performed better when the questions were straightforward, familiar and where all the required information was available in the question. This indicates PSTs acquired procedural knowledge linked to practised situations, and encountered difficulties when the question/item focused deliberately on conceptual knowledge or in which conceptual knowledge was needed as a tool in the solution process. Areas where the majority of PSTs needed support to enhance their content knowledge included many arithmetic concepts that were basic to primary school mathematics, such as place value, pattern recognition, comparing fractions, determining equivalent fractions, ratio and not being able to make connections among the parts of division operation (dividend, divisor, quotient and remainder).</p> <p>The study also found that the majority of the PSTs lack conceptual understanding of concepts of area and perimeter. For instance, when finding the area of shapes such as triangles of non-rectilinear shapes many students applied the area formula of a rectangle (length × breadth).</p> <p>Overall, the study found that only a small number of PSTs had acquired adequate breadth and depth of primary mathematics content knowledge across all four strands. This was indicated by the large numbers of partially correct responses in both MCIs and FRQs across all four strands. The majority of the PSTs attained content knowledge at a surface level which did not appear to be an appropriate basis for teaching. In addition, knowledge gaps in all four strands were evident.</p> <p>The findings highlight a major challenge for the colleges of education in Bhutan. The majority of the PSTs struggled with the fundamental knowledge, skills and understanding in primary mathematics. Without this, it appears problematic that new primary teachers will be capable of meeting the learning needs of their students.</p>