A diagnostic approach to STEM-based learning of ratio and proportion

Abstract

This thesis describes a design-based research project to design, develop, implement and evaluate an error-informed STEM-based teaching package aimed to reduce the errors made by resit GCSE mathematics course students in England and 9th-grade vocational high school students in Turkey when learning about the topic of ratio and proportion. There are several reasons for preferring STEM education in this study. Ratio and proportion is perceived as more abstract than many other topics. STEM education is a unique approach that explores teaching and learning and solving real-world problems across/between any two or more STEM disciplines. Moreover, STEM-based education enables students to contextualise concepts and challenges, as well as engage and study in a collaborative learning environment. One of the main objectives of this research is to focus on the errors made by students when learning about ratio and proportion and the causes of these mistakes. For this reason, this study is aimed at two similar contexts; resit GCSE students in England and first-year vocational high school students in Turkey. The first phase of this research involved exploring the similarities and differences in the teaching of ratio and proportion in England and Turkey at the end of the literature chapter. According to the results of this phase of the research, students encounter the topic of ratio and proportion at similar grade levels in both countries, although there are differences in the sequencing within the topic. In the second phase, an error-informed STEM-based teaching package was designed and trialled to reduce the errors made by both sets of students. There were three phases of the design process. The first two phases aimed to determine the ratio and proportion errors made by Turkish and English students. For this purpose, a literature review, lesson observations, diagnostic tests and teachers’ interviews were carried out. In addition, a new error analysis model was developed to analyse students` errors and the causes of these errors. The results revealed the identification of 38 different types of errors and 79 different causes associated with these errors. These errors were; reading and decoding errors, understanding errors, mathematisation errors, processing skills errors, and encoding errors. In the final phase of the design, STEM-based lesson plans were developed, considering the student errors identified and the causes of these errors. Notably, there were differences between the types and frequencies of mistakes made by students from the two countries. As a result of these differences, tailored schemes of work were designed for each country. Subsequently, the frequency and variety of mistakes made by the students significantly decreased following the implementation of the STEM-based lessons. This thesis offers insights and contributions to both theory and practice, as would be expected from a design-based research project. The first of these is detailed information about the place of ratio and proportion in the curriculum of both countries. The teaching package provides detailed information about student errors related to ratio and proportion and the causes of these errors. Moreover, the error analysis model developed, makes a significant contribution to the classification of students' mistakes and their causes. The final contribution is the developed STEM-based teaching package. These lesson plans were developed iteratively through three cycles and by providing accounts of the design changes after each study together with the process involved, the outcomes of the lessons, and what worked and what did not, they are intended to offer detailed information to inform future research and practice.