Maths was fine until they brought the alphabet into it: An examination of Irish 14-year-olds' knowledge of initial algebra
Healy O'Brien, Aoife
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The aim of this research is to establish what second-year students (age approximately 14 years) in Ireland know about initial algebra. To measure this knowledge, a standardised criterion referenced screener has been developed. No such standardised assessment for algebra exists in the Irish context, nor a comprehensive understanding of students’ algebraic knowledge. There has been a shift in the method of teaching initial algebra from the transformative-based to the functions-based approach, both nationally and internationally. Despite progress made with pedagogical approaches to initial algebra, it remains a difficult area of mathematics for students as they grapple with the many prerequisite and algebraic concepts required for proficiency. Evidence in Ireland shows that students here encounter the same difficulties as their international counterparts as reported by teachers and evidenced in state examinations and international testing. A mixed methods approach, framed within the post-positivist viewpoint, was utilised to explore the research problem. An exploratory sequential design was employed as is appropriate when development is an objective of a study. The qualitative approach was used to identify the construct of initial algebra and an appropriate conceptual model. Additionally, task items were identified in the literature and adapted for use in the screener. The quantitative approach, which was dominant, was used in the statistical analysis of the task items and to refine the screener, while providing a profile of the students’ knowledge of initial algebra. This research identifies key content areas with which students’ struggle. These include fractions, decimal number magnitude, exponents, integers, order of operations and variables, all of which are identified in the literature as difficult for students. This knowledge can help mathematics teachers by allowing them to focus on these areas in their instruction and development of resources, while the screener can be utilised as a formative assessment tool in the classroom.
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