A profile of Irish second year post-primary students' knowledge of initial algebra

This research focuses on initial algebra as students transition from arithmetic to algebra, an area of mathematics education known for its difficulties (Demonty et al., 2018; Kieran, 2007). Algebra is identified by many as the language of mathematics and considered a prerequisite for further study in mathematics in many disciplines such as science, technology, and engineering (Gavin & Sheffield, 2015; Stacey & Chick, 2004). It has been argued that algebra is not only the gatekeeper for higher education but also for citizenship.Objectives of the Study: This report provides a profile of Irish second years students’ knowledge of initial algebra. Students need to develop knowledge, skills, and abilities across a wide range of content areas to ensure success with initial algebra. The prerequisite content areas include ratio and proportional reasoning, fractions, decimals, percentages, integers, exponents, order of operations and equality. The algebra content areas include variables, expressions, equations, functions, and patterns (Bush & Karp, 2013; Warren & Cooper, 2008).The central objective of the study was to develop a profile of Irish second year students’ knowledge of initial algebra and from this: 1. Identify students’ strengths and weaknesses in the pertinent content areas for initial algebra. 2. Identify prevalent errors and misconceptions that hinder students’ understanding and progression with initial algebra. 3. Provide the empirical evidence to help mathematics teachers effectively guide their instruction given the limited time available in the classroom. 4. Develop key recommendations to support mathematics teachers and researchers in the area of initial algebra. Evidence has emerged, through various government reports, research, and international testing, that students in Ireland, like their international counterparts, are experiencing difficulties with algebra (Chief Examiner, 2015a; Shiel & Kelleher, 2017). This study provides empirical evidence based on the assessment of over 500 second year post-primary students during the academic year 2016-2017, as part of a PhD study. This report provides a summary of the results from this assessment and identifies key content areas with which our students are struggling. This empirical evidence has heretofore been unavailable