Algebra readiness for students with learning difficulties in grades 4–8: Support through the study of number

Developing proficiency in algebra is the focus of instruction in high school mathematics courses and is a minimum expectation for high school completion for all students including those with learning difficulties. However, the foundation for success is laid in grades 4–8 (aged 9–14). In this paper, we assert that students' development of algebraic reasoning skills and knowledge is influenced by their understanding of numeracy. We propose that students in grades 4–8 need targeted instruction on three interconnected numeracy concepts. First, we propose that students need a strong conceptual foundation of number and number systems to facilitate computation, estimation and problem solving across number systems. Second, we identify students' understanding of basic number properties as foundational to lawful application of operations. Finally, we note that procedural proficiency, including computational fluency and conceptual understanding, provides a foundation for generalised application of algorithms for solving arithmetic and algebraic problems. Combined, these skills and knowledge enable students to employ algebraic reasoning by generalising their knowledge for solving abstract problems.