Algebra and Equivalence
Camilla K. Gilmore, Silke Melanie Göbel, Matthew Inglis · 2018
This chapter reviews studies that have sought to understand children&s;s difficulties with algebra and the approaches to instruction that have been proposed to address these difficulties, before turning to the topic of mathematical equivalence and how children&s;s understanding of equivalence impacts on their performance in algebra and mathematics. One reason often given for these difficulties is that moving from arithmetic to algebra involves a conceptual shift. One consequence of difficulties transitioning from arithmetic to algebra has been calls to integrate algebraic reasoning throughout early mathematics learning. Children&s;s responses to this, and equivalent items, were explored both before they had received any algebra instruction, and after 8 weeks of standard curriculum algebra lessons. Although the studies by M. MacGregor, K. Stacey and E. J. Knuth et al. provide a more favourable picture of children&s;s grasp of the concept of a variable, there are limitations to children&s;s understanding.