Number and algebra

Many children and adults have reservations about algebra. Why? The abstractness of algebra partly lies in its use of variables and pronumerals. Nonetheless, algebra expressed in a mathematical principle to solve a range of problems is what makes it powerful (Kieran, 1992). Indeed, algebra is a topical theme in mathematics that requires an extensive use of problem-solving skills. Mathematics education researchers regard algebra skills as a 'gatekeeper' to higher-order mathematical thinking skills in advanced mathematics (Carpenter, Franke & Levi, 2003). Algebra skills are useful not only for solving real-life problems (e.g. 'If your father wants to increase your weekly allowance of $20 by 5%, what is your new allowance?') (Ngu, Yeung & Tobias, 2014), but are also transferrable to other curriculum domains such as physics and chemistry (e.g. 'A solution contains 1.1 g of sodium nitrate NaN03 in 250 ml, what is the molarity of this solution?') (Ngu & Yeung, 2012, 2013; Ngu, Yeung & Phan, 2015). Despite the prominent role of algebra in the secondary mathematics curriculum, there is limited evidence of an efficient use of algebra, particularly in middle school students (Stacey & MacGregor, 1999). Such findings suggest that secondary students perceive algebra as a challenging topic to learn and master. To assist secondary students in building a foundation in algebra knowledge, this chapter will highlight several aspects of teaching and learning algebra based on the Australian Curriculum: Mathematics.