Preservice elementary school teachers’ knowledge of fractions: a mirror of students’ knowledge?

Semantic and Syntactic Fraction Understanding

“…In a parallel manner, while local, syntactic interactions can be equated to instrumental or procedural understanding (using processes and algorithms to produce results) of mathematics, global semantic interactions hold similarities with conceptual understanding (the ability to see interconnections among ideas) (Hallett, Nunes, & Bryant, 2010). While some have recognized elementary students' difficulties with fractions concepts (e.g., Braithwaite, Pyke, & Siegler, 2017;Bulgar, 2003;Gabriel et al, 2013;Siegler et al, 2011;Tirosh, 2000;Van Steenbrugge, Lesage, Valcke, & Desoete, 2014), some equate this to students primarily possessing procedural knowledge of fractions and operations (e.g., Byrnes & Wasik, 1991;Kerslake, 1986;Rittle-Johnson, Siegler, & Alibali, 2001). Interestingly, while Kerslake (1986) has determined that some students can have success with some fraction operations using primarily procedural knowledge, Byrnes and Wasik (1991) contend that conceptual knowledge regarding fractions is the prerequisite and Hallett, Nunes, and Bryant (2010) suggest that some students rely more on procedural understanding and others on conceptual understanding.…”

“…Interestingly, while Kerslake (1986) has determined that some students can have success with some fraction operations using primarily procedural knowledge, Byrnes and Wasik (1991) contend that conceptual knowledge regarding fractions is the prerequisite and Hallett, Nunes, and Bryant (2010) suggest that some students rely more on procedural understanding and others on conceptual understanding. However, when students demonstrate lesser conceptual understanding and greater procedural understanding, this may limit their understanding of fractions (Van Steenbrugge et al, 2014) and lead to the development of misunderstandings (Hallett Nunes, & Bryant, 2010;Kerslake, 1986).…”

“…Based on whole number bias and other misconceptions, students' understanding and communication of fractions continues to be investigated (e.g., Bartelet, Ansari, Vaessen, & Blomert, 2014;DeWolf, Rapp, Bassok, & Holyoak, 2014;Iuculano & Butterworth, 2011;Kallai & Tzelgov, 2009;Lyons, Price, Vaessen, Blomert, & Ansari1, 2014;Meert, Grégoire, & Noël, 2009;Opfer & DeVries, 2008;Schneider & Siegler, 2010). Research reveals that some student difficulties with fractions are born from misunderstandings with natural numbers (e.g., Siegler, Thompson, & Schneider, 2011;Stafylidou & Vosniadou, 2004;Van Steenbrugge et al, 2014). This is because, children's knowledge of natural numbers can inhibit later fraction learning (Siegler et al, 2011).…”

“…The primary reason may be due in part to the fact that fractions are inconsistent with the counting principles, counting-based algorithms, and numerical ordering applicable to natural numbers (Stafylidou & Vosniadou, 2004). This results in whole number bias leading to misconceptions (Van Steenbrugge et al, 2014). Additionally, the multi-dimensional nature of the fraction construct also leads to student difficulties (e.g., Charalambous & Pitta-Pantazi, 2007;Kieren, 1976;Van Steenbrugge et al, 2014).…”

“…This results in whole number bias leading to misconceptions (Van Steenbrugge et al, 2014). Additionally, the multi-dimensional nature of the fraction construct also leads to student difficulties (e.g., Charalambous & Pitta-Pantazi, 2007;Kieren, 1976;Van Steenbrugge et al, 2014). To overcome this, fractions must be considered through interconnected subconstructs (i.e., ratio, operator, quotient, and measure) (Kieren, 1976) and the part-whole construct (Behr, Lesh, Post, & Silver, 1983), all defined by Charalambous and Pitta-Pantazi (2007) and Van Steenbrugge et al (2014).…”