Poster #34 - Multifaceted assessment of children’s inversion understanding

• In Event: 2-055 - Poster Session 06
  In Poster Session: PS 06 Section - Cognitive Processes

Integrative Statement

The understanding of the inversion principle (e.g., A + B – B = A) is an important component of conceptual knowledge in mathematics. While a lot of studies have been conducted to investigate children’s understanding of the inversion principle (Canobi, 2009; Dube & Robinson, 2018; Rasmussen, Ho, & Bisanz, 2003; Robinson, Price, & Demyen, 2018; Vilette, 2002; Watchorn et al., 2014), most of them mainly rely on the application of procedures task. Participants who are able to apply the inversion shortcut in arithmetic problem solving are considered to have mastered the inversion principle. Such assessment may not provide a comprehensive picture concerning children’s inversion understanding because the understanding of the inversion principle is multifaceted in nature (Bisanz, Watchorn, Piatt, & Sherman, 2009; Prather & Alibali, 2009). For instance, children who are aware of a particular arithmetic principle may not apply the relevant shortcut (Siegler & Crowley, 1994), while those who apply a particular shortcut may not fully understand the logic behind (Baroody, Wilkins, & Tiilikainen, 2003).

To address the issue of single-facet assessment, the current study examined children’s inversion understanding using three different assessment methods: evaluation of examples (Dixon, Deets, & Bangert, 2001), explicit recognition (Dixon et al., 2001; Wong, 2017), and application of procedures (Torbeyns, Peters, De Smedt, Ghesquière, & Verschaffel, 2016; see Table 1 for details). A total of 110 fourth to sixth graders were assessed on these three inversion measures as well as two mathematics achievement tests. Based on their performance in these three measures, the participants were subjected to a latent profile analysis. A seven-class solution emerged, with each class having a different inversion profile (see Figure 1). While some of the classes demonstrated uniform profile (e.g., scoring uniformly high or low in all measures), some classes scored high in some of the measures but not others. The seven classes were unevenly distributed across the three grades, and more importantly, they demonstrated different levels of mathematics achievement, with classes having superior performance in both the explicit recognition task and the application of procedures task being the higher math achievers. The current findings provide supporting evidence to the multifaceted nature of inversion understanding and thus point to the need for multifaceted assessment. Furthermore, the findings empirically support the relation between children’s inversion understanding and their mathematics achievement and thus highlight arithmetic principle knowledge as an important cognitive predictor of children’s mathematics achievement.

Author

• Terry Tin Yau Wong, The University of Hong Kong
  Presenting Author