Investigating Instructions on Rational Number Arithmetic in Elementary School
Conceptual understanding of rational numbers and performing their algorithmic operations is the key to success not only for more advanced mathematics (Booth, Newton, & Twiss-Garrity, 2014), but also for occupational success (Handel, 2016). Despite this importance, many students (Kloosterman, 2010; Martin, Strutchens, & Elliott, 2007; Siegler & Lortie-Forgues, 2015), adults and even some mathematics teachers (Hanson & Hogan, 2000) have shown limited knowledge of rational numbers.
There are several reasons why children struggle when learning rational numbers, such as their multiple representations with the multiple interpretations, the complexity of rational number magnitudes and rational number arithmetic and many more (Lortie-Forgues, Tian, & Siegler, 2015). However, in a recent study, it has been shown that the difficulties with learning rational numbers might (at least partly) originate from how rational numbers and rational number tasks are presented in mathematics textbooks (Braithwaite & Siegler, 2018).
My PhD-project comprises three studies. In Study 1, I aim at analyzing (Swiss-)German mathematics textbooks to replicate the findings of Braithwaite and Siegler (2018). Then, I will investigate how the selection of tasks in mathematics textbooks may bias children’s understanding of rational number arithmetic. In Study 2 and Study 3, I will experimentally investigate how different instructional sequences may enhance children’s ability to understand the multiple representations of rational numbers and to conduct arithmetic operations with them. To this aim, both studies will take up well-researched instructional approaches from educational psychology on interleaving problems (Brunmair & Richter, 2019), which have not yet been applied to teaching and learning of rational numbers.
(Dissertationsprojekt von Parvaneh Babari; Projektleitung: Prof. Dr. Lennart Schalk [PHSZ]; Betreuung: Prof. Dr. Elsbeth Stern [ETHZ]; Finanzierung: Innosuisse und OFP PHSZ)