Making sense of fraction division: domain and representation knowledge of preservice elementary teachers on a fraction division task

Strategic competence for multistep fraction word problems: an overlooked aspect of mathematical knowledge for teaching

“…The errors teachers made in this study were different from those reported in prior studies. This could again be due to differences in the study population as well as in prior use of onestep problems versus our use of multistep word problems (e.g., Adu-Gyamfi et al, 2019;Lee, 2017). Unlike in the majority of studies, we used multistep word problems; therefore, the errors teachers made when solving one-step word problems may have been different from the kinds of errors they made when solving multistep problems.…”

“…Prior work on teachers' strategic competence is relatively sparse. Most research to date has been conducted with preservice teachers (Adu-Gyamfi, Schwartz, Sinicrope, & Bossé, 2019; Baek et al, 2017;Cullen et al, 2017;Lee, 2017;Nillas, 2003;Olanoff et al, 2014;Taplin, 1998) and suffered from several methodological limitations, such as using a single problem to investigate teachers' strategic competence, requiring participants to use certain strategies or representations, and collecting data from a group of preservice teachers who were taking the same methods class (e.g., Adu-Gyamfi et al, 2019;Baek et al, 2017;Cullen et al, 2017;Li & Kulm, 2008;Lo & Luo, 2012;Son & Lee, 2016). Partly because of these limitations, evidence is mixed regarding preservice teachers' strategic competence (cf.…”

“…Partly because of these limitations, evidence is mixed regarding preservice teachers' strategic competence (cf. Adu-Gyamfi et al, 2019;Baek et al, 2017;Cullen et al, 2017;Lee, 2017;Nillas, 2003). For instance, Lee (2017) analyzed 111 preservice teachers' written solutions to a one-step fraction division word problem that required them to use a drawn length model.…”

“…In contrast, Baek et al (2017) reported in their analysis of 93 solutions provided by 77 preservice teachers to a multistep fraction word problem requiring them to use pictorial representations, that 81% of the solutions devised a valid strategy and arrived at a correct answer. Such variation across studies in teachers' arriving at a correct answer could also be related to the fact that most of the prior work has documented teachers' strategic competence on a single problem (e.g., Adu-Gyamfi et al, 2019;Lee, 2017). Single word problems are limited in terms of their ability to capture teachers' strategic competence adequately because a single item can capture only a limited amount of information.…”

Prospective Teachers Understanding Fraction Division Using Rectangle Representation

“…There are many ways to understand about the fraction division problems, and maybe if we are a creative person, it can be a new method to understand the fraction division problems. There are some ways to understand fraction division problems (Adu-Gyamfi et al, 2019) (see Table 1).…”