Pre-service teachers’ figurative and operative graphing actions

Student difficulties in solving covariational problems

“…Based on research data, these data show that 88% of students have difficulties when faced with problems that require covariational reasoning. These results indicate that the results of this study have similar results with previous studies (Carlson, 1998;Carlson et al, 2002;Carlson, Larsen, & Jacobs, 2001;Madison et al, 2015;Moore & Carlson, 2012;Moore et al, 2019;Paoletti & Moore, 2017;Weber & Thompson, 2014;Wilkie, 2019) that, problems that require covariational reasoning are still difficult for most students. Specifically, in Indonesia, mathematics is identical to the calculation operation.…”

United States and South Korean citizens’ interpretation and assessment of COVID-19 quantitative data

“…The data representations varied (e.g., text, graphs, charts, tables) and relied on mathematical concepts including rate of change, comparisons of relative size, exponential growth, probability, accumulation, and mathematical modeling. Mathematics education researchers have created models of how students and teachers understand these representations and concepts ( Behr, Harel, Post, & Lesh, 1992 ; Byerley & Thompson, 2014 ; Byerley, 2019 ; Castillo-Garsow, 2013 ; Ellis, Ozgur, Kulow, Dogan, & Amidon, 2016 ; Harel & Confrey, 1994 ; Johnson, 2012 ; Konold, 1989 ; Lesh & Lehrer, 2003 ; Lobato & Siebert, 2002 ; Moore, Stevens, Paoletti, Hobson, & Liang, 2019 ; Steffe & Olive, 2009 ; Steffe, Liss, & Lee, 2014 ; Thompson, 1994a , 1994b ; Thompson, Hatfield, Yoon, Joshua, & Byerley, 2017 ), but independent of the COVID-19 pandemic and data. These same researchers have argued people’s schemes for these concepts and representations vary in their productivity, but again these claims have been independent of a major event like the COVID-19 pandemic.…”

“…As we identify in the following sections, productive schemes afford an individual conceiving equivalent mathematical properties across various representations despite differences in those representations (e.g., comparing a cases per day graph with an accumulation graph or comparing graphs using different scales). Productive schemes are generative in their capacity to accommodate to novel data representations due to their foregrounding quantities and their relationships ( Ellis, 2007 ; Liang & Moore, 2020 , online; Moore et al, 2019 ; Smith & Thompson, 2007 ; Thompson, 2013a ).…”

“…To distinguish various schemes for graphs and slope, we leverage a distinction between figurative thought and operative thought that Moore, Thompson, and colleagues adopted to characterizing students’ graphical meanings ( Moore, in press ; Moore et al, 2019 ; Moore & Thompson, 2015 ). Piaget (2001) developed the figurative and operative thought distinction to differentiate between thought constrained to states such that actions are indissociable from results and thought foregrounding the coordination of internalized mental actions so that results are subordinate to this coordination.…”

Opportunities for Reasoning: Digital Task Design to Promote Students’ Conceptions of Graphs as Representing Relationships between Quantities

“…Although digital technology has brought many affordances (Drijvers 2015;Lobato et al 2019) both university and secondary school students continue to have difficulties with graphs. Moore et al (2019) found that university mathematics students' perceptual interpretations of graphs can account for their struggles, while Vitale et al (2019) found that the designer's goal for a task can impact secondary science students' focus on relationships represented in graphs. By conceiving of graphs as representing relationships between quantities, students could interpret trends and issues represented by graphs encountered in their daily lives.…”