Beyond Doing Mathematics: Engaging Talented Students in Mathematically Creative Writing

Abstract

With recent increased attention to engaging students in written mathematical communication, the Elementary Mathematical Writing Task Force has recommended specific types of and purposes for mathematical writing with the ultimate goals of communicating and reasoning: Exploratory, Informative/ Explanatory, Argumentative, and Mathematically Creative. While it is recommended that all students engage in all types of writing, the mathematically creative type has specific implications for mathematically talented students. Justification for and ways to engage talented students in mathematically creative writing are presented and address the following questions: What is mathematical creativity? How can mathematically creative writing help meet the needs of talented students? And, what are the characteristics of a learning environment that fosters mathematical creativity and written communication?

Gifted Classroom Environments and the Creative Process: A Systematic Review

“…Westberg and Leppien (2018) discussed the importance of independent “investigations of real problems and solutions” (p. 13), and Coxon (2012) suggested that “children be provided with problems” that “require them to decide what evidence is relevant and to offer their own interpretations of what the evidence means” (p. 281). These learning experiences used interest-based inquiry to examine real-life issues that students wanted to solve in domains of interest (e.g., science, math, community activism; Firmender et al, 2017; Gavin & Casa, 2013; Jo & Ku, 2011; Thompson, 2017) that were relevant to their current situations in school (e.g., bullying; Groman, 2019). The literature suggested that teachers harness student interest in local or global problems (e.g., environmental concerns, Beason-Manes, 2018; accessibility, Schroth & Helfer, 2017).…”

“…Hines et al (2019) advocated for the use of Torrance and Safter’s (1990) Incubation Model of Teaching to incorporate more opportunities for gifted students to seek “connections between content and ideas, or events from past experiences, present problems, and future images” (p. 39) beyond the classroom. Beyond just providing time for ideas to incubate, authors advocated for explicitly teaching students to defer judgment when they consider an idea (Beason-Manes, 2018; Firmender et al, 2017; Gavin & Casa, 2013; Groman, 2019). Deferring judgment allowed students to record and carefully consider ideas before discarding them (Thompson, 2017) and required teachers to provide “adequate time” instead of asking students to complete tasks “on-demand” or on a “preset schedule” (Firmender et al, 2017, pp.…”

“…Beyond just providing time for ideas to incubate, authors advocated for explicitly teaching students to defer judgment when they consider an idea (Beason-Manes, 2018; Firmender et al, 2017; Gavin & Casa, 2013; Groman, 2019). Deferring judgment allowed students to record and carefully consider ideas before discarding them (Thompson, 2017) and required teachers to provide “adequate time” instead of asking students to complete tasks “on-demand” or on a “preset schedule” (Firmender et al, 2017, pp. 207–208).…”

“…Authors argued that providing appropriately challenging opportunities and instruction aligned with student abilities supports student motivation to be creative (Chan & Yuen, 2015; Fletcher, 2011; Gavin & Casa, 2013; Renzulli, 2012; Renzulli & Reis, 2012), which aligns with research on developing talent (e.g., Talent Search Model; Stanley, 1976; Subotnik et al, 2011). Classroom structures that allowed high-ability students to build psychosocial skills and move through appropriately challenging instructional content (e.g., required curriculum, state standards, and interest-based investigations) flexibly at their own pace opened time to engage in more creative endeavors (Firmender et al, 2017; Hines et al, 2019; Westberg & Leppien, 2018) and supported creative production (Hébert et al, 2014; Subotnik, 2015; Subotnik et al, 2011).…”

“…Five empirical articles were reviewed, of which two were qualitative (Chan & Yuen, 2015;Wu et al, 2019) and three were quantitative (Jo & Ku, 2011;Kettler & Bower, 2017;Sak, 2013). Of the remaining articles, most (n = 16) were practitioner-focused and written with classroom teachers as the primary audience (Beason-Manes, 2018;Chandra Handa, 2015;Coxon, 2012;Firmender et al, 2017;Fletcher, 2011;Gavin & Casa, 2013;Groman, 2019;Hagge, 2017;Hébert et al, 2014;Hines et al, 2019;Schroth & Helfer, 2017;Scott, 2011;Senne et al, 2016;Shively et al, 2018;Thompson, 2017;Westberg & Leppien, 2018), but several (n = 5) were more theoretical in nature with a broader audience that included researchers and school personnel (Miller, 2012;Renzulli, 2012;Renzulli & Reis, 2012;Subotnik, 2015;Subotnik et al, 2011). Overall, the 26 articles described learning environments for gifted students with an emphasis on classroom systems that promote and support creativity and the creative process.…”