Static Versus Dynamic Disposition: The Role of GeoGebra in Representing Polynomial-Rational Inequalities and Exponential-Logarithmic Functions

Abstract

This study investigates prospective secondary mathematics teachers' visual representations of polynomial and rational inequalities, and graphs of exponential and logarithmic functions with GeoGebra Dynamic Software. Five prospective teachers in a university in the United States participated in this research study, which was situated within a framework of productive disposition and visual representations in pre-calculus. The main result was that the role of GeoGebra as a cognitive tool fostered the research participants' productive disposition, despite recurrent mismatches between the algebraic and visualized formalisms. Moreover, participants exhibiting dynamic productive disposition seemed to understand and make better sense of the conceptual underpinnings of the mathematical content they explored in contrast to those embracing static productive disposition.Visual representations play a crucial role in understanding and making sense of mathematics. Students' favorite mathematics textbooks and teachers are often ones that use a variety of colorful figures, diagrams, pictures, and graphs

Effects of Using Dynamic Geometry Activities on Eighth Grade Students’ Achievement Levels and Estimation Performances in Triangles

“…In other words, instruction supported by dynamic geometry tasks has positive effect on students' performances in both estimation and academic achievement in triangles. This enhancement in performance corresponds with previous research in which it is stated that dynamic geometry software has a positive effect on students' learning and performance on mathematics (Baki, Kosa, & Guven, 2011;Caglayan, 2014;Doğan & İçel, 2011;Gecü, 2011;Güven & Karataş, 2009;Hall & Chamblee, 2013;Hohenwarter, Hohenwarter & Lavicza, 2010;Idris, 2007;Jiang & White, 2012).…”

The effect ofGeoGebra software–supportedmathematics instruction on eighth‐grade students' conceptual understanding and retention

“…Similarly, Doktoroğlu (2013) and Tayan (2011) have revealed that GeoGebra software on linear equations and graphics in seventh grade is more effective on students' mathematics achievement than textbook‐based instruction. Also, in several studies conducted at different grade levels, it is indicated that DGS has positively increased students' mathematics achievement and conceptual learning regarding functions and graphics (Dayi, 2015; Hutkemri et al, 2017; Önür, 2008; Reis & Özdemir, 2010), analytic geometry (Delice & Karaaslan, 2015; Işıksal & Aşkar, 2005), limit (Hutkemri & Zakaria, 2014), continuity (Kepçeoğlu & Yavuz, 2017), derivative applications (Öçal, 2017; Zengin, 2018), integral (Tatar & Zengin, 2016), exponential and logarithmic functions (Birgin & Acar, 2020; Caglayan, 2014) in comparison to textbook‐based instruction. In addition, it is revealed in meta‐analysis research results (Chan & Leung, 2014; Günhan & Açan, 2016) that DGS has a positive effect and large effect size on students' mathematics achievement compared with traditional paper‐and‐ruler instruction.…”

“…It has been expressed in many studies that dynamic geometry software (DGS) provides students opportunities to establish connections between mathematical objects and graphical representations (Öçal, 2017; Shadaan & Leong, 2013; Taş, 2016) and supports the active construction of mathematics knowledge within a dynamic learning environment (Dayi, 2015; Hohenwarter & Fuchs, 2004; Hutkemri & Zakaria, 2014) and enables conceptual learning with the aid of animation and visual materials (Diković, 2009; Tatar & Zengin, 2016). Moreover, it has shown in the results of some studies that using DGS has positively increases students' mathematics/geometry achievement (Chan & Leung, 2014; Erbaş & Yenmez, 2011; Günhan & Açan, 2016; Köklü & Topçu, 2012; Özmen, 2019; Pilli & Aksu, 2013; Topuz, 2017; Turk & Akyuz, 2016) and conceptual learning (Caglayan, 2014; Hutkemri & Zakaria, 2012, 2014; Zengin, 2018). However, only a few studies (Delice & Karaaslan, 2015; Doktoroğlu, 2013; Işıksal & Aşkar, 2005; Önür, 2008) focus on the effect of educational software on linear functions and graphs related to students' mathematics achievement for seventh‐grade and high school students but not for eighth graders.…”

Development of a GeoGebra-Assisted Calculus Worksheet to Enhance Students’ Understanding

“…It can foster mathematical reasoning and mathematical thinking [6]. Using technology (technology-supported environment) in calculus learning specifically the use of GeoGebra in Riemann sums [14].…”

“…Visual representations play an important role in understanding and making sense of mathematics. Students and teachers are more likely to use a variety of colorful [1], [14]. For teachers, GeoGebra provides opportunity to create interactive learning climate [16]- [18].…”