Can Geometry Achievement and Geometric Habits of Mind Be Improved Online? Reflections From a Computer-Aided Intervention

Abstract

This article aims to examine the impact of an online learning environment enriched with computer activities on geometry achievement and geometric habits of mind (GHoM). The study includes reflections from an online application of a one-term computer-aided mathematics teaching course in which the participants were preservice teachers (PTs) enrolled in a faculty of education. A test was used to measure all participating PTs’ learning outcome and determine their GHoM. In addition, clinical interviews were administered before and after the intervention to examine the opinions of the PTs regarding the online learning environment. The results revealed that the design provided for positive development in terms of both geometry achievement and GHoM. However, the impact was found to be very limited for some components of GHoM. The article presents a discussion of the effective aspects of the intervention.

Factors affecting prospective mathematics teachers beliefs about geometric habits of mind

“…The definition of GHoM used here indicates that they are intertwined with problem-solving. Studies have shown that there is a positive significant relationship between beliefs about mathematical habits of mind in general, and GHoM in particular, and students" problem-solving achievement (Bülbül & Güler, 2021;Driscoll et al, 2007;Driscoll et al, 2008;Gordon, 2011;Jacobbe & Millman, 2009;Lai & Donsing, 2018;Matsuura et al, 2013). This means that a relationship can be found between students" beliefs about GHoM and beliefs about problemsolving.…”

The Effects of an Online Learning Environment Prepared by Considering the Problem Solving Steps and Strategies on Geometric Habits of Mind and Geometry Achievement

“…Geometric habits of mind are the solution-oriented approaches of individuals when they faced with a geometry problem (Driscoll et al, 2007). So, geometric habits of mind can also positively or negatively affect individuals' problem-solving achievements (Bülbül & Güven, 2019;Bülbül & Güven, 2020;Bülbül & Güler, 2021;Cuoco et al, 1996;Driscoll et al, 2007;Driscoll et al, 2008). This situation reveals the necessity for students to use their geometric habits of mind as good level in order to learn geometry concepts and solve geometry problems.…”

The Effect of the 7th Grade Students’ Geometry Oriented Self-Efficacy on the Geometric Habits of the Mind

“…When we look at the studies in the literature, there are a limited number of studies that determine the geometric thinking habits of students (Bülbül, 2016;Bülbül and Güven, 2019;Bülbül and Güven, 2020;Bülbül and Güler, 2021;Özen, 2015;Driscoll et al, 2007;Driscoll et al, 2008;Goldenberg, Cuoco and Mark, 1998). It is thought that increasing the studies on this subject will be effective in determining the reasons for the students' failures in geometry and increasing their success in geometry.…”

“…Researchers generally focused on studies about examining teacher competencies and teachers' geometric thinking levels (İlhan and Oral, 2012;Toluk-Uçar, 2009;Uygun, Ergen and Öztürk, 2011), students' geometric thinking levels (Duatepe-Paksu, 2013;Kılıç, 2003;Yenilmez and Korkmaz, 2013); students' and teachers' geometric habits of the mind (Bülbül, 2016;Bülbül and Güven, 2019;Bülbül and Güven, 2020;Bülbül and Güler, 2021;Köse and Tanışlı, 2014;Özen, 2015;Uygan, 2016) and the relationship between affective components and success (Erşen, 2017;Gülten and Soytürk, 2013). In order to develop students ability to relate from different angles, to gain the skills to think, to question and to explore, geometric learning theories should be utilized.…”