Self-Learning Geometric Transformations: A Framework for the “Before and After” Style of Exercises

Abstract

After the long period of mandatory distance learning, either synchronous or asynchronous, caused by the COVID-19 pandemic, the existence of learning tools to support students in similar scenarios is welcomed in many curriculum subjects. Geometric transformations are relevant in mathematics and an omnipresent topic in the computer graphics curriculum that needs plenty of visual tools and learning-by-doing environments. In this work, we propose a framework based on an extended Translation-Rotation-Scale (TRS) pattern to generate composite transformations to support a specific style of learning exercises that we call “before and after”. The pattern, together with specific constraints to reduce the domain into a finite set of cases, allows the automatic exercises generation, evaluation, and real-time feedback. Two pieces of software, called GTVisualizer and GTCards, were developed to empirically test the proposed framework embedding it in a gaming environment. The first tool supports the initial instruction and introduces the formal matrix-based methodology to specify composite transformations; the second one provides a ludic environment where students can drill and reinforce the subject by playing. Our initial results suggest that these tools are suitable for learning geometric transformations; they helped students in simulated self-study mode achieve comparable results to those students receiving the regular lecture materials and explanations in the classroom. Moreover, the usage of the tools appears to favor a similar increasing effect on students’ visual-spatial abilities, similar to the obtained by taking an in-person course on computer graphics, as measured with the Purdue Spatial Visualization Test.

Teachers Underutilize Their Learning Styles in Developing Thought-Provoking Questions: A Case Study

“…Dostov et al (2022), Lee and Hwang (2022), Lo (2020), Umbara et al (2020), and Moffett and Eaton (2018) confirm that visual representation is needed in mathematics, as this subject matter contains a different set of related abstractions. The impact of teachers who cannot transform abstractions into a certain format allows students to link mathematics with what they learned, and then students study without understanding (Coskun & Bostan, 2022;González-Campos et al, 2022). Another consideration affecting Kurnia in emphasizing the use of visual objects is students' cognitive development during the period of concrete operations.…”