The effectiveness of goal-free problems for studying triangle similarity in collaborative groups

Abstract

Similarity is a topic in Geometry which investigates similar elements of a plane. This topic has a high complexity that generates cognitive load in working memory. A deep understanding of the concept is needed to solve similarity problems. Based on cognitive load theory, learning by goal-free problems is suggested since it can minimize cognitive load. This research examined the effectiveness of presenting similarity inquiries using goal-free problems for learning by collaboration. Using a factorial design: 2 presentation techniques (goal-free vs. goal-given problems) x 2 groupings (collaborative vs. individual) in authentic classrooms, the experiment consisted of four consecutive phases: introductory, learning phase, retention test, and transfer test. One-hundred eleven eighth-graders from four classrooms in a junior high school in Yogyakarta, Indonesia, served as research participants. The findings showed that students who were learning using goal-free problems possessed significantly higher scores of retention and transfer tests, as well as experience lower cognitive load during both tests. On the contrary, it was found that studying individually yielded a significantly higher transfer score than studying collaboratively. Since there was no interaction effect, it may be concluded that goal-free problems can be effective for either collaborative or individual learning.

Evolution of Pre-Service Mathematics Teachers’ Spatial Visualisation Skills During a Cognitive Load Theory-Based Education

“…In such cases, guiding and encouraging learners to invest more time and effort in defining the problem and finding solutions allows them to reflect on the quality of their own representations and solutions (Law et al, 2021). Various studies (Azimah et al, 2020;Dhlamini, 2016;Zahara et al, 2020) also stated that CLT-based education could effectively develop and strengthen learners' problem-solving skills and schemas and their learnings, as demonstrated by research focusing on problem-solving first approach (Likourezos & Kalyuga, 2017), goal-free tasks (Purnama & Retnowati, 2020), worked examples (Sentz & Stefaniak, 2019), self-explanations (Joo et al, 2020), imagination (Leopold & Mayer, 2015) and guided learning (Simamora et al, 2019).…”

“…These studies reported the following. Goal-free problems help students develop their flexible thinking skills (Maulidya et al, 2017;Purnama & Retnowati, 2020;Youssef-Shalala et al, 2014) guidance (Kirschner et al, 2006;Sweller et al, 2007). Worked examples and self-explanation have a positive effect on learning conceptual and procedural knowledge (Atkinson et al, 2000;Renkl, 2017;Wittwer & Renkl, 2010;Wynder et al, 2017) and on acquiring complex skills, including spatial skills (Chen et al, 2015;Pillay, 1994).…”

Mathematics education research in Indonesia: A scoping review

“…Misconceptions and error analysis are topics of study related to cognitive processes that are often discussed (Agustiani, 2021). Furthermore, cognitive load theory has been studied in various perspectives, including mathematical literacy skills (Purnama & Retnowati, 2020) and worked examples (Irwansyah & Retnowati, 2019).…”

Content validity of D-MESS: Articulate storyline 3-based learning media in sport massage courses

“…Articulate Storyline 3 also has other advantages, such as ease of use and support for various formats, including HTML5, to produce attractive tutorial presentations. Articulate Storyline 3 in the form of web-based media could also be run on various devices, such as software on tablets, laptops, and applications on smartphones (Purnama & Retnowati, 2020). Multimedia based on Articulate Storyline 3 is easy to use, just by sharing the link via the Google Drive link or an application that the user could download independently.…”