Contribution of Conceptual Understanding, Creativity Skill and Motivation to Student’s Problem-Solving Skill in Learning Plane Geometry Based on Visually Assisted with Guided Discovery Based Learning Model
This quasi-experimental study involving 96 Grade 10 students in Ethiopia demonstrates that conceptual understanding, creativity, and motivation significantly contribute to problem-solving skills in plane geometry when taught through a visually assisted, guided discovery-based learning model.
Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer
Mathematics is often taught as a set of rigid rules to memorize, but solving a real problem requires something far more flexible: the ability to understand the underlying ideas, to think of new ways to approach a challenge, and to care enough to keep trying when things get difficult. This is especially true in geometry, a subject where students must visualize shapes and relationships in space. For decades, educators have known that simply listening to a teacher explain a concept is not enough for deep learning. Instead, students need to actively discover these ideas for themselves, often with help from visual tools that make abstract shapes concrete. When a student truly grasps a concept, feels motivated to learn, and can think creatively, they are better equipped to solve complex problems. The question researchers have long asked is how these three internal qualities—understanding, creativity, and motivation—work together to help a student succeed in mathematics.
In a study conducted in the high schools of Woldia City, Ethiopia, a team of researchers set out to measure exactly how these factors influence a student's ability to solve geometry problems. They focused on tenth-grade students, a critical time in their education, and compared three different ways of teaching the same material. One group of students learned through a traditional method where the teacher led the class and students listened. A second group used a "guided discovery" approach, where the teacher guided them to find answers on their own. The third group used a combination of that guided discovery method with visual aids, such as diagrams and physical models, to help them see the geometry in action. The researchers wanted to know which of these teaching styles helped students the most, and specifically, how much of a student's success came from their understanding of the concepts, their creative thinking, and their drive to learn.
The study involved 96 students divided into these three groups. Before the lessons began, the students took tests to measure their current skills. After a month of instruction, they took the tests again. The researchers then looked at the results to see how much the students improved and what factors predicted that improvement. They found that all three factors—conceptual understanding, creativity, and motivation—were linked to better problem-solving skills, but their importance changed depending on how the students were taught. In the group that used the visually assisted guided discovery method, the students' deep understanding of the concepts was the single most powerful driver of their success. This group showed that when students could see the geometry and were guided to discover the rules themselves, their ability to understand the material became the primary key to solving problems.
The findings revealed a clear hierarchy of influence within this specific teaching model. For the students using the visual and guided approach, their grasp of the concepts explained nearly twenty-nine percent of their success in solving problems. While creativity and motivation were still present and helpful, their direct contribution to the final score in this specific group was much smaller, accounting for less than one percent each. This suggests that in a classroom rich with visual tools and guided discovery, the most critical factor is ensuring the student truly understands the "why" and "how" of the shapes they are studying. The study also showed that in the group taught with the standard, traditional method, motivation played a much larger role, explaining over twenty-five percent of the success, while creativity had almost no measurable impact on the results.
The researchers concluded that while motivation and creativity are valuable traits, the foundation of problem-solving in geometry is a solid conceptual understanding, especially when the teaching method encourages students to explore and visualize the material. The study did not claim that motivation or creativity are unimportant, but rather that in the context of learning geometry with visual aids, a student's ability to comprehend the core ideas is the dominant force that allows them to solve problems. The results suggest that teachers should focus on instructional models that help students build this deep understanding, using visual tools to make abstract ideas visible. By doing so, they can create an environment where students are not just memorizing formulas, but are developing the fundamental skills needed to tackle mathematical challenges with confidence.
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