Effects of Variation Theory Integrated Guided Inquiry-Based Instruction on Grade Ten Students Self-Belief in Learning Solid Geometry

In mathematics education, students’ beliefs that could take many different forms like students' beliefs about mathematics learning mathematics teaching; and about themselves play a significant role in their learning and achievement. In particular, self-belief (SB) that is students’ evaluation and judgment about themselves in learning solid geometry, which encompassing control belief (CB), goal orientation (GO), self-concept (SC), self-efficacy (SE), and task value (TV), is critical to their success in learning solid geometry. Addressing these SB dimensions can substantially improve students' learning outcomes in solid geometry. Innovative, student-centered instructional approaches like GIBI, especially when combined with variation theory, offer a potential solution for overcoming Ethiopian secondary schools’ educational challenges by promoting active learning and providing varied examples to enhance engagement and achievement. However, there is a lack of research on the effectiveness of this combined approach in Ethiopia context. This study aims to fill this gap by investigating the effects of variation theory integrated GIBI on grade ten students' SB in learning solid geometry in Ethiopia. Employing a quasi-experimental with non-equivalent control group pretest-posttest design, 102 students from three public secondary schools in Debre Tabor city, Amhara region were randomly assigned into three groups: Experimental Group 1 (EG1) received GIBI with variation theory, Experimental Group 2 (EG2) received GIBI without variation theory, and the Control Group (CG) received traditional teaching methods. A SB questionnaire was used to measure students' CB, GO, SC, SE, and TV before and after the intervention. The results revealed significant improvements in the SB dimensions among students in EG1 compared to those in EG2 and CG. Specifically, EG1 students showed higher post-test scores in CB (F (2,99)=40.29, p=0.000, η²=0.449); GO (F (2,99)=3.43, p=0.036, η²=0.065); SC (F (2,99)=32.09, p=0.000, η²=0.393); SE (F (2,99)=24.02, p=0.000, η²=0.327); and TV (F (2,99)=5.35, p=0.000, η²=0.097). Tukey post hoc tests indicated that EG1 students' scores were significantly higher than those of the CG in CB and GO, and higher than EG2 and CG in SC, SE, and TV. These findings suggest that the integration of variation theory with GIBI effectively enhances students' SB in learning solid geometry, thereby addressing the educational challenges faced by Ethiopian students. The study recommends adopting this instructional approach more widely to improve student outcomes in mathematics.