Using a Latin Square Design to Determine the Most Effective Mathematics Teaching Method

Abstract

Pages 64-69 64 www.ijntr.org  Abstract -This study determined the most effective teaching method among four (4) teaching methods (i.e., direct instruction, inquiry-based, cooperative, and guided discovery).The study adopted a 4 x 4 Latin-Square design, using four (4) classes, four (4) teachers and four (4) teaching methods to record students' scores. Participants consisted of forty (40) public high school students and four (4) teachers in a school district in the western region. The results indicated that main effect for teacher was significant, F (3, 15) = 37.50, p < 0.05, = 0.95, main effect for class was significant, F (3, 15) =755.83, p < 0.05, = 0.99, main effect for teaching method was significant, F (3, 15) = 37.50, p < 0.05, = 0.98. (i.e., there were significant differences in students' scores at all levels with respect to teacher, class, and teaching method). Tukey's HSD post hoc multiple comparison tests indicated that students' scores for direct instruction was significantly lower than their scores for cooperative, t (6) = -9.50, p < 0.05,C.I = [-11.95, -7.05], students' scores for direct instruction were significantly lower than their scores for guided-discovery, t (6 ) = -15.50, p < 0.05, C. I = [-17.95, -13.05], students' scores for inquiry-based instruction were significantly lower than their scores for cooperative, t (6) =-9.50, p < 0.05, C. I = [-11.95, -7.05], students' scores for inquiry-based instruction were significantly lower than their scores for guided- discovery, t (6) = -15.50, p < 0.05, C.I = [-17.95, -13.05]. Nonetheless, students' scores for direct instruction were not significantly different from their scores for inquiry-based instruction, t (6) = .00, p > 0.05, and students' scores for inquiry-based instruction were not significantly different from their scores for guided-discovery, t (6) = -15.50, p > 0.05.This study has demonstrated that a Latin-Square design has a greater ability and robustness in detecting treatment differences as compared to a one-way analysis of variance. The study finally concluded that mathematics teachers should be encouraged to use more guided-discovery and cooperative learning methods, in their instructions. Index Terms ─ Effective teaching methods, instruction, Latin-Square design, multiple comparison tests, main effect.

University Mathematics Major Students’ Ratings of Their Lecturers’ Preferred Teaching Methods: A Repeated-Measures Design

“…Lecturers could use the following order of instruction to improve their teaching: guided discovery, cooperative, inquiry-based instruction, and direct instruction (Assuah, 2019). These students' ratings corroborate Assuah's (2019) earlier finding that highly rated teaching methods corresponded to those in which students performed well, after instruction.…”

“…Lecturers could use the following order of instruction to improve their teaching: guided discovery, cooperative, inquiry-based instruction, and direct instruction (Assuah, 2019). These students' ratings corroborate Assuah's (2019) earlier finding that highly rated teaching methods corresponded to those in which students performed well, after instruction. While research on the best mathematics teaching method is still inconclusive, strong evidence suggests that teachers can improve students' conceptual mathematics understanding by giving them opportunities to develop their own ideas of the underlying concepts through exploration, but this is best achieved when teachers provide some reasonable degree of guidance to students (Marshal & Horton, 2011;Lazonder & Harmsen, 2016).…”

“…In their proper order, lecturers could use the following teaching methods to improve their teaching: guided discovery, cooperative, inquiry-based instruction, and direct instruction. While research on the best mathematics teaching method remains inconclusive, strong evidence suggests that teachers can improve students' conceptual mathematics understanding by giving them opportunities to develop their ideas of the underlying concepts through exploration, but this is best achieved when lecturers provide some reasonable degree of guidance to students (Assuah, 2019;Marshal & Horton, 2011;Lazonder & Harmsen, 2016).…”