Comparative Study of Reasoning Capability and Mathematical Understanding of Student between Application of Open Ended Approches and Expository Approches and Relatioan to student Early Capablities

— The problem in research is the low reoning ability and mathematical unnderstanding of students is the lecturer-centered learning outcomes. Change in the learning process into student-centerd learning must be done, one of wich is learning that applies the Open-Ended approach. This research is aimed to comparing : (1) Reasoning skills and mathematical understanding of groups between Open Ended approaches and expository learning. (2) Reasoning skills of mathematical between learning and early math ability of student mathematical learning result. (3) Mathematical understanding between learning and early math ability of student mathematical learning result.This research is quasi-experiment. The subjects of this study were students of Mathematics Education Study Program who were randomly selected by two classes. Class B was treated with 32 students by Open ended approaches and Class C was treated with 32 students by Expository Learning. The instrument used was a description test from reasoning and mathematical understanding test, observations of student activities, diversity and answer patterns given by students. Data analysis was performed by t-test and Kruskal-Wallis Non-Parametric Test to see the mean difference and Anova of two Factorial 2 x 3 lines. The main result of this study is that students who study with the Open Ended Approach significantly have higher reasoning and mathematical comprehension skills than students who learn with the Expository Approach. Students with high abilities significantly have higher reasoning and mathematical comprehension skills than students with moderate abilities compared to low ability students, except mathematical reasoning abilities in groups of students with expository learning. There is no interaction between learning factors and students ability factors that influence students' reasoning and mathematical understanding abilities