<![CDATA[Abstract: The objective of this research was to investigate the effect of the learning models on the learning achievement in Mathematics viewed from the reasoning ability of the students. The learning models compared were the problem based learning model, the problem posing learning model, and the direct learning model. This research used the quasi experimental research method. Its population was all of the students in Grade VIII of State Junior Secondary Schools of Banyumas regency in Academic Year 2013/2014. The samples of the research were the students of State Junior Secondary School 4 of Purwokerto, State Junior Secondary School 2 of Sokaraja, and State Junior Secondary School 2 of Baturraden. They were taken by using the stratified cluster random sampling. The instruments used to gather the data of the research were test of learning achievement in Mathematics and test of reasoning abilities. The data were analyzed by using the two-way analysis of variance with unbalanced cells. The results of the research are as follows. 1) The problem-based learning model results in the same good learning achievement in Mathematics as the problem posing learning model but results in a better learning achievement in Mathematics than the direct learning model, and the problem posing learning model results in a better learning achievement in Mathematics than the direct learning model. 2) The students with the high reasoning ability have a better learning achievement in Mathematics than those with the moderate and low reasoning abilities, and the students with the moderate reasoning ability have a better learning achievement in Mathematics than those with the low reasoning ability. 3) In the students with the high reasoning ability, the problem-based learning results in the same good learning achievement in Mathematics as the problem posing model but results in a better learning achievement in Mathematics than the direct learning model, and the problem posing model results in the same good learning achievement in Mathematics as the direct learning model. In the students with the moderate and low reasoning abilities, the problem-based learning, the problem posing learning model, and the direct learning model result in the same learning achievement in Mathematics. 4) In the problem-based learning, the students with the high reasoning ability have a better learning achievement in Mathematics than those with the moderate an low reasoning abilities, and the students with the moderate reasoning ability have the same learning achievement in Mathematics as those with the low reasoning ability. In the problem posing learning model, the students with the high reasoning ability have the same learning achievement in Mathematics as those with the moderate reasoning ability, but the students both with the high and moderate reasoning abilities have a better learning achievement in Mathematics than those with the low reasoning ability. In the direct learning model, the students with the high, moderate, and low reasoning abilities have the same learning achievement in Mathematics.Key words: Problem Based Learning, Problem Posing, and Reasoning ability.]]>
