Prospective Teachers' Expectations of Students' Mathematical Thinking Processes in Solving Problems

This research aims to describe the expectations of prospective teachers for students' mathematical thinking processes in solving problem-based on the Polya model. This model is perceived by the theory of mathematical thought processes proposed by Mason. A descriptive method with a qualitative approach was used in this research. The research subjects were 25 students from the Department of Mathematics Education, Ibrahimy University. The test was given to collect data related to mathematical thinking processes expected by prospective teachers to students. Collected data including observations, tests, and interviews were tested in the aspect of their validity by triangulation. The qualitative descriptive was used to analyze the data. The results indicated that:(1) The average GPA (Grade Point Average) of the high, medium, and low group prospective teachers' were 93.25; 89.89; and 83.63 with a standard deviation of 1.754 each; 1.054; and 5.370, respectively (2) The prospective teachers expected that the students' mathematical thinking processes were able to carry out all of four mathematical thinking processes based on Mason Theory;(3) The prospective teachers expected that students were able to use Mason Theory on every stage of the Polya model problem solving; and (4) The expectation of prospective teachers were specializing (89%), generalizing (75%), conjecturing (62%), and convincing (59%). The results suggest for following up in a teachers or lecturer’s meeting in order to find out the expectations of their students' mathematical thinking processes, both in mathematics or other disciplines.

The development of comparison material tool with problem based learning based on caring community and its effect on the students' connection ability

This research was intended to develop the mathematics learning device with Problem Based Learning which also based on Caring Community and find out the effect on the students’ connection abilities. The method used was Mixed Method, in which it used R and D Methods of Thiagarajan Model and quantitative method used quasi experimental pretestpostest together. The students of SMP Ibrahimy 1 Sukorejo, which was class VII L was selected as the control class, whereas class VII M was chosen as the experimental class. The students’ connection abilities were measured by using essay test. Before analyzing the data, normality test and homogeneity of variance were performed. The data were normal distributed, so that T-test was performed. From the result of this research, it was obtained (1) the development of comparison material with problem besed learning which also based on caring community could be said valid, practical and effective (2) According to the result of difference test, the increase on students’ connection abilities showed its significance value (2-tailed) as much as 0,000 (p < 0,05) showed that the implementation of Problem Based Learning which also based on Caring Community had a significant effect on the students’ connection abilities.