“İstatistik ve Olasılık” Dersinin Senaryo ile Öğretim Süreci Sonunda Öğrencilerin Eleştirel Düşünme Eğilimlerindeki Değişim

The most effective way in improving critical thinking skills is the application of appropriate learning method (Burris, 2005). Problem-Based Learning (PBL) method used in mathematics is one of the effective ways in determining the students‘ critical thinking skills. The research is of importance in terms of manifesting whether the subject of ―Statistics and Probability-I‖ increases the students‘ critical thinking skills and whether this education leaves an impression on the students. Of the testing models, the testing model with pretest-posttest control group was used in the study. The study was conducted with the third grade students of Dokuz Eylül University, Buca, Faculty of Education, Department of Elementary Mathematics Teaching. The students of Branch-A (n=56) constitutes the experimental group and students of Branch-B (n=56) the control group. The students of experimental group completed the process with scenario practices, while the students of control group completed the process with the traditional methods. As data collection tools, the scenario developed by the researchers and ―California Critical Thinking Disposition Scale‖ adapted to Turkish by Kökdemir (2003) were used in the study. The teaching objectives were primarily determined in the preparation phase of the scenario developed by the researchers. The teaching objectives belonging to the scenario were established as: conditional probability, BAYES‘ theorem, product theorem belonging to conditional probability and the proof of BAYES‘ theorem. The scenario used in the study was arranged in accordance with the steps of analysis, synthesis and assessment enabling the transition to high-level thinking. The questions towards the attitudes such as inferencing, determining the guidelines of the scenario, hypothesizing, finding the problem, finding a way of solution to the problem, associating the sessions, showing the ways of solution with figure, table and graph were arranged in the analysis step of the students. In the synthesis step, on the other hand, students‘ obtaining new information by adding the new ones to those they learned in the scenario was aimed. In addition, they were expected to reach permanent information by associating the acquired gains with prelearnings. In the synthesis step, students exhibit new behaviours by producing new information by starting from the samples in the scenario, making sense of information again and combining the all information. In the assessment step, on the other hand, students reach a conclusion for the solution of the problem in the scenario. In the assessment step, the roles of the training directors are effective. The assessment of the scenarios is of use in the organization of learning-teaching activities and in performing the assessment in a reliable way. The arranged scenario is made up of three sessions. The first and second sessions are formed of two parts, and the third sessions is, on the other hand, composed of one part. In the first session; the learning objective of the first part was arranged as conditional probability, the learning objective of the second part was arranged as BAYES‘ theorem.The first part was intended for conditional probability learning objective. After the definition of conditional probability had been reminded, sessions over the possibility that more than two events happen concurrently were prepared. In the second part of the first session, probabilities of the results, that is to say, the learning objectives according to BAYES‘ theorem were prepared. In the second part, the results were included as to the appearance of the events such as the appearance of a single event, of two events simultaneously and of the events depending on the conditions. At this stage, when the probability of this result related to a specific event was determined after the result became clear, it was stated that the probabilities of the results are in question. In the second session; the learning objective of the first part was arranged as product theorem belonging to conditional probability, the learning objective of the second part was arranged as the proof of BAYES‘ theorem. The proof of product theorem belonging to conditional probability was included in the first part in order to repeat the first session. Students were asked to prove the product theorem belonging to conditional probability in order to test whether they understood conditional probability in the previous session. With the participation of the training director in the process, the product theorem belonging to the conditional probability of P(A∩B)=P(B).P(A\B) was proved by making use of A∩B=B∩A feature. In the second part, by reminding the BAYES‘ theorem, a distribution A1, A2,…, An of sample space S and for in B, there is an event apart from Ai (i=1,…n)s, for each i; the equation of P(Ai\B)=P(Ai)P(B\Ai)\P(A1)P(B\A1)+...+ P(An)P(B\An) was obtained. The third session was arranged as the application session covering the samples containing the first two sessions. The problems were re-assessed by going back as long as there was a problem in attaining the learning objectives. In the third session, it was observed that students had difficulty in understanding the BAYES‘ theorem. In consequence, it became apparent that the effect of applied teaching method was positive. The fact that posttest critical thinking tendency scores of the experimental group students were higher than posttest scores of the control group revealed that the provided training improved the students‘ critical thinking skills. As a result of the teaching via scenario used in ―Statistics and Probability-I‖ subject, significant differences came up between the students‘ critical thinking tendency and analyticity, open-mindedness, inquisitiveness, self-confidence, truthseeking and systematicty which are the sub-scales of critical thinking scales. It became apparent that according to the analyticity sub-scale, students couldn‘t sufficiently acquire the tendency of reasoning and utilizing objective evidence in view of difficult problems; to open-mindedness sub-scale, students were aware of their own mistakes and were sensible to them; to inquisitive sub-scale, their tendency to learn was high without expecting any benefit according to the provided method of training and they were open to new information; to self-confidence subscale, the trust which they had in their own reasoning processes was positive; to the results of truth-seeking sub-scale, their tendency to assess the views and thoughts different from one another was positive; and to the systematicity sub-scale scores, the students had more tendency to study in a planned and careful way. It was concluded in the study that the instruction provided employing scenario in mathematics teaching made the individual acquire the skills such as discovering the similarities and contrasts, being able to analyze and to assess in the thinking process, that is to say, it contributed positively to his/her acquiring critical thinking skill.