The most effective way in improving critical thinking skills is theapplication of appropriate learning method (Burris, 2005). Problem-Based Learning (PBL)method used in mathematics is one of the effective ways in determining the students criticalthinking 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 thiseducation leaves an impression on the students. Of the testing models, the testing model withpretest-posttest control group was used in the study. The study was conducted with the thirdgrade students of Dokuz Eylül University, Buca, Faculty of Education, Department ofElementary Mathematics Teaching. The students of Branch-A (n=56) constitutes theexperimental group and students of Branch-B (n=56) the control group. The students ofexperimental group completed the process with scenario practices, while the students of controlgroup completed the process with the traditional methods.As data collection tools, the scenario developed by the researchers and ―California CriticalThinking 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 scenariodeveloped by the researchers. The teaching objectives belonging to the scenario wereestablished as: conditional probability, BAYES theorem, product theorem belonging toconditional probability and the proof of BAYES theorem. The scenario used in the study wasarranged in accordance with the steps of analysis, synthesis and assessment enabling thetransition to high-level thinking.The questions towards the attitudes such as inferencing, determining the guidelines of thescenario, 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 werearranged in the analysis step of the students.In the synthesis step, on the other hand, students obtaining new information by adding thenew ones to those they learned in the scenario was aimed. In addition, they were expected toreach permanent information by associating the acquired gains with prelearnings. In thesynthesis step, students exhibit new behaviours by producing new information by starting fromthe samples in the scenario, making sense of information again and combining the allinformation.In the assessment step, on the other hand, students reach a conclusion for the solution of theproblem 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 andin performing the assessment in a reliable way.The arranged scenario is made up of three sessions. The first and second sessions are formed oftwo parts, and the third sessions is, on the other hand, composed of one part. In the first session; The first part was intended for conditional probability learning objective. After the definition ofconditional probability had been reminded, sessions over the possibility that more than twoevents happen concurrently were prepared.In the second part of the first session, probabilities of the results, that is to say, the learningobjectives according to BAYES theorem were prepared. In the second part, the results wereincluded as to the appearance of the events such as the appearance of a single event, of twoevents simultaneously and of the events depending on the conditions. At this stage, when theprobability 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 toconditional 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 partin order to repeat the first session. Students were asked to prove the product theorem belongingto conditional probability in order to test whether they understood conditional probability inthe previous session. With the participation of the training director in the process, the producttheorem belonging to the conditional probability of P(A∩B)=P(B).P(AB) was proved bymaking use of A∩B=B∩A feature.In the second part, by reminding the BAYES theorem, a distribution A1, A2, , An of samplespace S and for in B, there is an event apart from Ai (i=1, n)s, for each i; the equation ofP(AiB)=P(Ai)P(BAi)P(A1)P(BA1)+...+ P(An)P(BAn) was obtained.The third session was arranged as the application session covering the samples containing thefirst two sessions. The problems were re-assessed by going back as long as there was a problemin attaining the learning objectives. In the third session, it was observed that students haddifficulty in understanding the BAYES theorem.In consequence, it became apparent that the effect of applied teaching method was positive. Thefact that posttest critical thinking tendency scores of the experimental group students werehigher than posttest scores of the control group revealed that the provided training improvedthe students critical thinking skills. As a result of the teaching via scenario used in ―Statisticsand Probability-I‖ subject, significant differences came up between the students criticalthinking tendency and analyticity, open-mindedness, inquisitiveness, self-confidence, truth seeking and systematicty which are the sub-scales of critical thinking scales. It became apparentthat according to the analyticity sub-scale, students c