Students’ intuitively-based misconceptions in probability: teachers’ awarenesses and teaching practices in middle and high schools

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2014
Öçal, Mehmet Fatih
The purpose of this study was to investigate 8th and 11th grade students’ intuitively-based misconceptions in probability and to what extend their teachers’ awareness and teaching practices in their regular instructions resolve these misconceptions. This study was designed as a multiple case study with middle and high school mathematics teachers and their students as cases. The participants were two middle school teachers and their 59 students in the first case, and three high school teachers and their 59 students in the second case. Data were collected through interviews, classroom observations, and pre- and post-tests consisting of open-ended diagnostic questions about intuitively-based misconceptions in probability. While the interviews and the classroom observations were analyzed through content analysis method, students’ responses in the diagnostic test were analyzed through descriptive analysis method. Frequency tables were also provided for the findings from the test. Students’ responses to open ended questions showed that students had various intuitively-based misconceptions including availability and representativeness heuristics, simple and compound events, conjunction fallacy, time-axis probability, and misconceptions from Stavy and Tirosh’s theory of intuitive rules. The findings gathered from interviews indicated that teachers had awareness of and knowledge of methods for teaching probability, students’ difficulties in probability, and the possible reasons for their difficulties. Based on the classroom observations, it was found that what teachers aware of and what teaching practices they performed in the classrooms were contradictory. Although there were many teaching practices such as developing concepts for the content, constructing relation between the probability and other topics, using physical materials, giving related examples, solving related questions, and constructing shortcuts for the event types and formulas, it was observed that teachers teaching practices was not effective in resolving students’ intuitively-based misconceptions. According to the post-test results, it was observed that some misconceptions appeared in the pre-tests slightly decreased among both middle and high schools, while some others stayed still. In the case of outcome approach misconception, the occurrence frequency among students increased slightly after students received regular instruction. In conclusion, teachers in this study focused on the high school and university entrance exams in their instructions and did not have much effort on resolving students’ intuitively-based misconceptions. These findings implied that teachers focused on completing the curriculum (or course content) before the academic year finishes instead of considering students’ comprehension of the ideas and concept, and possible misconceptions in probability. Teachers should be equipped with the knowledge of students’ cognition and prepare their instructional practices accordingly.