2013 Conference Proceedings - University of Nevada, Las Vegas

sample misconception). All four of the students who chose Adam on the pre-test correctly choseAshley on the post-test, and three of the four students who chose Keisha on the pre-test choseAshley on the post-test.Table 1Number of Students Choosing Each Sampling PlanAshley Jake Adam KeishaPre-test 13 0 4 4Post-test 21 0 0 1Students’ reasons for choosing their preferred sampling plan varied widely. An analysis ofthe pre and post interview data revealed a three tiered structure to the misconceptions thestudents had regarding appropriate sampling methods. At the lowest level, students had threedistinct general misconceptions. Some students placed an inordinate amount of attention onwhether or not the sampling plan was efficient. If a sampling plan was too difficult to carry out,it was dismissed. For instance, some students said it was too difficult for Ashley to fit all thenames of the students in a hat, so she shouldn’t do it. While efficiency should be attended to (forinstance, it would not be advisable to conduct a census in this study), some students had anunderdeveloped sense of efficiency that interfered with their understanding of the benefits ofchoosing a random sample in this case. A second misconception at this lower level is the beliefthat researchers must have an extremely large sample in order to produce reliable results.Finally, many students held the belief that it is critical to the success of the study for people inthe sample to care about the survey topic.Students with a more developed understanding of issues involved in sampling recognized thebenefits of having a random sample, but they possessed misconceptions of what makes for arandom sample. Some students felt that if the sample was diverse, then it was random. So longas there was a good mix of people, it was random. Others expressed that if there was ahaphazard way of selecting sample participants (“no rhyme or reason”), then the sample wasrandom. Finally, some students felt that if the sample was a volunteer sample, then it wasrandom. Since the sample participants “randomly” came up to the researcher and were notchosen by the researcher, the sample was random. In part, these misconceptions likely stem froma colloquial understanding of random as a surprising or unexpected event.Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 81