2013 Conference Proceedings - University of Nevada, Las Vegas

opinion of the student body. This question is designed to reflect a situation where a simplerandom sample is required in order to analyze the data with standard inferential statisticalmethods taught in an introductory statistics course. The question is a modified version of aquestion found at the NSF funded ARTIST (Assessment Resource Tools for ImprovingStatistical Thinking) website (Garfield, 2006) and is as follows:Four students at XYZ University (Ashley, Jake, Adam, and Keisha) conductsurveys to gauge the opinion of the student body on various political issues. Thestudent body is 30,000 students. Ashley got the names of all students at XYZU,put them on pieces of paper in a large plastic container, mixed them well, andchose 120 students to ask. Jake asked 50 students at a meeting of the computergaming club. Adam asked all 8,293 students who are sophomores. Keisha set upa booth outside of the student union and asked people passing by to fill out asurvey. She stopped collecting surveys when she got 120 students to completethem. Discuss the benefits and limitations of each person’s sampling method.Which method do you think is best?At the beginning of the semester, students provided written feedback to this question and all22 students explained their thinking during a video recorded semi-structured interview.Subsequently, students learned standard introductory statistics topics including samplingdistributions, confidence intervals, and hypothesis testing through ANOVA and linearregression. Lessons that targeted issues in the above modified ARTIST question included onetask that utilized the TI-Nspire and empirical sampling distributions to investigate how largerandom samples need to be for a sample mean or proportion to provide a good estimate of thepopulation mean or proportion (Strayer, in press). Another task used decks of cards to simulatethe problems with taking convenience samples (see Appendix). At the end of the semester, the22 participants completed the same assessment as a post-test and were again interviewed toinvestigate their thinking on the above question. Student answers to the question were recordedand the video interviews were transcribed. An analysis of data from the transcripts and writtenresponses was conducted using qualitative grounded theory methods of open coding, memowriting, axial coding, and theory construction.ResultsStudents’ choices for their preferred sampling plans at the beginning and end of the semesterare shown in Table 1. In the pre-test, 59% of the students chose the correct answer of Ashley,while 95% chose Ashley on the post-test. Incorrect answers were split evenly on the pre-test with18% choosing Adam (large sample misconception) and 18% choosing Keisha (convenienceProceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 80