The Problem Within an Elementary Statistics course, the sampling distribution is labeled by some as being a threshold concept. It is hypothesized that if students are able to develop a true understanding of the sampling distribution, then the conceptual understanding and practical application of related inferential methods will naturally follow. Alternatively, a lack of understanding of the sampling distribution is thought to lead to difficulty in learning the corresponding inferential methods. We examine student learning of the sampling distribution and its association with student performance of key procedural and conceptual elements from the course. Our aim is to assess to what extent the sampling distribution truly is a threshold concept.

Evidence of Student Learning & Methods of Analysis Student understanding of the sampling distribution was assessed using concept mapping projects (Lipson, 2003). Students were given a suggested list of key terms and asked to arrange them into a map that shows relationships and structure. The concept maps were scored using a 3 point rubric. Student conceptual and procedural understanding of inferential methods was assessed using corresponding exam questions. These questions appeared on the 3rd midterm exam of the course, the 4th midterm exam, and the final exam. Factor analysis was used to convert the scores that students received on each of several exam questions into a single procedural and two conceptual numeric scores. Multivariate analysis of variance was used to test if the average conceptual and procedural scores differ significantly between those scoring a level 1, 2, and 3 on the concept mapping activities.

Tier 1 example concept map

Tier 3 example concept map

Project Summary This project focuses on students taking Elementary Statistics. The objective of the project is to correlate students' learning of sampling distributions to their procedural and conceptual understanding of inferential statistics. We are interesed in gaining a better understanding of the role that sampling distributions play in student learning of inferential methods. We assess student learning of sampling distributions through concept mapping activities. Students' procedural and conceptual understanding of inferential methods are assessed using problem solving activities and exam questions.

Helpful Resources & References Schau, C. and Mattern, N., Use of Map Techniques in Teaching Applied Statistics Courses, The American Statistician, Vol. 51, No. 2 (May, 1997), pp. 171-175 http://www.jstor.org/stable/2685413 Hubbard, R., Assessment and the Process of Learning Statistics, Journal of Statistics Education, Vol. 5, No. 1 (1997) Lipson, K., The Role of the Sampling Distribution in Understanding Statistical Inference, Mathematics Education Research Journal, Vol. 15, No. 3, 2003, pp. 270-287 Kennedy, P.E., Teaching Undergraduate Econometrics: A Suggestion for Fundamental Change, The American Economic Review, Vol. 88, No. 2, Papers and Proceedings of the Hundred and Tenth Annual Meeting of the American Economic Association, (May, 1998), pp. 487-492 http://www.jstor.org/stable/116972 Nesbit, J.C. and Adesope, O.O., Learning With Concept and Knowledge Maps: A Meta-Analysis, Review of Educational Research, Fall 2006, Vol. 76, No. 3, pp. 413-448

Career Relevance & Impact Involvement in the Wisconsin Teaching Fellows and Scholars program has prompted me take a new, broader view of teaching and learning. The professional development provided through WTFS is very unique in my experiences. I have especially valued the interaction with a variety of other disciplines and levels of teaching experience.

Results & Conclusions Within the two classes of students included in this study, a general trend was observed showing that increased understanding of the sampling distribution as demonstrated through concept maps is associated with higher average procedural and conceptual scores. However, the trend seen within the observed sample is not statistically significant and therefore may not generalize to a broader population of Elementary Statistics students. Further study is needed to assess the extent to which the sampling distribution truly is a threshold concept. Students' procedural and conceptual understandings of inferential methods are not adequately represented by a single procedural score and conceptual score as some previous research has suggested (Lipson, 2001). In particular, students' conceptual understandings seem to be multidimensional. Data from this study suggests that conceptual understanding can be broken down into at least two meaningful dimensions: one related to sample size concepts and another related to interpreting inferential results.

For further study Gauge the repeatability and reliability of concept mapping tasks at measuring student understanding of sampling distribution. I conjecture that the lack of statistical significance in the current study is largely associated with measurement error. Further investigate the multiple facets of conceptual understanding in Elementary Statistcs. This type of investigation would require asking and analyzing a greater number and greater variety of conceptual tasks. Review and develop strategies for addressing common misconceptions and misunderstandings that appeared in student concept maps.