Literature Index

In a residential home, energy consumption is closely related to the outdoor temperature and size of the house. In a home of a given size, fuel consumption varies fairly predictably through the year. When homeowners add a room, other things being equal, energy consumption should increase. This dataset permits students to estimate the energy demand, make forecasts for future months, and investigate other relationships.

Teaching statistics to students aspiring to other professions can be both frustrating and rewarding. The frustration arises from (a) having limited time to cover everything from introductory to advanced material, (b) receiving little input from staff in the client profession, (c) the concepts of unpredictability and randomness being alien to students' thinking, particularly for engineering students, and (d) students not having the background knowledge or skills necessary to understand the methods fully. The reward comes from seeing students understand both basic and advanced concepts and methods, and from requests for assistance with later work as former students discover the relevance of statistics. This paper will address some methods used to overcome the frustration and to enhance the rewards in teaching a first course in statistics to engineering students. Although situations vary, these ideas will hopefully provide helpful tools.

Statistics is not about numbers, statistics is about numbers in context. Statistics is not the same as probability. But some probability is necessary to understand certain statistical topics, while other statistical topics do not depend on probability. Statistics is not the same as mathematics. But an appropriate level of mathematics is needed to understand any statistical topic, and understanding statistics can contribute to an understanding of mathematics. Statistics is not the same as the scientific method. Yet statistics helps solve problems in science, engineering, medicine, business, and many other fields. Using statistics is inherently interdisciplinary. While using statistics demands that one understand the problem, the reason that statistics is so powerful is that key statistical concepts, methods and ideas are applicable in so many different problem contexts. This paper discusses the key concepts in statistics that students must learn in the K-12 curriculum so that all high school graduates can become productive citizens and use quantitative information effectively. The topics are organized and discussed in terms of number sense, planning studies, data analysis, probability, and statistical or inferential reasoning.

Performance based assessments of statistical thinking provide teachers with a window to students' conceptual development. With this aim in mind, we examined the performance of a pair of fourth/fifth-grade students working collaboratively on a probabilistic assessment task developed by the California Department of Education. To account for student performance, we developed a cognitive model of the knowledge guiding student performance. Using this cognitive model, we revised the assessment to provide opportunities for assisted performance. We believe that performance assessments of statistical thinking should be designed with ways to assist performance, a view consistent with visions of teaching and learning as assisted performance.