Tim Jacobbe

Teachers’ Understanding of Averages

The concept of average has been a part of the curriculum for well over 100 years. Consequently, research on students’ understanding of average has been one of widest areas explored in mathematics and statistics education research; however, research focused on teachers is still very scarce. In this chapter, research related to school students’ understanding is first described and then research dealing with teachers’ understanding or professional knowledge is analysed. Some final implications for research on the training of teachers are provided.

Statistics Education in the K-12 Schools of the United States: A Brief History

The purpose of this paper is to provide a brief history of statistics in the K-12 setting in the United States. This is intended to serve as a reminder of how far the discipline has come in its inclusion in the standard curriculum for all students as well as to highlight the need for research in this area.

The Effects of a Family Math Night on Preservice Teachers’ Perceptions of Parental Involvement

This study examined the impact of a Family Math Night on preservice teachers’ perceptions of low-income parents and their engagement in their children’s education. Participants were enrolled in an elementary mathematics methods course; one section served as the treatment group. Participants were required to aid in the planning and implementation of a Family Math Night held at a school serving a predominantly African American, high-poverty community. Results of a pre- and post-survey analysis indicate that the treatment group had more positive perceptions of parental involvement overall. These results were not sustained 1 year later, suggesting important implications for mathematics teacher educators.

Encouraging Sixth-Grade Students' Problem-Solving Performance by Teaching through Problem Solving.

Abstract This teaching experiment provided students with continuous engagement in a problem-solving based instructional approach during one mathematics unit. Three sections of sixth-grade mathematics were sampled from a school in Florida, U.S.A. and one section was randomly assigned to experience teaching through problem solving. Students’ problem-solving performance and performance on a unit test were analyzed. The intervention had a positive effect on students’ problem-solving performance whereas the comparison group experienced no changes. ANCOVA analyses suggest that intervention students solved more problems on the posttest than their peers, but the comparison group outperformed the intervention group on the unit test.

Toward an understanding of p-values: Simulation-based inference in a traditional statistics course

ABSTRACT The study presented in this article examined the impact of two simulation-based inference activities on students’ understanding of p-values in a second undergraduate statistics course. In the study, students familiar with traditional inference methods used physical and computer simulations to estimate p-values. To examine students’ conceptions before and after participation, students were prompted to write brief explanations of p-values, to apply these explanations in different contexts, and to self-evaluate their understanding. This article describes students’ varying conceptions of p-values and the ways in which students demonstrated improvement after engaging in simulation-based inference activities. Qualitative analysis of student responses suggests that students hold a range of conceptions of p-values even after a full semester of instruction; further, this study suggests that incorporating simulation-based inference into traditional courses has the potential to improve understanding of p-values and is a promising area for future research.

Students' Understanding of Bar Graphs and Histograms: Results from the LOCUS Assessments.

ABSTRACT Bar graphs and histograms are core statistical tools that are widely used in statistical practice and commonly taught in classrooms. Despite their importance and the instructional time devoted to them, many students demonstrate misunderstandings when asked to read and interpret bar graphs and histograms. Much of the research that has been conducted about these misunderstandings has been with students in introductory statistics classes at the college level. In this article, students in grades 6–12 completed multiple-choice and constructed-response questions about bar graphs and histograms as part of a larger study. The same misunderstandings that college-level students demonstrate were found in these younger students.

The Levels of Conceptual Understanding in Statistics (LOCUS) Project: Results of the Pilot Study

The Levels of Conceptual Understanding in Statistics (LOCUS) project (NSF DRL-111868) has created assessments that measure conceptual (rather than procedural) understanding of statistics as outlined in GAISE Framework (Franklin et al., 2007, Guidelines for Assessment and Instruction in Statistics Education, American Statistical Association). Here we provide a brief overview of the LOCUS project and present results from multiple-choice items on the pilot administration of the assessments with data collected from over 3400 students in grades 6-12 across six states. These results help illustrate students’ understanding of statistical topics prior to the implementation of the Common Core State Standards. Using the four components of the statistical problem-solving process outlined in the GAISE Framework, middle and high school students tended to perform better on questions assessing Formulate Questions and Collect Data; both groups also tended to perform relatively worse on the Analyze Data questions.

An Analysis of the Statistical Content in Textbooks for Prospective Elementary Teachers

We analyzed the statistical content within mathematics textbooks used in courses for preparing elementary teachers. Six textbooks commonly used in the United States comprised our sample. Each task in statistical sections was analyzed using both the levels of the GAISE framework (Franklin et al. 2007) and phases of the statistical problem solving process (Formulate Questions, Collect Data, Analyze Data, and Interpret Results). Tasks within the Analyze Data phase were also classified as creating or reading a display, performing a mathematical computation, or using statistical reasoning beyond mathematical computations. The majority of statistical tasks in each book required data analysis. Two textbooks primarily consisted of tasks addressing statistical concepts beyond computations, while three series focused on graphical displays and computational procedures.

Department of Research on K-12 Statistics Education

The release and widespread adoption of the Common Core State Standards for Mathematics (CCSSM) have dramatically increased the expectations for teaching statistics in grades 6 through 12 (Common Core State Standards Initiative, 2010). The inclusion of statistics in the K-12 setting has been an ongoing effort of the statistics education community dating back to the work of Fred Mosteller and the creation of the Joint Committee on Curriculum in Statistics between the National Council of Teachers of Mathematics (NCTM) and the American Statistical Association (ASA), as well as many others in the 20 century.