Learning Math: Data Analysis, Statistics, and Probability
Classroom Case Studies, Grades 6-8
This is the final session of the Data Analysis, Statistics, and Probability course! In this session, we will examine how statistical thinking from the previous nine sessions might look when applied to situations in your own classroom. This session is customized for three grade levels. Select the grade level most relevant to your teaching.
In This Grade Band
Part A: Statistics as a Problem-Solving Process
Part B: Developing Statistical Reasoning
Part C: Inferences and Predictions
Part D: Examining Children’s Reasoning
In the previous sessions, we explored statistics as a problem-solving process that seeks answers to questions through data. You put yourself in the position of a mathematics learner, both to analyze your individual approach to solving problems and to get some insights into your own conception of statistical reasoning. It may have been difficult to separate your thinking as a mathematics learner from your thinking as a mathematics teacher. Not surprisingly, this is often the case. In this session, however, we shift the focus to your own classroom and to the approaches your students might take to mathematical tasks involving statistics. See
As in other sessions, you will be prompted to view short video segments throughout the session; you may also choose to watch the full-length video for this session.
In this session, you will do the following:
• Explore the development of statistical reasoning at your grade level
• Analyze the use of the four-step process for solving statistical problems in your classroom
• Review mathematical tasks and their connection to the mathematical themes in this course
• Examine children’s understanding of statistical concepts
Notes for Session 10
This session uses classroom case studies to examine how children at your grade level think about and work with data. If possible, work on this session with another teacher or a group of teachers. A group discussion will allow you to use your own classroom, and the classrooms of fellow teachers, as case studies to make additional observations.
stem and leaf plot
Session 1 Statistics As Problem Solving
Consider statistics as a problem-solving process and examine its four components: asking questions, collecting appropriate data, analyzing the data, and interpreting the results. This session investigates the nature of data and its potential sources of variation. Variables, bias, and random sampling are introduced.
Session 2 Data Organization and Representation
Explore different ways of representing, analyzing, and interpreting data, including line plots, frequency tables, cumulative and relative frequency tables, and bar graphs. Learn how to use intervals to describe variation in data. Learn how to determine and understand the median.
Session 3 Describing Distributions
Continue learning about organizing and grouping data in different graphs and tables. Learn how to analyze and interpret variation in data by using stem and leaf plots and histograms. Learn about relative and cumulative frequency.
Session 4 Min, Max and the Five-Number Summary
Investigate various approaches for summarizing variation in data, and learn how dividing data into groups can help provide other types of answers to statistical questions. Understand numerical and graphic representations of the minimum, the maximum, the median, and quartiles. Learn how to create a box plot.
Session 5 Variation About the Mean
Explore the concept of the mean and how variation in data can be described relative to the mean. Concepts include fair and unfair allocations, and how to measure variation about the mean.
Session 6 Designing Experiments
Examine how to collect and compare data from observational and experimental studies, and learn how to set up your own experimental studies.
Session 7 Bivariate Data and Analysis
Analyze bivariate data and understand the concepts of association and co-variation between two quantitative variables. Explore scatter plots, the least squares line, and modeling linear relationships.
Session 8 Probability
Investigate some basic concepts of probability and the relationship between statistics and probability. Learn about random events, games of chance, mathematical and experimental probability, tree diagrams, and the binomial probability model.
Session 9 Random Sampling and Estimation
Learn how to select a random sample and use it to estimate characteristics of an entire population. Learn how to describe variation in estimates, and the effect of sample size on an estimate's accuracy.
Session 10 Classroom Case Studies, Grades K-2
Explore how the concepts developed in this course can be applied through a case study of a K-2 teacher, Ellen Sabanosh, a former course participant who has adapted her new knowledge to her classroom.
Session 11 Classroom Case Studies, Grades 3-5
Explore how the concepts developed in this course can be applied through case studies of a grade 3-5 teacher, Suzanne L'Esperance and grade 6-8 teacher, Paul Snowden, both former course participants who have adapted their new knowledge to their classrooms.