|
The National Council of Teachers of Mathematics (NCTM, 2000) identifies data analysis and probability as a strand in its Principles and Standards for School Mathematics. In grades pre-K through 12, instructional programs should enable all students to do the following:
• | Formulate questions that can be addressed with data, and collect, organize, and display relevant data to answer them |
• | Select and use appropriate statistical methods to analyze data |
• | Develop and evaluate inferences and predictions that are based on data |
• | Understand and apply basic concepts of probability |
In grades 3-5 classrooms, students are expected to use appropriate statistical methods to do the following:
• | Describe the shape and important features of a data set and compare related data sets, with an emphasis on how the data are distributed |
• | Use measures of center, focusing on the median, and understand what each does and does not indicate about the data set |
• | Compare different representations of the same data and evaluate how well each representation shows important aspects of the data |
In grades 3-5, children readily notice individual data points and are able to describe parts of the data -- where their own data falls on the graph, which value occurs most frequently, and which values are the largest and smallest. A significant development in children's understanding occurs as they begin to think about the set of data as a whole. Our goal for children is for them to see a data set as a distribution of values with important features, such as center, spread, and shape.
To focus students' attention on the shape and distribution of the data, it is helpful to build from children's informal language to describe where most of the data are, where there are no data, and where there are isolated pieces of data. The words clusters, clumps, bumps, and hills highlight concentrations of data. The words gaps and holes emphasize places in the distribution that have no data. The phrases spread out and bunched together underscore the overall distribution. Teachers must also continually emphasize and help students see that what they notice about the shape and distribution of the data implies something about the real-world phenomena being studied.
In grades 3-5, students learn to use measures of center to summarize a data set. Building on children's informal understanding of what is the most, what is the middle, and what is typical, teachers can help students develop understanding about the mode, median, and the mean. But students need to learn more than simply how to identify the mode or median in a data set and how to find the mean: They need to develop an understanding of what these measures of center tell us about the data, and what each does and does not indicate about the data set. The emphasis in these grade levels should be on the median, with informal exploration of the mean. Children can see where the median is located among the data, but the mean is much more abstract, as it has no clear identity within the data themselves.
When viewing the video segment, keep the following questions in mind:
• | Thinking back to the big ideas of this course, what are some statistical ideas that these students are developing? |
• | What questions could be posed to determine the extent of students' understandings of what the mode, mean, median, and range do and do not indicate about the data set? |
|
