Dear Matt,

I am having trouble incorporating the statistics standards into my Algebra 2 course when there are so many other topics that I need to cover.  Do you have any suggestions about how to get this done?

Struggling Second Year Teacher

Response:

Dear Struggling:

In the last issue of MathBits we talked about dealing with the crowded algebra curriculum, so you may want to reread that first. But let’s talk about how to incorporate statistics today.

Oftentimes we don’t believe that statistics and probability are very important, especially when compared to the ideas of algebra. However, there is a lot of evidence that the study of statistics is one of the most useful applications of mathematics for all students. Those who enroll in post-secondary institutions will find that studying statistics is required in nearly every field of study. Students who progress to the workplace will discover that today’s careers often demand a good understanding of statistical processes. Responsible citizenship demands that everyone be able to analyze data, interpret likelihoods, and evaluate research studies presented to the public. In other words, we all need to understand statistics.

The Minnesota 2007 Academic Standards in Mathematics require that students in grades 3-5 begin displaying data in simple forms. Students in grades 6 and 7 begin the study of elementary probability. In grades 7 and 8, students extend their ability to display and interpret data. This prepares students for the many important components of the study of statistics and probability in high school.

There are three big ideas at the high school level: creating and using data, evaluating data, and using probability. Most of this content can fit very nicely into an advanced algebra course. Real data, often gathered by students, or taken from events from their lives, can provide the raw material for analyzing data, and using the analysis to predict or make recommendations. A simple experiment in the classroom can provide the context and data for introducing the Five Number Summary and dual box-and-whisker graphs. This might be asking students, working in pairs, to record each person’s resting heart rate, and then their heart rate after exercise such as jumping jacks (or modified low impact jumping jacks). You could extend this idea to see what happens when they keep doing jumping jacks for several minutes, and plot each person’s heart rate every 30 seconds, starting before they jump , during 2 minutes of jumping, and for 2 minutes after they finish. Is it a function? If so, what kind? Can you find an equation describing it? Do all students’ graphs look alike? The statistical functions on graphing calculators or computers also provide powerful tools for analyzing data and predicting trends and correlations. Integrating statistics into the algebra early in the course rather than simply appending one or several statistics units to the end of the course reinforces and connects understanding of both strands. A longer term project, where students work in groups over time on a question of interest to them can pull together their learning, and might integrate algebra and statistics.

Though your question does not address probability explicitly, the advanced study of statistics, which is begun at the high school level, includes inferential statistics, which incorporates probability into statistics, by analyzing how likely it is that a certain result happens by chance. Thus, students need to have a good grasp of basic probability in order to continue their work in statistics.

There are several good places to begin looking for resources. Be sure to match the goals of the materials you pick to the standards. For example, students should not need a lesson on calculating the mean, but are expected to learn how to find summary statistics such as the Five Number Summary on their calculator.

As always, the National Council of Teachers of Mathematics has high quality resources, including Illuminations, an online data base of lessons, and the Navigations series, with booklets on both Data and Probability at the high school level. The 2006 Yearbook, Thinking and Reasoning with Data and Chance as well as the November 2008 Focus issue of the Mathematics Teacher on Data and Probability are additional useful resources. A new resource includes both book and ebook, Focus in High School Mathematics: Statistics and Probability, and offers up to date support for teachers. See the catalog or website for more information.

The American Statistical Association has for many years used their expertise and resources to assist K-12 teachers with statistics. They have a comprehensive framework, Guidelines for Assessment and Instruction in Statistics Education (GAISE) that gives Pre-K-12 teachers an excellent overview and rationale for the study of statistics, as well as many specifics. Their website is replete with resources for teachers, including data sets and videos. One of their many resources is the Chance Project, a rich resource especially for current articles incorporating statistics that is especially helpful for evaluating statistical studies.

A computer resource is the Fathom statistical software published by Key Curriculum Press. In addition to the software, they publish books, often including blackline masters, to support teachers and students and also textbooks. A wonderful source for interesting national, state and local data is the U. S. Census site. They produce many varied reports, and the newest report (March 2011) will be the basis of congressional redistricting.

A final resource is the Advanced Placement site. Since there is an AP Statistics course which is growing greatly in popularity, there are more and more resources on the AP statistics sites for teachers. Though the expectations for this course go beyond what is expected in the Minnesota standards, many components of the two overlap. And maybe as you incorporate more and more statistics in your courses, you will become so enthused that you can initiate an AP Statistics course in your school, if you do not already have one!

Happy Teaching!

Matt

Matt Mentor, a wise and experienced teacher, offers advice about teaching mathematics topics to beginning teachers. Of course, experienced teachers can join in as well.

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