Central Tendencies: Do Kids Really Know What Average “Means”?

In a math workshop last week, several math teachers commented that their students understood how to compute mean, median, and mode but they didn’t always understand that all three measures of central tendency were types of averages.  When asked for an average of a set of data, their students continually referred to mean.

To help students understand that mean was not always the best measure of central tendency, I had the teachers try the following activity from ASCD’s, Meaningful Mathematics:  Leading Students Toward Understanding and Application. The things we liked most about the activity  were:  the use of a concrete manipulative to create the set of data, the use of a concrete manipulative to find mean, and the use of an outlier to drastically change the mean.

Teachers were asked to make a stack of unifix cubes the height of the number of letters in their first name; ie., Renee took five unifix cubes.  When everyone at a table group had their stack, the information collected was transferred to a bar graph.  This would be the time to review the elements of a graph, if necessary.  Next, the teachers were asked to find the mode and median of their set of data.   A discussion of modes could occur at this point; does a set of data always have a mode and can a set of data have more than one mode?  Finally, I asked the teachers to find a way to make all their stacks have the same number of unifix cubes.  This resulted in a discussion of what to do with the cubes that were remainders; an excellent way to determine whether students have a good grasp of fractions.  At this point, students had determined mode, median, and mean.

To help students understand that mode or median might be a better measure of average than mean, I asked the teachers to pretend a new teacher was joining their group.   The new teacher’s name was “Tikki tikki tembo-no sa rembo-chari ruchi-pip peri pembo” which contains 46 letters and would be an outlier in their set of data.  I displayed the size of the bar using the unifix cubes.  They were asked to add this new name to their bar graph, and then determine the new mode, median, and mean.  The teachers were excited about this activity because they thought it would make a real impression on their students. The median and mode usually did not change but the mean changed drastically from a central number due to the size of the new name.

Just “sum”thing to think about!

Hi, I am Renee' Smith and I began teaching math in, of all places, a maximum security prison. “I was 21 years old and 99 lbs. soaking wet. Some of my students were convicted murderers and as scary as it sounds, it was incredibly sad. Many of those men had failed in the school system and then turned to crime.” That early experience with public school dropouts, cemented my resolve to help future students understand and succeed in the area of mathematics. To that end I dedicated 16 years to the classroom, teaching 5th grade math through algebra. After obtaining my Masters in Education from Baker University, I joined the ESSDACK team in 2007. I have presented at the local, state, and national levels but my most worthwhile experience at ESSDACK has been working to take the fear out of math for teachers and students alike. Although my primary focus has been providing professional development in mathematics, I also devote time to podcasting and creating materials for teachers to use in their classrooms. My podcasts include, By the Numbers, Just Desserts and Math Snacks. Working at ESSDACK has provided me the opportunity to do many of the things I love. “I have the time to research current educational practices, I get to be creative, collaborative, and I meet tons of new people."

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