Flaws and Fallacies (cont.) AND Types of Data

As we transition into the second portion of the lesson, I pull up the PowerPoint slide with Big Bird on it and tell the students that they have 2 minutes to write down as many descriptors as possible about him (gather the data). 

After the students have gathered the data, I tell them to turn to their thinking groups and group all of their data into two piles.  (Circulate the “Thinking Group” Data Sorting Template”)  DO NOT tell them how to classify the two piles!  It is up to the students to talk about and agree on how this needs to be done.  Almost every group will group the data quantitatively and qualitatively, although they will not likely use these exact classifications.  After allowing 5-6 minutes for these discussions to occur, I have each group send a representative to the board to show their 2 categories and 3 of the data points that lie under each category – not all of them.  The students will come up with a wide variety of titles that align to quantitative and qualitative, but it is up to the teacher to package them all together and reveal the common terminology!  Because the directions were intentionally vague, be sure to give attention to the 1 or 2 groups who classified the data in a different way.  As long as they can explain their reasoning to the class when given the opportunity, emphasize to the students that these groups are equally correct, although it was not what we were specifically looking for.  This goes a long way to creating a safe learning environment (and emphasizing the math practice standards) early on in the semester.  There is not “one set way” to do things! 

After defining Qualitative and Quantitative data using the student responses, it is time to break the Quantitative data into two subgroups.  Ultimately we are “fishing” for discrete and continuous from the students, although it is NOT likely that they will come up with this actual terminology on their own.  I ask the class to do this with me at the board.  I jump from group to group asking for a quantitative data point which we discuss how to group as a class.  This does two things: 

#1  Ensures that all groups participate, even those groups who initially grouped differently than qualitative/quantitative. 

#2  Informally assesses the students level of understanding as you go along. 

NOTE:  The discrete/continuous discussion will likely take time with the students!  It is not as clear to them as the quantitative/qualitative grouping.  Be creative during the discussion, and do not be afraid to pull in additional examples!

The student’s work alone to complete the Exit Quiz shown in the PowerPoint.  This gives me a feel at the end of the day if the students have mastered the concepts enough to use them in a new setting.  This is vitally important before we attach the real math associated with data collection, and begin to take things to the next level.