# Data Associations: All About Your Students

I like Statistics and Data!  You should see the look on kid’s faces when I shout that out enthusiastically in class.  I really dislike looking at textbook options when it comes to Data, kids are more engaged when they collect their own (or are looking at unlabeled graphs).  This is one that activity I always look forward to in any class I teach.

I have students brainstorm what types of data they can collect from students in their grade (that is also school appropriate).  List those on the board, and then limit the data collection to 10 different types through class discussion.  Students in my classroom typically collect data on these topics

1. Height
2. Weight
3. Shoe Size
4. Hand Size
5. Eye Color
6. Hair Color
7. Handedness
8. Employed
9. Dating
10. Favorite Clothing Brand
11. Favorite Shoe Brand
12. Favorite Game System
13. Favorite Food
14. Favorite TV Show
15. Favorite Music

As you can see, there are more than 10.  It is a good discussion to have students thinking about which ones we could omit (without explicitly telling them about association or correlation).  When you have your 10 sample items, collect data from all the students in the grade.

I typically ask my class if they want to sample just a class, grade or school.  Since I teach mainly middle school students, they have a good understanding about how sample size effects your data.  They are a social, nosy lot- so students typically pick a school sample.  Depending on how large of a student body you have, or how co-operative your co-workers are you may need to limit the survey to the grade.

After collecting our data (of which I typically compile a spreadsheet of values), we shift our focus to association.  I have a few associations I want the students to explore, but I always ask students which ones we should examine.  We create a list of 10 different associations, and I ask students to predict what type of associations exist with those data sets. When they are done, we discuss those predictions and make conjectures for two relationships as a whole group, using graphs to determine the validity of those predictions.  After we do this, I have students break out into groups again and determine if all their predictions are correct- or if they want to change them.  While students are in their small groups, I wander around the classroom and listen to them discuss- and I learn.  I really enjoy listening to student reasoning and justifications on why certain associations do or do not exist.

We come back together as a whole group and discuss the list.  If we encounter a relationship we can’t agree on, we graph it.  When we complete the list, they are ready for “homework.”  Their assignment:

1. Create a list of 3 relationships that would have a positive association
2. Create a list of 3 relationships that would have a negative association
3. Create a list of 3 relationships that would have no association

The second part of this homework- to list any misconceptions students had with associations, whether it was individual or small group.  They also need to describe what math talk took place which corrected the misconception.  I find this last part the most important for me, having student language on ways to correct errors is invaluable.