## Wednesday, September 12, 2012

### Update to conflict and discussion in descriptive stats

Well now, yesterday I gave a brief diagnostic quiz about finding mean and median from a frequency table. I wanted to test retention of the methods we had developed the previous lesson. The results were... interesting.

• About half the class could find the mean, and a bit less than half could find the median. Some students wrote out the raw data first to find these values, and some didn't. I would of course prefer that they didn't have to write out the raw data, however even the fact that they spontaneously make the connection from frequency table to raw data is an important improvement that shows understanding of how the two representations fit together. In the previous lesson, no one started out being able to find mean and median, so overall it's an improvement to see that about half the class now could do it.
• The other half that couldn't find the mean and median seemed to use the same, incorrect and illogical, methods that they had suggested the previous class, almost as if they hadn't already seen that the method was faulty.
• After a very brief go-through of finding the mean and median, we moved on to measures of spread. At the very end of the hour, students received another frequency table and were asked to solve for central tendencies and also measures of spread. This time, it looked to me that all the students in class could find the mean, though some still struggled with the median. Likewise, finding quartiles does not come easy to my students.

What I'm wondering:
• Did some of the students practice understanding and procedures between the two lessons, and might this account for the differences in retention?
• When solving the last example at the end of the lesson, were students doing solving it through understanding, or were they simply copying the procedure of the worked example that we did together?
• Why is it so tricky to find the median and quartiles? Are the students simply not as used to this as they are to the mean? Are they still struggling to get the feel of what the numbers in a frequency table represents?
• Is the retention better than students would normally have after a guided-discovery or direct instruction lesson?