Day 130 Central Tendency Quiz

6th Grade Math Standards: 6.SP.2 Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.

6.SP.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.

6.SP.5 Summarize numerical data sets in relation to their context, such as by:
a. Reporting the number of observations.
b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
c. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.
d. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.

The Objective: Determine a median, mode, and mean of a data set. Analyze mistakes in finding a mean. Determine a missing value from a data set given the mean and almost all data values.

Agenda: 

1. Collect the Weekly Quiz while students do the grades of Elvis vs. Elvida
2. Take the central tendency quiz
3. Make necessary changes to the weekly quiz 
4. Retake any previous math assessment (inequalities or the functions test)
5. Read silently

The Assessment: The quiz and weekly quiz. As far as the quiz goes, question 8 was difficult for students because they left Friday out of the data set. Question 9 was difficult because for lack of a better phrase it was difficult. Students actually did better on question 10 which makes sense because there was a concrete data set. I was surprised by the amount of students that knew Taylor's mistake in question 11. 

Glass Half-Full: The first seven questions of the quiz were handled well by the class. If a mistake was made, it was not as if the student was guessing aimlessly. The pepper practice we had with the vocabulary proved worthwhile and perhaps it also helped students to have a very concrete example of what median is as we reviewed it. Going forward we are going to need these skills as fundamentals in studying dot plots, box and whisker plots, and measures of variation such as interquartile range and mean absolute deviation. It is comforting to know that the students shouldn't be lost with the prerequisite steps toward all of these topics. 

One Regret: I have two regrets today. The first regret is that I wish that items three through five were not a part of the agenda. I overestimated the amount of time that the quiz would take. The reason that I overestimated can likely be attributed to the anticipated difficulty of questions eight through twelve. These questions were difficult, but the amount of time spent on them by the students did not change which led to students having an entire block of time to work on potential retakes and the weekly quiz. The trouble with retakes and the weekly quiz is that both of these items are heavily reliant on getting assistance from me. Students would not be retaking a quiz or fixing a weekly quiz if they understood the material in the first place. I also have to coach students on the process for what problems they need to fix, remind them how poorly they did, and stop for a moment to cue the students that are being disruptive to get back to task. Overall the process of an entire class spending an entire block on fixing holes in their learning sounds utopian in theory, but in execution it's extremely stressful and partially chaotic. 

The other issue of course is with those problems eight through eleven that students struggled more with. On the first day of statistics I asked students how long they would spend before giving up on a problem. Perhaps that is what I lead off with when reviewing this quiz. Students were not nearly as persistent as I would like with the problems in which they had to finding a missing data value. 

I learned today that even though on the surface students should be motivated by the prospect of being able to retake a quiz and bring their grade up, that students could care less. I kind of already knew this, but it was safely confirmed for me today. Students crave diversions. They do not want to do more of the same. For all the complaining I do about students being over-tested I was guilty of adding to the problem today.