## Tuesday, July 3, 2018

### Ten Weeks of Summer: Analyzing THE Exam (Week 3)

Right before school ended, AP teachers at my school got an email from the person in charge of our AP program saying that the AP exam books from 2017 were available.  They were put in my mailbox and I didn't have time to look at them at that point.  I remember thinking that it probably would have been more helpful to get them before the students took the AP exam on May 17th.

At my most recent workshop, participants wondered how it worked to get AP exam books back.  Here is what I found.  It cost us about \$300, because we got all the exam books back for all of our students for all our AP courses, and the exam books arrived at our school somewhere between October and December.  This makes me wonder where they were from December through May.  It is a bit frustrating, because I could have reviewed the material in the books and used what I learned with my current AP Stat students.

Today I finally had a chance to look at my exam books and I used the rubrics to determine each student's score.  I was happy to see that no student left a question blank and it appears that some students got the highest possible score for a few of the questions!  But what were some of the big things I noticed? Do I need to modify my instruction or emphasize certain things more?  Here is what I discovered.

1) From question #1, I noticed that many students interpreted slope correctly, but did not mention a predicted change in the response variable.  Using words the words on average, approximately or predicted, would have indicated the non-deterministic nature of a LSRL.

2) From question #2, almost all my students used their graphing calculator to do a one sample z-interval for a proportion.  However, not all students named the procedure or checked to see if the conditions for doing the procedure were met. A few students did not have the correct confidence interval procedure at all, but all students gave a correct interpretation of the interval they found.

3) From question #3, almost all of the students could do the normal distribution calculation correctly for part a.  However, to get full credit for this, they needed to show boundary and direction.  If the student had simply drawn a normal distribution and marked it appropriately, they would have received full credit for part a.

4) In general, I noticed that students weren't showing their work for probability calculations.  Students may get partial credit on probability calculations if you have a wrong answer, but the work must be shown.  The directions on the exam even state, "Show all your work.  Indicate clearly the methods you use, because you will be scored on the correctness of your methods as well as on the accuracy and completeness of your results and explanations."  I need to emphasize that more.

5) From question #5, I had many students leaving off the expected counts condition entirely or comparing the sample size of 207 to 30.  But on the plus side, almost all students were able to draw the correct conclusion in context and included linkage between their p-value and a chose alpha level.

The Positives - Students are using context, making correct inference conclusions and correctly interpreting confidence intervals!

Areas to Work On - I need to model drawing a normal distribution and require students to draw a well labeled/shaded normal distribution for any normal distribution calculation.  We need to spend more time on mixed review of identifying inference procedures and their associated conditions.

Consider - I currently split up LSRL between the two semesters.  LSRL, residuals, standard error, correlation and coefficient of determination are in the first semester and inference for LSRL is in the second semester.  Interpreting slope (and y-intercept) with non-deterministic language can be challenging, because students don't really understand that one sample produced that one very specific LSRL and that it is not likely to be the true regression line for the population.  In addition, they don't understand the concept of sampling variability early in the first semester.  Perhaps moving all the LSRL topics to the second semester would make this better, I think. This is the approach used by some stats teachers I know and one that I may want to use myself.

The remainder of this week I will be working on reading the AB Calculus Course Description from the College Board and identifying my areas of weakness relative to AB topics.  For example, I remember learning about slope fields in differential equations in college, but that was in 1990 - twenty-eight years ago!!  Since I haven't seen that topic since then, it is safe to assume that I am rusty in that area.  Perhaps next week I'll blog about AB Calculus or I'll blog about meta-analysis of my teach 180 blog from last year. (Spoiler: I am about 1/3 of the way through and definite themes are emerging!!)