## Grading for Probability and Statistics

Here is what I came up with for grading my probability and statistics course. First, I came up with standards my students should know:

“Interpreting” standards (these correspond to expectations for a student who will earn a C for the course.

1. Means, Medians, and Such
2. Standard Deviation
3. z-scores
4. Correlation vs. Causation and Study Types
5. Linear Regression and Correlation
6. Simple Probability
7. Confidence Intervals
8. p-values
9. Statistical Significance

“Creating” standards (these correspond to a “B” grade):

1. Means, Medians, and Standard Deviations
2. Probability
3. Probability
4. Probability
5. Confidence Intervals
6. z-scores, t-scores, and p-values
7. z-scores, t-scores, and p-values

(I repeat some standards to give them higher weight).

Finally, I have “Advanced” standards (these correspond to an “A” grade):

1. Sign Test
2. Chi-Square Test

Here is how the grading works: students take quizzes. Each quiz question is tied to a standard. Here are examples of some quiz questions:

(Interpreting: Means, Medians, and Such) Suppose the mean salary at a company is \$50,000 with a standard deviation of \$8,000, and the median salary is \$42,000. Suppose everyone gets a raise of \$3,000. What is the best answer to the following question: what is the new mean salary at the company?

(Interpreting: Standard Deviation) Pick four whole numbers from 1, . . . , 9 such that the standard deviation is as large as possible (you are allowed to repeat numbers).

(Creating: Means, Medians, and Standard Deviations) Find the mean, median, and standard
deviation of the data set below. It must be clear how you arrived at the answer (i.e. reading the answer off of the calculator is not sufficient). Here are the numbers: 48, 51, 37, 23, 49.

Advanced standard questions will look similar to Creating questions.

At the end of the semester, for each standard, I count how many questions the students gets completely correct in each standard. If the number is at least 3 (for Creating and Advanced) or at least 4 (for Interpreting), the student is said to have “completed” that standard (the student may opt to stop doing those quiz questions once the student has “completed” the standard).

If a student has “completed” every standard within the Interpreting standards, we say the student has “completed” the Interpreting standards. Similarly with Creating and Advanced.

Here are the grading guidelines (an “AB” is our grade that is between an A and a B):

-A student gets at least a C for a semester grade if and only if the student “completes” the Interpreting standards and gets at least a CD on the final exam.
-A student gets at least a B for the semester grade if and only if the student “completes” the Interpreting and Creating standards and gets at least a BC on the final exam.
-A student gets an A for the semester grade if and only if the student “completes” all of the standards, gets at least an AB on the final exam, and completes a project.

The project will be to do some experiment or observational study that uses a z-test, t-test, chi-square test, or sign test. It can be on any topic they want, and they can choose to collect data or use existing data. The students will have a poster presentation at my school’s Scholarship and Creativity Day.

I would appreciate any feedback that you have, although we are 1.5 weeks into the semester, so I am unlikely to incorporate it.

### 11 Responses to “Grading for Probability and Statistics”

1. TJ Says:

I like this. It seems like a good first cut. Keep your fingers crossed and let us know when you figure out what is wrong with it.

• bretbenesh Says:

Here is the first thing that is wrong with it: I want to give them quizzes most days, and this requires about 10 minutes of class. This extra class time is itself a problem, but the larger problem is that I need to be aware when there is 10 minutes left in class.

I did not realize that in my second class today; they did not get a quiz today.

But I suppose that is separate from the content of this post, which will also fail somewhere soon enough. Bret

• gasstationwithoutpumps Says:

I have always had trouble scheduling things at the end of class. Do the quiz at the beginning, then adjust the rest of the class to fit the time.

• bretbenesh Says:

See, I feel the opposite. If a student finishes the quiz early, I want them to be able to leave rather than to wait around for everyone else. It just seems like a more efficient use of everyone’s time.

• gasstationwithoutpumps Says:

My problem is that I always have so many things to talk about with the students and so poor a time sense, that I tend to run over. I don’t think that I could leave 10 minutes at the end of class for a quiz without having a big timer that interrupted us in the middle of doing something.

• bretbenesh Says:

Yeah, I had to train myself to end class early. The trick that worked: I started telling myself that class ended at 10:40 rather than 10:50. I completely fell for it (thankfully). Bret

2. Joshua Bowman (@Thalesdisciple) Says:

I like your scaffolding of the standards in a way that shows how some of them require more advanced thinking, or a greater mastery of the material. As in my system, this seems to have a lot of flexibility for assigning the final grades, but you also seem to have a clear sense of how much students will have to rely on the “interpreting” and “creating” standards to get the “advanced” ones.

I wonder if I shouldn’t add quizzes into my assessment tools, rather than just homework and three tests… But I understand the difficulty with remembering to leave the time at the end.

• bretbenesh Says:

Unfortunately, I think that the scaffolding is less clear to me than you think—I think you might be giving me too much credit. I was _hoping_ to do that, but I do not think that I succeeded. The main problem is that this is my first time teaching the course and I am not a content expert, so I do not really fully know how everything works together. But I am happy that you like my _plan_ to do that.

I have come to rely heavily on quizzes. I prefer them to tests because they are similar, but with lowered stakes (although I do have a final). I want homework to to be for feedback, so that is out (although your system has potential). Basically, quizzes simply work for me until I figure out a way to do more “authentic” assessments.

3. Joss Ives Says:

Bret. I quite like the quiz questions you posted. They get at the heart of the concepts instead of allowing them to blindly mash numbers into a calculator.

My quizzes are always of somewhat indeterminate length such that I have to give them at the start of class instead of the end.

Do you also use the projects to assess standards?

• bretbenesh Says:

Hi Joss,

I probably should give the quizzes at the beginning of class, too, but I want to protect my class time. I feel that this is okay because each quiz is such low stakes that students don’t need to do all of it.

I do not use projects. The main reason for this is: I haven’t figured out how to do it yet. In principle, I would like to use projects; furthermore, I would like the students to figure out which standards they have been assessed on on those projects. But that is a task for another semester.

It would be great if you wrote a blog post on how to do that! Bret

4. Assessment Idea for Calculus I: Feedback desperately wanted! | Solvable by Radicals Says:

[…] differs from how I did things in the past, in that I used to list “learning goals” as very broad topics (so they weren’t learning goals at all, but rather “topics” or “types of […]