Posts Tagged ‘policies’

Grading for Probability and Statistics

January 23, 2013

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.

Gaming the Classroom

February 23, 2011

I had previously heard about Lee Shelton‘s effort to turn a classroom into a video game-type experience from several sources, although I did not know that he had created a website for it until Professor Hacker pointed me there.

Before viewing his website, I was simultaneously intrigued and concerned about his approach. I was intrigued because games clearly have a quality that gets people to devote large quantities of time and effort to them for very little outside purpose. It would be great to create an educational situation which causes students to have sustained, near-obsessional interest.

I was concerned it seems like such a set-up could easily devolve into a series of external motivators that ultimately decrease the student’s intrinsic motivation for the academic subject. Since I believe that we should be fostering an interest in learning for its own sake—not just to earn points—I was concerned about how the class was set up.

I have now looked through the site. I have only skimmed it, and I am far from an expert on gaming. Considering this, please take this next sentence with a grain of salt: I now no longer feel intrigued nor concerned; I just feel a little disappointed.

Largely from looking at the syllabus, it seems to me that the main difference in this class is that everything has a cute, gaming-type name. There are no “quizzes,” but rather “monsters to fight.” There are no “points,” but rather “XP” (“eXperience Points,” for those non-gamers out there). “Groups” of students are “guilds,” and “doing well on a midterm” is “defeating the level Boss.”

One feature I like is that it appears to have some sort of 0-1 grading scheme (you either get the XPs or you don’t), although I cannot tell if there is a mechanism for re-doing work that students attempt but do not succeed on. My opinion is that this is an essential component of a 0-1 grading system.

Largely, I feel that I am missing something. In the words of a mathematician, this seems “isomorphic” to any other classroom. Please let me know why this class structure deserves all of the buzz it is receiving—I want to go back to being intrigued and/or concerned about it.

Cooperative Homework Update

January 21, 2010

I finished grading my first assignment for my abstract algebra class, and all is well. I was particularly concerned about how the cooperative homework component would be perceived by the students—I worry about student reaction whenever I change the usual school procedure. In particular, I was concerned that students would not like having other students responsible for their grade.

It turns out that my students enjoyed it. I took a straw poll in one of my classes when I first introduced this policy, and only one student (out of 13) said he was nervous about the system. Everyone else felt either positively or neutral about the policy.

I used some class time to give students an anonymous evaluation of how the first cooperative homework assignment went. I asked some open-ended questions (“What went well?,” “What could your team improve upon?,” and “What could Bret do to help?”). I also asked the students to rank their experience on a scale of 1 (Bad Experience) to 10 (Great Experience). The high score was 10, the low was 5 (only 1 occurrence), and I think that the mode was 9. There seems to be good support for this policy.

Course Collaboration Project—Part 4 (Homework Policies)

January 2, 2010

With goals and content in mind, I can now focus on how to best get the students to learn the material. One aspect of this is homework.

This is a proof-based course. My theory is that there are three things that need to happen if you are going to learn how to successfully do proofs:

  1. You must read a lot of proofs.
  2. You must write a lot of proofs.
  3. You must analyze the proofs you read.

The third point will largely be done in class, since I do not think I can expect students to know how to analyze proofs. I have several ideas for formats that will allow the students to read and write a lot of proofs:

  1. I might have students evaluate their own homework. Students would give me a photocopy of their homework, but keep the original for themselves. I would create a solution key/rubric. They would use the rubric to evaluate the homework outside of class; perhaps students could comment on the “differences, omissions, and additions” of their proofs compared to mine, and comment on how important these differences/omissions/additions are. Students would email me their evaluation, noting the strengths and weakness of their proofs. I would spot-check their work by using the photocopied homework.
  2. I might allow students to resubmit unlimited attempts on homework problems to me. Problems would have two possible grades: “Near-perfect” and “Incomplete.” Students would resubmit until they received a grade of “Near-perfect.” I would provided detailed comments on their proofs to help them with the next draft.
  3. I might have students evaluate other students’ proofs as part of their homework. I would create a packet of 3-5 student attempts at proofs. Students would be expected to contribute to class discussions on the proofs.
  4. I might have “homework committees.” This idea comes from from Patrick Bahls. Here, a committee of 2-3 students would look 1-2 selected problems from the homework assignment. This committee would look at all of the student solutions that were submitted, categorize the different approaches that students used, and discuss the relative strengths, weaknesses, and validity of each approach. The committee would give a short summary of what students did in class.

I think a combination of these approaches would work well to get students to read, write, and analyze a variety of proofs. I am leaning toward a combination of the first three approaches. I am planning on giving 3-5 problems that the students will self-evaluate each “cycle” (6 school days=1 cycle). Students would additionally get 1-2 problems that students would be allowed to revise as many times as needed. I would use these revisable problems to create the packets for students to evaluate. On the fourth approach, I am in agreement with Patrick that the homework committees might create more overhead than I care to handle.

I am strongly considering following Patrick’s lead and teaching the class LaTeX. I would then require students to use LaTeX on the revisable homework, which would make their revisions easier.

The one point that have not settled on: I would like students to give presentations. I have not yet determine how this should relate to the homework. I welcome input on how I should organize the course—on the subject of presentations, or any other aspect of homework.