The first assessment I provide is the last homework for Introduction to Statistics. It covers the topic of the One-way ANOVA test. I don't frequently get to cover all the end matter in our course textbook, which includes Chi-Square test, ANOVA, and Inference on Regression. Generally, I will choose one chapter and cover it on the last day of class. I have taught one-way ANOVA twice in my four semesters. I've assigned the problems you see both times.
I have several goals for this particular homework assignment. I break them down into three sections:
I chose homework problems that give insight into the ANOVA method. That is, I chose problems that (a) would have the students explore the data in order to check required ANOVA conditions, (b) would have the students execute ANOVA, and (c) would require students to analyze their data.
I allow students to use R to aid with the analysis in each problem. I do this so that students may have a small experience of what problems a modern day statistician might attempt to solve and how a modern day statistician might solve them.
In my class, homework is used as a learning experience, and so they aren't weighted heavily. Primarily, I care about completion because exposure is very important. However, I do give feedback on each problem so that students will have something to use when they study for exams.
The primary difference between the times I have assigned homework is that the first time I assigned the homework as recommended and the second time the homework was a requirement. The first time I assigned the homework as recommended because I believed students would do it in order to prepare for the final exam which required their knowledge of ANOVA. I found this not to be true. Therefore, I made the homework a graded assignment the second time, though the grade is not a significant portion of their final homework grade.
In the sample homework I provide, it is clear I did not meet many goals. For instance, my goal of exposure. This particular student did not do all the problems, nor did they complete all the problems they began. Additionally, my goal of mimicking a statistician's approach was not met since this student did not use R in their write up.
I did meet part of my first goal, however. This student did explore the data in order to verify conditions, even if their conditions weren't always correct. This student also successfully analyzed what the F-statistic and P-value indicate in the beginning problems.
The goals that are met or unmet seem to depend on the student. There were many students who enjoyed this homework and fulfilled each of the goals. I chose a homework where I was unsuccessful in order to display contrasting assessments. To fulfill each of my three goals in the future for all students, I may
Place more emphasis on how homework problems are written up. The homework on display is pretty sparse and could have all steps on scratch paper.
Place more emphasis on the use of R in homework. The statistical software is not separate from statistics, and should be not be treated as such.
Grade homework more heavily so that students take it more seriously. I am reluctant to do this because then homework can damage a student who is slower to learn than others. In addition, doing this makes homework more intimidating than the simple practice students need.
For the second assessment, I provide two exams for Linear Algebra. I choose exams from Linear Algebra because I taught this course for one term only. I want to demonstrate that my teaching is constantly modifying while I am teaching a course, not simply between semesters as artifacts from Introduction to Statistics illustrate. As a graduate student, I was a teacher assistant three times for a linear algebra course. However, there is a stark difference between simply grading material based on a solution set and creating your own material so that students who understand can do well and students who do not understand will find out. Exam 1 is my first attempt at creating an exam for this course. Exam 3 is the result after trial and error during the term.
I have several goals for my exams.
I want to test how comfortable students are with material they have already seen by
giving slightly modified versions of problems already solved in order to determine whether they've learned from earlier experiences,
giving brand new problems that require students to think critically prior to solving the problem.
I want an exam length such that no student needs more than 55 minutes but no student will be able to complete the exam in less than 40 minutes.
An exam, to me, is not the proper place for surprises. Therefore, I attempt to avoid problems that will take students longer than 10 minutes.
Although the student's exam 1 has a decent grade, I did not meet all my goals. Goals 2 and 3 are failed.
For example, the first problem is a modification of a problem the students have experience with and they knew how time consuming finding a 3x3 inverse can be, even when done correctly step-by-step. Many students made mistakes along the way and had to redo the Gaussian Elimination. I made the mistake of assuming that the students can do Gaussian Elimination as seamlessly as Matlab.
Additionally, problem two is also not a new problem but students spent quite some time learning to find a basis for a subspace. This problem did not take 10 minutes, on average. In addition, like the example shown, students did not show their set of vectors were linearly independent or span the subspace. They stated this fact without checking. Because their statement was true, I felt I could not remove points since I did not ask them to check.
Finally, the third problem was completely new to students, and poorly written. I began with example matrices A and B. I wanted students to solve (a), (b), and (c) for the general case. Again, I could not remove points since it was my fault that they did the problem for the specific A and B.
Many students did not do well on this exam, even students I knew understood the material relatively well. There are only 4 problems and each problem was 25 points. I chose 4 problems so that students could complete the exam in 55 minutes. However, I did not foresee the number of mistakes the students would make. I learned that what I feel is an easy exam is not to those who are learning the material for the first time. My goal for future exams was to design them based on the failures of the first exam.
I display the third exam because it should meet all my goals for exams.
The first goal is met once again. The following problems are modified versions of problems from a practice exam: 2 and bonus. The following problems are modified versions of homework problems: 4 and 5. The remaining problems were new but tested them on material the students have seen prior to the exam. Problem 1 is tricky and I expected only the students who understood the material well to find a solution. I was quite surprised when most of the students did so.
I believe the second goal was also met. Many students attempted the bonus problem, as the student artifact shows.
Since there are 5 problems and a bonus and many students reached the bonus, it must be that my third goal is also met.
I chose problems that were not as time consuming. The students were also better prepared for the exam thanks to an increased number of homework problems and a practice exam from which I chose their problems. In addition, I provided the students with more problems, reducing the number of points each problem is worth. These seemed to helped students do better. In the future, I will follow a similar plan of action regarding exams.