# What is a healthy and effective way for a math educator to evaluate his or her performance?

Educators are constantly evaluated by at least the following methods:

• Anonymous evaluations collected from students by the school
• Anonymous evaluations posted online by students
• Grades or pass-rates of the students in the class

Experienced educators have all learned to not read too much into any of these.

So, if you would like to evaluate your own performance, what is an effective method?

I think some good answers may be specific to mathematics, otherwise I would post the question elsewhere.

One place to look is in the following source:

National Research Council. Evaluating and Improving Undergraduate Teaching in Science, Technology, Engineering, and Mathematics. Washington, DC: The National Academies Press, 2003.

There is free online access, and Chapter 5 (Evaluation Methodologies), includes a section specifically on Self-Evaluation for STEM instructors at the undergraduate level.

Chapter 6 (Evaluation of Individual Faculty: Criteria and Benchmarks) may be worth a read, as well.

For more information on the book, see the Executive Summary and Background on Committee Members.

• Thanks! I think Jim's answer is the most fascinating and interesting, but I'm accepting this one as the one that best answers the question. Commented Mar 28, 2014 at 20:43
• The only thing I would add, if it is not listed in the sources above, is that the regular use of formative assessments can help you judge the effectiveness of your teaching before the end of the semester, which helps you make changes when they will make a difference for this group of students. Commented Apr 7, 2014 at 10:44

Though faculty are often skeptical of student evaluations, research suggests that student evaluations are an effective tool for evaluating teaching. Here is a link to a meta-study that surveys the results of approximately 1500 other studies on student evaluations:

Cashin, "Student Ratings on Teaching: The Research Revisited"

Here are some of the major conclusions of the paper:

Correlation to Exam Scores

In courses with multiple sections and a common exam, there is between a 0.3 and 0.5 correlation between an instructor's evaluation scores and the students' scores on the common exams. The paper notes that it is rare to ever find correlations above 0.5 in the social sciences when studying complex phenomena.

Correlation to Instructor Self-Ratings

When instructors are asked to rate their own teaching effectiveness, the answers they give have approximately a 0.29 correlation with student evaluations. In addition, when instructors are asked to rate how their effectiveness varied over different courses they have taught, the instructor's answers have roughly a 0.45 correlation with student variation in evaluations across those courses.

Correlation to Ratings of Administrators and Colleagues

When instructors are rated by either their colleagues or by administrators, the scores they receive have between a 0.45 and 0.7 correlation with student evaluation scores. Of course, colleagues and administrators might be basing their score on student evaluation scores that they have seen.

However, ratings by trained classroom observers (who have not seen student evaluation scores) also have 0.5 correlation with student evaluation scores.

Further Discussion

Based on this research, I think that it is reasonable to take student evaluation scores into account when analyzing the effectiveness of your own teaching. From a particular instructor's point of view, the 0.45 correlation highlighted above has the most relevance: it means that you can tell which courses you did a good job in based on student evaluations.

Of course, there are some other effects that need to be taken into account. Classes full of highly motivated students tend to give higher ratings than classes of reluctant students. Students in advanced courses also tend to give higher ratings than students in introductory courses. If your abstract algebra students consistently rate you higher than your calculus students, that doesn't necessarily mean that you're doing a better job in abstract algebra.

Finally, it should be pointed out in any discussion of evaluating teaching that there is no universally accepted definition of good teaching. You may perceive advantages or disadvantages in your teaching style that the students do not see, and there's no objective way to determine whether you are right. Ultimately, it's part of every teacher's job to form their own opinions on what constitutes good teaching.

dtldarek asks below whether the correlation between student evaluations and student exam scores might be due to instructors grading their own class's exams.

Cashin's study cites two other meta-studies for the results on exam scores: one by Cohen and one by Feldman. I haven't looked through the Feldman study, but Cohen's meta-study analyzes several methodological features, including who grades the exams. Of the 68 studies that Cohen analyzes, 10 had each teacher grade their own class's exam, 28 had some external evaluator grade all of the exams, and the remaining 30 had some other system (e.g. each instructor grades one question from all of the exams). From Cohen:

The only other methodological variable that correlated significantly with effect size was evaluation bias. The correlation between ratings and achievement was large when an external grader was used or when each instructor evaluated one part of the test for all students. For 10 studies in which achievement tests were evaluated by students' own instructors, the effect size was much smaller.

That is, the correlation between good evaluations and good exam scores is stronger when the exams are not graded by the teacher themselves.

• I found the correlation between an instructor's own ratings of their own classes to be compelling at first, but then highly suspect -- essentially, aren't you arguing that I should believe student evaluations because they correlate with my own self-evaluation? If this is the basis for deciding if ratings are "accurate," why not just use a self-evaluation to begin with? Or, instead, are you saying that student evaluations' correlation with all the other evaluations makes it likely that it does have intrinsic meaning? Commented Mar 26, 2014 at 19:00
• @ChrisCunningham The idea is that professors and students in general tend to agree on whether a course turned out well. So if you're trying to figure out whether a course turned out well, it makes sense to listen to the students. Commented Mar 26, 2014 at 19:17
• @ChrisCunningham I also find it interesting that this correlation (.45) is so much higher than the correlation (.29) for overall teaching effectiveness. If you trust instructors' opinions, this means that the students are better at comparing different courses by the same instructor than they are at comparing different instructors. (Or you might trust students' opinions more, in which case this says that instructors are better at comparing their own courses than they are at comparing themselves with other instructors.) Commented Mar 26, 2014 at 19:20

This is just a minor addition, but I talk to my students about it. In class I sometimes stop to take little show of hands surveys, e.g. "do you guys like it better if I start with an example and move on to the general formula, or vice versa?" After each exam and quiz I ask students personally how they felt about it, whether it was too hard or too easy, when they come up and turn it in. I don't mind criticism at all, and I encourage them to be honest with me about how things are going. And I have more lengthly discussions during office hours with those who show up. Of course this isn't a one hundred percent reliable way to quantify performance, but it helps me make little qualitative improvements to my teaching, with the side effect of making the students feel more empowered.

My own assessment is:

• Teaching training: do training, a lot:
• Enroll courses (better outside your area)
• Non-local knowledge:
• Do you know latest teaching theories
• Do you know what other countries do?
• Do you know any rellevant teacher outside your country?
• Non isolament:
• Do you know any other collegues outside your school?
• Do you collaborate with them?

If you answer 'yes' to many, then you are a good teacher.

It works for me.

There only one reliable way to do this, and it's also very straightforward and easy to do. Give your students a well-constructed, research-based test that measures their knowledge of the subject. Do this once at the beginning of the semester and once at the end. Subtract.

This gives you a number, which has interest only if you have something else to compare with. You can try to compare with your own past results, or with the results of your colleagues at your school, but generally the random and systematic errors make this difficult, and it also won't alert you to the case where you and your colleagues are both doing something wrong. It's better to compare with published results that have large sample sizes.

It's easy to do this. What's harder is to identify ways of improving your results (if they appear sub-optimal) and sustaining any such improvements over time against countervailing forces.