## What oral exams taught me

In my course for elementary education students, I once again gave oral exams—this time for the final exam. Here are two take-aways from the oral exams.

First, I need to do some peer instruction next time. In particular, students had a difficult time understanding the difference between the “whole” of a fraction and the “denominator” of a fraction (Consider “$\frac{1}{2}$ of a mouse” and “$\frac{1}{2}$ of an elephant.” Both have a denominator of “2,” but the whole of the first is “mouse” and the whole of the second is “elephant.” This leads to different meanings. I think that three clicker questions would eliminate this.

Second, I was shocked at how ineffective my lectures were. The oral exam questions (which they also had to create screencasts for) were ones that were previous done in class (for example: why does inverting and multiplying give the correct answer to a division problem?). The process was this: students would figure out why the algorithm works, and then present at the end of a class period. I begin the next class period by giving the same argument. Other class periods begin with students presenting on similar questions, the class evaluating the presentations, and—if needed—me presenting the correct explanation.

Furthermore, I gave the answers to each of the oral exam questions on the last day of class. Test test So students saw the answer to each oral exam question at least three times, and probably more (especially since I had students view other students’ video solutions).

I was concerned that students would simply memorize these explanations. This simply did not happen. Either students understood the algorithm (I can tell from the oral exams—these students could answer any question that I had on the algorithm) or students did not understand any portion of the algorithm.

Most puzzling is that, in my student evaluations, some of my students complained that they were never shown how to do the algorithms correctly. This is in spite of seeing a completely correct solution to every problem between 3 and 10 times. I can only explain this in two ways:

1. Somehow students did not understand that the solutions they saw were solutions to the problems from the oral exams and screencasts. This would mean that I did not clearly communicate the intent of presenting the solutions.
2. Lecture was monumentally ineffective in helping them learn—so much so that students did not even remember that they occurred.

Do you have any other ideas?

### 14 Responses to “What oral exams taught me”

1. Joss Ives Says:

Hi Bret,

There’s nothing quite like those moments of clarity when you discover how ineffective your lectures are: “But I explained it clearly to you three different times!” 😦

• bretbenesh Says:

Hi Joss,

I know! I had come to terms with students having misconceptions from my lectures, but not even knowing that they had been lectured to (repeatedly)? That was shocking to me.

Also, I am glad that you can read my post. I am having severe problems with text disappearing. Bret

2. Hitchman Says:

The complaint about “not having been shown the algorithm” is expected, disappointing and baffling.

But maybe it really shows this: Those students haven’t taken responsibility for their learning. I mean, it sounds like everyone had the message that these were important. Somehow, these students still think it is your fault they don’t understand it. It is _their_ problem. They have to see it gets fixed. So, I would work on something that helps bring out the message that students are responsible for learning, and you are responsible only(!) for making an environment where that can happen.

• bretbenesh Says:

I think that this sounds right. This means that I need to improve my communication in this realm, too (Repeated “Part of the purpose of this class is for you to develop the skills so that you can teach yourself a new topic if you need to teach it 7 years from now while teaching” did not seem to work). Bret

3. Andy "SuperFly" Rundquist Says:

I think I agree with Hitchman about student responsibility. I think, though, that I might use the word “ownership” instead. Students watch you and other do something, but maybe don’t quite get that they’re supposed to own it. That’s one thing I’ve seen improve as I’ve done standards based grading.

4. gasstationwithoutpumps Says:

Frightening that these students are the teachers of tomorrow, isn’t it?

• bretbenesh Says:

Definitely for some of them (particular the ones I was thinking about while writing this post). On the other hand, I really think that the most will be competent at teaching mathematics, and a few will be fantastic. Most made huge strides this semester; it is understandably difficult to change your mode of thinking about mathematics in one semester.

So I feel like we are making slow progress. But I agree that even this progress is not really fast enough for what our children will need (which makes homeschooling that much more appealing, right?). Bret

• gasstationwithoutpumps Says:

Unfortunately, even the teachers who are competent at teaching the average students sometimes fail miserably at teaching the gifted students. It takes a greater depth and breadth of understanding of the math to be able to teach past the level of “proficient”.

I’m not sure that the “part-whole” mental model for fractions is the most robust one—especially if it leads to confusions like the one you describe here. Will these teachers be able to explain fractions like -7/-5 to the kids who jump to ideas like that without prompting?

• bretbenesh Says:

With all due respect to you and your son, gifted students are the least of my concern in these teacher education courses. I consider the course to be a success if a large percentage of the future teachers are to a point where they will be able to teach the average students. I do not see a way of training future teachers to teach gifted students without first getting to the point of being able to teach average students.

Similarly, I agree that the part-whole model is not the most robust one. However, I am skeptical that teaching more complicated notions of fractions before the part-whole model will lead to better understanding for the future teachers.

I am happy to be proven wrong here.

• gasstationwithoutpumps Says:

I agree that getting the teachers to the point where they can teach the average students effectively is an important goal, and that it has to be met before we can work on getting the teachers past that point to where they can effectively work with gifted students.

Unfortunately “gifted students are the least of my concern in these teacher education courses” seems to be the rule for almost all teacher education courses, with the result that there are very few teachers being produced who know anything about teaching gifted students. It may not be your biggest concern, but it is a huge concern for the parents of the 5–10% of kids who are gifted. That’s a lot of kids whose needs are being ignored.

5. Kinder, Gentler Oral Exams « Science Learnification Says:

[…] Benesh wrote a couple of posts (1, 2) discussing his use of oral exams. His format it closer to mine than it is to Andy’s, but […]

6. Kim Nicholas Says:

I wonder if the problem is inherent with lectures, rather than the lecturers or the lecture recipients. See the learning pyramid for knowledge retention: http://pegasus.cc.ucf.edu/~tbayston/eme6313/learn_retention.html

This would imply that lectures are the least effective way to convey information, and we would be better off designing/using fewer, high quality activities rather than more, overwhelming, fancy lectures. When I taught a class in Korea this summer, I ended up using the board (rather than ppt) because of language barriers, and I found I really liked it, it made me slow down and go at a more reasonable pace, and I think the students were more engaged. However designing meaningful activities for student learning is a lot more work and more variable than lectures! (and more pushing the comfort zone.) Some good ideas here: http://sciencecases.lib.buffalo.edu/cs/collection/websites.asp

• bretbenesh Says:

Hi Kim,

This is definitely the direction I am trying to move. Everything that I have read suggests that the benefits of lectures can mostly be achieved through other methods that have fewer drawbacks. So I am making the transition.

And it is nice for you to come over to the blackboard side—the mathematical community welcomes you!
Bret