I’m spending a good chunk of the morning grading the exam that I gave yesterday, so here’s a poll on what you might call exam philosophy. Our classes are small, so the bulk of our exams are free-response problems, and we tend to break those problems into sub-parts (1a, 1b, 1c, etc.). There are two approaches to writing these questions that I have seen: one is to use the sub-parts to break a single problem into steps, thus leading students through the question; the other is to write questions where the sub-parts are independent, so that a student who has no clue how to answer part a can still go on to parts b-f without needing the answer from a.
There are reasonable arguments for each of these, so I’m interested to hear what other people think:
The exam in question is about classical E&M, so you can only choose one answer, not a superposition of multiple answers.
Cumulative answers are more reflective of how most real use of the physics goes, and I think occasionally students can actually learn from such an the exam, if it’s constructed well. That said, it’s important for grading with cumulative answers to propagate answers (so that if they get part a wrong, but correctly do part b with the wrong answer from part a, they get full credit for part b.) Which is a pain to grade.
Not physics here, but math and statistics. I usually don’t give multi-part in-seat tests, but do use those types of questions on assignments and examples. I also explain that the problems are broken down into parts to illustrate the components of the entire process, and my students (should) know that a single question on an in-seat exam quite often requires them to put all of the individual pieces together, without prompts from me.
It’s funny how I know immediately what you mean…To a certain extent you can combine both approaches. For example, you can have them derive some equations (but giving them the answer, i.e :derive X using y), then they solve those equations the next step. Or you can ask them to find the equations themselves, and then let them solve similar ones you give them (that’s still a multi-poart question if they are related to the equations they had to derive).
But, if I had to choose, all parts should be independent. I can imagine it being extremely frustrating to get stuck in the first part of a multi-part question, without being able to proceed. Besides, how would you grade a part that was done correctly, but started with the wrong premise? Can you even tell the difference always?
I voted for (b), but what Andrew Foland said. As long as you propagate answers you won’t be unfairly penalising someone who made a simple mistake in the first part but correctly answered the rest.
I voted A, but otherwise agree with Moshe… I always tried to make it cumulative, but you could still do part B without part A…
My tests are often about 50% multiple choice on conceptual questions (MC being faster to grade for three classes of students than short paragraph answers) and 50% problems. Many problems are independent questions, but I also ask questions where part a needs to be used to answer part b. However, when I grade part b, I assume that their answer to part a was the right value. Instead of marking it with a check though (meaning its the correct answer), I mark it with an “OK” to say they did the right thing with wrong values.
It is a pain to grade, but I feel that students need to be exposed to problems that aren’t just one-step solutions. Most problems encountered in the workplace aren’t one-step solutions, or the boss would have done it himself and saved the company your paycheck…
Giving multiple guess bubble sheet exams is the no-brainer: much quicker to grade and students who contest the grade can’t claim subjectivity in the scoring of responses.
I’m Attention Deficit– Oh, Shiny! but if I’m focusing on a test, multipart questions really aren’t harder in that regard than taking each question one at a time. Maybe less so, because one isn’t having to visualize a new set-up from scratch each time, and it allows time to hyper-focus, whereas changing problems is an interruption of thought requiring refocus.
I do love it when answering one question correctly leads to an easier answer for the next question, BUT, the issue of cumulative error is scary for the student. OTOH, sometimes the second part *leads* to catching and correcting the error in the first, when you get to the “that can’t be true” moment.
So it’s a hard decision, but I think a few multiparters can be good for the students and lead to deeper understanding and doesn’t trip up the ADD kids unduly.
But I clicked the “being of pure thought” button because I saw the question as too complicated for a simple answer. 🙂
The question is, can you grade freely or are you subject to a curve and a “minimum pass” requirement? I always thought cumulative questions give the A students the spot to shine and separate out those that can only deal with memorized answers for given problems. But as a result you get a lot of A and a lot of low scores, which can get you in trouble if you’re supposed to curve to pass 90% or so (bimodal distributions hate Gauss curves).
Sorry, but I do cumulative and independent about equally, particularly in E+M. Further, I consider “independent” parts to be a distinction without a difference because they could easily be numbered separately, as in “for the same situation described in problem 5 …”
For example, I frequently have circuit problems where later results depend on earlier ones, but I am pretty careful to have the hardest sub-parts independent of each other. On the other hand, it is just convenient to ask several independent questions about various Gauss, Ampere, or Faraday situations.
@1 and @4:
Careful design is critical. You don’t want to make part b depend on part a if there are, say, 20 different wrong answers possible in a class of 30 students. That way lies madness. You also need to decide in advance how to grade a “solution” where a wrong answer to part a leads to a correct answer to part b, whether it is by “equation grabbing” the answer (skipping the physics introduced in part a) or cancelling math or physics errors.
I also learned to avoid asking them to set up and then evaluate an integral, given the odds that a minor error can turn an easy problem into a nearly impossible one. Set up is enough to find out if they know what they are doing.
I do both independent and cumulative questions. I do make sure that if students get part A wrong but use that answer correctly in part B to get an answer consistent with their part A, they get most of the part B credit.
It’s harder to grade, but more forgiving of an early error and still allows for a complex problem set-up.
Although cumulative would better represent professional experience, I voted for independent just to avoid penalizing student who actually know the stuff but made a stupid error in the beginning.
Most of my undergrad physics classes used type A questions but rarely more than 4-5 layers deep.
One thing most of my professors did however is if you got stuck on part A they would give you the answer and deducts the relevant number of points. Typically by writing it all in red pen right at the time. This may only work however in small classes.
To give a feel for the department size the biggest upper level physics class I ever had had 13 people for first semester E&M 1. 3-6 students was typical. I never has any single person classes but they were not uncommon.
Philip