Fun, visual ways to give students a 1:4 probability

May 31, 2018 4:12 AM

My students will take 4 quizzes. To prepare for each quiz, I will allow them to fill one index card with notes or formulas that they will have a 1 in 4 chance of being able to use during the quiz. Just the act of writing down notes concise enough to fit on a card helps students organize and prepare very well, but they are more motivated to use this method with an incentive. I picked giving them a 1:4 probability of being able to use their notecard during the quiz, making it 'open note,' and am now brainstorming fun ways to carry this out. I could do a double coin flip, where either heads or tails is called, and two coins have to display what was called. Or I thought about filling 4 beakers full of water and adding food coloring to one and then covering them and getting someone to randomly pick one. Any other fun things I could try?
posted by cristalina to Education (20 answers total)

I'm a teacher and I think this is a really swell concept, but I would rethink the payoff. You may not get a lot of buy in for a 25% chance.

Maybe raise the probability to 50% or even 75%, or better yet, change it so they can use their notes, but it will be for either 25%, 50%, 75% or 100% of quiz time. I think of my more challenged students, and they would totally make those notecards if they knew that they would be able to use them, always, for even 25% of the quiz time.
posted by yes I said yes I will Yes at 4:25 AM on May 31, 2018 [25 favorites]

Like a classic combinatorics question. Put m black and n white marbles in a bag. Draw # of balls. Is the number of white balls drawn in tne 1st, 2nd, 3rd, or 4th quartile of tne expectrd distribution?
posted by SemiSalt at 4:31 AM on May 31, 2018

They can write their names on 4 cards, fill in one, and you hand out one of the cards at every quiz. The way my brain works, even having an empty card would help me visualize what was on the filled-in one.

An additional incentive could be that if they have a study card, but don’t get to use it, they get bonus points, 5 extra minutes, something like that.
posted by tchemgrrl at 4:54 AM on May 31, 2018 [1 favorite]

If you don't mind bumping the probability up to 1/e (about 37%), here's a neat trick. Put a bunch of labeled items in one bag, and the same set of labeled items in another bag. Draw one item from each bag simultaneously. If they're the same, no notes; if they're different, set the drawn items aside and draw again. If you empty the bags without ever drawing the same item from both at the same time, they get notes.

The interesting thing about this is that it's not particularly dependent on how many items you put in the bags in the first place: as long as there are at least 4 per bag, the success probability is about 37%. This is known as the Derangement Problem; a search on that name can bring up explanations of the mathematical phenomenon dictating its probability.
posted by jackbishop at 4:56 AM on May 31, 2018 [9 favorites]

Obviously you know your students, but I just thought back to my school days and feel compelled to say that the inherent unfairness of arbitrarily deciding who gets to use their notes would have made me anxious and upset to the point of deincentivizing me to write them.
posted by STFUDonnie at 5:05 AM on May 31, 2018 [39 favorites]

Roll a ginormous d20.

(d20 so you can do other probabilities too)
posted by GCU Sweet and Full of Grace at 5:11 AM on May 31, 2018

I just thought back to my school days and feel compelled to say that the inherent unfairness of arbitrarily deciding who gets to use their notes would have made me anxious and upset to the point of deincentivizing me to write them.

Actually yeah; can you clarify this? I took it to mean that the probability question will apply to all students, and they will either get to use their notes in 1 of 4 tests, 2 of 4, 3 of 4, or all 4. If the probability is individualized to each student, this would not be fair.

I still think it's a better idea to let all the kids use their notes and have the probability determine how many minutes they get to use them for all the quizzes, not how many quizzes out of 4 they will get to use the notes. This will also teach them good test-taking strategies; knowing you can only access your notes for a few minutes will help them develop focus.

(Being a good teacher is hard.)
posted by yes I said yes I will Yes at 5:30 AM on May 31, 2018 [9 favorites]

I didn’t see an age? 9 year olds tend to like different things than 17 year olds.
I like urn problems as much as the next guy but not sure they have mass appeal.

This sounds like a good excuse to build a plinking machine, everyone loves Plinko.

Also agree the chance is too low, the kids who will get the most help will mostly skip, and this could well serve to favor those who are already high achievers.
posted by SaltySalticid at 5:38 AM on May 31, 2018 [3 favorites]

I teach high school, and I have a specific test where I let the students bring in a note card for the discussion portion of the test. They do not use the car for the fact-based multiple choice. They think this is fair.
posted by Sauter Vaguely at 6:26 AM on May 31, 2018 [2 favorites]

I'll just second the anxiety bit...I was thinking of answering earlier but I didn't want to derail the question, and I know your intentions are really good.

If these are low-stakes tests then I think it would be okay, with the additional explanation that creating the index card has a benefit to me as a student. But if these tests count for a lot of marks in aggregate, I would have found it a situation that would throw me off, and especially in math, that could torpedo my ability to think clearly for part or all of the test. One of my two kids is the same way. I didn't know what it was when I was in school but I now recognize it as anxiety.

I think there are so many fun ways to demonstrate probability that it seems like it could be easily separated from a situation where students are being evaluated. I know that sounds like being a wet blanket but quiet honestly, this kind of game that teachers play to "make students think on their feet" or whatever is one of the reasons I went from loving school to becoming distrustful of school.
posted by warriorqueen at 7:14 AM on May 31, 2018 [1 favorite]

I thought about filling 4 beakers full of water and adding food coloring to one and then covering them and getting someone to randomly pick one.

I wouldn't do anything that requires a single student to participate in the outcome, even if it truly is 100% blind. Kids are mean to each other and if a Not-So-Popular Kid chooses one of the "wrong" beakers, there's a non-negligible change their classmates will them a hard time over it.
posted by schroedingersgirl at 7:24 AM on May 31, 2018 [5 favorites]

Any student who brings in their filled-out notecard gets a 1-in-4 chance of an automatic A on the quiz.
posted by xo at 7:31 AM on May 31, 2018 [2 favorites]

I feel like this could be disappointing to your students because understanding probability is hard. Even I, as an adult and former math teacher, read your scenario and initially thought, okay, cool, the students will definitely get to use notes on at least one of the four quizzes, but that's not actually the case if each quiz has a 1 in 4 chance of getting to use the cheat sheet.
posted by coppermoss at 8:05 AM on May 31, 2018 [1 favorite]

Besides the problems others have pointed out, how are you going to write this quiz. That is, what will the questions look like, because the kind of questions you write for an open-book test are very different from the kind of questions you write for a closed-book test. Will you have two stacks of tests ready to go?
posted by If only I had a penguin... at 8:17 AM on May 31, 2018 [1 favorite]

I appreciate the intentions here, but putting the ability to score better on a test to chance, even if it's a perceived ability, is really really going to stress a bunch of people out and have unintended consequences. I too didn't want to answer at first for fear of derailing the question, but my initial thought was that this was not going to go well at all.

I love the idea of using real-world examples to teach probability, but tying it to a score on a test is not the right way to do it.
posted by cgg at 8:38 AM on May 31, 2018 [4 favorites]

I would be extremely resentful of this, because I would want my evaluations to reflect what I've learned - not whether or not I was lucky. I probably wouldn't bring a card at all, although I would have studied. Applying it to the whole class is slightly less unfair, but not entirely unfair, and believe me, students are perfectly capable of feeling aggrieved as a group. And there will also be students who will resent making a card and not being able to use it, in the likely even that they lose.

From an instructor's point of view, I think that this undermines the purpose of an evaluation, because you've left what you're evaluating partially up to chance (memorization and application vs. application).

I just see this backfiring on you. If you want to demonstrate probability with the quiz, can you do something with this idea that doesn't affect the evaluation? E.g., deciding which portion of the quiz they do first, what color copy the students get, etc.
posted by Kutsuwamushi at 9:35 AM on May 31, 2018

A different way to do this might be to cut index cards in half so that students have multiple mini-cards. Then roll a d4 or do another method of randomly determining how many of those cards they get to have available for the test. This way they always get to bring at least one card with them, and it forces them to prioritize the information?
posted by Garm at 9:37 AM on May 31, 2018

If there are a ton of formulas, asking them to MAYBE commit them to memory may be setting them up to fail. Being given a list of formulas and knowing what to do with them are two different things. Perhaps yes I said yes I will Yes's idea of giving it between a 25% and 75% of the time of the test with your card but maybe give them a short list of formulas. I dunno, I went back to school as an adult and I feel like it's given me a perspective on test taking I lacked before. In chemistry, stat, and physics, there are just so many formulas and, in the real world, you are going to have the ability to look that formula up. Knowing how to use it is the real skill.
posted by Foam Pants at 9:45 AM on May 31, 2018 [1 favorite]

Response by poster: Thanks for the discussion here, everyone-- lots of great points I hadn't considered.

For more context, these are adult students of a terminal trade school for a manual skill where final grades do not have any real bearing on their future profession... essentially, you either pass or fail the entire program, and it is definitely designed to keep graduation rates high. Which is to say, the quizzes aren't especially stressful to most students as the real coursework is a project.

I shouldn't have said formulas in my question, since there are only really two testable concepts that use a fairly basic formula... I just remember being encouraged to use the index card strategy in my science classes, and had formulas on my mind.

I wouldn't have had some students have an advantage of notes and others not, the whole class would be able to use them. And I didn't intend for it to demonstrate probability or chance events... its just very common for instructors here to drop the lowest 1 of the 4 quizzes and I was considering doing something a little different this time around, but I will be reconsidering that approach with your input in mind.

Sorry to have concerned some of you with how this idea might have really stressed you out as a student! Thanks again for your feedback!
posted by cristalina at 10:06 AM on May 31, 2018 [4 favorites]

I share others' concerns about the idea as I originally read it, and am happy to see the followup response.

One idea that would make the whole thing a lot less stressful might be to hold the draw a week ahead of time. Finding out whether or not you get a note card while you still have time to change your study choices would have made me a lot happier as a student. It doesn't add motivation to write note cards for the other tests. But, no draw will be more motivating than just letting them use notes for all four tests. (Which sounds like a fine option to me.)

Assuming you do choose a lottery, how about tying it to something unpredictable that exists in the real world? For example, "was there an Earthquake somewhere in the world above magnitude 6.0 during any specific 14 hour period" gives you very nearly a 1:4 chance. (source)
posted by eotvos at 2:00 PM on May 31, 2018 [1 favorite]