Surely not every question on a New York State math Regents should be completely straight forward. You want a test with a mix of some challenging questions so that students prepare for a test that is going to require a lot of thinking. But a challenging question should not be challenging just because it is poorly worded or ambiguous. In examining the recent Algebra II Regents, I have found way too many examples of ‘bad’ questions.
What is the appropriate number of ‘bad’ questions that should be permissible? If by ‘bad’ you mean poorly worded, confusing, ambiguous, or mathematically inaccurate, then there should be none of those. But I suppose it is a matter of taste how many ‘challenging’ questions there should be. For me these extra ‘challenging’ questions belong at the end of a unit test about a topic and not as 2 point multiple choice question on the Regents, but I suppose I should expect one or two of those that, in my opinion, were too difficult for the test, if the goal is to accurately assess how well students in New York State understand Algebra II.
I’m absolutely sure that when a curve is made EVEN BEFORE THE TEST IS ADMINISTERED saying that a 30% is going to be curved to a 65%, that is a serious issue. Making a test too hard, whether it is the good kind of hard because it required a lot of good mathematical thinking or the bad kind of hard where the question was worded poorly or ambiguous or just otherwise ‘bad’ is a mistake for a Regents. The Regents should be reasonable and should have no curve whatsoever. That should be one of the first goals in the creation of the test.
This is my last post about this particular exam, though I could do a similar thing for the Algebra I test and others, particularly Patrick Honner, have done a great job on the Geometry test.
One problem with multiple choice questions is that there is no partial credit for getting the ‘second best’ answer. So especially for a Regents test, you want to make the questions pretty clear otherwise you can’t distinguish a student who knows most of the material from a student who knows little of the material. For this question the part about “If she plans to run the unit for 3 months out of the year” is an unnecessary twist. I know that sometimes test makers like to put in extraneous information to check if a student can distinguish the relevant information from the irrelevant, but in this case I could see a student thinking this is relevant information, using it, and creating an equation based on this, which would already have an extra twist since it asking for cost per year instead of the typical total cost question, and still get no credit.
For a unit test on just this topic I wouldn’t have a problem with this being one out of 15 questions or something, just to make it tricky to get a 100 on the test, but for a Regents exam, it is not good test making to throw in this extra piece of irrelevant information with no opportunity for partial credit for following through on the question correctly after not realizing this.
This is an example of how a question can be simultaneously ‘interesting’ and also a ‘bad’ Regents question. This is a great application of the finite geometric series problem, and it is something that I do with my classes. But it is something that works well as a twenty minute activity, not as something that you try to do during a Regents in the multiple choice section. If students have not been exposed to this exact question, this would be a big challenge to decipher in the moment during the test.
And even if they really want to do this question, because it is ‘rigorous’ for them to apply the formula to an unfamiliar situation like this, the wording of this question is terrible. Earlier in the test they have a probability question that takes an entire page and is still confusing. In this one, they make this explanation way too short. It is also ambiguous since the answer depends on when she puts the money in and when she eventually takes it out. It seems to me that she puts the money in at the beginning of each month, but must take it out instantly after she makes her last deposit since if she waits until the end of the year, there will be more money in the account. If I needed to give this question, I would say
“Jasmine decides to open a savings account. On January 1st 2017 she puts $100 into the account. The account earns 3% a month compounded monthly. On February 1st 2017 she puts another $100 into the account. She continues this until December 1st 2017. Right after her final deposit, she withdraws all the money in the account. Which expression is equivalent to the amount of money she withdraws?”
Again, this would still not be a great question since it has way too much going on in it. It could be made more reasonable by instead of doing 12 months, have her make a deposit once a year for 12 years, still compounding, but not having to deal with the converting the annual interest rate to a monthly interest rate.
Ironically, if students were to just type the four answers into the calculator, only choices (3) and (4) would be over $1200 so they are the only reasonable answers here anyway.
So it’s an interesting problem that makes for a good classroom activity, but not good for testing the sum of a finite geometric series formula on the Regents.
This is one of the open ended questions which was already basically tested in the multiple choice question number 16. I think I’d rather have seen question 24 with the compound interest made into an open ended question and have some better multiple choice question in its place.
The 4 point questions are an opportunity to make a question that is more interesting and that students can demonstrate their thinking. This question is just an exercise in typing very carefully into a calculator. The bigger problem is with the second part since the thing they are asking for, the down payment, is not part of the formula at all so students would have to be familiar with the idea that when you take a mortgage out you sometimes make a down payment first to cut money off the principal and to lower the mortgage payment. This is a pretty sophisticated idea and one that is not explained very clearly in the statement of the problem. The idea of ‘down payment’ is just slipped in there and very easy to overlook. Personally, I read this question too fast the first time and didn’t even notice the ‘down payment’ thing and answered the question that I thought they were asking, which was what principal would lead to an $1100 payment, so I would have lost at least a point there.
I don’t know who the team is that made this test. I’d hope that whoever assembled the team and gave them direction is held ‘accountable’ and not permitted to do this for future exams.
Making a good Regents exam is not a task to be taken lightly, so many people are depending on you to do it right. I don’t know if New York State really cares that much about how good of a test it is. The curve makes it that roughly the same percent of people pass this ‘more rigorous’ test, so in that way it makes politicians happier even if it is really frustrating for students and teachers who worked hard all year expecting to get a fair test.
I know a lot of people, including myself, who could single-handedly make better math Regents exams than we are currently seeing. If whoever was responsible for putting together the team that created this round of Regents exams ever wants my advice on defining a better philosophy of what the tests should be like, or about the selection process for being on the team that writes the question, or if they want to let me look at a draft of the test to do this kind of critique before the test is finalized, I’d be willing to participate in that.