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C'est la Z

APCS A - The Hardest Question

There was some discussion the other day resulting from some info released by the College Board on this past years APCS-A exam.The "hardest" question was the 2D Array free response. As it happened, 34% of test takers earned 0 out of 9 points on the question. What's interesting is that the College Board noted that at the same time, students did very well on the multiple choice 2D array questions.

What does that mean and what does that tell us. Let's explore.

You can find the question in the released exam questions starting on page 14.

Was it really a hard question?

In my opinion, not really. APCS-A is supposed to be a college level CS1 class and following instructions to traverse or manipulate a 2D array should be pretty easily handled by CS1 students.

Once you get to the meat of the question it was pretty straightforward. Of course, getting to the meat, particularly under time pressure could be a considerable challenge. More on that below.

The first part of the question was basically just a scan down a column and reassign elements with a couple of conditions. The "to do" items were listed pretty clearly in the question so a student would just have to take the bulleted instructions as an outline and code it out.

The second part involved scanning through a 2D array. Pretty standard stuff but you had to pay attention to the specific order of your traversal which was hidden in a mountain of text.

There have certainly been harder and trickier questions in past years. I can think of one "encryption" question that I remember to be harder and I seem to recall others that required shifted values in a 2D array which is certainly harder than what was asked here. It would be interesting to see the score data on the "hard" question from past years and see how they compare.

Whose fault is it?

One of the comments I read was that if 34% of test takers score 0 points on a question the test write is at fault. This is probably correct but not necessarily because the question was bad or that the exam was bad. This is a deeper question. I plan to address this in a later post.

Blank question or blank test?

This question was raised in one of the forums. Each year, so I'm told, there are large swaths of AP exams that are just blank. This can be for a variety of reason - an unprepared kid, one who never wanted to take the exam, cases where the kid's already decided on college (or not college at all) and the exam won't do anything for them and possibly other reasons. Obviously this question would be blank if the entire exam was blank. What percent of otherwise completed tests had this question scoring 0 points. Better, but maybe impossible to figure out now, how many questions were left blank vs had totally incorrect answers? All of this would be interesting.

Is this a CS test or is this reading?

Another comment pointed out that this question was a wall of text. Hard enough for a native English speaker but a particular challenge for an English Language Learner. How badly did this affect the results? It took me a reasonable amount of time and effort to make sense of the question. It was somewhat contrived and arbitrary and you really had to get into the weeds of the text to know exactly what to do. How big of an effect was this? Did it cause kids to give up? Did they misinterpret things? Who knows. While understanding a problem statement is important, in the real world, a professional programmer can always ask for clarification. Not on an exam. I get it - since its one way communication, the test writers have to put everything in the question and leave no ambiguity but if the result is a long winded obtuse question, maybe come up with another question. Strip away the story and this particular question is pretty easy. With it, it's much harder for most high school kids and maybe intractable for an English Language learner.

Did they run out of time?

Maybe it wasn't that it was a hard question but seeing the wall of text or the topic of 2D arrays, students left it for last. This is not an uncommon strategy. For years, across all subjects, teachers tell students not to get caught up on one time consuming problem. The strategy is to maximize your points. When I taught APCS, my students never had trouble with the time for the free response but the multiple choice was a race - probably because I never did any explicit prep for it. It's frequently better to skip a couple of time consuming ones and get all the others right.

Same strategy can be used for the free response. How many students focused on getting maximum points on the other questions and just ran out of time. This would jive with the fact that students did well on the multiple choice 2D array questions.

Was it a strategic omission to maximize score?

What if it was left for last and by "it" I mean teaching 2D arrays. This has long been a teaching strategy when high stakes tests are at play. Arrange the topics taught and the amount of time to allocate so as to maximize student performance on the exam.

This seems to have happened far and wide in New York City in Geometry. In NY, students have to pass a number of high stakes tests called regents exams. Many schools allocate 2 years to Algebra and most students pass. Then, they allocate one year to Geometry - a much harder, richer curriculum. Based on the design of the exam, teachers have realized that in spite of the fact that the course is really supposed to be about deductive reasoning and proof, that proof only comprises a very small number of points on the exam. So, if you don't teach proof - a notoriously hard subject to teach and learn or merely pay it lip service, students won't get any points on the proof section but the hope is that they'll know the other subjects better and end up passing and in fact scoring better overall.

Last time I graded the geometry regents, before I left for Hunter College, the number of proof answers that were entirely blank backs the theory of this approach.

Now, for geometry this certainly hurts kids down the road since deductive reasoning and proof is more fundamental and important than say, circle geometry but since teachers and students are being judged by standardized test scores you can't really blame them.

Could it be that APCS-A teachers have decided to do something similar with 2D arrays. It's even more plausible given that most high school CS teachers are currently much newer to and weaker in CS than math teachers are to math.

Final thoughts

As you see, there's a lot to explore based on the simple statistic of 34% of students scored 0 on a question. There are probably more factors and potential explanations than the ones I've shared but the next, more interesting question is the one posited at the top - is the College Board to blame or someone else? I think it is a College Board issue and it's an issue with the basic AP model. I'll explore that in a future post.

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