Teaching

The release of student test data from 2013 has educators, administrators, politicians, and parents abuzz in New York.  These are the first state exams aligned to the Common Core standards, and as widely predicted, proficiency rates have plummeted, leaving everyone scrambling to explain what has happened.

The most common explanation offered is that these new tests are substantially more rigorous than the old ones, so lower student performance is to be expected.  I was curious about the claim that the new tests are more rigorous, and while the state does not release the exams to the public, they do publish a small number of questions from each grade level.

The new tests were administered in grades 3-8.  As a high school teacher, I am not well-versed in elementary school tests, but I have spent a substantial amount of time scrutinizing New York state math Regents exams, so I thought I’d look at the 8th grade math questions that were released to the public.  I was quite surprised by what I saw.

The “representative sample” of 8th grade math questions does not seem more rigorous to me.  They do not seem to emphasize “deep analysis” or “creative problem solving over short answers and memorization”, which is often how the new standards are characterized.  I can’t say I was surprised to discover this.

What did surprise me, however, was how many of these 8th grade math questions were virtually identical to questions that have recently appeared on high school math Regents exams.

Here is the first example from the set of 8th grade math questions released to the public:

This problem is essentially the same as #4 from the January, 2013 Integrated Algebra exam

The second example from the set of 8th grade math questions released to the public

is quite similar to #4 from the January, 2013 Geometry exam

And the fourth example from the set of 8th grade math questions released to the public

is essentially the same as #9 from the January, 2013 Integrated Algebra exam

This surprising discovery left me with a lot of questions.

First, why are 8th graders facing the same kinds of questions on this state exam that 9th, 10th, 11th, and even 12th graders faced this year?  Were teachers and students prepared to see this kind of content on the 8th grade exam?

Second, how can it be argued that this new test is more rigorous if it is comprised of the same kinds of questions that appear on the old tests?  Simply moving a question from a 10th-grade test to an 8th-grade test doesn’t transform the question into one that requires deep analysis or creative problem solving.  More rigorous questions would ask students to construct mathematical objects, explore concepts from different perspectives, and demonstrate mathematical reasoning.  None of the above questions do this:  they are not especially challenging, deep, or novel.  In short, they are typical standardized test fare.

And perhaps the most important question is this:  if these are the hand-picked exemplar questions released to the public, what must the rest of the test look like?  Only by releasing the entire test to the public can we truly assess what we are assessing.

A version of this post appears at GothamSchools.

Here is another installment in my series reviewing the NY State Regents exams in mathematics.

Some of the worst exam questions aren’t merely erroneous, but actually encourage students to exercise bad mathematical habits.  Consider these questions from the June 2013 Algebra 2 / Trig exam.

Notice that the problem doesn’t specify what kind of series this is:  the student is expected to assume that the series is geometric.  This is a terrible habit to encourage, and I wrote about this the last time it happened on a Regents exam.  I guess no one is listening.

In order to determine whether a relation is one-to-one or onto, it is necessary to know the relation’s domain and range.  Here, the student is expected to assume that the oval on the left represents the domain of the relation and the oval on the right represents the range.  Perhaps these assumptions are reasonable given the nature of the diagrams, but this just seems sloppy to me.  I wouldn’t accept imprecise formulations of functions and relations like this from my students; I would demand they be more explicit.  (It’s also worth noting that the relation in (2) is one-to-one and onto its image in the right-hand oval.)

Here’s another example of sloppiness in question construction.

Is it supposed to be obvious that the i here is the imaginary unit?  The letter i could be just a variable, like, say, the m that also appears in the question.  The available answers support the assumption that , but why are we forcing students to play test-detective?

The Regents exams also continue with their long-standing tradition of presenting unscaled graphs, another bad mathematical habit to encourage.

I believe these tests should stand as exemplars of proper mathematics.  Maybe I’m alone in thinking this, but it seems to me that repeated exposure to these sloppy exam questions might actually interfere with a student’s ability to truly understand the underlying mathematics.