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Math Photo: Between the Octagons

Between the Octagons

Sometimes the sun and surroundings cooperate and create an opportunity for a perfect profile picture.

Regents Recap — June 2014: Common Core Algebra Structure

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

June, 2014 saw the administration of the first official Common Core Regents exam in New York state,  Algebra I (Common Core).  Roughly speaking, this exam replaces the Integrated Algebra Regents exam, which is the first of the three high school level math Regents exams in New York.

The Algebra I (Common Core) exam was structured differently than the Integrated Algebra exam.  Algebra I (Common Core) contained 24 multiple choice questions, while Integrated Algebra contained 30 multiple choice questions.  This change, in and of itself, likely translates to lower average scores on the Algebra I (Common Core) exam:  merely guessing on those 6 extra multiple choice questions would yield an extra 3 points on average, and multiple choice questions are generally easier to score points on than free response.

The free response sections are structured slightly differently, as well, but not substantially so.  In fact, apart from some significant content differences, not much distinguishes the new Common Core exam from the old Integrated Algebra exam.

Many of the questions on the Algebra I (Common Core) exam are similar in style and content to questions on other math Regents exams.  For example, here is number 1 from the Common Core exam compared with number 5 from the Integrated Algebra exam.

common core comparison 1

And here is number 3 from the Common Core exam compared with number 14 from the Integrated Algebra exam.

common core comparison 2

A few of the questions on the Algebra I (Common Core) exam do show improvement over similar items on other exams.  Consider number 8 from the Common Core exam, compared with number 8 from the Integrated Algebra exam.

common core comparison 3

The two questions address the same issue, but the top is more mathematically precise.  (I really dislike the “Which step could be used?”-type problems).

Overall, in terms of the way questions and posed and structured, there is not much of a difference between the new and old exams.  The Algebra I (Common Core) exam is pretty much standard test fare.  When the current testing culture is criticized, a common response is that we just need to make better tests.  This is easy enough to say, but surprisingly hard to do.  And it doesn’t look like this first Common Core Regents exam is substantially different, or better, than its predecessor.

Regents Recap — June 2014: Common Core Content

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

June, 2014 saw the administration of the first official Common Core Regents exam in New York state,  Algebra I (Common Core).  Roughly speaking, this exam replaces the Integrated Algebra Regents exam, which is the first of the three high school level math Regents exams in New York.

So how does the new Algebra I (Common Core) exam compare with the old Integrated Algebra exam?  In terms of mathematical content, one difference jumps out immediately:  functions.

On the 2014 Algebra I (Common Core) exam, the word “function” appears 17 times.  On the 2014 Integrated Algebra exam, the word “function” appears once.

An informal reading indicates that functions play a part in 14 of the Algebra I (Common Core) exam questions, which are worth a total of 36 points.   This is around 42% of the exam (36/86 points).  In addition to several direct, function-related questions, like about domains and modeling, we see a number of familiar questions recast in the language of functions.

For example, number 12 from the Algebra I (Common Core) exam asks about “zeros of the function”.  On an Integrated Algebra exam, the same type of question would likely have been asked in the context of “solving an equation”.

common core -- functionI’m not going to dispute the importance of this concept:  functions are central objects in mathematics, and in high school math in particular.  But this is clearly a substantial change in focus for this exam, and I doubt many could have predicted the extent of this change.  Functions should be covered in any algebra course, but this dramatic shift in assessment undoubtedly penalized many students.  A student with a weak grasp on this one concept would face a huge obstacle on the Algebra I (Common Core) exam.

In addition to this major shift in emphasis, several topics which were previously covered in the highest-level exam (Algebra 2 / Trig)  are now on the Algebra I (Common Core) exam:  recursively defined functions; correlation coefficient; and the quadratic formula.  This does not come as a surprise, but it’s worth noting that these topics have been moved ahead by 2-3 years in the typical student sequence.  Also of note was that students were asked to factor a fourth-degree polynomial (of quadratic type) on the Algebra I (Common Core) exam, which as far as I know has only previously appeared on the Algebra 2 / Trig exam.

Will the next iteration of Algebra I (Common Core) emphasize functions so heavily?  What will the first iteration of Geometry (Common Core) exams look like?  Our initial experience with Common Core Regents exams in New York suggest it will be hard to predict.

Regents Recap — June 2014: Subtle Changes

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

The following item appeared on the 2014 Geometry exam.  It was the highest-valued item on the exam, the only six-point question.

2014 Regents Geom -- coordinate proof

There’s nothing particularly unusual about this problem.  In fact, similar problems have appeared on prior exams.  Here we see the lone six-point problems from the 2013, 2011, and 2010 Geometry exams.

other six-point geom questions

The problems are all very similar, yet there is one subtle difference between the 2014 version and these three prior versions:  the 2014 version contains one less substantial task than the three previous versions.  That is, it requires less work than previous versions, but is still worth six points.

In 2014, the student is asked to prove that a given quadrilateral is a parallelogram, but not a rhombus.  In 2010, the student had to do these two things, but in addition prove that the quadrilateral wasn’t a rectangle.

In 2013 and 2011, the student was asked to prove two similar results, but first had to construct a new quadrilateral from the given quadrilateral.  This preliminary work involves repeated application of the midpoint formula.

I don’t really think this is a big deal, but it does point to the subtle ways in which tests, scores, and results can be manipulated.  Test results have become highly politicized in recent times:  politicians routinely take credit for improving graduation rates and closing achievement gaps.  But without scrutiny of the tests themselves–their content, their construction, their scoring–it’s difficult to put such claims in their proper perspective.

Regents Recap — June 2014: Are They Reading?

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

I have been reviewing New York State Math Regents exams for several years now, and I occasionally wonder if anyone involved in the production of the exams pays attention to what I say.

Well, last year I wrote about a problem on the Geometry exam that asked students to graph a compound locus but then incorrectly penalized them if they didn’t graph each individual locus.  The supervisor at the grading site didn’t take our complaints seriously, but It seems the exam authors eventually realized that this was wrong.

This is from the 2014 Geometry exam.

2014 Regents Geom -- locus

Notice how this question explicitly asks the student to graph both individual loci.

I doubt that my post instigated the change, but it is nice to see errors on these exams addressed every once in a while.