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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.

Math Photo: City Grid

City Grid

This view of the city through this rectangular netting puts me in mind of projecting three-dimensional space onto a two-dimensional coordinate system.  The rectangular grid seems a bit oblique, relative to the buildings, which makes me wonder what angle I’d have to look through in order for make everything to line up straight.

Regents Recap — June 2014: Lack of Scale

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

The following question appeared on the June, 2014 Algebra 2 / Trig exam.

2014 alg 2 trig 35 -- lack of scaleGraphs without scales are common on Regents exams (I’ve written about this before).  Personally, it’s not a huge deal to me–I’m a lazy grapher, myself.  However, a colleague of mine regularly complains about this, and she made an excellent point regarding the grading of this particular problem.

The solution to this problem involves translating the graph one-unit to the left and two units up.  But since no scale is given on the graph, it’s not clear what one unit to the left would be.  If we assume the box on the graph indicates one unit, then the red graph below would be appropriate.  But if we assume a box to represent half-a-unit, the purple graph would be correct.

unscaled graphs -- possibilitiesIf no scale is explicitly given, it seems like both graphs should be considered correct and receive full credit.  But the rubric doesn’t address this possibility, and it’s unlikely students were given the benefit of the doubt.

Math Photo: Obtuse Art

Obtuse Art

I really like the shape of this midtown-Manhattan sculpture.  Whenever attempts are made to define or quantify beauty, symmetry is one of the first considerations.  But this obtuse,scalene triangle is decidedly unsymmetric.

Maybe its lack of symmetry makes it more noticeable as a piece of public art.