Another bad math question from NY State
How can New York State test kids in math when it can no longer consistently write appropriate questions? This gaffe is almost two years old, but it looks like no one noticed the problem, until it showed up on the Association of Mathematics Teachers of New York State (AMTNYS) listserve this week.
On the August 2013 geometry regents, students were asked to find the slant height of a cone, given the lateral area.
It’s easier than it sounds. There is a formula sheet in the back that gives
L = πrl,
where L = lateral area and l = slant height and r = radius.
Heres’s the question:
14. The lateral area of a right circular cone is equal to 120π cm. If the base of the cone has a diameter of 24 cm, what is the length of the slant height, in centimeters? (1) 2.5 (3) 10 (2) 5 (4) 15.7
Since radius is half the diameter, r = 12 and plugging in: 120π = π(12)l, or l = 10, choice 3.
But wait. The height of the cone (like a flagpole from the base to the highest point), the radius (like a stripe from the base of the flagpole to the edge of the cone), and the “slant height” form a right triangle, with the slant height being the hypotenuse. So how is the hypotenuse (10) shorter than the base (12)? Can’t happen in the real world… but in New York State?
Here is an insightful comment from the listserve:
This is another example of the type of error that has been occurring on Regents exams since the early 1990s when the math bureau of NYSED was downsized from 7 very experienced and talented people (a bureau chief + 6 math specialists) to an inexperienced few. It is also a product of contracting out the writing of exams to rich companies that had no experience in this area.The errors often occur from the creation of questions that require substitution into formulas without looking at a drawing to see if the numbers are possible.