Wednesday, July 19, 2017

June 2016 NYS Geometry Regents Question 24 has no correct answer!

July 25, 2017 note:  I have just received word that NYSED has deemed all 4 answers to be granted credit for this question.
Here is a question from last months new York State Regents Exam in Geometry (Common Core)
This question, to be answered best, requires you to identify three which are sufficient. The one left over would be the answer. Wouldn't it?

The Regents "powers that be" have decreed that choice "2" is the correct answer. They are wrong. There is no correct answer: all 4 choices are sufficient for the task.

A key item in analyzing this question is recognizing that point C in the diagram is between points A and E and between points B and D. This information is embedded in the diagram.  Should a blind student be taking this test, this information must be verbally communicated (maybe using the sense of touch is possible, but I will not deal with that here.)

If the diagram has been totally omitted from the question, all bets are off. As a matter of fact, a better question would have been to leave out the diagram and leave out the word "not" in the question.

Although this does not constitute a proof, it illustrates what a proof for choice "2" would be dealing with. I did not use the same point names, but the lengths are correct. Points A, B, E can be dragged.

A more detailed proof has been written and the link can be found at https://www.change.org/p/nysed-mark-q-24-on-the-june-2017-geometry-regents-as-correct

Monday, July 10, 2017

Learn something new...

Math students (or anybody, for that matter) should try to learn something new everyday.
This might help meet that need for somebody out there.

Saturday, July 8, 2017

Meanderings on a rainy afternoon

Just a bit of doodling in Geogebra, trying to keep from getting mentally rusty.
Students should be working with GeoGebra.
It's free, it's fun, and it's educational. A trifecta.
The file can be found here.

Friday, July 7, 2017

Cavalieri's What?

Here is question 27 from the New York State Geometry Regents exam of June 2016.

One thing specifically stands out in this question. Cavalieri's Principle.

Students in New York do not have to remember the quadratic formula, how many feet in a mile, or even the Pythagorean Theorem. Those items are all on the Common Core High School Math Reference Sheet with which each student is supplied. 

But Cavalieri's Principle? That stands out. After all, everyone should know the main success of Felix Cavalieri, lead singer of the Lovin' Spoonful.

Oh, sorry, Wrong Cavalieri.

This Cavalieri is actually the gentleman who proved the formula for the volume of a general prism (which can be found on the reference sheet). 

I will admit that when I first read this question, I said to myself "what the heck is Cavalieri's Principle?" After a little research I was reminded that I had confronted it somewhere in my mathematical meanderings.

It does please me that NY has risen its standards and now expects students to remember and be able to apply Cavalieri's Principle. Now if they could only do that with the other items on the reference sheet...

Wednesday, July 5, 2017

NYS Regents Algebra 1 Questions 18 and 19

The above question bothers me.  The statement of the problem makes no claim about any domain, and the answer key's choice of (2) actually requires that the problem be interpreted by the student as a question regarding a recursive sequence. This question appears to result from a mashup of two different issues: recursive sequences on the one hand, and definition of function on the other.

Obtaining the answer that is deemed "correct" requires that the student assume that every result from the formula (normally associated with the concept of "range") can then be used as an input into the formula (normally associated with the concept of "domain"). 

Although the topics of recursive sequences and function definitions are both legitimate for first year algebra, this question still does not belong.

Here is question 19:
This question can be answered by simple substitution and calculation. A student need show no skill regarding solving linear equations to answer it correctly. 

Compare that question to this from Ninth Year Mathematics from 1969 (the one I took)
(The [5,1] indicates 5 points for solving and 1 for checking. ) Admittedly, this question was 1 of 7 ten pointers out of which the student had to answer 4. To see what the choices were, check out the exam here

For that matter, compare June 1969 with June 2017 and then tell me that our standards have really been raised. (Keep in mind that hand held calculators of any kind did not exist back then.)