What if...................

Today has just been one of those days when I wonder what it would be like to be in the classroom with technology such as GeoGebra. For some reason, I think that Common Core would be promoting such technologies, but the testing that has grown up around it would be forcing me to forego such things. Who knows. Here is just a "doodle" from this morning. Enjoy.

 

Algebra 1 and pencils

The New York State Common Core Sample Questions for the Regents exam in Algebra 1 (Common Core) from fall 2013 (see it here) includes the following situation in question 12:

At an office supply store, if a customer purchases fewer than 10 pencils, the cost of each pencil is $1.75. If a customer purchases 10 or more pencils, the cost of each pencil is $1.25.

I find this question to be a microcosm of our society in the new millennium.  Overlooking the fact that a dozen pencils should cost less than two bucks, let's let the costs be as stated.

I need 9 pencils. Do I overspend and pay out $15.75 (eight times $1.75) or do I buy 10 for $12.50 and just toss the one I do not need?  Do I waste money or waste product? (I use those last two words wisely.)

Which is the intelligent choice?

Regents Examination in Geometry (Common Core) Sample Items Fall 2014: Question 4 is BAD!!!!!

Here is question 4 from the Fall 2014 New York State Common Core Sample Questions for the Regents Examination in Geometry (Common Core) You can find it here.

Here is the sample solution.

This question is a RED FLAG!!  The question is misleading and the answer is wrong!!!

The answer assumes that the vertex of angle B is at the center of the circle. There is nothing in the statement of the question that stipulates this.  In point of fact, the angle can change depending upon exactly where in the circle that vertex is. Drag that vertex in the diagram below.


A major MAJOR point in any Geometry course is, and must be, that care must be taken about making assumptions based on appearance. Just because the vertex looks like it could be the center does not mean it is.

Who says you must use tangent?

I am beginning an analysis of the questions recently posted in the Fall 2014 New York State Common Core Sample Questions for the Regents Examination in Geometry (Common Core) You can find it here.

Here is the first question posed, along with sample solutions. (My part continued below.)
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The answers to the above include, in addition to the correct choice, some key "distractors".  Replace "tan" with "sin" above and you obtain answer choice (3). Switch the 69 and 102, and you will get choice (4). Replace 69 with 59 and 102 with 86, and your result is choice (2). 

Please take note that should you make one of these errors, you will have a 0% chance for a correct answer, whereas if you randomly make a selection, your chances are 25%. 

Also, please recognize that the correct solution to this question begins with careful and accurate reading. The ability to read the question is paramount. The best math student is blinded if they cannot read the question. 

During my years in the classroom I many many times discovered students who could do such problems perfectly fine if I read the problem to them, but could not handle it on their own. In constructing tests, care has to be taken in controlling how much of the grade should be dependent on the ability to read, and how much actually is dependent on that ability.

Please take note that a student who has absolutely no knowledge of tangent can solve this problem perfectly should they begin by using the Pythagorean Theorem to find the hypotenuse length, then properly apply either sine or cosine. The phrase "tangent must be used" is mathematically incorrect.

My final note is that to obtain feedback about a student's skills and knowledge, I would never make such a question "multiple choice".  This type of question creates easy, but hardly useful, data.

Carefulness must accompany caring

Errors happen. That is inevitable. Mistakes abound.  New media have fact checkers, writers have proofreaders, weight lifters have spotters, and so on. Nobody is perfect.

So why do so many errors that are avoidable remain undetected?  I have compiled a gathering of those I have seen while I have had a camera with me (see here). I have limited my collection to printed media, either hard copy or digital. No audio or video here. The picture below I have not included in my collection because I have not yet convinced myself that it is an error. It might have been the intention to write "french fries" while showing mashed potatoes.

What amazes me is that each of these is (was) made by more than just one person. Perhaps just one made the initial error, but the non-detection of it makes others equally responsible, if not more so.

Note I do not call them careless errors. Carelessness implies that one just doesn't care, and, not being a mind reader, I cannot make that claim in any of these cases. Who knows whether or not the initial mistake was called by indifference. However, the failure to rectify the mistake is a sign of indifference. In each case (except the automobile photo) a business either saw the error and did not care about it, or was careless in not. (The automobile photo I place in a different category since the sign was inside the car over a couple weeks while its owner was home and had actually moved the care once or twice.)

These items become newsworthy as they indicate a sense of complacency, which brings to mind Thomas Edison's quote “We shall have no better conditions in the future if we are satisfied with all those which we have at present." We have to jump start our culture and society into being more careful, not just more caring.

Albert Einstein said “Whoever is careless with the truth in small matters cannot be trusted with important matters.”

Samuel Johnson stated "It is more from carelessness about truth than from intentionally lying that there is so much falsehood in the world."

Where have you gone Joe DiMaggio, er, I mean decent cable TV?

Back on September 12 of this year Dane Wigington had an article online titled The Weather Channel Switches To Reality Shows (see it here). I do not wish to repeat it, but I will add to it the comment that this weekend the channel outdid itself. A whole weekend of "Prospectors", a show whose content I do not know and care not to know. I turn on The Weather Channel to find out about the weather. That wish is met with decreasing frequency, and this weekend almost not at all.

Finding weather on The Weather Channel is about as difficult as watching shows about travel on The Travel Channel. Perhaps I have missed something: maybe the word "travel" has now morphed into a synonym for "food", as most of its shows revolve around some unhealthy or just strange aspect of eating.

I will not even go into looking for history on The History Channel.

Maybe big business is really truly trying to dumb down society. Does intelligence scare them?

Fresh?

A few days ago I wrote a post about taking thought-provoking photos. Here is one I took a couple years ago. Needless to say, it was not taken in the US. I cannot think of a single place in the US where live chickens would be allowed to roam in front of a fast food restaurant, and I cannot imagine a Colonel Sanders franchisee tolerating live fowl outside the front door.  This picture was taken, however, near downtown George Town in Grand Cayman.

I know this photo is not unique (just do a Google image search of"Grand Cayman KFC") but I thought it thought provoking anyway. It at least got me checking on chicken in the wild in US towns and cities.