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Wednesday, April 22, 2015

STEM is not synonymous with education

My local NBC channel, WNYT channel 13, has been bludgeoning its viewers lately with stories it relates to STEM, the Science-Technology-Engineering-Mathematics push, with its STEM13. One would think that I, as a career math teacher, would appreciate such coverage and clamor for more. But no.

There is a strong linkage between the four subject areas, but in promoting it uber alles (in its true translation as "more than anything else"), it has belittled each of the 4 subject areas, deeming them each subservient to some higher academic god.  That is to say nothing of what it does to history, language, art, music, physical education, and so on.

STEM has a place, once the basic footings of mathematics, science, history, literature, language, art, music, and physical education have been put in place.  (I leave out technology, for it, as Oxford dictionaries states, is  "the application of scientific knowledge for practical purposes, especially in industry". Seems to me, before it can be applied, science must be known.)

Sure, in the professional setting, all these areas are interwoven frequently. They naturally would, once the foundations have been laid.  But stressing them to the exclusion of anything else is putting the cart well in front of the horse. 

Gottfried Leibniz is quoted as saying "Music is the pleasure the human mind experiences from counting without being aware that it is counting." Just being able to appreciate that sentence requires one to know something about Leibniz, music, and math. The mathematics in music is astounding, almost magical.  If you have any doubts about how key mathematics is in music, take a look at the wikipedia page for Pythagorean tuning. That's right, Pythagoras. The same guy who worked with triangles.
To quote Wikipedia
According to legend, the way Pythagoras discovered that musical notes could be translated into mathematical equations was when he passed blacksmiths at work one day and thought that the sounds emanating from their anvils were beautiful and harmonious and decided that whatever scientific law caused this to happen must be mathematical and could be applied to music. He went to the blacksmiths to learn how the sounds were produced by looking at their tools. He discovered that it was because the hammers were "simple ratios of each other, one was half the size of the first, another was 2/3 the size, and so on".
Imagine if Pythagoras had no concept of ratios. Sure, there is a slight chance that such an event might spur someone to invent a concept of ratios. A very slight chance. 

While on the topic of music and math, stop and watch a short video from TED. It is part of a web page from the site ed.ted.com which can be found here. After watching that video, just ask yourself again as to whether or not music and math travel together.

It might be that our nation would be more prosperous with more "STEM" people. What is more important is that the foundation of mathematics be fully grounded, and the inclusion of music can only help make that happen. The tunnel vision of "STEM" seems to be pushing subjects like music to the sidelines. That has to stop.

Tuesday, April 21, 2015

The Family of Nobodies

Here is a question from last January's Algebra I (Common Core) regents Exam in New York state. Read it carefully.

This "predicting function" is based on household size as input and number of devices as output. Hence the household size falls into the domain.

Here I show a quote from www.cliffnotes.com (see it here)
When you first learned to count, you started with 1, 2, 3 and kept going until you couldn't remember what came next or grew tired of counting. These positive counting numbers (1, 2, 3, 4, ...) are called natural numbers. The ... means the number list continues on infinitely.
If you add the number 0 to the natural numbers, you get the whole numbers (0, 1, 2, 3, ...). You also get an example of how a number can be classified as more than one type. For example, the number 2 is both a natural number and a whole number. In fact, all natural numbers are whole numbers, but not all whole numbers are natural numbers. Why? The number 0 is a whole number but not a natural number.
I may be missing something here, but it seems to me that question 6 above is missing the correct answer. Unless you find it common to talk about the number of families with zero members, the answer to question 6 must be the natural numbers ("counting numbers" is an accepted synonym). The question asked for the most appropriate. As long as you are willing to include elements in the domain that are nonsensical, any of the answer choices are okay.

As for a benefit of including households with 0 members: Uninhabited homes can be considered as householder-occupied, vagrant iPhones can be given a place to live. Wolfram (seen here) even acknowledges lack of a standard, and recommends the following:


I do grant Wolfram a certain amount of respect in the world of mathematics.

While we are at it, a a standard convention in mathematics is, in the absence of a specified domain, to use the largest domain for which the function makes sense. In this case, that is the positive integers, or natural numbers, or counting numbers. However here, as in many elections, the correct answer is just not one of the choices.


Now we have question 13 from the same test.



Give me a break: 79 cents?  Not 75, not 80. Seventy-nine cents?

This question writer(s) seem to have concluded that 75 or 80 would have made the question too easy. For someone who can do arithmetic mentally, it would be easier. Or would it? This problem requires absolutely no calculations of any kind! That 79 just sends up a red flag saying "don't take this test seriously".

Monday, April 20, 2015

What's your plinth?


The following quote was allegedly used in the New York State 6th grade Common Core ELA test, according to Valerie Strauss of The Washington Post (see here)
As a result, the location of the cloud is an important aspect, as it is the setting for his creation and art of the artwork.  In his favorite piece, Nimbus D’Aspremont, the architecture of the D’Aspremont-Lynden Castle in Rekem, Belgium, plays a significant role in the feel of the picture. “The contrast between the original castle and its former use as a military hospital and mental institution is still visible,” he writes. “You could say the spaces function as a plinth for the work.”
I copied this text and pasted it into Microsoft Word  so I could check some readability measures. Irs Flesch-Kincaid readability level is grade 11.0.

I took it to and received the following:
I was surprised at the 10.9 to 11.0 discrepancy of the Flesch-Kincaid rating, but noted that they all came in quite higher than the 6th grade level of the test.

Let me add a disclaimer: until I read Ms. Strauss' article, I can honestly say that the word "plinth" was not part of my vocabulary. I know that in the absence of a dictionary, the essence of this paragraph would have been totally lost to me. Were students allowed a dictionary during this test? I would hope that the skills we are allegedly teaching our youth include the basic skill of looking up a word of unknown meaning. So do they get dictionaries? Do you know?

The New York State Testing Grade 3-8 Common Core English Language Arts and Mathematics Tests School Administrator's Manual (that's a title!) states the following:
Bilingual Dictionaries and Glossaries——English language learners may use bilingual dictionaries and glossaries when taking the 2013 Grades 3–8 Common Core English Language Arts and Mathematics Tests. These bilingual dictionaries and glossaries may provide only direct translations of words. Bilingual dictionaries or glossaries that provide definitions or explanations of words are not permitted. 
I am extremely curious as to whether or not the "other" language edition's of this test used a word as exotic as "plinth", and, if so, were they translated by the accepted dictionaries and glossaries as "plinth".

This is just indicative of a poorly run and disastrously implemented testing program.

What is beginning to really annoy me is that the political climate of our culture is making it very very difficult to be in favor of outside assessments while being dead-set against what is currently being done.  The testing system being implemented just has to get tossed. It may be making a few people richer in the short run, but in the long run it will help impoverish our society and culture.

If you have read this far, you might be able to tell me why these tests are being given in April, two months before the end of the school year? Who made that call? I'll bet it was for the convenience of some corporation. 

Cuomo wants to these tests as 50% of teacher evaluations, while testing only 80% of the school year. That is weird. But consider the source.

The first step in fixing this fiasco must be to get Cuomo out of office, and then get rid of any and all politicos who signed off on this debacle.

Thursday, April 9, 2015

Which way did he go?

I have had this animated graphic for years. I do not remember where I first got it (I did not make it), but I do know that it has spurred a number of conversations where no one left feeling mentally competent.

The situation is simple: count the number of people both before and after the animation. Explain.