Tuesday, April 29, 2014

Why do we have schools and why do they need a common core?

Having read, seen, and heard a number of stories regarding Common Core and, more specifically, testing related to Common Core, I keep coming back to one nagging question: Why do we have schools?

I am not trying to be funny. I am really and truly asking WHY schools exist? Is it to train a work force? Is it to create an informed population? Is it to babysit children?

Here is a column from the JacksonHerald Today web site, from December 2010
What is the purpose of education? That question may seem obvious, but ask 100 people why schools exist and there will be 100 different opinions.

Among those opinions, a popular one is that education is for the training of workers in our economy. Indeed, over the last two decades secondary schools have increasingly put an emphasis on workforce development. A growth in vocational programs has ridden that wave and today is a large part of school programs.

But perhaps that idea has gone too far. Schools don’t exist just to train worker-bees for economic development. Students shouldn’t be viewed as mere “products” of an assembly line.

At their core, schools should prepare people to be constructive citizens. A part of that is the building of a common base of civic, cultural, social and political knowledge.

But all too often, that core is missing, either through neglect or extreme political correctness. The common body of knowledge has fragmented such that it really doesn’t exist.

The result is that schools are churning out people who have some specific technical skills, but no understanding of the larger world around them. They can’t balance a checkbook, evaluate political candidates, or understand information that is put into a historical context because they themselves have little historical context. And too many have no concept of how to express their ideas either verbally or in written form.

While schools tend to focus on language and math skills, that doesn’t seem to be working. Take a look at the terrible grammar and spelling by those who put comments on any of the various mainstreetnews.com websites — the inability to communicate clearly is obvious. And while some students do conquer math, many high school graduates can’t compute simple math formulas.

Maybe it’s time for school systems to focus less on developing worker-widgets and more on developing well-rounded citizens.
A more wordy dissertation can be found here  in an article from WholeSchooling.net.

Thomas Jefferson wrote to George Wythe (find it here):
I think by far the most important bill in our whole code is that for the diffusion of knowledge among the people. No other sure foundation can be devised, for the preservation of freedom and happiness...Preach, my dear Sir, a crusade against ignorance; establish & improve the law for educating the common people. Let our countrymen know that the people alone can protect us against these evils [tyranny, oppression, etc.] and that the tax which will be paid for this purpose is not more than the thousandth part of what will be paid to kings, priests and nobles who will rise up among us if we leave the people in ignorance.
Needless to say, we do have schools, we do have this entity called the Common Core having a strong impact, and we have people all over the place complaining about Common Core tests, and complaining that we have too many teachers "teaching to the test", as the saying goes. With that idea in mind, I do have to quote Diane Ravitch, who, in an article entitled "Why So Many Parents Hate the Common Core" on CNN Opinion (see it here), wrote "It is time to stop testing students on material they have not been taught."

I find it a bit enlightening to come across diametrically opposite complaints about the same thing: the Common Core is bad because it forces teachers to teach to the test, then tests on things that have not been taught. Which is it?  Actually, I believe the real basis for the dislike of Common Core is neither of those.  I have the sense that everybody who dislikes Common Core has his/her own rationale for that dislike, and the only reason those complaints sound so loud is because they have a common enemy. 

When New Yorkers complained to the New York State Education Department in the past, it was generally in regards to a local concern.  People in Oregon were little concerned, and probably largely unaware, about the complaints that surrounded the demise on Regents Competency Tests as New York went to a "Regents for all" standard with its Math A/Math B program. I cannot reverse that direction, since being an upstate New Yorker, very little news came about the status of the Oregon Department of Education.  Both states, however, are wrapped up in Common Core issues. (See here for Oregon and here for New York).

Should we have a common core? In some respects, yes, in other respects, no. Should there be some common knowledge between and among school graduates throughout the country? Definitely yes. Should big business be behind it and federal aid be tied to it? Definitely not. I cannot get past the fact that the business world was responsible for sending millions of jobs overseas, and keeps what it does in the US only when it helps their own bottom lines. Business is patriotic only when it is convenient.  Sorry, Bill Gates.  We must remember that in our society, business is there to help the citizens, not the other way around.

When we consider how much involvement big business should have in education, we must consider the impact it has had in the world of health care.

One nice thing about Common Core is the "common" part. In this day and age when people listen to music and podcasts and books on headphones, and DVR or Tivo a couple of the thousand TV channels (when they are not streaming other media) and read a digital book they cannot lend to their neighbor or watch one of the 35 professional or college sports games on at any one time, it is nice to have something in common.

Thursday, April 24, 2014

Who is to be trusted?

The state of Georgia has now expanded the people and places where guns can be, and in many cases has paced the burden of their presence or absence not on the gun carrier, but elsewhere. It seems that a restaurant owner cannot ban guns, but can ban people carrying guns, which means he/she needs to know who is carrying a gun.  I believe the burden of proof has been tragically misplaced.

Suppose we passed a law that allowed a person stopped for DWI on the highway a "free pass" provided that they agreed to stop driving in that location for a while. Why not? A person can bring a gun into a Georgia airport, and get away freely as long as they leave the premises when asked. Evidently the only way a person can break the law with a gun is by actually committing some crime with it. Walking in an airport with a gun is not to be considered a crime.  By the same logic, a person drunk who is driving is not committing a crime: driving is legal.

The way I understand it, the lawmakers really do not want guns in the airport, but see no legal way to stop them except by asking nicely, please, "could you and your gun leave."  If the person refuses to leave, what law would they be breaking? Unwillingness to submit to authority? Isn't that what this business is really all about?

A well regulated Militia, being necessary to the security of a free State, the right of the people to keep and bear Arms, shall not be infringed.

These are the words that many gun owners hide behind.  I must admit that I have not seen a militia in my lifetime, but there must be one hiding in Hartsfield-Jackson International Airport.

I also cannot help but wonder if counterfeiters are going to enter the business of gun permits.

While we are at it, the 7th amendment says: In Suits at common law, where the value in controversy shall exceed twenty dollars, the right of trial by jury shall be preserved, and no fact tried by a jury, shall be otherwise re-examined in any Court of the United States, than according to the rules of the common law.

I hope that all those NRA people are also campaigning to see that the $20 limit is stringently followed. After all, this is our Constitution.

Tuesday, April 22, 2014

NY Times Cancellation Torture

Today I went on the web to cancel my NY Times digital subscription. I decided it was no longer worth the cost. So I went to the web and logged on and clicked on "cancel subscription".

That is where I saw the message that in order to cancel I had to call a special number.

I called. Ten minutes on hold. Then silence.

I called again. More time on hold. More silence.

I then looked for "customer care" on line and found a different number. I called, played the phone tag, and got forwarded. This time I was told the wait would be 9 minutes. I waited.

A gentleman came on the line. I had to give him my email address so he could enter it. I told him what I wanted to do. Twice he wanted to put me on hold so he could talk to a supervisor about a better rate. Twice I had to tell him I was calling to cancel, not get a better rate. He then proceeded to ask me about how I was using the subscription. Twice he tried. Twice I had to tell him that was irrelevant, as I was calling to cancel.

Finally, a full 45 minutes or more after my first attempt at calling, the message got through and he went to cancel my subscription.

I was about to cancel my subscription to the NY Times crossword, but I had an "aha" moment: My credit card expires before my next renewal date. This time they will have to come to me, and then I can be the one in control!

Friday, April 11, 2014

Have you ever....

Have you ever wondered how business like UPS or FedEx pick their routes? Identifying the most efficient way to deliver packages is a massively complex mathematical problem, but all complex solutions begin as small solutions to simpler problems.

Here is a simple variation in which the shortest route from "start" to "end is in red. Drag the points around and you will see the route change. This file was created using the free GeoGebra software.

Note: lines that cross below without a point labelled can be thought of like those interstate bridges, where two roads cross without actually intersecting.

I put this same file on the web at geogebratube. Click here


UPS is in the process of rolling out a massive program to help deal with its efficiency. You can read about it at FastCompany.

Search for info on the Traveling Salesman Problem and you will be amazed at what you find.

Thursday, April 10, 2014

Stupid or not?....

Ezra Klein writes a blog at the website www.vox.com, and his April 6 entry "How Politics Makes Us Stupid" is worth reading. Just make sure that it is not the only article you read on this topic.  You can find it here. In it he addresses the interface between the "more information hypothesis" and politics.

I must admit that I had never heard of Ezra Klein until this morning. A little blurb at the top of the Perspective section of today's Albany Times Union makes mention of him and the above-mentioned blog, although not mentioning the vox.com site, so finding Klein'a actual blog took a bit of searching.

Having read Klein's blog entry, some things seemed a bit unsettling, so I did my usual further search, and came across an entry at thefederalist.com called  "How Vox makes us stupid". In this article, David Harsanyi makes mention of author Caleb Crain's analysis of Kahan's column. Crain's work is titled "who's Wonking Who", and it, too, is worth reading. Find Crain's work here.

This whole debate just keeps bringing me back to the distinction between that which we know and can do without deep thought and that which we know and can do only because of deep thought. Notice I do not refer to what we "believe".  I consider beliefs and knowledge as distinct, even if only distinct insofar as they are different places on a continuum, far enough apart to be considered unique. (We seem to accept that with the naming of Europe and Asia as two continents.)

With all this debate going on, I cannot help but wonder what we would all think about global warming if there were no such things as huge power and oil companies and automakers. Could our opinions on the science be effected by our feelings about the economics?

Wednesday, April 9, 2014

Have You Ever Been Deceived?

Eat Forever!!
Here is a graphic that could easily explain our tax situation here in New York state.

If you look closely, you see that a way has been found to take an item (in this case a candy bar), divide it into 20 pieces, rearrange those pieces into the same candy bar, and have a piece to eat as well.

Now, you may say, "that is not possible!"  To which I could reply that at a time in history a spherical earth was also considered impossible.

You could say that this defies all the rules of logic as we know it. To which I could reply, do we really know logic.

Now, the idea the whole being more than the sum of its parts has been around for a long long time, at least going back to Aristotle.  Could it be that Hershey has proved it?

(I am not a Facebook user, so the best I could do is supply the link.)

12 or 13?
Here is another case where people seem to appear out of nowhere (or disappear to nowhere) for no apparent reason.

I would like to think that all of you out there believe that both this pictures are illusions of things that are really and truly impossible.  But I do not know that.

In color here you can see an illusion where a white square seems to be unaccounted for. An Algebra 1 student should be able to rectify this situation. At least they should have the mathematical tools necessary.

We should all be aware that only the conscious mind can reason its way through such illusions. We fall victim to illusions all the time without even knowing it.
Here is one that is great. I remember it whenever I hear stories better known as "eyewitness accounts. 

What brings all this to mind is that as a culture we are so willing to admit the existence of optical illusions and so willing to admit that we can get tricked, yet when it comes to politics we are so convinced that we are correct and that others are deceived or ignorant.

More later...

Saturday, April 5, 2014

The Fuzziness Continues

Taken from  the New York State Testing Guide’s Educator Guide to the Regents Examination in Geometry (Common Core)

Students will be expected to know grade-level mathematical content with fluency and to know which mathematical concepts to employ to solve real-world mathematics problems. Students will be expected to know grade-level mathematical content with fluency and to know which mathematical concepts to employ to solve real-world mathematics problems.

Upon reading this statement I immediately became focused on the word “fluency”.  Just to check my vocabulary, I went to http://www.merriam-webster.com/dictionary/fluency and found two definitions.
1)    the ability to speak easily and smoothly; especially : the ability to speak a foreign language easily and effectively
2)      the ability to do something in a way that seems very easy

I suspected that definition #1 was not relevant (unless the regents Exams will be oral exams), so definition #2 has to be the meaning intended. But is it?

Imagine the mathematical content in a Geometry course actually being described as “easy” by the end of the year. What a goal! What a target! Is it realistic as an expectation?

Being a natural skeptic, I went searching for more information. I checked the NYS Testing Guide for Algebra 1 (here) and found this: Students will be expected to know grade-level mathematical content with fluency and to know which mathematical concepts to employ to solve real-world mathematics problems.

In both documents, the statements were attached to categories labelled Shift 5: Application and Shift 6: Dual Intensity.  So naturally I needed to delve more.

When I wade through the http://www.engageny.org/ site I find that “Shift 6: Dual Intensity” is the tag for this:   Students are practicing and understanding. There is more than a balance between these two things in the classroom – both are occurring with intensity.

What does that mean? I get the practicing and understanding, but what do “more than a balance” and “occurring with intensity” mean?  I find these phrases being used all over the country in all kinds of “Common Core” related documents. This is scary stuff. Do a google search on this statement: “Students are practicing and understanding. There is more than a balance between these two things in the classroom – both are occurring with intensity.”  It’s an education in the making.

As a sample, this is from El Toro High School in California:
Shifts in Mathematics

Shift 1
Teachers significantly narrow and deepen the scope of how time and energy is spent in the math classroom.  They do so in order to focus deeply on only the concepts that are prioritized in the standards
Shift 2
Teachers carefully connect the learning within and across grades so that students can build new understanding onto foundations built in previous years.
Shift 3
Students are expected to have speed and accuracy with simple calculations, teacher structure class time and/or homework time for students to memorize through repetition, core functions.
Shift 4
Deep Understanding
Students deeply understand and can operate easily within a math concept before moving on.  They learn more than the trick to get the right answer.  They learn the math.
Shift 5
Students are expected to use math and choose the appropriate concept for application even when they are not prompted to do so.
Shift 6
Dual Intensity
Students are practicing and understanding.  There is more than a balance between these two things in the classroom – both are occurring with intensity.

Note these are called “shifts.” The implication is that it is all new and different. Some are not new, but some might be, depending on the meaning of the words used. What is the meaning of “Teachers significantly narrow and deepen the scope of how time and energy is spent in the math classroom”?  I can guess at what it is supposed to mean: fewer concepts so those dealt with can be handled better.  But does it mean that? I cannot tell.  I do know that the authors of that statement did not display much fluency with it.

The more I delve into Common Core documents at the state, district, and school levels the more I see a strange and unfortunate gathering of words. Delaware even says “Mathematics is not a list of disconnected tricks or mnemonics.” That can be found here.
Oops! Sorry Delaware! That idea was previously written as “Mathematics is not a list of disconnected topics, tricks, or mnemonics; it is a coherent body of knowledge made up of interconnected concepts. Therefore, the standards are designed around coherent progressions from grade to grade.” This appears in Key Shifts in Mathematics in the original Common Core postings. 

I find it insulting that such a statement appears. Thinking it is fine, even encouraged, but to find it relevant and meaningful enough to place in a formal document is an insult to all the people who have been teaching mathematics. If you need to insult some, so be it. But to insult all? That’s terrible.

Am I against the Common Core? Absolutely not. Am I pleased with it as it is? Absolutely not. 

Friday, April 4, 2014

Math Test or Reading Test?

I ask you to carefully compare two test questions. (You do not have to solve them.)

From the top of an apartment building, the angle of depression to a car parked on the street below is 38 degrees, as shown in the diagram below. The car is parked 80 feet from the base of the building. Find the height of the building, to the nearest tenth of a foot.


Solve for length x:

What's the big difference? Well it's twofold.
First, the second problem is a trig question. The first problem is a trig question embedded in, ummmm.., words?  Ignoring random error, more students should get the second one correct than the first one. Why? Less reading!!!!

The second difference is that the first problem was question 36 on the NYS Algebra Regents from this past January. the second was not on that test. 

Is there any reason why, on a math test, questions would be buried in verbiage?  NYS already has massive amounts of reading tests. Why turn a math test into a reading test?

Tuesday, April 1, 2014

Thinking Fast and Slow

I am only a third of the way through this book, but it is time to recommend it.

Any review I might post will wait.

For now, just read it!