Wednesday, December 31, 2014

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.)
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.

Tuesday, December 9, 2014

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."

Sunday, December 7, 2014

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?

Wednesday, December 3, 2014


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. 

Saturday, November 29, 2014

What happened?

Whenever I travel I try to take as many photos as I can that are worthwhile but not find-able all over the web. No sense taking pictures that have already been taken. I look for unique pictures. Even more so, I like them to be though-provoking.

This one I took while walking on a dock in St. Thomas, USVI, a bit over a year ago. I can tell you that the hat was floating, although some people to whom I have shown the picture thought I had caught it in midair. That led me to consider how we describe what we see, and how we extrapolate in the process.

Anyone who describes the hat as in midair must presume some person, or some thing, as the thrower, unless perhaps it was windblown.  Even knowing it is floating, the question could still be asked: How did it get there?

So, if I was to ask you to write the history of this hat, as best you can, how would you respond?

Friday, November 21, 2014

FOILed again?

The statement in red here is one I came across while taking another look at Common Core standards. I decided to Google the statement. I did discover that Google will not let you use more than 32 words between quotes, so I Googled just the 1st sentence in quotes (so Google looks for an exact match), and got 14,100 hits. Listed below are just a few of them.

There is a world of difference between a student who can summon a mnemonic device to expand a product such as (a + b)(x + y) and a student who can explain where the mnemonic comes from. The student who can explain the rule understands the mathematics, and may have a better chance to succeed at a less familiar task such as expanding (a + b + c)(x + y).

It's a bit misleading. The second sentence says "may have a better chance". Anyone who really and truly understands what binomial multiplication is and why it is, WILL have a better chance. A much much better chance.

It's also interesting that the statements refer to "a mnemonic device" and gives it a bad flavor. I suspect the device the authors had in mind was the old FOIL method for binomial multiplication, and the impetus behind the statements was the knowledge that there are teachers who taught only FOIL, and nothing more. (Could it be in use here only because F-O-I-L actually spells a word in English? Could this be why US math is falling behind?!? Imagine!?!) Do you know the meaning of FACE? Does it help or hinder in music studies?

I find it odd that a statement which embodies such a major thrust in educational philosophy is phrased in the context of binomial multiplication.  Multiplying binomials is something most people never do in their lives. However, if binomial (and polynomial) multiplication where actually dealt with carefully and fully they would be recognized as the foundation behind most algorithms for multiplication. Multiplying a pair of two digit numbers is actually a binomial multiplication. Multiplying 564 and 37 is actually multiplying a trinomial and a binomial. (I find it interesting that my spell-checker just marked "trinomial" as a misspelled word. For the record, it does not acknowledge "pf" as a possible error.)

The 4th grade standards include this: Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

The arrays and area models referred to here are exactly the same devices that are, or could be, used to describe the distributive process applied when multiplying polynomials. It would be nice if our educational system would recognize this and capitalize this, and perhaps gather 4th grade and high school teachers together to carefully comb out more connections. I an willing to bet that a substantial number of 4th grade teachers are not tuned in to the distributive rule as it relates to polynomial multiplication. A few visuals are here.

Whatever happens with Common Core, let's at least recognize that it doesn't have all the right answers, but it could be spurring people into asking the right questions. I hope.

Thursday, November 6, 2014

GeoGebra no later than middle school...

This is just a continuing saga of options that teachers and students now have that I hope they are using.  with the technology we have now students can be introduced to new things in dynamic ways making them accessible as never before.

I just made this in GeoGebra as an example of check boxes in case I needed one at the AMTNYS conference presentation next week.

Wednesday, November 5, 2014

A Heart for Mathematics

Basic geometry as work. Circles with radii 1, 3, and 6, centered at the origin and 3 units below. Two points rotating counterclockwise at the same rotational speed, one clockwise at twice that speed. Those points are connected to form a triangle, and two angle bisectors shown. The trace shows the path of the point of intersection of those medians, the incenter.

There is a lot of mathematics in this diagram. I believe that creations such as these can be used with young students to "hook" them into mathematics long before they know the math needed to write equations for such graphs. Although the equation would be heavy into trig, the creation of the graph requires no trig at all. Basic geometric concepts such as circle, line, bisection, rotation are just about all that is needed. 

A tremendous amount of mathematics can be learned by setting kids loose with GeoGebra and a basic knowledge of the GeoGebra toolbar. In many respects, kids would probably learn GeoGebra faster than adults.

Animations and GeoGebra will be the topic of my session at the AMTNYS (Association of Mathematics Teachers of New York State) annual conference in Syracuse next Monday.

Monday, October 13, 2014

Floating Midpoints

This image consists of a visual recording made while using GeoGebra which was then converted to an animated gif and then resized to fit the blogger window.

Friday, October 10, 2014

If only...

I wish I had this ability when I was teaching. For more details on animations and GeoGebra, come to my presentation at AMTNYS in Syracuse on Nov. 10. Click here for details. the sketch is online here.

Saturday, October 4, 2014

Avoid those errurs, I mean, errors.

During 30+years in the classroom, I developed a great appreciation for the impact of the careless error. Sometimes called "avoidable" errors, they crop up frequently in the mathematics classroom, and often are the root cause of a problem's seeming impossibility to the student solver.

Such an error is much more powerful in a student's math class than, perhaps, in his English class. Readers slide past spelling errors, often not even noticing them, while perhaps having a bit of a stronger jolt by a punctuation error. But even a tiny arithmetic error can turn a simple mathematics problem into an insurmountable task.

We may call them avoidable, because they can and should be avoided, and would be fixed if not avoided if we would only do such things as check our work, proofread, in short: be careful.

I have put together a small collection of such errors as they have appeared out in public. This collection is merely meant as a reminder to us all that double-checking our work is not a sinful task.

The first one here was snapped during a TV news broadcast, while the second was from a newspaper. Neither is a major error, but they both were avoidable.

Many many times the individual who made the error never notices it, which is why, I presume, the media has people on staff with the responsibility of checking each other's work. The reason I include them here is that they are evidence of a systemic failure in that regard.

I have put these and a few others on a web page, which can be found here. I pose the task to you to identify the errors. After all, somebody has to find them before anyone will fix them. That is the nature of avoiding an avoidable error.

Wednesday, August 27, 2014

Town of Kinderhook, your web page stinks!!!

I heard at one time in my life that town web sites were geared towards "open" government and keeping people informed.

Someone should convey that message to the town of Kinderhook, NY.
As of this morning, August 27, 2014, the page entitled "Town Board Meeting Minutes" looks like this:

Wed, Apr 2, 2014 2:56 PM
Wed, Apr 2, 2014 2:56 PM
Wed, Apr 2, 2014 2:55 PM
Wed, Apr 2, 2014 2:55 PM
Wed, Apr 2, 2014 2:54 PM
Wed, Apr 2, 2014 2:54 PM
Wed, Apr 2, 2014 2:54 PM
Thu, Dec 12, 2013 12:02 PM
Thu, Dec 12, 2013 12:01 PM
Thu, Dec 12, 2013 12:00 PM
Thu, Oct 10, 2013 11:53 AM
Thu, Oct 10, 2013 11:53 AM
Thu, Oct 10, 2013 11:52 AM
Thu, Oct 10, 2013 11:51 AM
Thu, Oct 10, 2013 11:50 AM
Thu, Oct 10, 2013 11:50 AM
Tue, May 21, 2013 1:04 PM
Tue, May 21, 2013 1:04 PM
Tue, May 21, 2013 1:04 PM
Tue, May 21, 2013 1:03 PM
The date on the left is the date the minutes were posted on the web,

That is the good stuff!!! The page titled "Agendas and Minutes" looks like this:
Agendas and Minutes

That's it!! Blank!!

That is how we are kept informed!!!  This is a town with no radio or TV or paper. (Oh, they do say our legal paper is the Hudson Register Star)

The town has a planning board. As of today, its page looks like this;
Planning Board Agendas
Thu, Feb 9, 2012 10:02 PM
Tue, Feb 7, 2012 7:12 PM
Thu, Jan 12, 2012 7:52 PM
There is more!
The Zoning Board of Appeals has a page. It looks like this:
ZBA Meeting Minutes
Sun, Jan 12, 2014 12:59 PM
Sun, Jan 12, 2014 12:59 PM
Sun, Jan 12, 2014 12:58 PM
Sun, Jan 12, 2014 12:56 PM
Sat, Dec 28, 2013 4:31 PM
Sat, Dec 28, 2013 4:30 PM
Wed, Sep 11, 2013 7:37 PM
Tue, Jul 2, 2013 9:57 PM
Tue, Jul 2, 2013 9:56 PM
Thu, Jul 5, 2012 6:19 PM
Thu, Jul 5, 2012 6:10 PM
Sun, Mar 25, 2012 12:12 PM
Thu, May 5, 2011 5:56 PM
Mon, Mar 7, 2011 5:20 PM
Mon, Mar 7, 2011 4:20 PM
Thu, Mar 18, 2010 8:07 PM
Tue, Dec 8, 2009 12:05 PM
Tue, Dec 8, 2009 12:05 PM
Wed, Sep 9, 2009 4:05 PM
I could go on, but I think the message is clear. 
Kinderhook, get your act together!

Monday, August 18, 2014

Can you drive while adding 2 digits numbers?

Today's Albany Times Union contains an Associated Press article written by Lauran Neergaard. Actually, the paper does not name the writer, just credits the story to the AP. A little searching discovered the article's author, and also some interesting headlines for the article. Here are three of them:

In math, memorizing counts out of Albany Times Union
Kids’ brains reorganize when learning math skills from Fallreporter.com out of Fond du Lac, Wisconsin

I find it interesting that each title creates a slightly different spin. The Fallreporter.com version promotes the stance that learning mathematics (which in this article is described as basic arithmetic) changes the way the brain operates. The KOB4 version might be taken to describe a more static brain which can reveal what is happening when kids learn math. The Times Union headline seems to stress the most basic form of remembering, known as memorization, as the big key.

I note that the Fond du Lac title matches the title used at ABC News (see it here)

Somehow, somewhere, somebody has to realize that memorization is only a short-term solution, and can only lead to a long-term skill if that which is memorized is then used repeatedly. In the case of arithmetic, this would require a delay in the use of calculators until arithmetic skills have been strongly embedded in the brain.

Take a moment to read Susan R. Barry's column from Psychology Today titled "Math and Memory", and  the Josef Parvizi (Stanford Medicine News Center) article "Mathematics or Memory?"

Start with the AP column and the two articles just named, and consider them in light of our big push to stop texting while driving. In what way is driving a car similar to doing arithmetic? Or is it the texting that is more like doing arithmetic? Can you text and do arithmetic simultaneously? Or is it easier to drive and do arithmetic easier? I would suspect that using a calculator while driving is very dangerous. Can you say that about doing basic arithmetic mentally and driving at the same time?

Unless and until you have carefully considered situations such as these, I would shy away from making claims that giving kids calculators is helping them.

Let's give the kids arithmetic, and keep the calculators away, until they are truly needed, not just wanted.

Tuesday, July 29, 2014

Think Again, Ms. Tucker

Cynthia Tucker's latest column (online here) which I first read in the Albany Times Union (7/29/14) is titled "Ineffective educators need to go". Brilliant.

Consider: Ineffective______________ need to go. I dare say you can pretty much fill in the blank with almost any profession and obtain a fairly accurate statement. For that matter, do not limit it to professions: fill it in with "toasters", "golf balls", "politicians", "garden hoses", "parents"...

The title of Ms. Tucker's column is probably meant to ignite the reader's passionate opinions, either for or against teachers. So be it. I agree with her title, but little else in her column.

One of her statements is:
It pains me to say this since I hail from a long line of educators, but schoolteachers have become a huge stumbling block to classroom reform.
She forgets to add the statement "Schoolteachers are some of the biggest proponents of classroom reform."

She also adds:
Good teachers deserve our whole-hearted support — higher salaries, better working conditions, more respect. But they ought to stop defending their weaker colleagues. Bad teachers need to be forced into another line of work.
A few items Ms. Tucker ought to recognize:

  1. Teachers are not the ones who hire and fire other teachers. Neither do teacher unions. That responsibility falls in the hands of administrators and school boards. 
  2. By state law (at least in NY) teacher salaries are the negotiated by unions with the districts.
  3. Nobody trusts anybody to be the judge of good teacher vs bad teacher.  Yet, someone would have to judge, if Ms. Tuckers utopia is to become a reality.
  4. No teacher gets tenure when hired. It is granted by school boards, generally upon recommendation by administrators.
Greensboro, NC newspaper "News & Record" had an article in its May 31, 2014 issue that included the statement 
Critics say teachers too often get tenure simply by continuing to show up for work and that bad teachers can be too expensive to fire.
Whose fault is that? Who gets the blame? That article, from the Associated Press, also talks about an ongoing North Carolina push to get teachers to waive their tenure rights in return for a pay raise. Imagine the general idea of giving up a right in exchange for cash!  

If the truth be told, spending all this time and energy addressing teachers, tenure, accountability and reform, is time spent addressing a symptom. If we want our schools to be more successful, we need a culture and society in which education is respected. A small start in that direction might be news media in this country taking a portion of their sports budget and instead reporting on successful students in the local schools. Imagine media slowly spreading the word about what academic success looks like and what it entails.

I am not saying that the world of teachers does not have room for improvement. What I am saying is that the end result will not be better if all we do is appease the gripes of those who blame it all on teachers, and it could, indeed, be much worse.

Tuesday, July 8, 2014

The News That is Missing

The clip here is from today's Albany Times Union, but I would expect, being an Associated Press story, that it also appeared elsewhere.  It strikes me for a few key reasons:
  1. With redeployment of 313 officers due to 48 more incidents, does it imply that, had there been a reduction of 48 shootings, the NYPD would have taken 313 officers out of those areas?
  2. Did the increase occur in the "high crime streets"?  I would have thought that the AP would have asked that, and included the answer in the story.
  3. Would the story have the same impact if the story had said that there was 1 shooting for every 14893 residents, up from 1 for every 16284 residents. Would the impact be stronger or weaker? (This is based on estimated 2012 population of 8.37 million.)
  4. The 313 officers redeployed. Where did they come from? Did crime rate in those areas go down?
  5. The officers have been redeployed for 90 days. Does that mean that mean NYPD expects the perceived need to decrease on October 6? To what would they attribute this?
  6. If 3 guns shoot 8 bullets in 1 "event", is that 1 shooting, 3 shootings, or 8 shootings?
  7. Is this increase attributable to more guns, more people with guns, or some other factor?
  8. If this increase is a random statistical bump, and due to the general process known as "regression to the mean" is followed by a comparable decrease, will this redeployment be called a success? (Just as I followed up my hole-in-one with a couple double bogies.)
The scary thing here is that in this age of tweets and texts, a lot of people are getting a lot of their "news" in digital strings shorter than this story. This is in direct competition with the push in the world of education to greater thinking and learning skills.  

If nothing else, people should be working to lengthen their attention spans and strengthen their skills. In aid to this cause, the news media should produce stories that promote both of those goals. What seems to be happening is that media has regressed in both those areas over time. Just look at the evolution of Time magazine.

The Chicago Tribune, on May 18 of this year, had this story on their web site:
Are words going out of style? At a time when the public's hunger for news reaches new heights, it is startling to hear the new word-count limits that Reuters and The Associated Press have imposed on their reporters.
Top editors at Reuters sent out a memo in early May that asks its writers in the Americas to trim their copy to 300 to 500 words for all but the most "distinctive" stories — meaning stories that offer something that nobody else does. A top editor at AP set similar limits for his staff.
The Washington Post on May 12 contributed (see here):
This is a short news article about how news articles are becoming shorter. 
The world’s largest independent news organization, the Associated Press, for one, has told its journalists to cut the fat — and keep their stories between 300 and 500 words, a length in which this story (301 words) would easily fit. 
That’s 500 words, max, on just about every one of the 2,000 or so stories AP journalists report each day, from ballgames to bomb blasts to the latest political skulduggery. 
Exceptions: AP has told its reporters that the top one or two stories in each state may run between 500 and 700 words, and the top global stories of the day may be a practically Faulknerian 700-plus words. Reporters in AP’s newly expanded investigative unit will be permitted to bust the limits. 
Why? The news service says many of its members — 15,000 or so newspapers, Web sites, and radio and TV stations around the world — lack the staff to trim stories to fit their shrinking news holes. What’s more, AP says, readers can get turned off by longer stories, especially on mobile devices, an increasingly popular way for people to get the day’s news. 
“We need to be more disciplined about what needs to be said,” Kathleen Carroll, AP’s executive editor, said in a (short) interview. “We don’t do enough distilling and honing, and we end up making our readers do more work.”
If anyone is concerned as to how to improve education, and wishes to get a clear sense of the Common Core, do not trust what you know, as the media has cut your information in a desire to keep it simple.

Come on America, we can do better. 

Wednesday, June 25, 2014

Those "aha!" Moments.

Here is a very simple application of GeoGebra that I created this morning in about half an hour.
Simply created, yet totally impossible when I was a student, and largely impossible and generally improbable when I was a teacher. It depends on the correct technology and a teacher who can make it or at least use it.

Little technological things like this have the potential for creating those "aha!" moments, the presence of which are mileposts in the life of the mathematician, the absence of which create the dead ends of the math phobic.

We need to go out of our way to enable these "aha!" moments.
Improving the mathematical skills and knowledge of our country requires it.
If you wish to download the file itself and make your own modifications, you can get it here.

Thursday, June 19, 2014

Correlation coefficient of linear fit?

The Common Core State Standards Initiative has, in its High School Statistics and Probability section, the statement 
Compute (using technology) and interpret the correlation coefficient of a linear fit.
You can find it here.

I suppose I can accept the utilitarian notion of being able to computer something on a calculator while having no idea where it comes from, as long as the result can be interpreted correctly.

I do have a problem with question 11 from the New York State Algebra I (Common Core) exam. 

I see nothing in here involving interpretation or understanding. All I see is a question asking whether or not the student could remember a cook-book recipe from their calculator's user manual. Pity the poor teacher whose students have the gamut of calculators. (After all, school cannot be a mandate for using a certain company's products.)  I must assume that this question is not testing the students ability to state the coordinate names for the points, as the question requires a number of steps beyond that.

What I do see here is a lousy test question. 

As for the relevance of the topic itself, well, that is debatable. If Algebra I is considered as an introductory high school course, I say absolutely not. Comprehension of correlation coefficient requires a skills base and a time commitment better suited to a later course. If Algebra I is considered an exit exam, perhaps the situation changes. Since New York now considers Algebra I regents exam as both an introductory course (anything below it is considered remedial) and an exit course, in a one-size-fits-all scenario, things are very confusing.

By the way, I looked at NYSED's page regarding this test. It is here, and as of today, all its links are password-protected. 

Monday, June 9, 2014

A Fee? Charging potential teachers for double-checking a grade?

If you believe that a score (not a condition code) on one or more rubrics was reported in error, you may submit a request for a score confirmation in writing. The fee is $200. Information about the score confirmation service is available on edtpa.com.
The above statement I found on the edtpa web site. Find the full page here.

This is an example of Pearson creating a process that both discourages complaints and creates cash flow all at the same time.  Whether or not you believe that evaluating new teachers should be contracted out to a foreign-based company, the job of that company is to get things correct. If and when they make mistakes, which they will, they should make financial amends to the affected individuals by refunding money already paid. They should not create a cash cow for themselves.

Speaking of edtpa, The Huffington Post has a must read written by Alan Singer of Hofstra University. His column The "Big Lie" Behind the High-Stakes Testing of Student Teachers describes many of the other issues surrounding the involvement of Pearson in the certification of New York State teachers.

The best thing that can happen in New York right now is for Pearson's involvement in anything be ended.

Wednesday, May 28, 2014

StartUpNY? Only politicians could make this up

So the problem in NY state according to our state government is high taxes.

Solution? Run a lottery for businesses in which the winners will pay no taxes! (Provided that you meet their criteria, of course! See http://startup.ny.gov/)

Will that help the business climate in New York? No.  As a matter of fact if these businesses do start up and pay no taxes, their existence will in effect increase the tax burden of the businesses already in place. Great solution!! That is, overlooking the fact that business "startups" usually don't generate a profit for a number of years, making the income tax issue kind of moot, and overlooking that a successful startup generally is at its smallest size when it is beginning, so the property tax issue isn't that big.

Spoiler alert: When all is said and done, these businesses are supposed to bring in new jobs. These people will presumably be voting in new York State. Whom do you think they will vote for? Perhaps the politicians who created these tax-free jobs for them? Remember, a business cannot vote but people can. The voting employees will be getting a meaningful tax break from day one.

What happens when the 10 years are up and the tax breaks are gone? Well, expect our creative politicians to have a solution! After all, they won't want these voters to follow the businesses out of state.


Tuesday, May 27, 2014

Common Core Needs a Rewrite

Fluently multiply multi-digit whole numbers using the standard algorithm.
Thus states 5.NBT.5 of the Common Core standards.

No doubt, I find it positive to include multiplication of multi-digit whole numbers, and I believe the intention of the statement is that people should be able to do it mentally or on paper, but without calculators.  But to mandate "the standard algorithm", whatever that is, and require "fluent" use is way out of line.
I suspect that by standard algorithm they mean something like this:

What I find interesting is the inclusion of the phrase "using the standard algorithm". That, together with the word "fluently".

I learned it that way. So did millions of others. But many did not master it.

In my teaching days it hit me that in a world that reads and writes left-to-right, we were expecting students to work right-to-left in their arithmetic.  I consider that one of the great fertilizing factors of math phobia.  Left-to-right processes can be helpful for several reasons:
  • The chance of error increases the further you get in an algorithm, and with numbers the most significant figures are to the left.
  • Estimation is much easier for a brain trained left-to-right.
  • Mental calculation skills improve when using the ability to read, write, and say numbers the same way.
  • When using the above algorithm, the brain focuses on digits and not numbers.
Now, when it comes to standard algorithms, there are many. A neat one, perhaps easy for those accustomed to it, is a Japanese technique using drawing segments and counting intersections. A video sample form YouTube is here.

Lattice multiplication is kind of neat, but I would not call it an algorithm that leads to greater understanding. 

Back to Common Core: time to do a rewrite. Get Pearson out of the way, get big business to the sidelines, and get some math people covering the gamut from K to 12. Just make sure that they all have at least a BA in math.  Just because Common Core means well doesn't mean it is doing it yet.

The web site freetestprep.net  acknowledges this on one of their pages (see here).

Thursday, May 22, 2014

Common Core is Fine, But its Application is Terrible

In my meanderings around the common core story, I came across a shocker. Here is one question from a snapshot of a test posted online. (the story is here and the snapshot is here)
The article this came from refers to the test as a first grade test. If that is the case, I am amazed and shocked.

Are typical first graders that good at reading? I just popped the problem into my word processor and came up with a Flesh-Kincaid reading level of 6th grade.

Here is another:
I am just a retired career math and computers teacher with BA and MA in Math and I can honestly say in my lifetime I have never seen such a question: indeed, I have never seen an addition fact referred to as a "subtraction sentence."

Back in February I posted an entry here question Pearson's role in Common Core. (It is here.)  I question their role even more now.

The two examples above are not the worst part. Question #1 is the worst, but I will let you click the link and see that for yourself.