McDonald's ambiguity

I have seen a lot over the years about the shape of the Golden Arches. Here I let you decide. Just drag the points to locations (anywhere, no special order) along the curve you are investigating, then click "show graph". Enjoy

 

Big business fails again...

Earlier this week this email was sent to Verizon Fios cable customers:

Dear Valued Verizon Customer, 

Verizon’s agreements to carry The Weather Channel and Weather Scan have expired, and have not been renewed.  In today’s environment, customers are increasingly accessing weather information not only from their TV but from a variety of online sources and apps.  Verizon is therefore pleased to launch the new AccuWeather Network, which will be available on FiOS® TV on channel 119/619 (HD) and on our free FiOS Mobile App starting March 10, 2015.  Verizon will also provide the FiOS TV WeatherBug “widget” application, which features hyper-local weather, on FiOS TV channel 49. WeatherBug can also be launched by pressing the “widget” button on the FiOS TV remote.

Sincerely,

Your Verizon Team

Please take note that the official Verizon review of the Weather Channel App includes:

Whether you’re hitting the beach, planning a picnic or taking a road trip, it’s helpful to know what kind of weather to expect out there. The Weather Channel app will help you do just that. It helps that the info in it is sourced from one of the most trusted weather outlets there is. 

Thus it appears that, for the benefit of its customers, Verizon cable is dumping its most trusted weather outlet.

There are a few aspects of this that help tarnish Verizon's image. First, it appears that Verizon was not honest in dealing with its customers. The email it sent out was virtually simultaneous with the disappearance of the weather channel.  If Verizon had the opinion it quotes in its email, it could and should have communicated with its customers well before "pulling the plug".  The last minute email makes it appear that Verizon was  surprised by The Weather Channel's not giving in to Verizon's contract demands, and was trying to cover its tracks. 

I suspect the real reason for this mess is that TWC wanted more than Verizon wanted to pay. Well thanks, cable TV, for protecting us from the TWC omnivores. Now how about the same for all those sports channels that really suck out pockets dry?  Why not stand up to them?  After all, most people get the most of their scores and sports information "not only from their TV but from a variety of online sources and apps."

Admit it, Verizon. You screwed up.

Solution? Reinstate The Weather Channel. It still has more weather than the History Channel had history and the Travel Channel has travel.

We have to do better..

After having been away for a while, I finally had the opportunity to look at the January 2015 New York State regents Exam in Algebra I (Common Core). I looked at the first question on it, and immediately my head was scratching.
The problem is:

I know that the answer expected is choice 2, which probably should have said "hours worked per week by employee". That ambiguity made me realize a few things about this question.

First, I presumed that profit is measured in dollars (as I took this as a problem for New York State). Placing that fact together with the mathematical knowledge that no units were given in the equation, and that only like terms can be subtracted, I came to the conclusion that the 8600 was really $8600. Now the 22 could be 22 of anything, but the nearness of $22 in the problem led me to accept that most would take it to mean $22.  Basic mathematical knowledge forces the conclusion that the x must then be "unit-free". That means that the x need not be the hours worked (by the employee".

Second, and this is probably due to some basic cynicism on my part, the use of a linear function for profit is as "unreal" as you can get. Do we wish students to be pushed a bit in their minds towards the notion that employee work-time is bad for business?  Is this the best we can do in the billion-dollar industry of education in New York under the guidance of Governor Cuomo?   Who creates these tests? 

Later on appears this questions:

This problem has some style points to its credit, but a big fat goose-egg when it comes to its realism.  The acceleration due to gravity on the Moon' surface is not .8 m/sec² but is, rounded, 1.6m/sec².  In the big quest to make problems "real", doesn't it make sense to use real information?

All is not so gloomy, however. Here is question #2, which to me is a masterpiece when it comes to a multiple choice question testing a meaningful skill.

Constructing a Pentagon from a Square

This is a total experiment put together today. I wanted to see how I could work with GeoGebra, PowerPoint, Office Mix, and Blogger together. For a first run, I am pleased. Now I can proceed...

More on NY Regents scaled scoring

The highest value (perfect score) is assigned 100, and the lowest possible is assigned 0. Passing is assigned 65 and passing with distinction is assigned 85. All values can then be converted to the scale using an algebraic transformation:scale score = (a)*(x**3) + (b)*(x**2) + (c)*(x) + d.In this equation, the value of x in each of four equations represents perfect scoring, lowest possible scoring, just passing, or just passing with distinction, respectively. The coefficients can be determined because each equation is set equal to the four known scale values: 0, 65, 85, and 100. These values yield four simultaneous equations. Thereafter, every logarithmic value, which, through equating has the exact same meaning in performance from test form to test form, can be assigned a scale value from 0 to 100 in which 65 is passing. In this way, a logarithmic scale having meaning with reference to achievement of State Learning Standards can be converted to a scale that ranges from 0 to 100 and carries the same meaning with reference to achieving State Learning Standards.

The above is a direct quite from an article written by Gerald E. DeMauro entitled How the Scale Scores Are Calculated for New York State Regents Examinations. (See entire article here). The excerpt does not seem too clear. What non-math people thought about I have no idea. Part of me wants to claim that Mr. DeMauro knew what he was writing about, but the exposition of his knowledge seemed quite cloudy. This article, as posted in 2002, helped feed my skepticism as to what was actually going to happen in New York State.

The Office of State Assessment has a page set up to describe how Regents exams are scored. This page, from 2009, says in its first two paragraphs

Test scoring is a complex process that derives student scores from the number of questions answered correctly on a test, the level of difficulty of the questions and the skills each question measures.  The final score on most Regents examinations is not a simple percentage or number of correct answers.  Nor is it the same as the raw score – the total number of points a student achieves on a test.

The New York State Education Department develops Regents examinations in accordance with the procedures for test development that are recognized by the American Education Research Association, the American Psychological Association, and the National Council on Measurement in Testing.  All major test developers, including SAT, NAEP, and AP, use these procedures and insist that all tests must be scaled as described above.

The last two words here surprised me. I searched and searched for what had been "described above" but could not find what was being referenced.

In my research on these issues, I came across an article from May 2014 by Gary Stern at The Journal News that stated

The state Education Department plans to set the scoring so that roughly the same percentage of students will pass the tests as in the past.

"We want to have stability in terms of passing rates," said Ken Wagner, deputy state education commissioner.

With this in mind, I realized I was completely befuddled by the direction NYSED was taking. I am still trying to square up the notion of standards-based testing, whereby all those who meet the standards have succeeded, and the acknowledged politico-economic push to get students through high school by age 18. To have two distinctly different goals such as these is mind-numbing, but to put Mr. Wagner's comments into the mix makes it nearly incomprehensible.

To give credence to Mr. Wagner's words we have the following slide from a June 2014 PowerPoint (find it all here)

Here we have information indicating that no matter how much better or worse performance on exams is, the scaling will get the passing results to conform to 2005 levels. It could seem that  the state is  telling everybody not to spend too much time with the weaker students, as it will not pay off.

Do not jump to conclusions without reading Determining “cut scores” as New York students take the first Common Core high school exams at Education by the Numbers thanks to The Hechinger Report.

More of my rambling later..

So the score is scaled...

Here is an Excel plot showing raw score on the January 2015 New York State regents in Algebra One (Common Core) at the bottom, and the scaled score (out of 100) to the left. The dividing spots for New York's 5 "Performance Levels" are given.

The 5 groups are described as such (from here:)

• NYS Level 5 Students performing at this level exceed Common Core expectations.
• NYS Level 4 Students performing at this level meet Common Core expectations.   
• NYS Level 3 Students performing at this level partially meet Common Core expectations (required for current Regents Diploma purposes).   
• NYS Level 2 (Safety Net) Students performing at this level partially meet Common Core expectations (required for Local Diploma purposes). 
• NYS Level 1 Students performing at this level do not demonstrate the knowledge and skills required for NYS Level 2.

Take note here, the New York State Education Department established in May, 2011, that "the local diploma option remains available to all students with disabilities provided they earn a score of 55-64 on one or more required Regents examinations." (see here) The state has a clearly established goal of getting these students to level 2, thus the steepness of the blue in region 1 above makes political sense.

Naturally, this quick run to level 2 needs a compensatory move in the opposite direction, but not too quickly. In this case, the state makes group 3 a narrow group. Raw score 19 means level 1, raw score 30 means level 3. That is the narrowest band on the raw score scale. A quick jump from "failure" to get over the "safety net." All students at level 3 get the same New York State credit that level 5 students get.

Once we begin the transition from level 3, we have to "toughen" up things. The minimums for Regents Diploma or Advance Regents Diploma require a score of 65 (scaled scores). To get "with Honors" tagged on, a student must average 90% on all required Regents exams. To get to scaled score 90 on this exam is a massive leap from getting that 65.  

The bulge at the low end requires a lessening rate of increase as we move to the higher end. In this case the rate decreases enough to create a concavity shift in region 4. This created the opportunity for a "finishing lap" in level 5 that conforms more closely to the "percentage score". Divide raw scores at the upper end by 86 and you will see they give results fairly close to the scaled score. This is valedictorian/salutatorian space, and the scaling here probably helps quiet arguments down the line.

Please take note that when New York shifted to its "Regents for all" philosophy, it created a scenario where political economics demanded the tests be easier to pass, yet national and international standards dictated that these tests could not be too simple, they could not be "easy A's".  These dual goals are addressed via the scaling above.

Perform a similar analysis on exams since the first math A that had a conversion chart. The data can be found by plodding through http://www.nysedregents.org/.

Chaos is in the mind of the beholder

It is time for even non-math people to understand the connection between randomness and order.
This triangle results by picking your 3 corner points, picking a starting point, and then rolling a die. If the die comes up 1 or 2, move halfway to point A. If it ends up 3 or 4, move halfway to B; 5 or 6 puts you halfway to C.
Rinse and repeat. Actually, do not rinse, just let it repeat. Again and again and again....