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Saturday, February 22, 2014

GeoGebra is known for its use in math, but it can be used elsewhere!
Here is a creation of mine to help you test your knowledge of the states of the US.
Find it here!

Sunday, February 16, 2014

This ad appeared in the Albany Times Union on February 13th this year. Keep in mind that the census population of Albany in 2010 was under 100,000.﻿

Having seen this add, I sent an email to the makers of the product asking where they got the data for the ad. their reply is here:﻿

We appreciate your inquiry regarding the information appearing in our Ads. As much as I'd love to help, the information you requested is not available. Most of the information appearing in our ads is provided by the outside advertising agencies that we hire to do our advertising.

Thanks again for taking the time to write.

Annica F.

Puffs Team

I found it very unnerving to find that the concept of truth in advertising apparently means nothing to this company (Procter & Gamble).

Wednesday, February 12, 2014

How Thin Can You Slice Your Pi?

3.1415926535897932384626433832795

That is the value of 

Students should use the π symbol and its corresponding value when applicable on the Regents Exams in Algebra I, Geometry, and Algebra II (Common Core). The approximate values of π, such as 3.1416, 3.14 or 227 , are unacceptable unless otherwise specified.

The statement above is from NYSED's document

What could possibly be "its corresponding value"?  Mathematicians throughout the world know that π is a transcendental number (worse than irrational, to the uninitiated). If the state's guidance wants to use an exact value in any place-value system, it is asking for the impossible. If it saying that the π button on a calculator must be used, it is just accepting the calculator's approximation as "better" than any others.

Before anyone passes judgment on my comments, I suggest that first read a column from the July 21, 2012 at Scientific American entitled "How Much Pi Do You Need?" (get it here).

Another good read is a page from BetterExplained.com  by entitled Learning Calculus: Overcoming Our Artificial Need for Precision (see it here) which says
...approximations are a part of Nature, yet everything works out. Why? We only need to be accurate within our scale. Uncertainty at the atomic level doesn’t matter when you’re dealing with human-sized objects.
Every major civilization has been aware of π and have relied on various approximate values.  Basically they’d find an approximation that was “good enough” to find the length around any circle given the length across it (the definition of π) and go with that.

One question I pose is this: knowing that  π is by definition the circumference of a circle divided by twice its radius, how large a circle would we need to get 8-digit accuracy in our approximation  if our measurements of length were no better than the nearest millimeter?

On a simpler note: take any circle you wish, and measure its circumference and radius (I say measure, not calculate), then divide the circumference by twice the radius. Take the result of your calculation, and see how closely it agrees to the decimal at the top of this post.

I think you will be amazed at how different it is.

Do not force students to try to pin down a value that cannot be pinned down, rely solely on a calculator's value (not all calculators have the same approximation), or depend on "otherwise specified".  Instead, use this famous number as a tool in teaching the need for approximations, helping students learn to deal with accuracy and its colleague precision, and developing skill in answering questions such as "how accurate do I need to be?".

Monday, February 10, 2014

Pearson: Friend or Foe?

As the country slowly realizes that the big issue with the Common Core is not the core itself but the testing aspect of school accountability, I feel it is my duty to help keep the debate focused.
As a preface to my comments, let me point out the existence of Pearson PLC, specifically its "North America" page, (see here) which as of today says
We are the largest provider of educational assessment services in the U.S. We mark large-scale school examinations for the U.S. federal government and more than 25 American states, scoring billions of multiple-choice tests and more than 111 million essays every year.
Uniform national standards do make it easier for such a company to offer products to a greater number of states. These states, deciding that there may be no need to invent their own wheel, may then see Pearson as a cost-effective option. Pearson (or any other such company) has no real interest in what those standards are, but a large interest in their adoption by as many states as possible. The sooner states were in lockstep, the better for Pearson.
The real push behind all the testing is the program known as Race to the Top. This program states, on its own web site,
Authorized under the American Recovery and Reinvestment Act of 2009 (ARRA), the Race to the Top Assessment Program provides funding to consortia of States to develop assessments that are valid, support and inform instruction, provide accurate information about what students know and can do, and measure student achievement against standards designed to ensure that all students gain the knowledge and skills needed to succeed in college and the workplace. These assessments are intended to play a critical role in educational systems; provide administrators, educators, parents, and students with the data and information needed to continuously improve teaching and learning; and help meet the President's goal of restoring, by 2020, the nation's position as the world leader in college graduates.
Note the phrase "consortia of states". The burden starts with states working together. Who benefits from that criterion alone? Does it really and truly matter to an 8th grade teacher whether the curricula standards they need to address have national, state, county, or district origins?  Does it matter to the students?  Does it presume that any state addressing the issue alone will be less successful?
Pearson says on their web site
Race to the Top is a federal competitive grant program designed to reward states and districts that have made innovative education reforms.
So does that contradict the stated goal of Race to the Top? Is the funding for "consortia of states" or is it a reward to states and districts?

In addition, Pearson has a link to a Race to the Top handbook for grants which states that the purpose of a grant is to:

Reward Local Education Agencies (LEAs) who have the leadership and vision to implement the strategies, structures and systems of support to move to personalized, student-focused approaches to teaching and learning that will use collaborative, data-based strategies and 21st century tools to deliver instruction and supports tailored to the needs and goals of each student, with the goal of enabling all students to graduate college- and career-ready.
What is a Local Education Agency?  Do you know? Look it up!

Pearson's handbook goes to the assert that  "Eligible applicants include only individual LEAs and consortia of LEAs." Further, it says
1. Minimum of 2000 participating students. Consortiums can serve fewer than 2,000 students, if the consortium has at least 10 LEAs and at least 75% of the students served by each LEA are participating students.
2. At least 40% of participating students must be from low-income families.
So its natural push is to deal with larger groups. Due to the first restriction my district would not have been allowed to apply by itself. The second item would rule out many school districts.

The handbook also points to this address for more info: www2.ed.gov/programs/racetothetop-district/index.html . Check that page out. Of course, the deadline for these grants was last October, so the page MIGHT have changed, but it seems to have very little to do with Race to the Top.

The American Recovery and Reinvestment Act of 2009, the parent of Race to the Top, stipulates
The overall goals of the ARRA are to stimulate the economy in the short term and invest in education and other essential public services to ensure the long-term economic health of our nation.

So the original motive is economics-based, which easily leads to the idea that the most crucial measures of the success of education is the "economic health of the nation." Is it really?

Back to the Race to the Top quote above: if we are to restore the US as the world leader in college graduates by 2020, we are focusing attention on students graduating from high school by 2016, which means those entering kindergarten by 2003. How does all the testing of grades K-8 in 2014 even come into play?

Late last year a group of New York state principals drafted a letter (see it here) regarding Common Core and testing in which they said "Since 2010, the amount of time spent on average taking the 3-8 ELA and Math tests has increased by a whopping 128%! The increase has been particularly hard on our younger students, with third graders seeing an increase of 163%". Who made big bucks on these tests?
During my time on a Strategic Planning Committee in the district where I taught, the recognition was made that we had to look at the system not K-12, but rather 12-K. We had to start with graduating standards and design in reverse, so that each level would seamlessly flow into the next. We were aware that the program had to remain in flux, since as students cohorts were progressing through the system, they would be different from the cohort before, and (hopefully) more successful.

I know that serious implementation of any curricular change arrives with its assessment piece, so I understand fully why the K-8 world is boiling, especially in my home state.  What I do not understand is what the K-8 world has to do with the 2020 goal. The K-8 years are extremely important, but who really gains by the mad rush into K-8 testing? Could it be Pearson?

Saturday, February 8, 2014

Common Core is not about testing

The  Common Core standards are all about  Math and English. They are not about testing.

Rex Smith of the Albany Times Union says in this morning's paper
People are blaming Common Core for a cluster of pressures in the schools, including excessive standardized testing and a revised scoring system that has shown student performance to be lower than previously thought. But a lot of the folks attacking the Common Core, I’m convinced, haven’t actually looked at the standards, or talked with education experts about them. Until we have heard more from a thoughtful review by educators, the calls to abandon the reform are premature.

Common Core does not prescribe tests, or modules, or most of the things that people are complaining about. In New York, all those things called modules are not from the Common Core. They are designed by the New York State Education Department. The EngageNY web site states

The optional curricular materials on EngageNY are designed to be adopted or adapted. Educators will find both PDF and Word versions available for their use. Some lessons provide detailed instructions or recommendations but it is important to note that the lessons are not scripts and rather they should be viewed as vignettes so that the reader can imagine how the class could look.
I added in the red to emphasize that even NY does not believe it knows "the way" to do things.
I also know that there are districts that have mandates that their teachers follow the modules. Those districts are naive, misled, misleading, and dangerous. Common Core is none of those.

I also find it misleading for Governor Andrew Cuomo to select Todd Hathaway, for one, as a member of his new committee. After all, Common Core is about math and English, and Hathaway is a high school history (social studies) teacher. The least he could have done would be to include a math teacher and an English teacher.

Friday, February 7, 2014

Don't Let Me Down...

Donna St. George wrote an article for The Washington Post of January 8, 2014, in which she says:
Duncan said that students should be removed from classrooms “as a last resort,” and only for serious infractions such as endangering the safety of other students or teachers.

Today's Albany Times Union  has an editorial which states:
Studies show that suspensions lower academic performance, increase the dropout rate, decrease graduation rates and increase crime and prison time.
I find both these statements indicative of a mindset that fails to consider the impact on the students who are not suspended: the rest of the class, in other words.

In my tears in the classroom there were numerous times when a class's best and most productive days were when a troublemaker (sometimes two) was absent, for whatever reason.  I know that some feel that the good students are a positive influence on the bad students, but I am not talking about a bad students.  I am talking about troublemakers. Before politicians discuss impacts on those suspended, they should discuss impacts on those not suspended. Good students can help bad students in many ways, if by "bad student" we mean one for whom the studies are harder, but those good students should not have to suffer because of the presence of disruptive troublemakers.

I also have problems with the Times Union editorial praising community service as an alternative to suspension. I would hate to see community service viewed as a punishment.

The Post article ends like this:
Duncan noted Wednesday that South Carolina suspended 12.7 percent of its students — at the high end of the spectrum — while North Dakota suspended just 2.2 percent.
“That huge disparity is not caused by differences in children,” he said. “It is caused by differences in training, professional development and discipline policies.”
The implication here is that the training, professional development, and discipline policies are that much "better" in North Dakota than in South Carolina. Perhaps, rather than giving speeches and pontificating his opinions, he should be up in Minot or Bismarck taking notes.

Just in passing, he might also want to take note that North Dakota's largest school district, in Bismarck, has about 11,000 students (see here), while South Carolina's largest district, Greenville, has over 70,000 and is one of the 50 largest in the country (see here). For that matter, North Dakota is almost 90% "non-Hispanic white" whereas South Carolina is under 65% "non-Hispanic white" (see here). Further, as of 2012 North Dakota had about 95,000 students and South Carolina had about 725,000 (see here). There are indeed vast differences in the makeup of school populations between North Dakota and South Carolina.

Many people will say that my last paragraph is a sign of bias on my part, despite the fact that I am only quoting statistics. Many of those same people will praise Arne Duncan's words, even though they are unsupported and, if true, describe knowledge upon which he is not acting.

Saturday, February 1, 2014

Separation anxiety...

Starting this month I will be separating my math-specific posts and placing them in a different blog: Mr. VL's Math Page. My other entries will be kept here, as long as Blogger keeps operating as it does now.

My main goal in doing this is to have a place for students and teachers to go for things that might relate to their courses, and to keep my political and social ramblings separate.

Wish me luck!