To err is human...

If we cannot avoid the avoidable errors, what kind of errors can we avoid?



Ask a student for help

We are now well into the second semester in most of our schools. Fairly soon final exams will be looming, along with Regents exams (at least in New York) and assorted other Common Core assessments as well.

It is my hope that over the next few months the arguing over Common Core, etc., can stop, and the energy be directed at getting the students to succeed.

Be it English, Math, Social Studies, Spanish, whatever they are studying, support them at it.

If you are one of those math-phobics who tells everyone that you are and never were any good at math, don't pass that along to the kids. Instead of telling them you cannot help them, ask them to help you. Have them explain what they are doing and what they are working on.  Many times just trying to explain something clarifies it for the explainer.

Just as an example, if the graphic here brings back memories of painful high school classes, then go out and find a high school student and have them explain what they can to you about it.

Remember, by asking a student to help you, you are helping them.

How can we recognize quality in baseball batters?

In the chart ...(see below)... are the 24 possible situations which a batter may confront when he takes the plate, numbered 1 to 24. In addition are the 24 situations possible after the plate appearance is done (numbered 2 to 25).

Judgment of the quality of hitters must begin with assigning values to the "steps" possible in a specific plate appearance. For example, "1,1" denotes a no-out home run, "8,1", "16,9", and "24,17" all denote grand slams. The sequence 1,9,17,25 would be the "three up, three down" pitchers strive for. The sequence "8,25" would be a triple play.

Mathematically speaking, most plate appearances can be described as a single ordered pair of digits, the first digit for the situation when the batter first comes to the plate, and the second for the result after that batter's plate appearance. There are 576 such pairs. These must be assigned relative values. Until that is done, comparisons of hitters will remain a quagmire of subjective opinions.

Note: After these relative values are complete, one can then address strings such as 2,9,10, in which a runner is thrown out before a batter completes his plate appearance. No sense adding these in too early.

Know your states!!

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!

Truth in Advertising?

 

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).

If they are so nonchalant about this ad, it brings into question their advertising in general.

 

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 ²²⁄₇ , are unacceptable unless otherwise specified.

The statement above is from NYSED's document Mathematics Tools for Regents Exams in Algebra I, Geometry, and Algebra II (Common Core) .

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.

The web site Ask a Mathematician/Ask a Physicist states (here)

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?".

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?