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Thursday, March 31, 2016

Doesn't memory matter anymore? (Revisited)

Here are two images from PARCC's math reference sheets. (F you do not know what PARCC is, find out. Everyone should know). Look at them closely, and tell me what you notice.

Did you get it? The thing that stands out?
Look for "1 mile = 5280 feet".

It is in both. It also happens to be in all the PARCC reference sheets for grades 6, 7, and 8 as well.

For some reason PARCC expects students every year to use this information. Heck, they think it is important enough to put it on a reference sheet.

Evidently what they do not expect is students to remember that 1 mile is 5280 feet.
Ditto for for  "1 quart = 2 pints", "1 pound = 16 ounces", "1 ton = 200 pounds", and others as well.

Take note. All is not lost!
They have left out "1 yard = 3 feet".

My guess is that with its emphasis on problem solving and the availability of calculators, PARCC presumes that a student can figure that out by dividing 5280 by 1760.

I think back to my years in school, before calculators, when answering the question "What is 5280 divided by 1760?" correctly showed an ability to do something.

Those who belittle that ability, please take out a piece of paper and a writing utensil, and without using any electronic devices, divide 34785 by 4638.

For more thoughts on this topic, please visit this.

Wednesday, March 30, 2016

If only I had this in class...

GeoGebra has a steep learning curve at first, but the benefits are many.

Here is a little example demonstrating how control buttons and check boxes can help you control what is displayed. while maintaining interactivity of the display.

I might have used this in class by asking students to first give what they think an angle bisector (or median) might be. I could have projected this on the board, had the class give its best, and then show what the results actually are.

When discussing compass and straightedge constructions, project this on the board, demonstrate the construction, then let compare work with the Geogebra results.

The only limitations are your imagination together with the skills you have learned.

Tuesday, March 29, 2016

Let me know what you think of this

GeoGebra has massive functionality and flexibility.
Here is something that I could never have done in class without GeoGebra. It compares a couple methods for generating ellipses.

Play with it and let me know how I could improve it. The file can be found here.

Monday, March 28, 2016

Sine, Sine, Everywhere a Sine

I just made this up as an aid in teaching/learning the relationship between the sine of an angle and the unit circle. I have left it to the teacher to take the final step and actually point out the angle.

Do not deny your teachers and students the opportunity to learn and use GeoGebra!

Thursday, March 24, 2016

Give GeoGebra a Chance

Dynamic Geometry can be used to gain efficiency and minimize careless errors in class. Here is another that I wish I had had in class. Imagine how much more I could have focused on the students in class by having presentations dynamic and almost error-free. Imagine students having access to the same dynamic files from home.

Here is an example that shows how the measures of the angles of a triangle can be found if the lengths of the three sides are known. Besides the basic algebra, the student would need to know the Pythagorean Theorem and basic right triangle trig definitions. Taking the last step, to the angle measures themselves, could use a trig table, a calculator, or even Google. (But Google will give angle measure in radians, not degrees, so its use should be guided.  If you wish, you can google "calculator", flip it into degree mode, and do the inverse calculation).

This file can be found here.

Tuesday, March 22, 2016

So yesterday Donald Trump told the world about his "foreign advisers". One of them is George Papadopoulos.

Having had, evidently, 5 jobs in the last year, and currently residing in London, I guess Mr. Drumpf considers him an expert in world affairs. (I am only quoting from Mr. Papadopoulos' LinkedIn page, which as of today shows what you see here:)

Perhaps compared to The Donald himself, George is an expert.

I could accept that Mr. Papadopoulos might be considered for an entry-level position in the State Department, but then again, why should Trump be expected to do better than those who vote and campaign for him.

By the way, Thomas Jefferson said "The man who reads nothing at all is better educated than the man who reads nothing but newspapers.". What would he say in the days of the internet?

Mr. Trump should be aware of these word from Robert Frost: Education is the ability to listen to almost anything without losing your temper or your self-confidence.

Thursday, March 17, 2016

STEAM (Science, Technology, Engineering, ART, and Mathematics)

Could you imagine how the world might go astray if an art student used math software in an art class?

Wednesday, March 16, 2016

Go Figure Again!

This is just an adaptation of yesterday's entry.
I continue my quest for the recognition of dynamic geometry, such as GeoGebra, as a major tool in the learning of mathematics. There is no need for geometry to be taught the same way it has for decades!

Tuesday, March 15, 2016

Go Figure!

Here is one of my old standards in GeoGebra, but with a twist.
Just like our US politics, part is a mystery.

Tuesday, March 8, 2016

Trump or NO Trump?

Be careful taking news only from networks and social media.

Before today, Trump has 12 primary/caucus victories (or at least pluralities).
Among them are:
Alabama
Arkansas
Georgia
New Hampshire
South Carolina
Tennessee
Virginia
What do these 7 states have in common? They are all open primary states. Any voter from any party or even not from a party can vote.

In addition, Trump tied Kasich in Vermont, and he won in Massachusetts, where voters not registered in a party can vote.

Trump lost these states:
Oklahoma
Kansas
Iowa
Maine
What do these states have in common? They are not open primary states.

In this chart, the states that went for Obama in 2008 are listed in bold. Red font indicates states where Trump did worse than Romney in 2012.
 Trump Wins Trump Loses Closed Nevada 45% Louisiana 41% Kentucky 36% South Carolina 33% Maine 33% Iowa 24% Alaska 34% Oklahoma 28% Kansas 23% Open Alabama 43% Arkansas 33% Georgia 39% Massachusetts 49% New Hampshire 35% South Carolina 33% Tennessee 39% Virginia 35% Vermont -tied 33% Texas 27% Minnesota 21%

Take note: the highest Trump percentages were in Nevada and Massachusetts, both of which were Obama states in 2008. In addition, Trump out-polled Romney in 9 so far, but did worse in 9 as well.

It does not look like Trump is blowing the filed away. Perhaps he can just pack up and fly away.