Please Promote Math Positively!!

Inspired by a New York Times reporter who wrote in the Home section that "trying tiling was sort of like choosing to spend your weekend at an algebra slam!"

If we can promote Math in a positive way, it will help teachers and parents and most importantly students!

Please consider the way we speak of Math and how it can influence our students and society.  

Tiling 102 read the first paragraph

The article had photos of tiling tools so below please find some Math tools

Education Online -- A Wave of the Future

While there will always be a need for teachers and classrooms, on-line learning is here to stay. The Internet and on-line learning offers a flexible and economical alternative to classroom learning. This article featured Staples High School in Westport, Connecticut and the success they have had with on-line learning in Algebra and other Math classes.

Grading without A's

Response to New York Times article "Report Cards Give Up As and Bs for 3s and 4s"
http://community.nytimes.com/article/comments/2009/03/25/education/25cards.html?permid=61#comment61

While parents, students, teachers and society at large would like to know how students are faring, a good grade is not the only measure of learning. In fact, for the bright student, an A may be a result of their excellent 'raw materials' yet once these bright students reach Algebra, most will have to buckle down and actually study to learn the quadratic formula.

In secondary Math, an 85 is an excellent grade since 15 points will be lost to 'fuzzy errors' made under the pressure of an exam. It is hard to get an A in Math. As Barbie said “Math is hard” and it can be -- while offering many other life skills such as
Problem-Solving, Critical Thinking, Optimizing Your Potential, Escaping the Perfectionism Trap, Appreciating Effort vs. Obsessing about Ability, Financial / Medical Information Fluency, Expanding your self-teaching Skills, Finding a (new) career, Lifelong Learning and Brain Fitness.

As a Math peak performance coach, I help students and their families to focus on the learning and the effort expended while quieting the quest for perfectionism.

As Jim Rohn says, "Make measurable progress in reasonable time".

Robin Schwartz, Math Confidence

Algebra as an Archfiend?

Education is about stretching knowledge, skills and attitude.
Last month, the headline of a New York Times article about a Math video game for middle schoolers designed by Dimension M:

"Video Game Helps Math Students Vanquish an Archfiend: Algebra"speaks volumes about attitudes about Math! In the print verson, the word "foe" was used.

How about "ally", "comrade", "challenge", "opportunity"?

"Students at Intermediate School 30 in Brooklyn played a video game on Monday, and learned a little algebra at the same time. " was the caption on a photo.
The juxtaposition of this sentence would be:
"Students at Intermediate School 30 in Brooklyn learned algebra on Monday and played a little bit of video game at the same time. "

http://www.nytimes.com/2008/10/08/nyregion/08video.html

What Do Students Need Help With?

Algebra
Generalizing from y = mx + b so that the result is an equation like y = 2x + 5.
Students benefit from being reminded that they are finding the equation that describes the entire line not just a point.
I like to ask them "How many points are on the line?" -- the answer I like the most is "Infinite" but "Too many to count" or "A real lot" are very acceptable answers.

It takes a while to see that (x-5)/(5-x) = -1!!


Calculus and Number Lines

The idea of limits and that inscribing an n-sided polygon in a circle, the more sides you have, the closer the area is to the area of the circle. So as n approaches infinity using a circle with a radius of 1, the area approaches pi (3.14159265....).

Secant and tangent lines have nothing to do with trig functions secant and tangent!!

A really cool problem was f(x) = [x] + [-x] which involves the greatest integer function.
The TI-84 function for greatest integer function is Int. The greatest integer function is best demonstrated with a number line and asking the student what was the last number that you passed. If you are exactly at an integer, then the answer is that number.
For example, [2.5] = 2 we passed 2 on the way to 2.5.
and [4] = 4
But [-2.5] = -3 we passed -3 on the way to -.25 (but we have not yet passed -2!!)
The cool thing about this problem is that for most x's, such as x = 2.5,
f(x) = [2.5] + [-2.5] which comes out to
f(x) = 2 + -3 = -1
The exception is at exactly an integer -- f(4) = [4] + [-4] = 4 + -4 = 0.
This graph looks like a straight line like y = -1, however at each integer value, there is a discontinuity, as y jumps to 0 at -3, -2, -1, 0, 1, 2, 3, etc.
This is best seen by setting xmin = 0.99 and xmax = 1.01 on the window menu -- at x = 1 there is a dot on the x axis!!

Trigonometry

The Law of Cosines is really the Pythagorean Theorem with a little extra.
We have always been using it except that if we can use the Pythagorean Theorem then we must have a right triangle!
If we rewrite a^2 + b^2 = c^2 as
c^2 = a^2 + b^2 - 2ab cos C (cos 90 = 0)
so we are used to seeing it as
c^2 = a^2 + b^2


General Math (Percents)

I love to work with students on 'trick questions' .

For example, you buy a stock at $100 -- it goes up 10% and then down 10%, what is its final price?

You buy a stock for $40 -- it goes up 50% and then down 50%, what is its final price?

And, you buy a stock for $60 -- it goes up 100% and down 100%, what is its final price?