Help desk - How much do focus groups cost?

Does anyone know?

How much does it cost to hire a firm or an individual to run focus groups and write a report?

What I would specifically like to know is the prices for a firm not associated with the public education world to do this.

How much would it cost to hire a political polling firm, for instance?

If any of you has information, I'd love to hear.

Help Desk - Best online flash cards

Any suggestions on the best websites for using and/or creating online flashcards for a Spanish language course?  There seem to be so many.

help desk - 'distributing the negative'

I'm working with a boy in a neighboring town who can solve equations with positive values like the following:

3 + 2(x + y) = 9

He is having difficulty solving equations that require him to distribute a negative:

3 - 2(x + y) = -3

I remember C. having trouble distributing a negative, and I remember stumbling over minus signs myself when I was a kid. At some point, I solved my problems by deciding to treat minus signs as either a -1 or the addition of a negative, depending on the expression I was dealing with.

Thus -x became (-1)(x) and x-8 became x + (-8).

I don't think anyone ever told me to translate expressions in this manner. Quite the contrary; I have vague memories of reasoning it out for myself on more than one occasion.


Here's the way a sheet I have from Glencoe says to teach distribution of the negative:

Use the Distributive Property to write each expression as an equivalent algebraic
expression.
a. 3(w – 7)
= 3[w + (-7)] Rewrite w – 7 as w + (-7).
= 3w + 3(-7) Distributive Property
= 3w + (-21) Simplify.
= 3w – 21 Definition of subtraction

Unfortunately, this sequence doesn't solve the problem. My student can simplify 3(w-7); what he can't do is simplify 3–2(x+y).

Today I tried having him draw huge brackets around 2(x+y), then simplify the 2(x+y), and then simplify the remaining expression:

3–2(x+y)
3–[2(x+y)]
3–[2x+2y]
3-2x-2y

In effect, I was turning the problem into two distributions: first the 2, then the negative sign.

This approach always worked for me, but the logic of it wasn't obvious to my student.

One more thing: this student probably had Everyday Math in elementary school, and his current class seems to be intensely procedural. The only textbook his teachers are using seems to be a NY state test prep book.

I'm eager to hear any thoughts you have both about procedural teaching (including mnemonics) and about how I might help this student make some sense of the math he's learning. Moreover, and I hate to say this, but if I'm going to help him make some sense of it, I have to do it on the fly. Our time together is extremely limited.

If anyone knows of a good set of "instructional worksheets," that would be fantastic. I'm combing through my own collection.

Last but not least, what do you think of this video?

help desk - fiscal multiplier

We quantify the fiscal multipliers in response to the American Recovery and Reinvestment Act (ARRA) of 2009. We extend the benchmark Smets-Wouters (2007) New Keynesian model, allowing for credit-constrained households, the zero lower bound, government capital and distortionary taxation. The posterior yields modestly positive short-run multipliers around 0.52 and modestly negative long-run multipliers around -0.42. The multiplier is sensitive to the fraction of transfers given to credit-constrained households, the duration of the zero lower bound and the capital. The stimulus results in negative welfare effects for unconstrained agents. The constrained agents gain, if they discount the future substantially.
Fiscal Stimulus and Distortionary Taxation
Thorsten Drautzburg, Harald Uhlig
NBER Working Paper No. 17111
Issued in June 2011
NBER Program(s): EFG

I'm confused about the concept of the fiscal multiplier.

I've read explanations characterizing the multiplier as a simple multiple: if the multiplier is 1.5 and the government spends $1 million, then the net spending beyond that $1 million is $500,000.

1.5 x 1,000,000 = 1,500,000

But that's not right, is it?

What does a multiplier of .52 actually mean in terms of what the public spends beyond the amount the government spent?

help desk - grammar

Inspired by an SAT question C. and I answered yesterday --

All of the editors at the magazine agreed.
All the editors at the magazine agreed.

What happens grammatically when you omit the preposition ('of')?

In the first sentence, 'all' is the subject.

Is 'all' the subject of the second sentence, too? Is the preposition ('of') implied?

Or does 'all' become an adjective modifying 'editors,' making 'editors' the subject of the sentence?

help desk - online tech

Does anyone know what technology they're using? I would love to be able to write out a problem and post.

The ShowMe SAT videos seem to be terrific, by the way. I've only looked at one or two, but they were very helpful.

Help Desk question: Can parents affect a curriculum change at a school?

I'm looking for success stories of parents affecting the math program taught in an elementary school.
I'd like to provide some encouragement to a commenter on my blog, who asked:

How does one get their school district to consider changing over to Singapore Math?

Most of the schools I have worked with have had teacher-led math curriculum initiatives. Does anyone have examples of parent-initiated changes to share?

help desk - probability

from Art of Problem Solving Introduction to Counting and Probability by David Patrick, p. 128:

8.2.4 A penny, nickel, and dime are simultaneously flipped. What is the probability that heads are showing on at least 6¢ worth of coins?

I can do this by brute force, but I don't see the math.

help desk - balls in boxes

from Art of Problem Solving's Introduction to Counting and Probability:

5.16 How many ways are there to put 4 balls in 3 boxes if:
(b) the balls are distinguishable but the boxes are not.

I don't understand the part of the solution that explains how many ways you could put 2 balls in one box, 2 balls in another box, and 0 balls in a third box:

(2,0,0): There are 4C2 = 6 ways to choose the balls for the first box, and the remaining go in the second box. However, the two pairs of balls are interchangeable, so we must divide by 2 to get 6/2 = 3 arrangements.

To me, it seems like there would have to be 6 ways to choose 2 balls from balls 1, 2, 3, and 4 for the first box:

1,2
1,3
1,4
2,3
2,4
3,4

What am I missing?

For the option of (2,1,1), the solution is 6, not 3:

There are 4C2 = 6 options for picking the two balls to go in one box, and each of the other two balls goes into its own box.

I don't see how (2,0,0) is different from (2,1,1) when the boxes are indistinguishable.

help desk - sine and arcs and circular functions

From Dolciani's Algebra and Trigonometry, Chapter 13-2 Circular Functions, p. 555:

sin s = y
cos s = x
tan s = sin s/cos s if cos s ≠ 0
cot s = cos s/sin s if sin s ≠ 0
sec s =1/cos s if cos s ≠ 0
csc s = 1/sin s if sin s ≠ 0

s is the length of an arc of a circle.

This may be asking too much, but I need help.

I have never seen sine, cosine, tangent, etc. applied to an arc. I've only learned sine and cosine in relation to angles in a right triangle.

I've looked back through chapter 12, but I don't see a section that explains this. I'm sure it's there, but it's not obviously there, and I'm in a hurry, sad to say.

Is there a short way anyone can explain to me how we get from sine, cosine, angles, and SOHCAHTOA to sine, cosine, and arcs?

Is there a website that has a succinct and lucid explanation? 

And is there a book you like for self-teaching trigonometry and algebra 2? (Do we know what book(s) homeschoolers use?)

I need a royal road to circular functions.