kitchen table math, the sequel

Saturday, June 12, 2010

'Math Strategies for Women'

from Gruber's Complete SAT Math Workbook:
These are questions that women found significantly more difficult than men did. However, after learning the strategies in this book, women scored just as high as men on these sections.

1. Carol has twice as many books a Beverly has. After Carol gives Beverly 5 books, she still has 10 more books than Beverly has. How many books did Carol originally have?

2. 5_2 x 9 = 5,2_8 (missing digits are different)

3. If s equals 1/2 percent of t, what percent of s is t?
I find this passage kind of charming: a remnant from a more innocent time. And I'm sure he's right. I'm sure these are problems Betty Draper would have struggled with.

Meanwhile, Gruber doesn't seem to have noticed the presence of algebra 2 on the new exam. If Betty's having trouble managing a simple story problem, she's really going to blow a gasket when somebody asks her to solve an inequality involving absolute value.

Education: Preparing Americans

I'm concerned that WEAK Common Core Math Standards
(especially regarding "authentic" Algebra 2) will diminish our students' preparedness to achieve their personal goals.

Here's why..


Adelman, C. 1999. Answers in the Tool Box: Academic Intensity, Attendance Patterns, and Bachelor's Degree Attainment.
Washington, DC: U.S. Department of Education.

In the "selected findings" section, you'll find:
"Of all pre-college curricula, the highest level of mathematics one studies in secondary school has the strongest continuing influence on bachelor's degree completion. Finishing a course beyond the level of Algebra 2 (for example, trigonometry or pre-calculus) more than doubles the odds that a student who enters postsecondary education will complete a bachelor's degree"


The Toolbox Revisited "Reiterations" [p. 108]

First, there was a story about curriculum, the content of schooling, that was compelling in its secondary school dimensions in the original Tool Box, and is even more compelling now on both secondary and postsecondary stages. What you study, how much of it, how deeply, and how intensely has a great deal to do with degree completion.

Second, this curriculum story, joined by nuances of attendance patterns that turn out to have significant leverage, continues into higher education.


It’s not merely getting beyond Algebra 2 in high school any more: The world demands advanced quantitative literacy, and no matter what a student’s postsecondary field of study—from occupationally-oriented programs through traditional liberal arts— more than a ceremonial visit to college-level mathematics is called for.

The Toolbox Revisited: Paths to Degree Completion from High School Through College

Friday, June 11, 2010

boys & girls & SAT math

here

I've only skimmed the post, but I don't see a passage where he controls for the higher number of boys dropping out of high school.

I got a book today that has a page dedicated to the specific problems girls have trouble with - pretty funny. (He could be right for all I know. However, I'm having lots of trouble with SAT math but none whatsoever with the problems the author cites.)

I'll post tomorrow.

"SAT work"

a 2008 blog

hours and hours

from Susan S:
The worst part about the hours and hours of project making and coloring is the neglect of basic skills that will be needed for high school.

Somewhere around the end of 7th grade, I realized my son could barely hold a pencil or pen for more than a couple of sentences. There was no flow to his writing. It was just torture for him. I thought I was done with afterschooling only to realize we had to start all over and get him caught up.

Even in a class like social studies, he was expected to write a couple of things in a notebook, but then illustrate the page. Of course, he'd been typing since the 4th grade, so he'd forgotten cursive. But it wasn't just cursive he had forgotten. He was even unsure of certain letters in block form.

When I would receive his middle school journal at the end of the year I would notice basic words misspelled consistently, thus searing the wrong spelling into his brain. It was a nightmare to go through all of that and get him straight.

It took a good 4-5 weeks of writing summaries, bios, etc. every other day just to get him to form the letters automatically and quickly and without fatigue.

I have no idea why they do this. I do sense that they get pressure from upstairs to have a certain amount of project work. I imagine if they didn't have extended response and essays on the state tests, they'd probably not have them write at all.

Like math facts, they believe that these things just take care of themselves.

the brick problem


The pattern shown above is composed of rectangles. This pattern is used repeatedly to completely cover a rectangular region 12L units long and 10L units wide. How many rectangles of dimension L by W are needed?

answer choices:
A) 30
B) 36
C) 100
D) 150
E) 180

solution here and here

The Official SAT Study Guide

standard celeration charts

I'm thinking it's time I finally figured out Celeration Charts.
ABSTRACT

Combining Pavlov’s (1960/1927) use of frequency as a standard unit in the measurement of scientific phenomena and Skinner’s (1938) use of frequency, free operant behavior, and the cumulative recorder with his knowledge of engineering and interest in navigation, Lindsley brought to psychology and education the most powerful and scientific use of measurement applied to human behavior. In 1965, he developed what was first called the Standard Behavior Chart, now more accurately described as a family of Standard Celeration Chart —standard measurement charts for human behavior in daily, weekly, monthly, and yearly time periods. This paper provides an overview of these four types of Standard Celeration Charts.

Since 1967, educators and others have used the Standard Behavior Chart (now called the Standard Celeration Chart) to observe human behavior and improve learning. The people behaving have ranged from fetuses to those in their 80s (Calkin, 1983; Cobane & Keenan, 2002; Edwards & Edwards, 1970). Some behaviors counted have included all day counts of fetal movement (Calkin, 1983), positive and negative feelings about self (Cobane & Keenan, 2002; Kostewicz, Kubina, & Cooper, 2000; Kubina, Haertel, & Cooper, 1994), as well as the more usual 1-minute timings of academic behaviors such as Hear Say question then answer (Zambolin, Fabrizio, & Isley, 2004), See Write math facts (Stromberg & Chappell, 1990), Think Say and Think Write American government facts (using 1-minute, 2-minute, and 5-minute timings) (Ellis, 1980), Write words (Albrecht, 1981), and See Say parts of a microscope or skeleton (Miller & Calkin 1980).

[snip]

Using the Standard Celeration Chart makes two critical elements apparent. First, behavior grows by multiplying, not by adding. If Janel wants to improve her learning, she knows that to grow from one to two is to double and is identical to growing from 50 to 100, not from 50 to 51. When she wants to learn something new or change a behavior or feeling, she wants change by doubling, not by adding or deleting one at a time. If Abigail says 35 Russian conversation words in one minute (to which no Russian will listen for long!) and grows by adding one a day, it will take 215 days, or 31 weeks, to reach fluent speech. If she learns by doubling each week, she can get from 35 words per minute to 250 in 50 days, or seven weeks. If Gemma is a slow reader and reads 62 words a minute at grade level and wants to read 200 words per minute, does her teacher want her to grow by adding or multiplying? If Alan has 100 suicide thoughts a day, does he want to reduce them by one or two per day or by ÷5.0 per week?

Secondly, the chart makes us look at not only the frequency of a person’s performance, but also at the growth of learning across time, (i.e., the celeration). Within the first five years of using the chart, several of its powerful elements became increasingly apparent. Frequency is performance: It tells what happened during one time period, but by itself it tells little about learning. To see whether performance accelerates or decelerates, we need to measure it across time. Since 1971, we have called this change in learning celeration.1 Acceleration indicates an increase in the growth of change of the frequency, in the learning of the behavior. Deceleration indicates a decrease in the learning of the behavior.

Frequency is the count per minute: the number of times Steve does independent or dependent actions per hour; the number of pieces of science equipment Greg names correctly and incorrectly in one minute; the number of words Chris reads correctly and incorrectly per minute; the number of pleasant and unpleasant self-thoughts Angie has per day. These behaviors show performance. Celeration is the count per minute per week. It shows change in performance, or learning across time. We measure celeration, (i.e., learning) by the week, or, if using larger time measures, changes by the month, year, or decade. Celeration: Steve’s actions per hour, each day, per week; Greg’s pieces of science equipment he points to and says per minute, each day, per week; Chris’s words read per minute, each day, per week; Angie’s thoughts about self per minute all day, each day, per week.

PRECISION TEACHING: THE STANDARD CELERATION CHARTS
ABIGAIL B. CALKIN, PH.D.
PRIVATE PRACTICE
THE BEHAVIOR ANALYST TODAY VOLUME NUMBER 6, ISSUE NUMBER 4, 2005

SAFMEDS

One of the DI-list folks wrote a post about learning Italian using SAFMEDS.

S- Say
A- All
F- Fast
M- Minute
E- Each
D- Day
S- Shuffled

SAFMEDS and celeration charts at University of North Texas.

And: applied behavior analysis SAFMEDS. Just in case.

Allison explains absolute value inequalities

Catherine: also, I have completely forgotten how to set up and solve a simple inequality involving absolute value

Allison: You need to think about what it means.

The absolute value of any number equal to or greater than 0 is itself. x-->x

The abs value of any number less than 0 is the number*-1, or the number with its sign dropped: x --> -x.

So break down the inequality you see into other inequalities.

|x| - 2 > 3

means
|x| > 5:

allowable positive values of x satisfy
x > 5

allowable negative values of x satisfy
-x > 5

you "solve" this by switching sides (do you know why you're allowed to do that?)
and that becomes
x < -5

Now, you do |x - 3| < 5 in a similar way. To make yourself less confused, write (x-3) = y
and work on
|y| < 5

Then after you've got that into equations without the abs value, sub back in the x-3.

time

Time is our most valuable nonrenewable resource, and if we want to treat it with respect, we need to set priorities.

Albert-László Barabási
Bursts
Dutton, 310 pages, $26.95

Hurry Up and Wait

redkudu on

from Redkudu:
The assigning of art projects is just lazy grading, as far as I'm concerned. You can spot-check for the required elements without the need to analyze whether the student has mastered the material. Plus, it all looks good when admin stops by and they see all this "student engagement" thrown up all over the walls.

At our school, no matter what class they visit, students inevitably have to create a poster about themselves containing descriptive words and pictures. Most of them end up being on the inappropriate side because students are given few guidelines of what to say about themselves, so they generally try to reinforce the more shallow exterior facade they would *like* to represent to their peers. (We live in a tough area.)

Last year one of my students asked if we were going to do an "All About Me" poster project. I said no, and asked if she minded.

She said no. "I'm really tired of having to tell people about myself."
This reminds me of a friend's son who, assigned another memoir in 8th grade, told his mom, "I'm running out of memories."

honors English

from Lisa:
For honors English dd had to create a Beowulf cereal box, complete with list of ingredients and prize inside. Crazy! I suggested they read the whole work instead. The teacher was unimpressed by my suggestion. Thank you Katharine for pointing this out to folks who don't have kids in the PS system.
Raising a Left-Brain Child in a Right-Brain World: Strategies for Helping Bright, Quirky, Socially Awkward Children to Thrive at Home and at School
by Katharine Beals

lgm on school board elections

Also take in to account that a large minority of potential voters are employees of the school district and that the union is actively ensuring that particular candidates be put up for election. An independent candidate has a lot of work to do to counteract the organization and get out the vote in my area.
This is one of the main reasons why we have mayoral control of the schools, right?

projects we have known and loved

from Barry Garelick:
Not only is the tissue box assignment real, but elsewhere in her book Katharine talks about how in language classes, kids have to make posters about their family. My daughter had to do a family tree chart with photos for her Spanish class. The teacher lost the poster, and called my daughter at home to ask her to do another one, and said it was important for her grade. (!!) My daughter, who didn't like the assignment to begin with was infuriated to have to do it again, and all because the teacher had lost the first one. The sadder aspect of all this is parents get drawn in to the "this project is worth a lot of points for your grade" type thinking, and are afraid to make waves by telling the teacher that the student is NOT going to do this; please give an alternative assignment.

For English class in 8th grade, the teacher gave the students a choice of projects for Lord of the Flies. One was a standard book report. Others included designing a T shirt about the book. My daughter hated the alternatives and chose writing the book report. And she is not fond of writing!

I'm reading Katharine's book right now and have nothing but praise for it. I am going to recommend it to several teachers I know at George Mason's ed school. I really think it should be required reading.

Googlemaster on the German tissue box

re: the German tissue box assignment:
That's awful! I can't decide whether I would refuse to turn one in or create one with variations of "Dies ist die dümmste Idee überhaupt" all over it.

help desk

If 20 percent of x equals 80 percent of y, which of the following expresses y in terms of x?

(A) y = 16% of x
(B) y = 25% of x
(C) y = 60% of x
(D) y = 100% of x
(E) y = 400% of x

The Official SAT Study Guide 2006
p. 550

I absolutely cannot do this question, and I don't know why.

Thursday, June 10, 2010

cranberry on how politics work

There's nothing wrong with public debate about the manner in which a town or city chooses to spend the majority of its budget.

Those who want to change public schools for the better are forced to use the bottom-up process. The internet makes this much more effective, as it's no longer possible for administrators to placate the discontented with different answers for different people. When parents can compare the answers they received online, with parents in other grades, it's no longer possible for school system insiders to "manage the message."
This is something I don't think I've ever posted, here or on the Forum: there were unnamed others who co-founded the Forum with me, one of whom gave me the "theory of the listserv." Which had to do with the fact that whenever a parent approached the administration about a problem, she was told, "Your child is the only one having a problem."

And/or: "You are the only parent complaining."

Once parents began posting on a public listserv, this parent said to me, "They'll know that we know that they know."

Miscommunication and distrust arise when people notice that they've been told different things, and when committees are thanked for their input, are patted on the head, and then the committees must watch their recommendations put on a shelf and ignored.

A top-down solution would need the superintendent's support. The choice of a superintendent falls to the school board. The only way to influence the school board is to influence its composition. The only way to influence its composition is to convince enough voters of the necessity for change. That process is bottom-up. It always has been. The internet has made it easier to reach and organize voters.
Right!

Outside grass-root politics, there is no way to induce a wealthy public school to provide direct instruction in synthetic phonics and "traditional" math. At least, none that I've seen or experienced. Public schools aren't collaborative, and they don't see parents as valued customers or clients. They do what they do.

So democratic politics is the only avenue to reform, but one difficulty is that affluent public schools (perhaps all public schools?) see themselves as existing outside the political realm; dissent is illegitimate. Heck, affluent public schools, at least in my experience, see school boards as illegitimate. I've spent the past year listening to our administrators mock, disrespect, and even denounce the most independent member of the board, a woman who ran on a reform platform and won.

More from cranberry:

I should add that by the time any school reform efforts bear fruit, the original malcontents' children have left the system, either by graduating or changing to private schools.
Exactly.

This is everywhere the case, including in the youth sports organizations, I'm told. The powers that be wait for the troublemakers to age out of the system.

That is an anomaly in my town, where more than a few people whose children have graduated are politically engaged in reform efforts. Another anomaly: voters whose primary concern is extremely high school taxes and spending are allied with voters whose primary concern is student achievement. For some voters, those two concerns are different faces of the same problem: they are convinced that too much spending on the wrong things lowers academic quality.

It's not a perfect process, by any means. I think in most years, school administrators tend to get what they want. People who don't have children in the system only start paying attention when money gets tight.

The state and federal government also get involved. At present, our state is proposing to drop standards which are thought to be the best in the nation for standards which have not yet been set (and thus, can't be compared.) I'd love to be able to act in a top-down way on this. As a single citizen, though, it's just not possible.

Without political organization, parents don't have a voice.

revolution

"A revolution takes time to settle in." ~Lanza del Vasto

(thanks to Concerned CT Parent)

Engineering Project Lifecycle

1) Enthusiasm
2) Disillusionment
3) Panic
4) Search for the Guilty
5) Punishing the Innocent
6) Rewarding those not involved

(thanks to Mark Roulo)

sequence

First they ignore you,
then they ridicule you,
then they fight you,
then you win.

-Ghandi

(thanks to Mark Roulo)