Middle School Mathematics Institute updates

Middle School Mathematics Institute (MSMI) is alive and well with lots of progress.

MSMI's mission is to help teachers, schools, and parents ensure students succeed at school algebra. Focused primarily on elementary and middle school grades 4-8, MSMI offers a variety of services that build the Bridge to Algebra.

We've got a nice new website: www.msmi-mn.org, we are now officially a 501(c)3 non-profit corporation (so donations to MSMI are federally tax deductible), and we're beginning to get some traction in our mission along all of the three prongs--teacher institutes, school curricular services, and parent outreach.

I'll be posting here in the next few days about MSMI 2011 institutes this summer in St. Paul, MN, one on fractions, and another on rational numbers. I'll also be posting about an upcoming event in April here in St. Paul, a workshop on "How to Use the Best Strategies of Singapore Math to Strengthen your Math Instruction." But for now, I'd like to talk about the parent component.

The parent outreach part is just starting to get underway. I gave a talk the other night on the Math on the SAT, Getting to Mastery to a group of parents. Their kids were mostly in elementary and middle school, and that's the time to start helping them understand just what's happening in their students' math curriculum--before it's triage and remediation. The talk highlighted that the SAT reasoning test math portion is a very good test of mathematical maturity, and that maturity simply isn't going to come from the American curricula and textbooks most students see. The talk gave some ideas on just what mastery looks like (both conceptual development and procedural fluency) and how to help students gain that mastery. I was surprised at how well received the talk was, actually, and I hope to do many more on similar topics.

The talk slides are available on the web site to anyone.

Along with that talk, I hope to develop another talk focused on what is needed to be on a college-prep track in high school, and what is needed for college entrance into a STEM career.

MSMI will also be writing some free pamphlets that help parents understand what's happening in math education. Immediately, I expect to have a pamphlet up explaining "curricula, standards, assessments, and all that" so that parents are familiar with these buzzwords. I hope to also get another pamphlet together talking about the false dichotomy between teaching and learning, a kind of mini-primer on what modern ideas of education mean for their student.

I hope to keep refining MSMI's focus on the parent side to maximize the good it can do. I was surprised after my talk that many parents want to organize to do something to help their students, but simply do not know what to do, and what suggestions on how to get their school to change direction. As you might guess, I didn't have a lot to say on that front; MSMI isn't designed for that kind of advocacy. I think for now, it shouldn't be, but I hope it will facilitate parents coming together to do that for their kids.

Anyway, have a look, download the slides, send suggestions (the web site needs pictures, I know, I know...) and drive traffic to www.msmi-mn.org, please! :)

help desk - questions for management

A friend of ours who sits on the board of a private school watched the Terc Investigations video a couple of weeks ago. Until he saw it, he believed boards should leave curriculum decisions up to school administration. Now he wants to write him a list of questions to ask "management" about the school's math curriculum.

Suggestions?

what is the effect of the Triborough Amendment over the long-term?

I want to check my reasoning with all of you.

Yesterday the Times carried a long editorial on the subject of New York's public sector unions and the state's fiscal crisis, which included these two factoids:

In April 2009, private sector income was down 9%.
In April 2009, public sector employees were given a 4% raise.

and

Average salary for New York’s full-time state employees in 2009 (prior to April raises): $63,382
Average personal income in NY state: $46,957

State Workers and N.Y.’s Fiscal Crisis
New York Times
3/6/2011

I assume these two facts are connected by the Triborough Amendment, a statute that is apparently unique to New York state. Under the Triborough Amendment, when a public sector union contract expires, its terms remain in effect until a new contract is signed.

This means that raises negotiated in good times must be awarded in bad times, which explains the 4% raises paid out in April 2009. It also means that the union has little incentive to negotiate during an economic downturn.

From the Times:

Last April, in the midst of one of the worst financial crises that New York and the nation have ever faced, the state’s unionized workers got a 4 percent pay raise that cost $400 million. It came on top of 3 percent raises in each of the previous three years. These raises were negotiated long before the recession began, by a Legislature that routinely gave in to unions that remain among the biggest political contributors in Albany.

During the same period, many private-sector workers had their pay or hours cut. Private-sector wages in New York dropped nearly 9 percent in 2008. In 2009, Gov. David Paterson pleaded with the unions to give up the raises to help the state out of its crisis. Union leaders attacked him in corrosive television ads, and Mr. Paterson eventually caved, settling for an agreement that reduced pension payments to new employees. The deal wasn’t enough to address New York’s serious fiscal problems.

The Triborough Amendment was adopted in 1972.

Here is the line of reasoning I want to vet with you.

What is the likely effect of the Triborough Amendment over time?

To me, it seems that over time the relative position of public sector to private sector employees would change, with public sector employees moving ahead and private sector employees falling behind.

Over time, the gap between public and private sector income would grow larger. If private sector employees take income cuts while public sector employees receive raises (or, at a minimum, do not take freezes or cuts) -- then each time the economy recovers, hasn't the ratio of public sector to private sector compensation changed?

Then, when the next recession arrives, doesn't the ratio change again?

If so, is that why we see average salary of full-time public sector workers in New York state at $63,382 while average personal income is $46,957?

I realize this comparison isn't apples to apples, but given that public sector employee incomes are presumably included in the $46,957, the actual ratio of public sector to private sector income must be even larger.

What it looks like to me -- and please tell me if I'm not thinking this through correctly -- is a  decades-long redistribution of wealth from one segment of the middle class to another segment.

Or is that wrong?

Do the incomes of private sector workers somehow bounce back up to where they were before each recession while the incomes of public sector workers 'stand still' long enough for the ratio to return to what it was before the downturn?

Magister Green on guerilla teaching

re: memorization is a dirty word, Magister Green offers this advice:

I have found that using "automaticity" in place of "memorization" lets me get around the stigma of the latter word while retaining its basic meaning. And "automaticity" sounds cool, so people don't press.

Guerrilla teaching forever!

Guerrilla teaching or marketing --- !

Daniel Ethier on cognitive load theory

on another thread, Daniel Ethier writes:

Cognitive load theory has much to say about the educational implications of our limited working memory on learning.

As I read various papers on cognitive load theory, I keep having aha moments as I find reasons for things I see in the classroom.

The key to getting around our limited working memory is automaticity. If you know something well enough to not have to think about it, it does not take up working memory. And so you are free to think about the problem you're trying to solve.

Use Google Scholar and read some of the many papers about various aspects of cognitive load theory. Well worth the time.

uh-oh

"when A.P. testing began in 1956, memorization was not yet a dirty word"

Rethinking Advanced Placement
By CHRISTOPHER DREW
Published: January 7, 2011

In theory, the new A.P. courses are going to replace "memorization" with "critical thinking."

In reality, critical thinking depends on memorization: you can't think critically without something to think about, and that something has to be stored in long-term memory. If you're going to think critically, you have to know (i.e. remember) what you're thinking about.

What happens when you try to think critically about a subject without memorizing its terms and concepts first?

What happens is that you can think about 4 items at most. That is the number of new, discrete elements you can hold in conscious, "working memory"^* at one time. Four. And four may be pushing it.

Of course, when it comes to critical thinking, 4 is a tiny number. Experts think critically about far more elements at one time; being able to think about a vast amount of complex material is pretty much the definition of an expert, as a matter of fact:

The sine qua non of skilled cognitive performance is the ability to access large amounts of domain specific information [i.e. knowledge]. For example, it is estimated that chess masters have access to as many as 100,000 familiar configurations of chess pieces (Chase & Simon, 1973). As another example, in order to make sense of what he or she is reading, a reader must have access to information gained from previously read text. This is particularly true when reading complex technical material filled with jargon.
summary of Ericsson, K. A., & Kintsch, W. (1995). Long-term working memory. Psychological Review, 102, 211-245.
David Zach Hambrick, 1998, gt8781a@prism.gatech.edu

basal ganglia lollapalooza

Here's an example from my own life.

As a nonfiction writer, I'm essentially a permanent student: I am constantly trying to write interesting articles and books (mostly books) about material that may be brand-new to me. My current project involves the basal ganglia, which I knew nothing about going in. The vocabulary alone is overwhelming: nucleus accumbens, orbitofrontal circuit, putamen, striatum --- and that's just for starters.

So here's the question. How exactly am I to (a) understand and (b) think critically about a passage that contains these four terms if I haven't memorized what these terms mean and how they are related to each other first?

The answer is: I can't.

If I don't memorize vocabulary, I have to look up the definitions and then try to hold the definitions in mind while also reading and trying to think about what I'm reading.

It can't be done, and the reason I know it can't be done is that I've spent a lot of time trying to do it. I always make the same mistake with each new project I tackle. Somehow I think I can just look things up (Google!) and remember them while I read a complex study or article.

But I can't. No one can. Looking up four new words and remembering four new meanings maxes out working memory. There's no capacity left to read and understand a text using those four new words and four new meanings, let alone think.

I don't know why this is. Logically speaking, shouldn't it take just as much working memory to hold 4 memorized terms in mind as it does to hold 4 non-memorized terms in mind?

The answer is no: knowledge - content stored in long-term memory - extends working memory.

When you know a lot about a subject - when you have a great deal of knowledge stored in long-term memory - you can think about more than just 4 things at once.


blackboards vs PowerPoints

^* Working memory is essentially consciousness: it's what you're thinking about and/or remembering right now. When you hold a phone number in memory while dialing it, you're using working memory.

contingency budget for NY schools

In another thread, lgm asked about the contingency budget for this year in New York.

The contingency budget is the budget schools can impose by fiat if voters reject the proposed budget.

Here is an explanation by the NYSUT:

the law defines the contingency budget cap as the lesser of 4 percent or 120 percent multiplied by the CPI increase

Assuming I'm reading this right (pdf file), the CPI for 2010 rose by 1.6%.

That would put the contingency budget cap at 1.92%.


(There are various categories that can't be excluded from a contingency budget, such as tax certs. I don't know how those relate to the cap.)

Inflation in one picture
David Leonhardt

corn on the cob

Have been meaning to post this --

A few weeks back David Letterman showed a print ad that reads:

Corn cobs 4 for $1.00
Works out to 25¢ a piece

Kitchen Table Math

So I was just over at Art of Problem Solving cruising their textbooks (I'm loving their Introduction to Counting and Probability, which may be a good example of what Barry calls guided discovery), when I saw a prominent reference to Kitchen Table Math:

How nice! I thought.

So I clicked on the link.

LIFO -- Connecticut Considers a Change

A new post on Throwing Curves considers the possible defenses of what the popular media has already decided must go -- LIFO rules. The system everyone loves to hate. I got that. It's easy to think that getting rid of LIFO solves the problem. But I've tried to dig deeper into the issue and spark a broader debate.

palisadesk on psychopaths in schools

re: Snakes in Suits, palisadesk writes:

*I* know how you came across this book -- I recommended it to you (about 2 years ago I think). I still recommend it. Robert Hare's first book, which has been revised a few times, is a don't-miss one: Without Conscience: The Disturbing World of the Psychopaths Among Us.

We tend to think of psychopaths as serial killers like Ted Bundy, but in fact the defining characteristic of psychopaths is a total lack of conscience. They are all about me, me, me and have no empathy for others, nor any scruples about exploiting or cheating others. Since they are totally focused on their own needs and goals, they usually are not criminals; however, they are often cunning manipulators, narcissistic power-trippers, and they wreak emotional havoc wherever they go. Snakes in Suits deals with such charmers in the workplace.

Robert Hare is a world-reknowned authority on the topic, and a lucid writer who gives insight into how to deal with such individuals. A rather high percentage of the population (something like 5% IIRC) has psychopathic tendencies, so we are all bound to encounter them.

They are less attracted to the "helping professions" than to other venues for their talents, but I have known more than one in public education, and these individuals taught very briefly before rising through the management ranks where they could do ever more damage on a wider scale.

Hare does share some useful strategies, as well as cautions against courses of action that are known to backfire badly. Counter-intuitively, therapy and counselling makes these individuals worse and more dangerous, since it enables them to con people even more effectively. They often fool mental health professionals.

True story.

A long ways back, I was trying to decide whether to sign with a particular agent.

I had some concerns, so after lunch with my possible new agent, I stopped in a bookstore and skimmed Without Conscience to see if he/she fit the profile for psychopathy.

I must have spent at least an hour with the book, finally reaching the conclusion that, no, my potential agent was not a psychopath.

The significance of the fact that I had just spent an hour of my life researching the question escaped me at the time.






Suffering Souls: The Search for the Roots of Psychopathy
by John Seabrook
The New Yorker | November 10, 2008

way off-topic: ALERTS TO TERROR THREATS IN 2011 EUROPE

Ed and I are sitting here guffawing, reading this.

Starts slow, then hits warp speed in paragraph 4, with the Scots.

Of course, I love anything to do with the Scots and their bloody-mindedness.^*



Born Fighting: How the Scots-Irish Shaped America


^* I'm probably using that term incorrectly. Good thing it's not likely to appear on the SAT.

the choice

in my district

Snakes in Suits

No idea how I came across this book --- but I may have to read it.

Robert Hare is a major researcher in the field.

for writers & writing

The Mumpsimus

I'm a huge fan of Scrivener's.

Have just ordered a copy of Patterns of English.

Downloading Bean next.

decline at the top - the best students fared worst

Back in 1977, having watched SAT scores fall for 15 years, the College Board, which developed and administers the SAT, engaged a panel to try to identify the underlying causes of the decline. A first hypothesis to be checked was whether the test had somehow become more demanding. But, no, to the contrary, indications were that scoring had become more lenient. A second prominent hypothesis was that the decline was due to changes in the demographics of the test takers. Analyses shows this hypothesis to be largely correct, but only for a brief while. Over the early 1960s, changes in the composition of the tested population accounted for as much as three-quarters of the test score decline—and, no wonder, for during this period the number of students taking the SAT tripled. Over the 1970s, however, though the test-taking population stabilized, the scores did not. Instead, the decline continued, even steeper than before, while the extent to which it could be ascribed to demographic shifts shrank to 30 percent at most. Furthermore, the scores that dropped most were those of the strongest students, the students in the top 10 percent of their class; the scores of students toward the bottom of the distribution held steady or even increased.

Advancing Our Students' Language and Literacy: The Challenge of Complex Texts
by Marilyn Jager Adams
American Educator | Winter 2010 - 2011

answer key - Glencoe Algebra 2 - Chapter 12

online (pdf file)

how many different groups of 4?

A school librarian would like to buy subscriptions to 7 new magazines. His budget, however, will allow him to buy only 4 new subscriptions. How many different groups of 4 magazines can he choose?

Counting Principle, Combinations, and Permutations Worksheet (pdf file)

The New Math SAT Game Plan

The New Math SAT Game Plan is a fantastic book.

Amazing.

Last night I read the section on counting.

Counting has been a massive struggle for me. I worked my way through Dolciani's chapter on combinations and permutations, did all the exercises, and ended up pretty much where I started out: basically, being "counting" blind: all the problems look alike. I can't tell the difference amongst them, and I can't tell when and where I would do what or why. I have been utterly flummoxed. ^*

Last night, reading Keller, everything clicked.^** From one moment to the next, I abruptly understood why all the problems look alike (to me) and what the solutions have in common logically. I finished up Keller's 5-page explanation and did all of his exercises quickly and correctly. Easy-peasy.

Later on, I'll try Dolciani's exercises and see how I fare.

Here's how Keller explains the counting principle:

Your favorite restaurant offers a combo-meal. You get to pick one each from a menu of 6 sandwiches, 4 side salads, 5 beverages, 10 desserts and 3 sounvenir toys. You decide to eat at this restaurant once every day, ordering a sandwich, salad, beverage, dessert and toy every time, until you have had every possible combination. To the nearest whole number, how many years will it take you??

Do NOT attempt to list all of the combinations. Instead, learn the Counting Principle:

In any situation where you are faced with a series of decisions keep asking yourself: 

     "Now, how many choices do I have?"

until the last decision has been made. Then to find the overall number of combinations, you multiply together all the numbers of choices you had for each decision.

So in the example I have given you, you have to choose your sandwich from 6 choices, then your salad from 4 choices, your beverage from 5, your dessert from 10 and your toy from 3. And then you are done making decisions. So you multiply and find that there are

6 x 4 x 5 x 10 x 3 =3600 combinations. And then we can divide by 365 days in a year and find that it would take just under 10 years to order every combination. That's a long time but don't be surprised. When you have lots of decisions, or lots of options you get big numbers.

The example I just gave you is one of the easiest kinds of counting problems you'll see on an SAT. Many of the other varieties are a little harder to recognize and a little trickier to answer, as the next few examples will show.

After this, Keller shows how the solution to the problem where you've got a family sitting in a row and the mom and dad have to sit on the end chairs while the four kids can sit on any of the in-between chairs (and how many combinations is that???!!!) follows exactly from the solution to the how-many-combinations-in-the-restaurant problem.

Fantastic!

I am SO happy to know how many ways a family of 6 can sit in 6 chairs with both parents occupying the end chairs.

Seriously.

Now how many choices do I have?





^* I have yet to use either of the two resources you all left for me: the Arlington Agebra Project and a web page created by a math professor who may have sent me the link via email (I don't remember - !). Since I don't remember, I won't link here. 

^** Well...not everything. Still having trouble with the SAT counting problem that nearly did me in last summer - but I now understand the first part of the problem.

data for students and teachers at Khan Academy

About Khan Academy

another year, another budget free-for-all

in Irvington

per pupil funding: $30k

superintendent compensation: $256k

district size: 1796 students

administrator to student ratio school year 1999-2000: 213.9 : 1

administrator to student ratio school year 2009-2010: 112.4 : 1

Time to re-litigate the curriculum director position.

And here's Andrew Cuomo on administrator compensation.