kitchen table math, the sequel

Friday, December 16, 2011

project

from Don Stewart: Preface to the Third Edition - Notes Toward a New Rhetoric by Francis Christensen and Bonniejean Christensen:
I first asked [Bonniejean] to tell me about the research that her husband, a professor at the University of Southern California, had done that led him to discover the secrets of the world's great authors. She first had me conjure up in my mind an image of the classic English professor's study, lined from floor to ceiling with book shelves containing volumes of all sorts of writing, both fiction and nonfiction. In the middle of the room was a large mahogany table, and on that table stood dozens of glass canning jars, each with a label taped to it displaying the name of a particular grammatical construction and its placement in the sentence: participial phrase in initial position, adverb clause in medial position, absolute phrase in final position. In front of those soldier-like jars was a pile of coffee beans. Whenever he could capture a moment between classes or late at night, Francis would pull a book from the shelf, open to his bookmark, and read -- very carefully. Sentence by sentence. If the sentence began with an adverb clause, he picked up a coffee bean and dropped it into the jar labeled "Adverb Clause in Initial Position." He watched the jars as they filled up with beans, and at the end of each week he would pour out each jar's contents and count. He recorded the results and made charts that showed what types of grammatical elements these authors used, where they placed them, and how often each grammatical unit occurred. And from this most primitive of bean counting he discovered the answer to that most mysterious of questions, How do writers write?
Reading this passage, I recalled a Grade 5 data-collection project from Math Trailblazers:


So I'm thinking ... if you want 5th grade students to collect data, which apparently you do, why not have them collect data on number of participial phrases, adverb clauses, and absolute phrases and their positions in the sentences of professional writers? That would be interdisciplinary

First we'd have to tell them what participial phrases, adverb clauses, and absolute phrases are, of course.

Someone would have to tell the teachers, too. I myself had never heard of these things until two years ago, when I started teaching composition at my local college. 

Today I have a reasonably firm grasp of participial phrases and adverb clauses. (Reasonably). 

Still working on absolutes.

No idea what contemporary linguistics thinks of these entities. It appears I have to acquire the old, outdated knowledge along with the new, updated knowledge in order to know what I'm doing inside the classroom.

Thursday, December 15, 2011

'Writing, writing, writing' - a skill lacking among too many college graduates

Jeff Selingo wrote in the Chronicle of Higher Ed about what he learned from employers who are having a difficult time finding qualified employees to hire among recent college graduates.  This was just one problem he found.
Writing, writing, writing. We keep throwing around the word “skills,” but it seems the one skill that almost every job requires is the ability to write well, and too many graduates are lacking in that area. That’s where many of the recruiters were quick to let colleges off the hook, for the most part. Students are supposed to learn to write in elementary and secondary school. They’re not forgetting how to write in college. It’s clear they’re not learning basic grammar, usage, and style in K-12.
Why are students not learning to write before they get to college?  Maybe a different type of writing instruction is needed?


(Cross-posted at Cost of College)

Tuesday, December 13, 2011

Absent Teachers

This is getting to be a real big issue with me. What are typical contract rules about this? My son has soooooo many substitute teachers. Nothing happens in those classes. His teachers talk of dire consequences for students who miss school without following protocol and keeping up to date. Some of the rules are draconian. You even have to come after school to make up gym or you will get a zero for that day.

I just got an email from my son (he got it out during advisory) saying that his English teacher is not in today. This is the teacher who doesn't put any explanation on homework or exams and expects students to come in after school to get any sort of feedback or explanation. You have to sign up for this meeting, and if you fail to come, he will add a zero into your grades. I'm not making this up. My son was emailing me because I had to pick him up from school after one of these scheduled meetings. The teacher and school don't care that getting normal feedback on tests requires special transportation. I don't know what they expect from parents who work far away.

And in precalc, they are on their third teacher while the regular teacher is on long-term leave. The latest teacher was complaining that her stay was longer than anticipated and that, in effect, she was not prepared and had no lesson plans. This was in response to students' questions that she couldn't answer or had answered wrong. That was her excuse to the students.

Monday, December 12, 2011

SAT - For those still interested

This is something I meant to post before. It's the relationship between the raw score and the SAT score for the May 2011 SAT. It demonstrates how much your SAT score will drop with each error.

54 - 800 No errors or skipped problems.
53 - 790 One strike (error).
52 - 760 Two strikes.
51 - 740 You can’t get here for most cases. You round down.
50 - 720 Three strikes - this error drops you 40 points.
49 - 710
48 - 700
47 - 680

For the Student-Produced Response section, you don't get the extra quarter point penalty for a wrong answer and the rounding jump is delayed. Skipped problems will also cause a delay in the rounding jump. However, at some points the roundings kick in. It's a real killer in the 700 range.

Sunday, December 11, 2011

More posts up on Kerrigan 'Writing to the Point'

I've completed two more assignments in my project to work my way through the Kerrigan Writing to the Point method of writing instruction.
I continue to appreciate how the Kerrigan method teaches writing by systematically moving through a hierarchy of skills.

Here's my original post in this series.

Thursday, December 8, 2011

Schools find Khan Academy works better than group learning

More schools are trying Khan Academy videos in their classrooms, and initial results look promising.  But when you start with an instructional method that includes lots of time-consuming group work, maybe almost anything else will work better.  Here's how it's going at one school.
In the past, math class at the Summit schools was always hands-on: the class worked on a problem, usually in small groups, sometimes for days at a time. But getting an entire class of ninth graders to master the fundamentals of math was never easy. Without those, the higher-level conceptual exercises were impossible.
They found that Khan Academy did a better job.  Not too surprising to me.

You can read more at Cost of College.

Monday, December 5, 2011

SAFMEDS instructions

SAFMEDS = Say All Fast a Minute Each Day

SAFMEDS on the web

The best set of directions I've seen so far: SAFMEDS cards: Instructions - begins with the words: "I’m going to show you a method that will make it easier to learn the NEW terms (i.e., facts or rules) contained in the CLM Course of Study."

Is Fluency Free-Operant Response-Response Chaining? by Ogden R. Lindsley - inventor of SAFMEDS; explains the rationale

Ogden R Lindsley and the History of Precision Teaching

update: Youtube video explaining SAFMEDS -- and, about 6 minutes in, celeration charts

Sunday, December 4, 2011

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.

from the archives: grading student writing

from 2009:
Students have long believed (on good evidence) that if the same paper is submitted to two teachers in two different sections of the same course, the paper is likely to receive two very different grades. In 1961, Paul Diederich and his colleagues proved that this student belief is no myth. When 30 student papers were graded by fifty-three graders (a total of 15,900 readings), more than one third of the papers received every possible grade. That is, 101 of the 300 papers received all nine grades: A, A-, B+, B, B-, C+, C, C-, and D. Diederich also reported that

94 percent [of the papers] received either seven, eight or nine different grades; and no essay received less than five different grades from fifty-three readers. Even when the raters were experienced teachers, the grades given to the papers by the different raters never attained a correlation greater than .40. Diederich, P.B., French, J.W., and Carlton, S.T. "Factors in judgments of writing ability." Research Bulletin RB-61-15. Princeton, N.J.: Educational Testing Service, 60 pp.
The Schools We Need and Why We Don’t Have Them
E. D. Hirsch
185-188

palisadesk on inclusion issues

Part 1
Part 2

prodigy

in the Times today:
Great things were expected of him. His math teacher at Greenwich High School in Connecticut, Stephen Willoughby, now a retiree in Tucson, Ariz., says he was a math prodigy. “I always expected Chris would win a Nobel. I just wasn’t sure what field it would be.”

Mr. Sims’s classmates voted him most likely to succeed. “In a class of intelligent people, he was exceptional,” says Joyce Tracksler, a high school friend who is now a mystery writer in Kittery Point, Me.

His parents were exceptional, too. His father, Albert, was a diplomat, and young Chris lived in Germany a few years as a child. The family later moved to the Washington suburbs before settling in Greenwich. His father became an executive at the Institute of International Education and at the College Entrance Examination Board in New York. During the Kennedy administration, he helped start the Peace Corps.

Because of his father’s College Board connections, Mr. Sims got hold of an old SAT exam, which he and Mr. Willoughby used to conduct a statistical analysis. They found that on multiple-choice questions in English and social studies, the “longer answers tended to be correct.” In math, they determined that the number that was “closest to all of the other numerical choices” was probably the right one. Mr. Willoughby says Mr. Sims got perfect scores on SATs, and his teacher assumed that the young man would later “do something involving math, statistics and probability.”
Good Morning. You're Nobel Laureates by Jeff Sommer | December 3, 2011

Friday, December 2, 2011

STEM careers and the small liberal arts college

I've just come across a passage that is relevant to this exchange between Mark R anonymous. and ChemProf:

Mark anonymous:
With STEM degrees and with physics undergraduate degrees in particular I'd be a little wary of the large research institutions. As an example Cal (UC Berkeley) is the top rated graduate school in chemistry but I sure wouldn't send my kids there as undergraduates with the 500 person classrooms taught by grad students with three weeks of training.

There are a few top notch undergraduate-centered places (Harvey Mudd leaps to mind) but failing getting into there I think there's a lot to be said for finding a strong 2nd tier liberal arts college with one or two solid STEM departments that are actually doing some research as well as teaching. Strong students get lots of attention and opportunities as well as stronger and more personal letters of recommendation.
chemprof:
I was one of those chem grad students at Cal, and we got two days of training. But yeah, for STEM and given the current economic environment, I'd suggest looking at second tier liberal arts colleges and see what scholarship money was out there, as well as which departments have a strong history. It does take a little more searching, but there are some gems. I used to think it was a problem to be the big fish in a little pond, but at least for now, that seems to be a good strategy for students.
from Liberal Arts Colleges in American Higher Education: Challenges and Opportunities (pdf file):
Liberal arts colleges have produced disproportionate numbers of career scientists, as the surveys conducted by Oberlin and Franklin & Marshall Colleges have shown over the years. This fact alone ought to be grounds for enormous federal investment in small colleges. What has not been as obvious has been the role of less well known liberal arts colleges in meeting the national need for scientists. For example, Elizabethtown College in Pennsylvania has a biology department that in 1985 consisted of six faculty members and 73 majors. Now it has nine faculty members and 195 majors. Elon University in North Carolina has steadily increased the number of mathematics majors, with two (of 10) majors going to graduate school in math in the year 2000, three (of nine) going to graduate school in 2001, four (of 12) in 2002, and eight (of 12) in 2003. Hendrix College in Arkansas ranks 24th in the nation in the number of its graduates per total enrollment who have received Ph.D.s in chemistry. Most dramatic may be Whitworth College in Washington State, which has increased the number of physics majors by almost 400 percent in five years, from 11 in 1997 to 41 in 2002.
I happen to know about these lesser-known liberal arts colleges that are doing such a good job of producing career scientists because the Council of Independent Colleges has, for the past three years, run a prize program that recognizes outstanding achievement in undergraduate science education. What has been interesting about the applicant pool for these Heuer Awards for Outstanding Achievement in Undergraduate Science Education (as they are called) is that only five out of the 60 institutions that were nominated in 2002 and eight out of the 47 institutions nominated in 2003 had enrollment of over 3,000 students. Almost all of the institutions that have good reason to believe that they are making significant contributions to society’s need for high-quality career scientists are very small.

Richard Ekman, "Selective and Non-Selective Alike: An Argument for the Superior Educational Effectiveness of Smaller Liberal Arts Colleges" in American Council of Learned Societies, ACLS OCCASIONAL PAPER, No. 59.

what is curriculum support specialist, please?

I was sitting here on the sofa going through ancient Education Weeks when I heard Pat Sajak introduce a contestant as "a curriculum support specialist."

"A curriculum support specialist," he said. "What is that?"

answer: "It's a teacher that goes into the classroom to support the curriculum and other teachers."

Who says times are hard? Back in the real Depression, curriculums and teachers didn't have support! Curriculums and teachers had to make do with a principal, a superintendent, and the occasional school nurse.

How fortunate we are today, here with our civilian employment ratio of zilch.

oops

I spoke too soon.

The curriculum support specialist just went bankrupt.

another question

Thanks SO much for the comments on teaching students how to distribute a negative -- I can't tell you how much I appreciate your taking the time.

You are all good deed doers!

Unfortunately, I haven't actually read all you've written.

I was in the midst of reading when I had to break off mid-stride, load Andrew into the car, and drive the two of us around a sketchy part of Yonkers* for one hourafter dark (not a lot of street lights in Yonkers, not a lot of street signs, either), with cars honking at us and drivers yelling out their windows (RUDE DRIVERS IN SKETCHY YONKERS!) searching for and not finding ARC,* where we had an appointment to try and get Andrew's weekend aide hired because the agency she's been working for is kaput. Ed called the guy who runs it and reported back that the owner had been 'vague' as to what has transpired. Distressing, because we thought the world of the guy, and so did everyone who worked for him, it seemed.

Anyway: Mission Not Accomplished.

Next time I am going to ask Garmin to take me to 265 Saw Mill River Road in Hawthorne. We'll see how that goes.

No time to read this morning, either, as I am attending a two-hour workshop at my local college on how to pass the course I teach. My college gives exit exams to students taking the remedial courses, which I think is a great idea. The workshop is for students, not teachers, but still. I figure I'll attend and find out what it is they think I'm teaching.

Then, if it just so happens that I am somehow not teaching what it is they think I'm teaching, I'm going to start teaching it right away.

For the moment, I have a quick follow-up question: what do you think of yourteacher.com? I discovered last night that yourteacher has an algebra app (update: a pre-algebra app, too!) Fifty bucks, but I'm seriously considering springing for it. I'm not experienced enough to be teaching the distributive property on the fly.

* No numbers on the buildings and a paucity of signs announcing who was inside or why: a neighborhood in which a number of the local establishments appeared to have concluded that it makes good business sense not to advertise their whereabouts or even their existence. Curious! Question: what kind of enterprise is housed in a run-down, low-rise office building with a dozen shiny late-model cars crammed together outdoors beneath an oversized carport? I spoke with the two proprietors, who came outside to ask me what I wanted (I wanted directions), and wish now I had asked what they wanted. 

Thursday, December 1, 2011

The Day of Reckoning, brought to us from India

Together, the rise of Reform Math, the reduction in ability-based grouping and AP classes, the demise of the close reading and the analytical essay (see also this), and the growing rarity of instruction in the finer points of English grammar and sentence construction, have caused current and future American high school graduates to be decreasingly prepared for college. As more and more American college students display skills in math, writing, and reading comprehension that are way below expectations (ending up, even in some of the more selective colleges, in remedial math and writing classes), college admissions committees are increasingly looking abroad.

While much of the news about overseas applicants centers on China, with its thousands of Ivy League-aspiring applicants and their glossy, high-production value applications (and the growing suspicion that a fair amount of cheating is involved), it's India, I predict, that will bring to the American K12 education system the day of reckoning that we so desperately need it to have. First, unlike their Chinese counterparts, college applicants from India face no linguistic barriers; many speak and write a much more eloquent English than American (and even British) students do. Second, there are apparently tons of extremely well-qualified Indian applicants pinning their hopes on America's top colleges.

Indeed, as an October New York Times article inadvertently suggests, the Day of Reckoning may be close at hand:
Moulshri Mohan was an excellent student at one of the top private high schools in New Delhi. When she applied to colleges, she received scholarship offers of $20,000 from Dartmouth and $15,000 from Smith. Her pile of acceptance letters would have made any ambitious teenager smile: Cornell, Bryn Mawr, Duke, Wesleyan, Barnard and the University of Virginia.

But because of her 93.5 percent cumulative score on her final high school examinations, which are the sole criteria for admission to most colleges here, Ms. Mohan was rejected by the top colleges at Delhi University, better known as D.U., her family’s first choice and one of India’s top schools.
...

Ms. Mohan, 18, is now one of a surging number of Indian students attending American colleges and universities, as competition in India has grown formidable, even for the best students. With about half of India’s 1.2 billion people under the age of 25, and with the ranks of the middle class swelling, the country’s handful of highly selective universities are overwhelmed.
True, another reason--indeed, the only reason mentioned in the Times article--why American recruiters are seizing on this opportunity is because so many of the crème de la crème of overseas students are wealthy enough to pay full tuition, unlike many of their American counterparts. But it also helps that the K12 schools they attend aren't using Reform Math, aren't renouncing ability-based grouping, and aren't failing to provide college prep classes that are truly college preparatory. Indeed, if it were primarily her parents' pocket books that make Moulshri Mohan so attractive to Dartmouth and Smith, why are they offering her so many thousands of dollars of scholarship money?

So here are my dire predictions. In the next ten years, as the effects of Reform Math continue to percolate up the American school system, and as the number of highly qualified Indian students continues to outpace the numbers of spots at the best Indian universities, there will be a the growing displacement of American students by Indian students. Only then will a large enough proportion of the Powers that Be start realizing how urgent it is to enact actual education reform--reform, that is, that reverses the century's-long tide that has pushed our K12 schools further and further away from what's happening in the most successful school systems overseas.

(Cross-posted at Out In Left Field)

Wednesday, November 30, 2011

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?

ture and flase

In the thread on reading kcab and the SAT, Glen writes:
As a child, my bête noire was always true-false tests. The more details you know about a topic, the more likely you are to see every answer as, "well, yes and no." True or False: Lincoln was well-educated? Well, he had very limited formal education, which the teacher mentioned and which is what people today tend to mean when they say "educated," so maybe she wants me to say false. But he had extensive self-education, which she also mentioned, and this may be a trap where she's going to argue, "No, education doesn't have to mean formal education, and I told you he was self-educated" which would make it true. But if I answer true, she'll end up marking it wrong and telling me, "Oh, come on, you know what I mean by 'educated'", and someone will tell me--they always do--to stop "overthinking" it. What does "overthinking" mean? Does it mean that answering correctly requires answering as if I knew less? How much less?

And what does "true" mean? Does it mean 100% true? In formal (binary) logic, something that is mostly true is false. So, on a true-false test, if something is mostly true, is it true or false?

Those %#$@ true-false tests drove me nuts.
I'm laughing!

Glen's story calls to mind my first year T.A.ing freshman rhetoric at the University of Iowa. I was young and wide-eyed.

I was so young and wide-eyed that I vividly recall to this day my shock at one of the older T.A.s* telling a group of us that his students so often misspelled "true" and "false" on true/false tests that he had once required everyone in the class to write "ture" and "flase"(which he pronounced "flace") instead of true and false.

Later on, he became my boyfriend, but I don't think the ture-flase episode had anything to do with it.

* I'm pretty sure there's supposed to be an apostrophe after "T.A.s," but I don't like an apostrophe after T.A.s, so I'm not putting on in.

Tuesday, November 29, 2011

Charles Murray on abolishing the SAT

Murray writes:
For most high school students who want to attend an elite college, the SAT is more than a test. It is one of life's landmarks. Waiting for the scores--one for Verbal, one for Math, and now one for Writing, with a posible 800 on each--is painfully suspenseful. The exact scores scores are commonly remembered forever after. So it has been for half a century. But events of recent years have challenged the SAt's position. In 2001, Richard Atkinson (2001), president of the University of California, proposed dropping the SAT as a requirement for admission. More and more prestigious small colleges, such as Middlebury and Bennington, are making the SAT optional. The charge that the SAT is slanted in favor of privileged students--"a wealth test," as Harvard law professor Lani Guinier calls it--has been ubiquitous (Zwick, 2004).

I have watched the attacks on the SAT with dismay. Back in 1961, the test helped get me into Harvard from a small Iowa town by giving me a way to show that I could compete with applicants from Exeter and Andover. Ever since, I have seen the SAT as the friend of the little guy, just as James Bryant Conant, president of Harvard, said it would be when he urged the SAT upon the nation in the 1940s.

Conant's cause was as unambiguously liberal in the 1940s as income redistribution is today. Then, America's elite colleges drew most of their students from a small set of elite secondary schools, concentrated in the northeastern United States, to which America's wealthy sent their children. The mission of the SAT was to identiy intellectual talent regardless of race, color, creed, money, or geography, and give that talent a chance to blowwom. Students from small towns and from poor neighborhoods in big cities were supposed to benefit--as I thought I did, and as many others think they did. But data trump gratitude. The evidence has become overwhelming that the SAT no longer serves a democratizing purpose. Worse, events have conspired to make the SAT a negative force in American life. And so I find myself arguing that the SAT should be abolished. Not just deemphasized, but no longer administered. Nothing important would be lost by so doing. Much would be gained.

Murray, Charles. (2011). Abolishing the SAT. In Soares, Joseph A. (Ed.), SAT Wars: The Case for Test-Optional College Admissions (pp. 69-81). New York: Teachers College Press.