Page 99

Ed's new book is out! Heroes of Empire: Five Charismatic Men and the Conquest of Africa 

The Scribner Arithmetic

I was just talking to a woman here who is working on a transparency project (I'm in!). She got her start in all this when her district adopted TERC and rejected all forms of acceleration for gifted kids; now she's asking local townships for budget docs and the like.

Never occurred to me that the math wars can also have consequences for local government.

heh

She mentioned that when she looked back at her old textbooks, as well as her father's books, she was impressed. Her dad used Scribner Arithmetic in the 1950s.

Does anyone know anything about it?



The Scribner Arithmetic: Book 5

I wish I could remember the math books my school bought when I was in 2nd grade, I think. I remember thinking they were beautiful. Not just beautiful but elegant, though I don't think I knew to apply that word to a book at the time.

accent

I love this!

Only problem: I can't figure out which accent is my accent.

I think I just heard Cassy T, so apparently I'm clicking on flags too far north...

free books

An Introduction to English Syntax by Jim Miller
Jim Miller

The English Language: From Sound to Sense by Gerald P. Delahunty and James J. Garvey
Table of Contents (pdf file)

Now all I need is some free time to read them.

off-topic

This is interesting:

Despite poorer health, shorter lives and more strenuous jobs, in 1950 the typical individual did not claim Social Security until age 68.5. In 1950, more than 20% of Americans worked in physically demanding jobs; today only about 8% do. While today's technology-driven service economy places demands on older workers, it is hard to imagine that things were easier when Americans typically worked on farms or in factories.
Raise the Early Retirement Age
by Andrew G. Biggs
LA Times 11/9/2010

I had no idea.

back to Illinois

Robert H. Johnson

off-topic - social media

Do the people you know on blogs affect your odds?

Algebra II Before Geometry

This is happening in our area (not at my son's HS), but I'm not sure why. Is it being driven by the CCSSO standards? Do high schools want to get most students through the material (pseudo-Algebra II) before it's too late or while the algebra "iron" is hot? If this is true, then the top math track in high school is under attack. It's one thing to channel students off to integrated math, like Core Plus, but with the current emphasis on the traditional sequence of math classes, there seems to be only one direction for the content to go. Traditional math won, but ends up losing. Is that what will happen in lower schools if they decide to use Singapore Math? Perhaps I'm reading too much into this. I don't have any strong feelings about whether geometry or algebra II should come first, but I do have strong feelings about rigor. What is the real driving force behind the switch? Do they use the same textbooks? One comment I heard once was that this would allow the geometry classes to delve more deeply into proofs because the students would be more mature and would have more math background. I don't buy it. What direction would algebra II go, even for the honors version?

Knowledge is good

Just heard from Barry - new article from Sweller, Clark, & Kirschner is out --

Problem solving is central to mathematics. Yet problem-solving skill is not what it seems. Indeed, the field of problem solving has recently undergone a surge in research interest and insight, but many of the results of this research are both counterintuitive and contrary to many widely held views. For example, many educators assume that general problem-solving strategies are not only learnable and teachable but are a critical adjunct to mathematical knowledge. The best known exposition of this view was provided by Pólya (1957)....[I]n over a half century, no systematic body of evidence demonstrating the effectiveness of any general problem-solving strategies has emerged. It is possible to teach learners to use general strategies such as those suggested by Pólya (Schoenfeld, 1985), but that is insufficient.

[snip]

The alternative route to acquiring problem-solving skill in mathematics derives from the work of a Dutch psychologist, De Groot (1946–1965), investigating the source of skill in chess. Researching
why chess masters always defeated weekend players, De Groot managed to find only one difference. He showed masters and weekend players a board configuration from a real game, removed it after five seconds, and asked them to reproduce the board. Masters could do so with an accuracy rate of about 70% compared with 30% for weekend players. Chase and Simon (1973) replicated these results and additionally demonstrated that when the experiment was repeated with random configurations rather than real-game configurations, masters and weekend players had equal accuracy (±30%). Masters were superior only for configurations taken from real games.

[snip]

The superiority of chess masters comes not from having acquired clever, sophisticated, general problem-solving strategies but rather from having stored innumerable configurations and the best moves associated with each in long-term memory.

[snip]

[L]ong-term memory, a critical component of human cognitive architecture, is not used to store random, isolated facts but rather to store huge complexes of closely integrated information that results in problem-solving skill. That skill is knowledge domain-specific, not domain-general. An experienced problem solver in any domain has constructed and stored huge numbers of schemas in long-term memory that allow problems in that domain to be categorized according to their solution moves.

[snip]

[D]omain-specific mathematical problem-solving skills can be taught. How? One simple answer is by emphasizing worked examples of problem-solution strategies. There is now a large body of evidence showing that studying worked examples is a more effective and efficient way of learning to solve problems than simply practicing problem solving without reference to worked examples (Paas & van Gog, 2006).

[snip]

For novice mathematics learners, the evidence is overwhelming that studying worked examples rather than solving the equivalent problems facilitates learning. Studying worked examples is a form of direct, explicit instruction that is vital in all curriculum areas, especially areas that many students find difficult and that are critical to modern societies. Mathematics is such a discipline. Minimal instructional guidance in mathematics leads to minimal learning (Kirschner, Sweller, & Clark, 2006).

Teaching General Problem-Solving Skills Is Not a Substitute for, or a Viable Addition to, Teaching Mathematics (pdf file)
by John Sweller, Richard Clark, and Paul Kirschner

the Arizona case

School Choice on Trial

punctuating by breath

from Sentence Diagramming: A Step-by-Step Approach to Learning Grammar Through Diagramming:

Before the 1960s, grammar and punctuation were taught as foundation blocks for writing instruction. In the 1960s, some research questioned the value of teaching grammar, and new ways of teaching grammar cast doubt on the traditional methods. In the midst of all this change, the baby was thrown out with the bath water where grammar was concerned, and when the 1970s rolled around, a new generation of teachers had not been trained to teach grammar and punctuation.

I am a member of that new generation of teachers, and a product of a writing education with little structured or sustained lessons in grammar. Thankfully, one of my teachers believed in teaching grammar and punctuation through sentence diagramming. Before this instruction, I lacked confidence in my writing because I didn't know for sure if my sentences were really sentences.

I can still remember the great "aha!" feeling I had when I realized that I could analyze a sentence without the teacher's assistance--I could mentally diagram the sentence to determine if it was grammatically correct. What a sense of power that gave me!

Marye Hefty

I find this remarkable.

Mary Hefty earned a Masters degree in English and then worked as an editor in a research laboratory, but as a child (or teen?) she could not tell whether she had or had not written a sentence.

Crazy!

She goes on:

When I left the research laboratory to become a college professor, teaching English composition and technical writing, I noticed during the first term that many of my students' papers were riddled with grammar and punctuation errors. I didn't know how to add the necessary instruction in grammar and punctuation skills to our limited class time without letting it take over the class like a weed. Typically, I tried a band-aid approach to teaching grammar and punctuation. When I saw sentence fragments in the students' papers, I talked about sentence fragments. When I saw comma splices, I talked about those. It didn't take long to realize that many of my students didn't recognize a sentence, so they couldn't solve the sentence problems. My students were just like I had been--needing structure and an organized way to learn grammar and punctuation without having the approach overwhelm them or make it difficult for them to learn the writing process in class.

In several classes, I decided to discard the band-aid approach and devote 10 percent of the class time to teaching the students grammar and punctuation, starting with the basics--What is a simple sentence? How do you diagram it? And guess what? It worked.

I've been teaching sentence diagramming in some of my courses for eight years now, and the students who begin my classes not being able to identify or define a simple sentence leave the class with the vocabulary and knowledge to identify simple, compound, and complex sentences; fragments; run-ons; and comma splices. Most importantly, the students have a foundation that enables them to learn more--without my help--after they leave the class.

Surprisingly, my university students don't mind having to learn grammar and punctuation through sentence diagramming because this approach quickly gives them the skills and confidence to fix the problems in their papers on their own. I have heard enough anecdotal evidence from my students to know that sentence diagramming works. For example, one of my former students told me that she was asked to edit letters for her boss. She said that before taking my class, she just put in the commas in where she thought she heard a pause and just guessed that the sentences were correct. "Now I know for sure, and I can really help," she said.

A lot of my students -- these are college freshmen -- "punctuate by breath."

Punctuating by breath is OK as far as it goes, I think. Now that I'm learning the formal rules of punctuation, I realize I've been breaking some of those rules for decades. I've been breaking the rules because a) I didn't know them, so b) I've been punctuating by breath.

Having thought it over, I've decided to carry on punctuating by breath when the occasion calls for it. If I want or don't want a comma somewhere,  then a comma there will or will not be. I'm the decider.

Still and all, the reason this works for me is that I have never, ever, in my entire adult life, failed to recognize a complete sentence. Nor have I failed to write a complete sentence if that's what I wanted to write.

I have come to the realization that a course about writing is a course about sentences.

Time

My dad died this week.

Didn't see it coming.

My mom reminded me that she and my dad stayed at our house when I was pregnant with the twins. Or maybe it was right after I had the twins, I don't remember. Every morning, Jimmy would get in bed with them and wake my dad, whom we all called Bob, because that was his name. We called my mom Pat & my dad Bob.

After a few days, Bob left to go back home and my mom stayed on.

Every morning after that, Jimmy would get in bed with my mom and chant, "No more Bob, no more Bob."

Back to Illinois on the weekend for the funeral.

Preconceived notions about place value

(Cross-posted at Out in Left Field--with some great comments)

One thing that struck me about the math talks given at this weekend's New England Conference on the Gifted and Talented was the emphasis on manipulatives and the concerns about whether children understand place value. Are these the most appropriate things to be focusing on when it comes to students who are gifted in math? The mathematically gifted kids I know grasp place value and other aspects of arithmetic with only minimal exposure to manipulatives, and quickly advance to higher levels of abstraction by the time they hit first or second grade. But the education establishment seems bent on convincing itself that children--however gifted--don't understand place value.

Why would you want to convince yourself of this? Because it gives you an excuse not to teach the standard algorithms of arithmetic. If children don't understand place value, then they can't understand borrowing and carrying (regrouping), let alone column multiplication and long division. And unless they understand how these procedures work from the get-go, educators claim (though mathematicians disagree), using them will permanently harm their mathematical development.

So, given how nice it would be not to feel any pressure to teach the standard algorithms (because, let's admit it, they are rather a pain to teach), wouldn't it nice to convince ourselves that our elementary school students, however gifted in math, don't understand place value?

But how do you convince yourself of this? As that ground-breaking math education theorist Constance Kamii has shown, it's child's play. All you have to do is ask a child the right sort of ill-formed question. Here's how it works:

1. Show the child a number like this:

27

2. Place your finger on the left-most digit and ask the child what number it is.

3. When the child answers "two" rather than "twenty," immediately conclude that he or she doesn't understand place value.

4. Banish from your mind any suspicion that a child who can read "27" as "twenty-seven" might simultaneously (a) know that the "2" in "27" is what contributes to twenty-seven the value of twenty and (b) be assuming that you were asking about "2" as a number rather than about "2" as a digit.

travelling salesman

solved by bees

metrics feel good

24/7

Sorry to be AWOL...I am CHAINED TO MY DESK!

(Teaching 2 courses I've never taught before, both of them composition & literature, which means lots of paper reading and lots of reading-reading.)

I'm doing no math at all. None. Not even the SAT Question of the Day.

I'm spending so much time on English literature, fables, folk tales, and short stories that I think I'll just start posting some of the work I'm doing there for the time being.

For starters, here's a fantastic site for English students:

Getting an A on an English paper

factoid

Spotted this in the Times Book Review last night:

Town, county and state governments no longer have much independent political identity. They are mere “conduits for federal mandates,” as Codevilla puts it. He notes that the 132 million Americans who inhabited the country in 1940 could vote on 117,000 school boards, while today a nation of 310 million votes in only 15,000 school districts.

The State of Conservatism
By CHRISTOPHER CALDWELL
Published: October 21, 2010

A couple of years ago, when busing costs were at issue here in Irvington, we learned that at some point in NY history the state 'incentivized' (hate that word) districts to consolidate by picking up some of the transportation costs. I no longer recall the details, and the story doesn't make sense given the fact that the town is paying transportation costs, not the state.

But I'm pretty sure the state-incentivizing part is correct in some way, and it's interesting in light of Codevilla's statistics.

help desk - sentence structure

Alicia took an earlier bus than she needed to, for she didn’t want to be late.

Is this sentence simple or complex?

Over Sixty Percent Remedial

Our state paper had an article today about how 60% of the kids entering our community college system need at least one remedial class. Fifty percent need at least 2. (I think this is true nationally.) It also says that these kids run the greatest risk of dropping out. There are other issues since the graduation rate is only 10%.

The state Education Commisioner says that "... we need more college-educated adults ..." and that "...even if they don’t go to college, they need a level of skills to be successful in life." and also “We have to understand that this builds over time, from the very first day of elementary school, ...”.

The community college gives a standard test to all incoming freshman. The state tests (K-12) align with this standard (it's pretty low), but K-12 schools still allow students to move on to the next grade without meeting the low proficiency grade-level cutoffs. What do they think is going to happen? If they place the entire onus of success in education on the kids (and parents), then how do they think they are going to fix the problem?

spelling alone

Deliberate Practice Spells Success: Why Grittier Competitors Triumph at the National Spelling Bee

Barry G on the Times story

The New York Times ran a story on September 30 about Singapore Math being used in some schools in the New York City area.  Like many newspaper stories about Singapore Math, this one was no different.  It described a program that strangely sounded like the math programs being promoted by reformers of math education, relying on the cherished staples of reform: manipulatives, open-ended problems, and classroom discussion of problems.  The only thing the article didn’t mention was that the students worked in small groups.

[snip]

The mistaken idea that gets repeated in many such articles is that Singapore Math differs from other programs by requiring or imparting a “deep understanding” and that such understanding comes about through a) manipulatives, b) pictures, and c) open-ended discussions.  In fact, what the articles represent is what the schools are telling the reporters. What newspapers frequently do not realize when reporting on Singapore Math, is that when a school takes on such a program, it means going against what many teachers believe math education to be about; it is definitely not how they are trained in ed schools.  The success of Singapore’s programs relies in many ways on more traditional approaches to math education, such as explicit instruction and giving students many problems to solve, in some ways its very success represented a slap in the face to American math reformers, many of whom have worked hard to eliminate such techniques being used.

[snip]

Singapore’s strength is the logical consistency of the development of mathematical concepts. And much to the chagrin of educators who may have learned differently, mastery of number facts and arithmetic procedures is part and parcel to conceptual understanding.  Starting with conceptual understanding and using procedures to underscore it is an invitation to disaster—such approach is making profits for  outfits like Sylvan, Huntington and Kumon.

[snip]

Fortunately, the logical structure and word problems in Singapore’s books are so good it will work in spite of the disciples of reform.  My friend is right.  If the education community wants to think that Singapore Math is student-centered and inquiry-based and the realization of US reforms, let them think it.  For those of us who know better, it will remain our dirty little secret.
Singapore Math Is “Our Dirty Little Secret”

Waiting for Superman

cross posted to the Irvington Parents Forum

Waiting for Superman

Tue, October 12 5:10 || 7:25 || 9:40
Wed, October 13 5:10 || 7:25 || 9:40
Thu, October 14 5:10 || 7:25 || 9:40

Jacob Burns Film Center Theater
364 Manville Rd., Pleasantville, NY 10570
Info-line: 914.747.5555
914.773.7663

============

Hi everyone -

Waiting for Superman is incredible. So moving. Entertaining, too; Geoffrey Canada in particular is riveting. The title comes from a story he tells about the day his mother told him Superman doesn’t exist.

The film follows 5 or 6 children whose families are trying to find good schools for their kids, including one mom who can no longer afford the Catholic school her daughter has been attending. The lottery scenes at the end are excruciating.

Amazingly, the film does **not** give wealthy, white suburban schools a pass. About three quarters of the way in, the film tells us that suburban schools have the same underachievemement problems urban schools do; then we see data showing that the top 5% of U.S. students rank far below the top 5% of students in other countries. Which is true.

Here’s a picture of the suburban girl waiting to see if her number will be called:

Here’s the trailer.

Catherine

What about the US's better students? When asked, Schmidt replied, "For some time now, Americans have comforted themselves when confronted with bad news about their educational system by believing that our better students can compare with similar students in any country in the world. We have preferred not to believe that we were doing a consistently bad job. Instead, many have believed that the problem was all those 'other' students who do poorly in school and who we, unlike other countries, include in international tests. That simply isn't true. TIMSS has burst another myth - our best students in mathematics and science are simply not 'world class'. Even the very small percentage of students taking Advanced Placement courses are not among the world’s best."

TIMSS - Trends in International Mathematics and Science Studies

MSMI for schools and homeschoolers?

In the Homeschooling by the Numbers thread, there was much back and forth critical of criticisms of homeschoolers lacking content knowledge--mostly centered around the ideas that a) schools have the same problems, and b) tailoring to one's child is a good thing.

Wrt to the first criticism, that school teachers lack content knowledge, I've created a not-for-profit corporation to address this. MSMI, the Middle School Mathematics Institute, is aimed at parents, teachers and schools serving students in grades 4-8, offering a variety of services to help build the bridge to Algebra 1.

For teachers, we offer intensive workshops, known as "institutes" that teach the math behind the school mathematics that teachers are teaching. It teaches the foundational pieces to help teachers understand that math is meant to be coherent and precise, and they must teach it that way as well. For schools, we help them to move away from their textbooks-as-curricula, and understand that nearly all available textbooks have incredibly great deficiencies, so great that only a very skilled teacher will be able to overcome them, We then help schools to address their standards and curricula to raise the difficulty and mathematical maturity slowing over those grades so students are prepared for algebra. For parents, we over free talks and pamphlets to help navigate what a good mathematics education would look like for their children.

One group I've not reached out to, even though I have many contacts in that group, is the homeschooling community. Should I? How? I'm happy to reach out to them as I do parents, but I haven't tried involving them as teachers.

My last institute was 5 full days. My next is going to be 9. It takes that many days just to begin to start to teach what mathematical reasoning looks like, even to experienced elementary math teachers.

I find that they homeschoolers I know are even less likely to find the time to attend such an event. One day workshops every month aren't enough. None of the homeschooling mothers I know, even if they are willing to afterschool Singapore, are willing to essentially take a course in learning elementary math if it required meeting weekly.

Am I pitching it wrong? Is there something I can do to reach them? I'm willing to admit that I must be all things to all people, but what would it take to get to them?

I already have to thread the needle--positioning MSMI as supporting teachers in a way that makes them not feel attacked for lacking content knowledge, but instead, supportive of their being asked to teach more and more sophisticated math. I have to reach administrators and tell them that their textbooks are terrible and teachers don't have the knowledge they need to do what their state has asked them to do, and they've basically been given no other options, since all US textbooks are terrible and elementary teacher certs don't require any math. I have to help parents to feel empowered even as I sound the alarm about their child's math program.

That's a lot of defensiveness to dance around. And yet, in homeschoolers, it seems even higher. So even as they admit to me that they don't know any math, and their children know more than they do, they don't want to learn more.

What should I do? How could I reach them? What would it look like?

onward and upward

party on

"University administrators are the equivalent of subprime mortgage brokers," he says, "selling you a story that you should go into debt massively, that it's not a consumption decision, it's an investment decision. Actually, no, it's a bad consumption decision. Most colleges are four-year parties."

Technology = Salvation

slippery slope

…[I]f once a man indulges himself in murder, very soon he comes to think little of robbing; and from robbing he comes next to drinking and Sabbath-breaking, and from that to incivility and procrastination. Once begin upon this downward path, you never know where you are to stop. Many a man has dated his ruin from some murder or other that perhaps he thought little of at the time.

Thomas De Quincey, "Second Paper on Murder"
via Fallacy Files

let's not and say we did

In Michigan’s Wayne County, prosecutor Kym Worthy plans to meet this month with the Detroit City Council to discuss an ordinance she’s proposing to require parents to attend conferences. The most severe penalty would be three days in jail. It troubles her when she hears of Detroit schools that have 300 students, and just two parents will show up for conferences. A lack of parental involvement often leads to truancy, which leads to crime, says Ms. Worthy. She knows her proposal may be challenged by civil libertarians, “but at least we’ll get the conversation started.”

How Would You Grade Parent-Teacher Conferences
by Jeffrey Zaslow
Wall Street Journal
October 6, 2010, 9:40 AM ET

That's going to be one short conversation.

Number one: yes, indeed, civil libertarians are going to object. Strenuously.

Number two: do they teach logic in law school?

Number three: perhaps prosecutor Kym Worthy should ask teachers whether they want parents showing up for parent-teacher meetings on pain of arrest and incarceration.

And that pretty much covers it.

Next.

let's not and say we did
let's not and say we did, part 2
let's not and say we did, part 3

iParent

Now that my son is in high school and getting real grades (not vague 1-5 and 6-10 rubric scores), I'm much happier. On top of that, I get to check all of his grades online at iParent. The high school apparently laid down the law and told teachers to get the grades uploaded as soon as possible. In fact, there were a couple of times when I knew his test scores before he did. This is quite different from middle school where I never saw a lot of work, let alone the grades. The weightings are all there and the current grade is given.

I expected grading in high school would be better defined and defendable, what with the importance of GPAs. At the open house last week, almost all of the teachers talked about grading and how grading in the different classes are coordinated. In math, they decided to reduce the weighting of math homework to just 5% because they felt that too many were using homework to pull out a passing grade. There is a sense that they really spend time on the issue. I never felt that way in K-8. It now seems like many more parents and kids are paying attention.

are we having fun yet?

Two memories of this math controversy in SCASD never fail to make me chuckle when I think back on them.  The first was a comment posted on the CDT site after the Ed Mahon wrote his first article on the subject, entitled “The Great Math Debate”.  The commenter wrote, “If you say ‘math debate’ over and over again, it sounds kind of funny.”

The second one happened at a math information session for parents last spring.  The district curriculum staff were telling the parents how much fun Investigations was for their children, and a parent raised his hand and said, “You know, it’s okay if my kids don’t have so much fun if they learn some more math.  They have plenty of fun at home.”

Parents for Quality Math Education

student loans

The privately held Drake College of Business, which trains people to be medical and dental assistants, relied on taxpayers for 87 percent of its revenue in 2007. Almost 5 percent of the student body at its Newark, New Jersey, branch is homeless, says Jean Aoun, director of admissions and student services there. Late in 2008, it began offering a $350 biweekly stipend to students who show up for 80 percent of classes and maintain a “C” average.

“It’s basically known in the community: If you’re homeless, and you need some money, go to Drake,” says Carmella Hutson, a case manager at the Goodwill Rescue Mission in Newark, where about 20 clients have enrolled at Drake in the past two years. “It would put money in my pocket, help me buy a car,” adds Jerome Nickens, 45, who lived at the mission when he talked to a Drake representative but decided not to enroll.

Homeless High School Dropouts Lured by For-Profit Colleges

college tuition

my money blog

[T]uition has been been increasing annually (7.88%) at more than three times the rate of inflation (2.37%) since 1978.

 Carpe Diem


You can't attribute the fantastic increase in college tuition to special education.

Or to unions, for that matter.


This has got to be a big part of it:

The Bankruptcy Abuse Prevention and Consumer Protection Act was enacted in 2005 to include private student loans as one of the 10 debts that can't be forgiven.

Robert Siegel talks with Stephen Burd, senior research fellow in the Education Policy Program at the New America Foundation, who says federal loans had long been included in this list, but private loans were included in 2005 because lenders had been reluctant to take on the risk of student loans.

Now that lenders have no risk, Burd says, student loans have become a very lucrative business.

2005 Law Made Student Loans More Lucrative

algebra I and optics...

Solve for x, given k = x + 1/x and that k is fixed.

This is a reduced and massively rearranged derivation of the lens equation, when the separation distance between an image and object is known, and the focal length of a lens known and fixed at a single value. x = d_o / d_i. (Or due to symmetry, it could just as well be the other way round.)

Mathematica kindly pointed out (as it solved the equation for me) that you could write it this way:

k = x + x^-1

which resembles a quadratic equation, oooh. kinda. In real life you already know every k (= S/f -2) determines two solutions from experiment, but I was trying to decide how symmetric the ratios theoretically were.

Algebraic equation solvers tell me the solution has approximately the same form as quadratic roots, taking the form p +/- sqrt(q). Kinda. The general solution is x = 0.5 [ k +/- sqrt(k² -4)]

Unlike most quadratics though, there is a gaping asymptote, and the function y=k rapidly changes from -inf to +inf as x passes from -c to c, where c is a number arbitrarily close to zero. When x is large, k is approximately x; when x is small, k is approximately 1/x.

I puzzle in my head how to solve it algebraically on paper -- this college student who has (up to this point) taken Calc III, linear algebra, and the mess of multiple equilibrium scenarios that tricky chemistry professors throw at you. How do you algebraically solve "inverse-order" polynomials? I mean, this equation should be simple to solve, right?

schoolbook simplification

a. Between 1860 and 1991, American publishers produced readers for the same grade at widely divergent LEX levels (e.g., in 1968, first grade readers were available between -68 and -31).

b. The most difficult readers were generally published before 1918. By modern standards, Professor McGuffy’s pre- and post- Civil War readers were very difficult.

c. After World War I, mean reader LEX levels for all grades were generally simplified.

d. After World War II, mean levels of readers for all grades but third became even simpler. These were the books used by the Baby Boomers and successive cohorts.

e. School publishers in Great Britain did not simplify heir first grade readers after World War II, implying that there was no compelling educational reason for American publishers to further simplify their readers.

f. Today’s mean sixth, seventh, and eighth grade readers are simpler than fifth grade readers were before World War II.

g. Sentences were also shortened, from about 20 words before World War II to about 14 words now in Grades 4—8.

h. Texts for grade x + 1 are typically more difficult (lexically) than those for grade x. When the early readers in a series are simplified by a publisher, so too (generally) are the readers for later grades.

American readers were rewritten after World War II for many reasons: to modernize their content and graphics; to incorporate principles from research in education, psychology and linguistics; to emphasize new kinds of social relations; and to respond to television, which was fast becoming an unprecedented rival for students’ attention. Those considerations required that readers be changed but not that they be simplified. Chall (1967) described the justifications given at the time for simplifying schoolbooks; they were to increase their accessibility for students and raise the level of reading success.

The extent of this simplification is notable. Apart from one extraordinarily simple text (LEX = -75), most first graders in the Baby Boom era used readers whose LEX levels were between -53 and -65; that is, on average, first grade readers were 12 LEX units less difficult than the readers used by their parents and grandparents between World Wars I and II and 15 LEX less difficult than the texts used by students in the same grade in Britian — where the students were a year younger in age. Since the empirical range for LEX is about 140 units, a 12 LEX simplification represents 9% of the empirical range. Workbooks are also designed by the same publisher as the readers and are used in conjunction with them. Given the workbooks’ format, we cannot measure their LEX levels. It is unlikely the publishers would make the workbooks harder than their own reader for the same grade level.

In simplifying the readers’ patterns of word choice, the publishers also shortened sentence length (Figure 5). From the fourth grade on, the average sentence length was contracted by about 6 words — this is the equivalent of dropping one to two clauses from every sentence. This reduced the students’ experience in working out the meanings of more complex sentences.

Widespread objections from teachers and parents, and media publicity over the simplified, often dull, Dick, Jane, and Spot-like readers, caused most publishers to acknowledge that they had oversimplified their first and second grade readers. In the 1963 —1991 era, the mean LEX levels for those grades was restored to pre-Worid War II levels — and without ill effects. While they made those early texts harder, the publishers made the fourth, fifth, sixth, seventh, and eighth grade readers even easier — to the point where these are now at their lowest level in American history.

Schoolbook Simplification and Its Relation to the Decline in SAT-Verbal Scores
Donald P. Hayes, Loreen T. Wolfer, Michael F. Wolfe
American Educational Research Journal
Summer 1996, Vol. 33, No. 2, pp. 489-508

schoolbook simplification & the 50-point drop in SAT scores

I'm sure I've posted this before, but it bears repeating:

The 50+ point decline in mean SAT-verbal scores between 1963 and 1979 is widely attributed to changes in the composition of the test-takers. Several inconsistencies in that explanation are identified. That explanation also ignores the pervasive decline In the difficulty of schoolbooks found by analyzing the texts of 800 elementary middle, and high school books published between 1919-1991. When this text simplification series is linked to the SAT verbal series, there is a general fit for the three major periods: before, during, and after the decline. Long-term exposure to simpler texts may induce a cumulating deficit in the breadth and depth of domain-specific knowledge, lowering reading comprehension and verbal achievement. The two time series are so sufficiently linked that the cumulating knowledge deficit hypothesis may be a major explanation for the changes in verbal achievement. Only an experiment can establish whether this is causal, so we describe a simple, low-cost experiment schools can use to test how schoolbook difficulty affects their students’ verbal achievement levels.

Schoolbook Simplification and Its Relation to the Decline in SAT-Verbal Scores
Donald P. Hayes, Loreen T. Wolfer, Michael F. Wolfe
American Educational Research Journal
Summer 1996, Vol. 33, No. 2, pp. 489-508

cumulating knowledge deficit...

junket

The perennial issue of foreign language instruction in the early grades is alive once again in my district. I say "perennial" because, where foreign language instruction in the elementary grades is concerned, administrators are perennially against it while parents and interested bystanders are perennially for it.

The question of Mandarin keeps cropping up, too.

Looking for articles on edu-junkets to China, I found this:

Top San Francisco schools officials, who will consider expanding Mandarin language programs later this summer, quietly accepted a free trip to China recently to visit schools and meet with government officials who hope to persuade U.S. educators to expand Chinese curriculum.

Interim Superintendent Gwen Chan, five school board members and four principals made the unannounced trip from June 28 to July 4, spending time in Beijing and visiting schools across several provinces.

A staff member from the district's "multilingual programs department" also joined the entourage, which included about 400 schools officials from across the United States.

"This trip is not costing the school district any money," said Chan, whose first job in the district nearly 40 years ago was teaching Mandarin. "It is a goodwill and educational journey to promote Chinese immersion programs."

The Chinese government picked up the tab as part of its efforts to persuade U.S. schools to teach Mandarin, the official language of China.

[snip]

The San Francisco contingent -- including board members Mar, Jill Wynns, Dan Kelly, Norman Yee and Eddie Chin -- said they found the trip inspirational.

"I feel it helps us understand a significant portion of our student body,'' said Mar.

Wynns said there was great value in seeing another society, "especially one from which so many of our students have come.''

The trip included excursions to the Great Wall of China and Tiananmen Square in addition to a speech by the Chinese minister of education in the Great Hall of the People.

Even though five elected school board members traveled together without a public announcement, Wynns said the trip did not violate California's open-meeting law known as the Ralph M. Brown Act because no official business was discussed.

Kelly put an even finer polish on the point:

"You could say it was a junket," he said. "Totally a junket. We did no real work at all."

China trip for top schools officials
- Jill Tucker, Nanette Asimov, Chronicle Staff Writers
Thursday, July 13, 2006

A: The point of junkets is to get junketeers to spend money. There is no free junket.

B: Open Meetings law applies to any gathering of a majority of the board. A special exception for junkets does not exist.

Good thing the Fed Govt is paying for more teachers

on the Ku-Klux Plan

at zero out of five

the best things in life are free

protractors for some, miniature American flags for others

Audacious Idea #2: Placement by mastery, not age

My apologies to Gas Station Without Pumps -- I forgot a direct link to the post Placement by Achievement, which is http://gasstationwithoutpumps.wordpress.com/2010/07/21/placement-by-achievement//

Somehow I got from Megan Golding's audacious idea (see here) to the blog Gas Station Without Pumps's discussion of eliminating age-based grade level instruction in math, and instituting placement by achievement.

This approach to placing kids has long been popular with parents of gifted children (though for some reason not with school teachers and administrators). It has gone by many names (subject acceleration, readiness grouping, grouping by ability or skill or mastery, … ). I prefer the name placement by achievement, since we are not accelerating students but letting them move at whatever velocity best suits them, and we can’t measure “readiness” but only what has already been achieved. Ability is not the point, achievement is. I guess that “grouping by mastery” is ok, but “mastery” seems to me a more cumbersome word than “achievement” and “mastering” a subject seems to me appropriate for post-baccalaureate studies.

Personally I prefer "placement by mastery", but reasonable people may differ.

In another post, GSWP discusses the recent article by Bill Evers and Ze'ev Wurman, advancing the idea that the California state math standards are superior to the proposed Common Core standards. (I believe California adopted the Common Core standards -- if Evers and Wurman are correct, look out, afterschooling! -- but I digress).

GSWP goes on:

My opinion is that the whole notion of age-based grade levels is wrong and twiddling with the standards won’t fix that. There is value to having standards that all schools and curricula must meet, but I wish that the standards were not labeled with grade levels. There are students ready for algebra long before 8th grade, and students who are barely ready for it by the end of high school. Having students progress through the standards based on mastery, rather than age, would be greatly helped by not labeling the standards with grade levels.

One specific criticism of the Common Core that Evers and Wurman raise, that there is a big jump at 8th grade because the K–7 standards are too weak to provide sufficient support for the 8th grade algebra standards, is probably a valid one and should certainly be considered by the State Board.

Discussions on the Common Core:

• Alternative to the Common Core
• Professor Milgram's Full Review of Grade Level Common Core Math Standards
  

Audacious Idea #1: Illustrate Every Math Standard

Megan Golding is a 10th grade math teacher in Georgia. She has come up with an audacious idea:

I have a simple, if huge, goal: I want to publish a podcast for every single [Georgia Performance Standard] standard and element.

Sure, I’ve seen Khan Academy. It’s great! My addition is real state standards correlation (most of what I’ve seen that’s supposedly correlated to Georgia’s math standards is of shallow, if at all, relevance).

I’ve found that in math, my students want me to repeat the same explanation several times until that light bulb comes on. The podcast allows me to put an explanation in a kid’s hands and let him rewind & replay as much as he needs. Build in a little practice, and you have a nice little remediation tool.

Go look at her first post & do leave comments there.

Wouldn't it be great if every state had a video library like that?

[Cross published at Academic Remediation]

Eight O'Clock Class

Three times a week this small assembly meets, With drooping eyelids and half-hidden yawn,
To hear, incredulous, how Shelley, Keats,
And Wordsworth rose to write before the dawn.

EIGHT O'CLOCK CLASS
Richard Armour

Source: College English, Vol. 21, No. 7 (Apr., 1960), p. 383

Big "Aha!" moment from the MSMI2010 follow-up day

Saturday 9/25 - late afternoon:

My notes from Wu discussing the teaching of division with remainder:

Actually, this was a big "Duh!" moment.

Prior posts from MSMI2010.

Homeschooling by the Numbers

Via Pat'sBlog who saw it at Maria Miller's "Homeschool Math Blog.

(Click to enlarge)

Via: DegreeSearch.org

Any thoughts on the accuracy of these figures?

gone fishing

Off to Illinois for the weekend - back Monday!

autonomy, mastery, purpose

Dan Dempsey just left a link to this fantastic YouTube on the Irvington Parents Forum ---

"it's the culture, stupid" part 2

Deborah Kenny on Harlem Village Academies

the sorting machine

$100 million to Newark public schools

I'm against it.

Seriously.

Public schools need the things money can't buy.

Modern math is a river in Egypt

It's been decades since any sort of traditional math has been taught in most K-6 schools, but we still hear the same arguments. Our schools have used Everyday Math for years, and before that, they used MathLand. When schools and the state look at the testing numbers and whether they go up or down, it has nothing to do with any sort of traditional approach to teaching math.

Kids get to middle school and high school and still can't show mastery of very basic skills. Even those who favor discovery methods claim that mastery is needed. It still doesn't happen even though mastery of basic skills is much easier to check and correct than vague critical thinking skills.

My conclusion is that it's a huge case of denial.

It's Anti-Math. It's anti-hard work because hard work and expectations separate kids. They claim that kids will learn when they are ready, but that just keeps them from the hard work of figuring out whether there are other causes. It allows them to avoid working on things they don't like. That's why we parents get messages telling us to work on math facts with our kids.

In 5th grade, my son's Everyday Math teacher realized that many kids were struggling with simple things like adding 7+8. She knew these kids were "ready". She tried to fix the problems, but then didn't get to 35% of the material in the course. She believed in mastery, but the other teachers were happy enough to "trust the spiral".

Everyday Math facilitates this denial. They want math to be a pump and not a filter, but what they are doing is pumping along the failure until its too late and then dumping that guilt trip on the kids.

LexAequitas on SAT Critical Reading

LexAequitas:

“As an instructor for TPR for several years, I had a breakthrough on the reading passages at one point after I made a realization. I was good at verbal sections before, generally able to complete them in just over 20 minutes with a 750+ score, but after the instructor training I could complete them in 11 minutes with a perfect score.

The SAT is rigorously vetted, and constantly challenged. For every answer, there needs to be a detailed explanation that ETS can just mail off to every student who challenges the question. They come up with these before the test is ever given. This means there *has* to be something that can be pointed to in order to differentiate answers. On difficult questions, it will be minor, even picayune. And I don't mean picayune in the normal sense, I mean picayune in the sense that you'd better start thinking like a 13-year old with Asperger's syndrome. Don't accept generalizations that people use in speech and writing all the time just to make communication more efficient.

It's also worthwhile to note that the SAT does not typically select great literature. The writing is often clumsy and arcane, and this is part of the challenge. I suspect a better exercise if you want casual reading that mimics the SAT is to pick foreign translations.”

This is fantastically helpful.

satreading
And fascinating on many levels....

David Kaplan on Sal Khan

In an undistinguished ranch house off the main freeway of Silicon Valley, in a converted walk-in closet filled with a few hundred dollars' worth of video equipment and bookshelves and his toddler's red Elmo underfoot, is the epicenter of the educational earthquake that has captivated Gates and others. It is here that Salman Khan produces online lessons on math, science, and a range of other subjects that have made him a web sensation.

Khan Academy, with Khan as the only teacher, appears on YouTube and elsewhere and is by any measure the most popular educational site on the web. Khan's playlist of 1,630 tutorials (at last count) are now seen an average of 70,000 times a day -- nearly double the student body at Harvard and Stanford combined. Since he began his tutorials in late 2006, Khan Academy has received 18 million page views worldwide, including from the Gates progeny. Most page views come from the U.S., followed by Canada, England, Australia, and India. In any given month, Khan says, he's reached about 200,000 students. "There's no reason it shouldn't be 20 million."

Sal Khan: Bill Gates' favorite teacher by David Kaplan

David Kaplan is one of the best writers on the Irvington Parents Forum. Probably the best, as a matter of fact, and that's saying something, because there are a lot of good writers on the Forum.

why is SAT reading so hard?

I've just recently focused on SAT reading ---

It's hard.

Until two weeks ago, I took SAT reading for granted. I had high verbal scores in high school, and when I took a sample SAT test a couple of years ago, I missed two questions on the reading, only one of which was a real miss in the sense that my answer was clearly wrong. On the other miss, I disagreed with the CollegeBoard's answer.

So I hadn't thought about the verbal section until I started working with C. and a couple of other juniors on SAT prep.

Now I find that working through the verbal section is a wretched, miserable experience, and this is true in spite of the fact that I get the answers right.

Here's Hack the SAT:

You know how some people have a gift?

[snip]

No one has a gift for Critical Reading.

Sure, plenty of people have a gift for reading.... [but] no one is particularly natural at critical reading, this seemingly endless stuff that jams the SAT full of tiny blue print and passages about the subtle revelations of medieval scientist nuns.

[snip]

[E]ven those students who get high scores on Critical Reading find it more draining than the Math or Grammar sections. 

True!

Working through a Critical Reading passage - especially a 'compare two passages' section (those are death) - I feel the brain equivalent of eye strain.

Why is that?

a man after my own heart

Glen wrote:

I have my fourth grader do a hundred fraction problems while I do his "cut pictures out of magazines" homework for him. I have him work through middle school math contest problems, tossing him hints when he gets stuck, while I draw on his poster board. I had him learn every country in Europe while I built miniature teepees in a shoebox diorama.

He gets good grades on his schoolwork, but other parents--I mean kids, of course--often cut and paste better than I do.

His teacher thinks he's a "natural" at math, but there's nothing natural about it. It's man-made. It's training--the same sort of training you'd do if you needed to teach someone to cut hair or build birdhouses: show them how, help them a few times, and put them to work.

She would be shocked if she actually knew the level of difficulty of the math and science work he can do, but we're careful not to let her find out. Last year the teacher found out and was nasty to him for the rest of the year. She liked him when she thought he was a natural, but when she found out that he had to work at math, she was outraged.

"It's not fair to me that you are willing to do that much work for your father, but aren't doing the same for me!" I thought that I--I mean my son, of course--was cutting enough pictures out of enough magazines for her, but she apparently thought she deserved more.

She wanted to discuss the "problem" with me. She was concerned about how I was using his time. (How ironic.) She said that their Everyday Mathematics emphasized "conceptual understanding" and was concerned that my approach might not lead to "actual understanding." The previous night he had solved,

"We have four times as many cows as horses on our ranch. If we sold 280 cows, we'd end up with twice as many horses as cows. How many cows do we have?"

He was in third grade. I almost asked her to go to the board and show me how SHE would have taught him to solve it, with "actual understanding," but that would have been cruel. I held my tongue to keep my son out of trouble and said that I tried my best to help him understand. We left it at that.

This is one of the top 5% of elementary schools in Silicon Valley, so almost all the kids are performing at grade level--and that's where they want to keep them.

And I've now found out that at higher levels, middle school and high school, it's almost standard practice for parents to take the mindless homework load off their kids' shoulders to free up time for them to do the portion of homework that is actually useful.

If I have to do even more mindless homework, I may have to outsource it to India.

Using sentence combining to improve reading scores

from Arthur Whimbey and Myra Linden:

Let us now examine the problem mentioned at the beginning of this chapter: the difficulty that some students have comprehending textbooks containing sentences with relative clauses. Here is a paragraph from the Encyclopedia Americana.

Infectious diseases are the only ones that can be transmitted. They may be spread by infected animals, infected people, or contaminated substances, such as food and water. Infectious diseases that can be transmitted to humans from infected animals are known as zoonoses. Zoonoses may be transmitted by carriers, such as insects; by the bite of an infected animal; by direct contact with an infected animals [sic] or its excretions; or by eating animal products.

College freshman were asked to read this paragraph and then answer the following questions.

Zoonoses are:

a. insects that carry diseases.

b. infected animals that transmit infectious diseases to humans.

c. infectious diseases that man gets from animals.

d. carriers that transmit infectious diseases.

College students with weak reading skills often pick alternative b. When asked why they picked b, some reply that zoonoses sounds like zoo and animals are kept in zoos, so they figured zoonoses are animals. This explanation reflects the thinking style of nonanalytical readers. They base their conclusions on superficial associations among bits of information rather than on careful step-by-step interpretations of chunks of information and gradual reconstruction of total meaning.

Other students who chose b explained that they got this answer from the last six words of the third sentence: infected animals are known as zoonoses. This, too, reflects the thinking style of weak readers. They read a little bit here, a little bit there, and then jump to a conclusion.

The correct answer is based on the third sentence, which reads:

Infectious diseases that can be transmitted to humans from infected animals are known as zoonoses.

This sentence contains the following relative clause:

that can be transmitted to humans from infected animals

Good readers work step-by-step through the sentence in obtaining its correct meaning. They begin with the subject: infectious diseases. Then they go on to the relative clause, an essential relative clause that indicates the type of infectious diseases being considered; those that animals can transmit to humans. Finally, they come to the predicate: are known as zoonoses. Therefore, in answering the question they pick alternative c.

Research studies have found that students with weak analytical skills can understand only simple sentences, just as they can solve only one-step math problems. They have difficulty understanding complicated sentences, just as they have difficulty solving multi-step math problems. In other words, they can handle just small chucks of information because they have not developed skill in working step-by-step through complicated information. They can understand sentences such as this:

Some infectious diseases are known as zoonoses.

But they cannot understand Sentence 3 in the paragraph.

Other research studies (reviewed in Why Johnny can't Write: How to Improve Writing Skills) have found that having students construct complex sentences from simple ones improves their scores on standardized reading tests. these studies have not explored whether having students add relative clauses to sentences improves their ability to comprehend specifically sentences with relative clauses. They have only found that constructing various types of complicated sentences from simpler ones (using the types of exercises shown in this book) improves overall reading comprehension ability, with the weakest readers making the greatest gains. As the P-C Approach^* is used more widely in our schools,^** we can expect the average reading comprehension ability of the nation to improve. And as this improvement becomes evident, researchers may conduct additional studies to determine exactly how and why having students manipulate, construct, and write sentences improves their reading skills.

Teaching and Learning Grammar: The Prototype-Construction Approach
pp. 90-92

^*prototype-construction method
^** I'm not holding my breath

help desk - sentence diagram

In the passage below, Terkoz the ape has kidnapped Jane; Tarzan is tracking Terkoz through the treetops.

At boughs’ ends, where the anthropoid swings from one tree to another, there is most to mark the trail, but least to point the direction of the quarry, for there the pressure is downward always, toward the small end of the branch, whether the ape be leaving or entering a tree. Nearer the center of the tree, where the signs of passages are fainter, the direction is plainly marked.

Tarzan of the Apes
Edgar Rice Burroughs
The Compact Bedford Introduction to Literature

p. 74

This was a fantastically difficult sentence for my college composition students to read; it was difficult for me to read, too.

Can someone diagram the first sentence?

You hear constantly that sentence diagramming doesn't help with writing, but I'm wondering whether it would help with reading. I'm tutoring a high school junior on the SAT, and the sentences are fantastically complex. The reading passage we worked on this weekend actually contained two sentence fragments in a row, both of which modified the complete sentence before them.

LD enrollment drops

After decades of what seemed to be an inexorable upward path, the number of students classified as learning-disabled declined from year to year over much of the past decade—a change in direction that is spurring debates among experts about the reasons why.

The percentage of 3- to 21-year-old students nationwide classified as having a “specific learning disability” dropped steadily from 6.1 percent in the 2000-01 school year to 5.2 percent in 2007-08, according to the most recent data available, which come from the U.S Department of Education’s 2009 Digest of Education Statistics. In numbers, that’s a drop from about 2.9 million to 2.6 million students.

A learning disability—a processing disorder that impairs learning but not a student’s overall cognitive ability—is the largest, by far, of the 13 disability classifications recognized by the main federal special education law. Forty percent of the approximately 6.6 million students covered under the Individuals with Disabilities Education Act, or IDEA, fall into that category.

The decrease in the category goes hand in hand with a decrease in special education enrollment overall, though that change is not as large. The percentage of all students covered under the IDEA fell from a high of 13.8 percent in the 2004-05 school year to 13.4 percent in 2007-08—from about 6.7 million students to about 6.6 million students. Enrollment in the categories of emotional disturbance and mental retardation also went down, but students in those groups make up a far smaller slice of the IDEA pie. At the same time, though, enrollment of students classified as having an autism spectrum disorder or “other health impairment” rose.

[snip]

About 80 percent of children who are classified as learning-disabled get the label because they’re struggling to read. So, scholars say, the dropping numbers could be linked to improvements in reading instruction overall; the adoption of “response to intervention,” which is an instructional model intended to halt the emergence of reading problems; and a federally backed push toward early intervention with younger students before they’re labeled.

Learning-Disabled Enrollment Dips After Long Climb Up
by Christina A. Samuels
Education Week

words, diagrams, & math

Nick Rowe

12-week column on drawing

in the New York Times

Before I got sidetracked teaching myself math, I was learning to draw --- Loved it.

Also, I used to knit. I used to knit a lot. A friend of mine told me that knitting and math yield the same pleasures, and she turned out to be right. So I haven't knitted anything in 5 years, either.

I need a couple more lives besides just the one I've got.

safety first

Coincidentally, we were discussing the "security" system here in my district at the very moment Ed and I were trekking back and forth to the U.S. Open.

At the Open, the threat level appears to be permanently set on orange and security is always high. Security is so high that, when I presented my bag for inspection, the gal behind the table said, "Is that a Kindle? You can't bring that in."

What?

As Ed said, if you can take a Kindle on an airplane, which you can, you should be able to take a Kindle to the Open.

But no. I was supposed to hike two blocks -- uphill and in the sun -- back the way I came in 'til I got to a tent where I could pay another employee five bucks to check my Kindle.

Or, alternatively, I could walk a couple hundred yards back to the ladies' room, secrete my Kindle on my person, present my bag for inspection a second time, and enter the grounds without further ado. Which is what I did.

I told Ed, "Any security system that relies on terrorists to pay some guy five bucks to check his explosive device isn't a security system."

More anon.

lost in translation

caption: Fight fire with fire!
engrish.comhttp://www.engrish.com/
via: km-wordsmith

20 most common errors

from:
The St. Martin's Handbook

via:
Texas Tech University Writing Center

the 20 errors

Another rude awakening

Last year, my first-born was in enrolled in our local public school in second grade, and although he spent 6 or 7 hours there each day, he came home with tons of homework and a good deal more learning remaining. I started to think, “Why am I sending my kids to school, when the school sends them back to me to educate?” A friend later complained to me that when they gave her son a book report, it meant at least 5 hours of her own time working on it with him. Another parent told me how great the tutoring was at the chain store down the street from her. All this got me to thinking: if I’m ultimately in charge of my kids’ education, why do I feel so powerless? . . .

I assumed that the government knows best what, and how, to teach my kids. It’s an assumption I was raised with, one I never challenged, until now. Well, you know what they say about you when you assume…

“It’s always worse than you think?” Well, that’s what we often say around here.

Another parent gobsmacked by our public schools

Back to School: Part One

Testing in Basic Math in Community College

I finally got a copy of Teach Like a Champion. Since I teach at a community college, not everything applies. But I do teach a basic math class. And the book has inspired me to start taking data on my tests. This led me to analyze my tests to see what and how much I test on each topic.

At the end of the summer semester, I used the department written final to see if I could determine how much mastery my students had on each topic that I taught. Unfortunately, I don't have data from the beginning of the semester. But what I found wasn't very good: I measured the mastery on 15 topics by calculating a percent correct for each topic. For example, there were 5 problems on whole number operations and 11 students. This gives a total of 55 problems. Only 76% were answered correctly. If I had to take a guess, I would say that the class probably had over 70% mastery on whole number operations before they came into class. My highest % mastery was decimal operations, fraction operations and dimensional analysis with 93%, 85% and 93% mastery respectively. My lowest topics were divisibility tests and lowest common multiple and prime factorization. I then analyzed each incorrect answer to see what the most common errors were. 66% of the errors were concept errors: either the student didn't answer the question or did not use the correct mathematical technique. 19% of the errors were process error. In this category are errors like the following: a student knows that when multiplying mixed numbers, he must turn the mixed number into an improper fraction, but he does this incorrectly. 7% of the errors were mathematical. Another 8 % were divided evenly between not reducing fractions and sign errors.

So I'm teaching basic math again this semester, and I am trying to determine what I should be doing to ensure mastery. I am going to try curriculum based measurement. This is a technique I read about that is used in some elementary schools. You give students very short exams on a particular topic. Instead of counting the number of problems that are correct, you count the number of correct digits. For example, if a student has to add 99 and 49, there is a possibility of 3 correct digits, not one correct problem. You then do some number crunching and adjust your teaching accordingly. (I realize I'm gliding over this.)

It doesn't seem like any of the other instructors at my community college are collecting and analyzing data like this. If anyone has any links or resources on this topic, I would love to hear about it.

Another article (or two): Is it bad to test students frequently?

Two recent New York Times articles fly in the face of conventional pop psychology and education theory.

An article in last week's Science Section on study habits cites cognitive science research indicating that the act of taking a test can enhance learning:

The process of retrieving an idea is not like pulling a book from a shelf; it seems to fundamentally alter the way the information is subsequently stored, making it far more accessible in the future.

As Henry L. Roediger III, a psychologist at Washington University in St. Louis puts it, “Testing not only measures knowledge but changes it.”

Next we have a front page article in this weekend's Week in Review on Testing, the Chinese Way, written by Elisabeth Rosenthal, whose children spent a year at the International School of Beijing where "taking tests was as much a part of the rhythm of their school day as recess or listening to stories." Citing personal experience, Rosenthal argues that:

>Young children aren't necessarily aware that they are being "tested."

>Frequent tests give children important feedback about how they are doing.

>Frequent tests offer a more meaningful way to improve self-esteem than frequent praise does.

On this past point, Rosenthal cites Gregory J. Cizek, a professor of educational measurement and evaluation at the University of North Carolina at Chapel Hill:

Professor Cizek, who started his career as a second-grade teacher, said the prevailing philosophy of offering young children unconditional praise and support was probably not the best prescription for successful education. “What’s best for kids is frequent testing, where even if they do badly, they can get help and improve and have the satisfaction of doing better."

Cizek's overall take on testing in schools? “Research has long shown that more frequent testing is beneficial to kids, but educators have resisted this finding:”

Rosenthal concludes on a particularly powerful note:

When testing is commonplace and the teachers are supportive — as my children’s were, for the most part — the tests felt like so many puzzles; not so much a judgment on your being, but an interesting challenge. It is a testament to the International School of Beijing — or to the malleability of childhood memory — that Andrew now says he did not realize that he was being tested. Will tests be like that in a national program, like Race to the Top?

When we moved back to New York City, my children, then 9 and 11, started at a progressive school with no real tests, no grades, not even auditions for the annual school musical. They didn’t last long. It turned out they had come to like the feedback of testing.

“How do I know if I get what’s going on in math class?” my daughter asked with obvious discomfort after a month. Primed with Beijing test-taking experience, they each soon tested into New York City’s academic public schools — where they have had tests aplenty and (probably not surprisingly) a high proportion of Asian classmates.