A model school's selling points: everything but the math

(Cross-posted at Out In Left Field)

A year of activities: Spelling Bee | Talent Shoe | Musical | Science Fair | Fall Festival | 100 Days | Opera Company | Reading Buddies | Spring Concert | Valentine's Dance

So goes the text along the margin of the glossy school newsletter that came home yesterday on the last day of school--along with color photographs of smiling students and staff, and articles about the school and the community.

You'd never know that one of the school's activities was the Continental Math League club, run by yours truly and another parent volunteer, and attended 1 1/2 hours a week from October to March by 20 eager 2nd and 3rd graders.

Especially since, despite the principal's earlier assurances, the information sheet about next year's Continental Math League club (and ways to practice for it over the summer) somehow didn't accompany the above newsletter into students' backpacks.

Concerned that this might happen, I had sent said principal an email reminder the day before the last day. Then, when I bumped into her on the morning of the last day, I'd asked her about the email.

"I deleted it," she said, a big grin on her face.

I guess she's happy it's summer vacation.

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For those who are interested in ways to polish up their math skills for Continental Math League, or for any other reason, here's what I spent several hours compiling for students at our school. Perhaps other schools and other principals will find this more worthwhile than ours did:

MATHPRACTICELINKS

Extracurricular gifted programs threatened as well!

I've just learned that the principal has faulted our Continental Math League for "widening the achievement gap."

It's been suggested that, instead of running a math club for gifted students, I instead run one for struggling students.

Maybe I'm being unreasonable, but I tend to think that it's the school's job, not mine, to educate struggling students.

A first step for the school would be to follow in the footsteps of the following school districts and drop the Investigations math curriculum: Framingham (Massachusetts), Inner Grove, Little Falls, Staples-Motley, Stillwater, & Waconia (Minnesota), Columbia (Missouri), Fairport, Greece, Penfield, Pittsford, & Syracuse (New York), Lebanon, Painesville, Three Rivers, & Wickliffe (Ohio), Gervais, Sutherline, & Chariot (Oregon), Arlington, Bellevue, Clover Park, Eastmont, Lake Stevens, Oak Harbor, & Richland (Washington), Black River Falls, La Crosse, River Falls, & Superior (Wisconsin).

If the Powers that Be have the guts to do this, I will be so grateful that I may, indeed, be willing to sacrifice additional time in the name of math education.

The more likely resolution, I'm afraid, will be that--for all our enthusiastic support among math-starved math buffs and their parents--said Powers will not grant us permission to resume our Continental Math League next year.

Why More Mathematicians Don't Oppose Reform Math: and why we desperately need them to

(Cross-posted at Out In Left Field).

Yesterday's NPR Weekend Edition Saturday featured an interview with Stanford University professor Keith Devlin on the importance of Algebra, and while I listened to it, it suddenly occured to me why more mathematicians don't oppose Reform Math.

Here's what I posted on the NPR website:

Keith Devlin suggests that, given calculators, students should focus less on accurate arithmetic calculations, and more on algebraic reasoning. But, as Devlin's fellow mathematicians (e.g., Howe, Klein, & Milgram) have argued, mastering the basic algorithms of arithmetic is essential preparation for algebra. And while the most mathematically inclined students--including Devlin himself--may be able to master these algorithms without much hands-on, numerical practice, the vast majority do need lots of practice, and striving for correct answers is an essential part of that practice.

Today's arithmetic, unfortunately, has been seriously watered down by the new "Reform Math". More mathematicians need to examine this curriculum and speak out against it; ironically, because they can get by without much arithmetic practice, and because so many of them found arithmetic boring, too few mathematicians have considered the potentially dire consequences that the latest trends in grade school math present to the rest of the population (and to the country as a whole).

When our most prominent, accomplished mathematicians, who themselves may well have gotten by without developing accurate arithmetic skills, discount the importance of teaching such skills to the general population, they do a terrible disservice to elementary school math education (and may themselves be horrified by the results, years later, when today's grade school students enter their classrooms).

Consider what one other NPR poster has taken away from the Devlin interview. As she writes in her post:

I want to thank Dr. Devlin for a great quote that I plan to post at the front of my classroom. "Mathematicians often make mistakes in elementary arithmetic because we have our minds on higher things." That will come in very handy!

Yikes!

Mathnasium

Anyone know anything about this program?

spaced repetition

Someone posted a link to Mnemosyne, an online experiment in efficient memorization, on the Direct Instruction listserv. Sounds exciting, but unfortunately I have don't have an Intel Mac.

Here's Mnemosyne on spaced repetition:

Spaced repetition

When you have memorised something, you need to review that material, otherwise you will forget it. However, as you probably know from experience, it is much more effective to space out these revisions over the course over several days, rather than cramming all the revisions in a single session. This is what is called the spacing effect.

During the past 120 years, there has been considerable research into these aspects of human memory (by e.g. Ebbinghaus, Mace, Leitner and Wozniak). Based on the work of these people, it was shown that in order to get the best results, the intervals between revisions of the same card should gradually increase. This allows you to focus on things you still haven't mastered, while not wasting time on cards you remember very well.

It is clear that a computer program can be very valuable in assisting you in this process, by keeping track of how difficult you find an card and by doing the scheduling of the revisions. Let's see how this works in practice in the Mnemosyne program.

I still haven't gotten around to trying Wozniak's SuperMemo -- which I need to do for math and for Spanish.

This year's self-improvement projects, fyi:

• Dolciani Algebra and Trigonetry Structure and Method Book 2 ISBN: 0-395-07725-8 (I'm tracking C's class at Hogwarts)
  
• Fluenz Spanish (love it! This educational telepresence idea may have promise -- )

Last school year I worked through all but the last 10 lessons of Saxon Math Algebra 2 3rd edition. Am now relearning the same material in Dolciani & it's great.

I'm thinking that if you're going to teach yourself math, two textbooks are better than one.

Am also limping along through GrammarTrainer with Andrew. I say "limping" because I'm not remotely keeping to a schedule. The program is fantastic. I strongly recommend it.

Grade compression at colleges and universities, II

It's inevitable that, the more students catch on that B's are the new low, the more fervently they want A's.

As the dual forces of student evaluations and cynical burnout continue to exert upwards pressure on faculty grading practices, wants becomes expects becomes deserves.

Only those few who believe that grades should still mean something, and that they should somehow reward those whose work is truly distinguished, get to see the somersaults that the mediocre majority will turn to argue for A's.

From two of my B+ students (all identifing details removed):

I am writing to you with concern regarding my grade... I was just wondering what areas you felt I needed to improve on to earn an A because I completed all of my work, papers and participated in class as best as I could have. Is there anything I can do to have my grade reconsidered?

-----

I just checked my final grade online and saw that I got a B+. Can you tell me the breakdown of my grades? Most of my problem sets were V+ [no, they weren't] and I attended every class and tried to participate in lectures. The only reason why I am asking is because I felt confident that I would receive an A in the course.

What surprised me about these two students in particular was that each seemed to be putting in so little effort (as evinced, for example, by their papers--thickets of typos in what looked like stream-of-consciousness keyboarding, printed out and never actually read) that I'd assumed they were at peace with B grades. It never dawned on me that they might be expecting A's.

At least as disturbing is the most likely explanation for this expectation: presumably, all their other professors are giving them A's--along with every other student who shows up and turns things in.

All the worse for those who actually deserve top grades--particularly the left-brained crowd whose greatest strengths are typically more in academics than in extracurriculars and other varieties of resume-stuffing, not to mention career networking, schmoozing, and grade grubbing.

(Cross-posted at Out In Left Field)

Grade compression at colleges and universities

Only in the last few months, thanks in part to Catherine, have I become aware of how grade compression has permeated our grade schools.

My first experience with this phenomenon was over a dozen years ago, when I finished up my PhD and began adjuncting at local colleges.

While the consequences of grade compression in colleges and universities are probably similar to its consequences in grade schools--among other things, disfavoring the brightest students by clumping grades together into an ever smaller number of slots--the underlying forces, my experience suggests, are quite different.

On the one hand, I'd get emails from deans bemoaning the institution's rampant grade inflation and asking instructors to be sparing with A's. On the other hand, I'd get complaints from students who received anything below a B. Sometimes those students would successfully lobby the very deans who'd sent the emails, who'd then ask me to change C's to B's.

The only way to keep everyone happy--a key consideration for adjuncts, whose standing is largely a function of student evaluations, and whose renewal is at the pleasure of deans-- was to make B the new C (and D, and sometimes F), and compress all grades into a B- to A range.

So I'd reserve the A's for the two or three best students, including some I'd prefer to give A-'s to; translate the B's and B+'s to A-'s, B-'s to B+'s, and everything else to a B. It was more important, I felt, to make finer distinctions at the top than the bottom. That way, the very best might still gain some distinction--albeit not nearly as much as they once did.

After a 4-year hiatus from teaching, I've returned to find that my A-B grade scale is no longer compressed enough for many students...

But more on that in my next post.

(Cross posted at Out in Left Field).

Any summer projects to share?

If your child has been assigned a summer project--particularly one that seems excessively complex, open-ended, off-topic, and/or demanding of time and/or "creativity"--I'm currently collecting anecdotes about these. I've just posted two of my own children's summer projects at Out In Left Field; I'd love to post more. You can share them as comments here, or at OILF.

Left-Brained Epiphanies

Our blogging colleague, Out in Left Field (who posts here as Lefty) is asking a question: Are all epiphanies right-brained? In other words, the common story is "introverted, scholarly type learns to embrace extroversion, play, and lack of structure."

Lefty is looking for stories of left-brain epiphanies:

How often, for example, does an outgoing musician learn that what makes him truly happy is retreating to his study to analyze business cycles and market equilibria?

Go and contribute your stories.

Some prompts:

Left-brain: logical, systematic, analytical, one-at-a-time, abstract, verbal, introverted.

Right-brain: emotional, incidental, intuitive, holistic, relational, nonverbal, social.

Reminder: don't post your stories here, go over to Out in Left Field

Problems with "real world" math problems

I've been complaining for years that all the hands-on, "real world" math activities that dominate Reform programs shortchange kids on the autistic spectrum. They confuse the many who have language delays and gaps in worldly knowledge, and are too full of distractions for those who require streamlined, structured learning environments.

Now a new study by Jennifer A. Kaminski, a research scientist at the Center for Cognitive Science at Ohio State, reported in today's NYTimes, suggests that this kind of hands-on math is bad for everyone.

Quoting the Times: "The problem with the real-world examples, Dr. Kaminski said, was that they obscured the underlying math, and students were not able to transfer their knowledge to new problems."

As the Times also remarks: "Dr. Kaminski and her colleagues Vladimir M. Sloutsky and Andrew F. Heckler did something relatively rare in education research: they performed a randomized, controlled experiment."

Mental Math link

I spent the morning with my new friend Angela McIver, who evaluates the math skills of middle-schoolers and older children. I saw some fascinating videos of children struggling through basic math problems in ways that suggested huge gaps in their elementary school instruction.

Angela is a big proponent of mental math, which Reform Math programs not only marginalize, but, in insisting on explained answers, actually mark children off for. Among other things, mental math forces you towards maximally efficient strategies, with all the mathematical insights this entails.

She recently searched the Internet for mental math activities, and just sent me a good link.

memorize this!

At Out in Left Field.

kindred spirit

Fantastic new blog!

Out in left field

In a post on the subject of grade deflation and extended response math tests, he writes:

The Pennsylvania Math Standards on which the Philadelphia public schools base their grades, in fact, include numerous non-mathematical factors: explaining in words, drawing pictures, manipulating objects. Perhaps my daughter's explanations and drawings aren't as elaborate as some of her peers'. Perhaps she doesn't complete hands-on tasks as quickly as others do. And perhaps her shyness and passivity keep her from making oral contributions that "demonstrate superior understanding of concepts, skills and strategies" and from "independently explor[ing] ideas and topics:" two of her report card's benchmarks for grades of 4.

It's of course way too early to say just how strong my daughter's mathematical talents are. But I can't help wondering how many math buffs are being lost in the new system, and what this means for both their future, and that of this country.

This worries me, too.

I went back and found this post Barry G made to the old ktm:

Here's a problem that appears in IMP for 9th grade It is known as the "Haybaler Problem"

“You have five bales of hay. For some reason, instead of being weighed individually, they were weighed in all possible combinations of two: bales 1 and 2, bales 1 and 3, bales 1 and 4, bales 1 and 5, bales 2 and 3, bales 2 and 4 and so on. The weights of each of these combinations were written down and arranged in numerical order, without keeping track of which weight matched which pair of bales. The weights in kilograms were 80, 82, 83, 84, 85, 86, 87, 88, 90 and 91. Find out how much each bale weighs. In particular, you should determine if there is more than one possible set of weights, and explain how you know.”

David Klein, a mathematics professor at California State University at Northridge comments on the problem. “The process of solving this problem made me resentful of the stupidity and pointlessness of it. There is nothing ‘real world’ about it. It is completely inappropriate for kids who likely have not been taught how to solve simultaneous linear equations, or exposed at most to two equations in two unknowns. If I had been given such problems at that age, I think that I would have hated math.”

Consistent with much of the philosophy of “real life math”, the goal of the exercise is to explore strategies and to be able to write about it. This is made apparent by the “student guide” that accompanies the problem. It is essentially a scoring sheet, containing categories, with points awarded for each, such as “Restate the problem in your own words” (4 points); describe all the methods you tried before reaching your solution(s) (4 points); describe the process that lead to your solution(s) (4 points); describe all assistance provided and how it helped you (2 points); state the solution (2 points); describe why your solution(s) is correct, include all supporting data (6 points). Out of a total of 50 points, only 2 are given for the solution. In fact more points are given for describing why the solution is correct.

Be sure to read his post explaining Why teach fractions?