Lockhart's Lament or You Should Read This Now!

I've read this before but apparently I didn't blog it. Can't imagine why--it's fabulous! Makes me want to go back and re-teach high school math to Wolfie. A living books approach probably would have kept him interested in math, which he isn't anymore. :(

Anyway, here is a bit of "A Mathematician's Lament"by Paul Lockhart, an elegant proof that we may be teaching our children about mathematics but we're certainly not teaching them mathematics.

"By concentrating on what, and leaving out why, mathematics is reduced to an empty shell. The art is not in the “truth” but in the explanation, the argument. It is the argument itself which gives the truth its context, and determines what is really being said and meant. Mathematics is the art of explanation. If you deny students the opportunity to engage in this activity— to pose their own problems, make their own conjectures and discoveries, to be wrong, to be creatively frustrated, to have an inspiration, and to cobble together their own explanations and proofs— you deny them mathematics itself. So no, I’m not complaining about the presence of facts and formulas in our mathematics classes, I’m complaining about the lack of mathematics in our mathematics classes. "

It's a great argument against schooling in general, since while he claims no other subject has been so sucked dry of life and reason for living, the same could be said about history, economics, and most science courses. I've even seen it done in English classes. Pretty much any class that uses a textbook is about as interesting as the pile of wood pulp used to make said textbook. Oh yeah, I went there!

I Learned How to Pronounce Words in Jamaica, Mon!

I found this kids website from the BBC the other day. It has educational games for English and Maths (which is British for math) for early elementary students. I tried several of the games and found them quite fun. The most fun part for me was called Space Spins. When you pull a virtual lever, a sentence appears on the screen and is read aloud to you, in a very strong West Indies accent! Wha? The idea is to learn to read, I believe, but the story reader is the only voice on the program that speaks anything other than Received Pronunciation. So why is the vocabulary program speaking like Miss Cleo? Who knows, but it's hilarious!

Attn: College-Bound High Schoolers!

According to EdWeek.org, "a study released today highlights the gap between what high schools are teaching in the college-preparatory courses and what colleges want incoming students to know." The survey, by ACT, Inc. (the testing people) "found that college professors generally want incoming students to have a deeper understanding of a selected number of topics and skills, while high school teachers in all content areas tend to rate a far broader array of content and skills as 'important' or 'very important.'"

Specifically, "In writing, postsecondary instructors tended to value the basic mechanics of writing (such as sentence structure and punctuation) more highly than high school teachers did. High school English teachers rated topic and idea development as the most important set of skills.

In mathematics, postsecondary instructors rated being able to understand and rigorously apply fundamental skills and processes as more important than exposure to more advanced math topics. High school math teachers tended to view the latter as important. Postsecondary instructors also placed far more emphasis on being able to understand new material by reading a textbook.

In reading, the survey found a general lack of reading courses in high school and a decline in the teaching of targeted reading strategies after the 9th grade. In contrast, college instructors of remedial courses rated such strategies as very important and reported devoting a large percentage of time to teaching them.

In science, high school teachers consistently rated content as more important to student success than science process or inquiry skills, in direct contrast to both middle school and postsecondary science teachers."

What does this mean for homeschoolers? I believe it gives us an edge over public school students in that we can more easily tailor our kids' education to what the colleges want, without having to overcome institutional bias.

Curriculum notes to myself:

Make sure the boys can write a grammatical sentence, create an outline with a strong thesis and write a persuasive essay following that outline, preferably in less than an hour. (Yes, I know that is a run-on sentence. ;-)

Make sure they can read and understand challenging literature.

Focus on fundamental math skills, no matter how much Wolfie complains. (Learning on their own from a textbook is pretty much standard procedure, isn't it?)

Continue to skip the make-work labs and "activities" in the science texts in favor of cramming more information into their little brains. Only do experiments when we genuinely don't know the results.

Cool Little Resource for Visual Teens

I just picked up a copy of The High School Learning System. It's an interesting package--multimedia presentations on English (with ebook texts), history (US and World), math (pre-algebra through calculus) and science (mostly biology) with Q&A and quizzes assess learning (if you want to do that). The presentation on the French Revolution lasted about 20 minutes of narration with period background music and pictures. They included a good amount of detail, covered the various governments between 1789 and 1799 and offered a 101 question online "quiz" (sounds like a test to me!) at the end.

I was less impressed with the math section. I noticed on their website that they have a stand-alone math learning system product, so that may be why this section is less comprehensive.

I have the 2006 version, which I bought on ebay for $13 (2 DVDs and 1 Spanish-English online dictionary). The 2007 version costs $40 and includes:

"• All core subjects covered
• 86 integrated educational titles
• 54 hours of multimedia presentations & video
• 37 hours of audio books
• 101 Barron’s Book Notes
• Printable tests to monitor progress
• PLUS new educational material for your iPodTM"

I think this would be a great resource for younger gifted kids working at a high school level, for homeschooling teens and/or as a review for regular high school classes.

Web Site Launched for Students Keen on Math, Science

BALTIMORE, Feb. 26 (AScribe Newswire) -- Imagine if a teen-age Stephen Hawking could have sparred with Einstein over physics. For gifted teens in the United States and worldwide -- perhaps including future Einsteins and Hawkings -- it's now possible, through Cogito.org ( http://www.cogito.org ).

Cogito.org, developed by the Johns Hopkins University Center for Talented Youth ( http://www.cty.jhu.edu ), offers a virtual home for the world's brightest students with strong interests and abilities in mathematics and science. The site offers free use to all visitors, who can access most of its resources and learn about everything from global warming to cold fusion.

Cogito's developers want the site to inspire its users to become the innovators, visionaries, and problem-solvers of the future. They also want Cogito.org to play a critical part in upgrading math, science, technology, and engineering education -- known as the STEM subjects -- for the estimated 1.5 million gifted middle and high school students in the United States and greater numbers worldwide.

These four areas are the subject of national efforts defined in President Bush's 2006 American Competitiveness Initiative. Improved education in STEM subjects is seen as critical to maintaining U.S. competitive advantage in science and technology.

The free, public-access section of Cogito.org is packed full of interviews with experts, profiles of young scientists, science news, Web resources and directories of summer programs, competitions and other academic opportunities.

Middle- and high-schoolers, for example, have interviewed a nanotechnologist, a scientist at the McMurdo Station in Antarctica, and a roboticist at Carnegie Mellon, to learn about research they would never hear about in science class.

The site also features a section that is open to membership by invitation. It is here that students can participate in online discussion forums with top math and science students worldwide -- where U.S. students can share math problems with their Chinese, Russian or Thai counterparts, for example. Membership is expected to expand rapidly as programs serving gifted students in programs around the world nominate their students for membership.

Early site activity is promising, with students using Cogito.org as developers had hoped. "For some of us, it's the first time we've been in contact with so many other gifted math and science kids in our lives," says Willow Smith, a senior from Palm Bay, Fla. "It's the first time we've been in a community with people who can stand up to our arguments and then return ones of their own that are just as convincing."

Expert participation in discussions is also important Cogito.org's members, according to Andrew Peters, a 14-year-old 10th grader from Rochester, Minn. "I especially liked it when an expert was brought in to discuss the issue of planet status for Pluto," he said. "The chance to hear an expert's opinion on a current event is a rare and excellent opportunity."

To that end, a key goal and need, say CTY's Cogito.org developers, is to attract and retain adult scientists and mathematicians who can serve as discussion leaders and mentors. "Along with the benefits the site holds for young people, we think this is a wonderful opportunity for scientists and others to offer their knowledge to students," said Lea Ybarra, executive director of CTY.

The name Cogito.org, which was chosen with input from gifted students, was taken from the Latin translation of Descartes' famous maxim Cogito, ergo sum or "I think; therefore, I am." The site was developed by CTY in partnership with these other leading centers serving gifted students: the Talent Identification Program at Duke University, the Center for Talent Development at Northwestern University, the Rocky Mountain Talent Search at the University of Denver, C-MITES at Carnegie Mellon University, the Belin-Blank Center at the University or Iowa, the Center for Excellence in Education, the Davidson Institute for Talent Development, and Science Service.

A $1.7 million grant from the John Templeton Foundation provided initial funding to develop and launch the site, and additional funds are being sought to sustain and expand it.

- - - -

CONTACT: Amy Lunday, JHU Media Relations, 443-287-9960, acl@jhu.edu

What's So Great About Long Division?

In my last post, I mentioned that Xavier hates long division. Here are a couple of sites questioning the need for long division in the first place, courtesy of Zany Mom: (And you thought I ignored your email, didn't you! LOL)

Senseless of School Math

"Math learned as a side effect of using it is easy. Kids learn to see the big picture and how things fit together and how numbers work.

When kids are made to do pencil and paper math, they get lost in the details. They have to figure out 11/17 of 87 before they have been casually exposed to hundreds of personally meaningful ways fractions are used around them.

I think one of the most helpful things parents can do is to solve everyday problems in their head out loud. It forces you to see things in simpler terms so that you can do it in your head. If one is faced with 103-56 and does it the way you were taught in school, you'll have to juggle and remember a lot of numbers that don't relate to the problem in your head. But if you can see the problem broken down into understandable pieces, then it's much easier and kids get to see how numbers work. (One of the big problems with pencil and paper math is that the numbers feel fixed. You can't alter the problem into something simpler.)

So for 103-56 you might ask how far 56 was from 100. Well, 4 gets you to 60 and 40 more gets you to 100 and 3 more gets you to 103. So 47." (emphasis mine)

Spoken like a true visual-spatial learner. ;-)
Not that there is anything wrong with that! I would do the same problem in my head the same way. But not all kids work this way. I never had trouble applying algorithms to math problems and I can multiply and divide fractions like a house on fire. LOL

Unschoolers and Mathematics

"People do NOT need to learn math the way it is taught in schools. In fact, they don't need to "learn math" at all. Math is INSEPERABLE from most everything else in life, and if you live a full life, you'll learn all the math you need because you need it. It's there. It's part of everything. You couldn't escape it if you tried really hard."

We're not unschoolers but I mostly agree with both of these sites. The problem comes in when the kids skip the lower difficulty stuff (with Wolfie it's dealing with polynomials) and then run into trouble with the higher level stuff they are interested in. We're having to go back and practice the polynomials and he hates it hates it hates it. The practice, not the math.

High Working Memory = Math Anxiety?

There's an interesting article in Education Week entitled "Math Anxiety" Confuses the Equation for Students I'm not sure the link will work, and Ed Week requires you register before reading the full article, so I'll pull the most interesting bits out here:

..."When he first began examining the impact of anxiety on math performance, Mr. Ashcraft [professor of cognitive psychology at UNLV] assumed that students’ unease or nervousness amounted to “an attitude,” as he recalls it, rather than a phobia with a direct link to the brain’s processes. “I was wrong,” he says now.

A number of researchers, including Mr. Ashcraft, say there is evidence that anxiety disrupts student performance in math by wreaking havoc with “working memory.” Such capacity is a type of short-term memory individuals use to retain a limited amount of information while working on a task—and block out distractions and irrelevant information. Anxiety can sap students’ working memory during tests, but in other problem-solving situations, too."...

..."In a 2001 study, published by Mr. Ashcraft and Elizabeth P. Kirk, now a postdoctoral fellow at the Georgia Institute of Technology, the researchers concluded that math-anxious students struggle on problems involving carrying, borrowing, and long division."...

Interestingly, researchers at the University of Chicago and Michigan State University have found that it's students with high working memory who have the most problem with math anxiety.

"Students with a good amount of working memory rely on “really intensive strategies” to solve math problems, such as keeping track of numbers in their heads as they move from step to step, [Sian] Beilock [assistant professor of psychology at U of Chicago] explained in an interview. That approach serves them well on relatively simple math problems, but not more complicated ones, she said.

In higher-pressure situations, such as timed tests, or where researchers put students under additional stress, those high-memory students fare more poorly. Performance pressure sucks the working-memory that has served them so well previously. By contrast, individuals with relatively little working-memory capacity do not seem to suffer as much, Ms. Beilock said."

I find this particularly interesting because this is exactly the case with Xavier. His IQ testing last year showed working memory was a real strength for him. Yet he says he hates math and definitely freezes when in high pressure situations, whether math-related or not. I have noticed in working with him that he tries to do all calculations in his head. The only exception to this is long division, which he's sure he's terrible at.

So, what to do about math anxiety?

..."Still, research has shown that students can learn to overcome anxiety, Ms. Beilock said. One strategy simply involves practice with math problems, which can make it easier to retrieve answers from memory. Another is to train students to become more accustomed to working under pressure by having them take timed practice tests, for example."...

I would add to this being able to move at his own pace through the material. The constant repetition in a scope-and-sequence math curriculum adds frustration, which adds stress. (In fourth grade, Xavier refused to do a math worksheet saying, "She should know I know this by now!") Using lined paper horizontally instead of vertically, so it's easier to line up columns of numbers, has helped tremendously, particularly with long division. After a semester of math at home, he now acknowledges that, although he still doesn't like math, he's pretty good at it. I think that's a good first step toward alleviating his math anxiety.

I Crack Myself Up

I was helping Xavier with fractions yesterday. He had to determine the least common denominator for 5/6 and 2/7.

X: 42

Me: Correct. And 5/6 is how many forty-twoths?

X: You said that wrong.

Me: I did?

X: Yeah, you said 'forty-twoths.'

Me: Oh, I'm sorry--"forty-teeth."

LOL He's so disappointed in me, but I just couldn't help myself.

No, Mr. Bond, I Expect You to Die

Klaus just showed me this web comic he's been following called XKCD. Velociraptors and Vanilla Ice are recurrent themes. Just thought I'd share. LOL

UK Spending Big Bucks for Gifted Online Classes

According to the article E-credits for more gifted pupils at BBC.com, "The government is arranging "e-credits" for schools to access extra lessons for an estimated 800,000 gifted pupils. The £65m scheme is part of its drive to ensure all children in England with special talents are given extra help."

Now you all know I think online classes for gifted kids are an excellent idea. Particularly for kids who are gifted in particular areas and working at grade level (or below) in others. I don't understand why schools are so resistant. Sending one first-grader to second grade for math and another to fifth grade for science is a logistical nightmare unless you can mandate that every grade in the school teach the same subject at the same time each day. Otherwise the child is likely to miss something relevant in his or her own classroom during the accelerated lesson time. Pulling kids from the classroom for gifted classes can give the same result. But if a child could go to the library or media center during math time, say,--whenever math is scheduled for that day--to work on Aleks.com, where is the harm in that? The child's academic needs are being met. The teacher doesn't have to deal with a bored student who is at best tuned out, at worst, disruptive. Sounds like a win-win to me.

Despite the title, the BBC's article is primarily about identifying gifted kids. The British government has suggested identifying the top 10% as GT--very generous according to US standards that usually run top 2-5%. One teacher quoted asks "what to tell a girl who said: "Miss, I really wanted to go to the giant insects workshop today, but I'm not clever enough," adding that the criteria for inclusion should be "good attendance, good behaviour, good citizenship - anything but natural ability". Sigh. I'm the parent of one of these borderline kids--sometimes he's considered gifted, at school he's not. I would suggest that if a child has high interest in a workshop on giant insects, she should be allowed to go.

But this quote smacks of a reverse elitism, particularly the bit about "anything but natural ability," and a basic lack of understanding about the purpose of gifted classes. Gifted programs are not rewards for being born with high ability. Gifted programs are (or at least, should be) appropriate education for high-ability students. Anyone with high ability in any subject(s) should be allowed/encouraged/assisted to develop those abilities. That's not elitism, that's what schools are supposed to do.

Time Flies When You're Focused on the End of the Week

Hey, it's the second week of November already! This homeschooling thing is really messing up my "me time," which is when I can sit and write a coherent blog entry, unfortunately. Pardon me while I play catch-up:

Iron Science Teacher is the name of a webcast from the Exploratorium in San Francisco, pitting science teachers head-to-head to create science experiments out of everyday objects. Click the link to read more about the show, then check out the show at WWW.Exploratorium.com.

Freshwater Fred's Free Lending Library has materials for math, science, history, etc in a searchable database. From their website:

"Freshwater Fred's Lending Library includes approximately 1,100 educational videos, software programs and curriculum - and the collection is always growing. Explore topics such as biology, zoology, anatomy, physics, math, history, geography, the arts and environmental science. Some materials come with study guides.

There is no charge for Lending Library materials. Freshwater Fred's Lending Library is brought to you by Hoosier Energy and its Environmental Education Center, located at the Turtle Creek Reservoir in Sullivan County, Ind. The service functions on the Honor System.

Materials are available to educators in Indiana, Illinois, Kentucky, Michigan, Ohio and Wisconsin for 30-day intervals. Renewals are subject to demand. Educators are limited to 10 items at any one time."

Yale has joined the group of universities which offer course lecture online for free through Open CourseWare. Click here for more info.

Fun (and...shhh...educational) Site for Kids

I found this awesome site this morning. ExploreLearning.com has over 300 "gizmos"--interactive, web-based games/simulations--that teach concepts in middle and high school math and science. It's particularly well-suited to visual and kinesthetic learners and works equally well for homeschool/after-schoolers/individual learners and class learning via computer/media lab.

ExploreLearning has already correlated their gizmos with major textbooks and state curriculum standards, so homeschoolers who are worried about keeping up with the public schools can be sure they're covering everything they need to. Just click on your state, the standards are copied word-for-word with the list of appropriate gizmos just beneath. The gizmos all come with five or so assessment questions at the end of the activity and reports the score to the student and to anyone designated as teacher, so you can keep track of how much your child is doing and comprehending easily.

Xavier and I played around with the Chicken Genetics gizmo and had lots of fun. You get five minutes to play without registering, which isn't quite enough time to complete an assessment. ExploreLearning does offer a free 30-day trial subscription, after that there is a subscription system available. I plan to use this to extend the boys learning come fall. Too many textbooks makes Jack a dull boy. :D