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2013 August 8

Hard Math for Elementary School

Filed under: Uncategorized — gasstationwithoutpumps @ 20:34
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Hard Math for Elementary School by Glenn Ellison: (ISBN 9781489507174) looks like a book I could have used with my son about 8 years ago (too bad it was just published a couple of months ago).

The premise is simple: it is a math enrichment textbook, intended to take the topics of elementary school math deeper for gifted students.

The presentation is good, but the students will have to be reading at the 4th grade level as well as doing math at that level to get much out of the book.  This is not a flashy book with lots of illustrations and stories—it is just cool math, presented as cool math.

Disclaimer: I don’t have a copy of the book, and I haven’t read much of it. I used Amazon’s “Look Inside” feature to look at the table of contents and a couple of pages, and saw such gems as calculation tricks for computing some squares (like 552=3025) quickly.  (The trick is based on (x+y)(x-y)=x^2-y^2, but the author wisely avoids algebraic notation.)

Reviews from people who have looked at it in more detail can be found at and

Glenn also has a book for middle school students: Hard Math for Middle School

2012 May 13

Advanced Placement for talent development

Filed under: home school — gasstationwithoutpumps @ 15:15
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Since we are in the middle of AP testing for this year, it is timely that Hoagies’ Gifted has just posted Dr. Joyce VanTassel-Baska’s keynote speech from August 2000: The Role of Advanced Placement in Talent Development.

In this speech to teachers of Advanced Placement courses, Dr. VanTassel-Baska argues that AP courses are critical for gifted students, as a means of differentiating instruction for them. She said things like

In the late 1970’s gifted students reported AP to be the most beneficial program taken during their high school years. This perception has not changed appreciably over the intervening decades (Kolitch & Brody, 1992).

Of course, since she gave the talk in 2000, there has been a big push to get more students into AP courses, so that many of the courses are no longer all that suited for gifted kids.  Even at that time, she pointed out

One issue that Advanced Placement teachers need to be aware of is the different levels of aptitude for a particular AP course. The range of ability in AP classes is typically very great. Even if all students were identified as gifted, the range would be as broad as in heterogeneous classes. Such differences in aptitude level require more attention to addressing individual needs. Because AP course work probes depth of understanding, it tends to reveal greater disparity in student learning. Level of aptitude may predict how much material students can handle well, how capable they are to work independently, and how strong they are conceptually with the material. Use of various forms of flexible grouping for in-class work may be an antidote to this problem. Organizing sections of AP by ability levels may also be useful in subjects where enrollments are sufficiently high.

The trend to lower the barrier to entry for AP courses over the last decade has made this problem worse. The teaching strategies that are most effective for the bottom half of a current AP course may be quite unsuitable for the kids in the top quarter, who don’t need many routine practice problems, but rather a smaller number of more challenging questions that stretch their minds.

While AP courses may still be the best option available to most gifted high school students, many need to look elsewhere for teaching at their level. Community college courses sometimes provide this, though that varies enormously, as many community college courses are intended to remediate inadequate high school preparation for college, and may be taught in an even less suitable way for gifted students than AP courses.

Sometimes sufficient challenge can be found by skipping prereqs—the review built into the beginning of most courses can serve as a fast-paced introduction to the material for a gifted student.  This is essentially what we did by teaching my son a course that covers AP Physics C: Mechanics, with no previous physics courses.  He had picked up almost everything from a conceptual physics course by reading various popular books about physics, and his math was strong enough that he did not need the crutch of algebra-based physics, but could jump right into calculus-based physics.  (Actually, I think that calculus-based physics is somewhat easier, if you have the math, since there are fewer formulas to memorize—a lot can be trivially rederived from the definitions of force as the derivative of momentum with respect to time and of potential energy with respect to displacement, for example.)

I think that one problem with AP classes as a primary means of teaching gifted high school students is an extension of a common problem in gifted education in lower grades: what the students need is work that is more complex and sophisticated, not more work.  Too many AP courses pile on drudgery, in the mistaken belief that this makes them more like college courses. (See my analysis in How many AP courses are too many?)  This overload of marginally useful work prevents them from taking on more independent, non-curricular projects (like science fair, debate, theater, or internships) from which they would actually learn more.

I’m not saying that I think that AP courses are a bad idea, nor that gifted students should avoid them.  There are times when an AP course is precisely what a gifted student needs and other times when it is the best available choice. Taking AP courses is one of many ways for gifted students to learn, just not always the best way.

2012 March 11

CS Summer Camp

Filed under: Uncategorized — gasstationwithoutpumps @ 21:54
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On the mailing lists for parents of gifted kids, people often ask about the best computer summer camps.  Even more often, they ask for people’s experiences with nationally advertised programs.  So far, the general consensus has been that none of the computer camps work particularly well for gifted kids:  the pace is too slow, the teachers don’t know enough, and most of the kids in the camp aren’t passionate enough about computers to be good peers.

That was my son’s experience a few years ago when he tried an idTech camp, and it seems to be a common experience for gifted kids in almost all the summer computer camps, no matter who is providing them.

There are several summer math camps that don’t have this problem, so it is not just a matter of gifted kids being hard to please. Rather, I think it is a deliberate attempt to reach the “average” kid that makes the usual computing summer camp useless for gifted kids.

Mark Guzdial, in his blog post The Best CS Summer Camp Paper: Sustainable, Effective, and Replicable, talks about a paper by his wife, Barbara Ericson, Sustainable and Effective Computing Summer Camps.  The paper talks about programs at Georgia Tech that are self-supporting and not very expensive (after a whole lot of initial expenses covered by grants). Since this was a paper for SIGCSE (special interest group in computer science education), the paper talks about the measurable outcomes as well as how the camp was funded and organized.

There is good evidence that their summer camp programs are doing what they set out to do:

improve access to computing, increase students’ confidence in their ability to succeed in computing, increase students’ knowledge of computing concepts, and change students’ attitudes about computing.

The programs themselves sound a lot like all the other summer camps: fun for average or above average kids, but offering nothing for the passionate gifted kids who want something more than playing with Scratch or App Inventor.

Where are the computer equivalents of Awesome Math Camp  (which I blogged about a couple of year ago) or RSI (Research Science Institute)?  I’ve not found them.

2012 February 3

Tamara Fisher’s “Walking a Tightrope”

Filed under: home school — gasstationwithoutpumps @ 09:51
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Tamara Fisher, in her Unwrapping the Gifted blog, had a nice post about the balancing act needed as a teacher and program coordinator for gifted education in a small district: Walking a Tightrope.

I was interested to see that most of her challenges were not in dealing with gifted kids, but in dealing with ungifted teachers and parents.

She ends with the question “Which fine lines do you walk for the gifted youth in your life?”

Most of her challenges do not resonate with me, as I have no need to educate administrators (a hopeless task—those who have a chance of understanding don’t need educating), correct teachers, choose who gets gifted services, and all the other challenges that come from working within a school system that barely admits that gifted students have a right to exist.

Some of her questions do resonate with me as a home-schooling parent of a gifted child though:

How do I teach my students about what it means to be gifted without also unintentionally “giving them the big head”?

We have been using advice based on Carol Dweck‘s work (though we’ve not read Mindset yet, just shorter summary articles) of praising effortful accomplishment rather than traits that may be innate, and encouraging a “growth” mindset.  We want to foster pride in accomplishment, rather than pride in ability.  We’ve not been as successful at getting him to try things he believes he is not good at  as I’d like, but he probably has a better balanced view of his capabilities than I had at his age.

How do I stay ahead of dozens of kids who are ahead of me?

I only have to stay ahead of one student, and then not in all subjects. Some things have required my brushing up on old skills (like integration by parts and trigonometric identities), some have required acquiring new skills (like calculus-based physics). It helps that in some of the subjects he is interested in (like linguistics), my wife is knowledgeable enough that I don’t have to be ahead of him—I just have to learn enough to follow the conversation.  There are a few topics he knows better than either of us (like HTML and Javascript), but he is capable of teaching himself when he reaches his limits in those areas.

How do I think outside the box to get their needs met within the box that is our current reality of School?

I finally gave up on this one, which is why we’re home schooling now.  We managed to squeeze all we could out of 10 years of public and private schools, but the “box that is our current reality of School” finally became too awkward a fit.  Getting his educational needs met is still a difficult problem, but removing the “within the box” constraints has simplified some things (by removing the need for accreditation and removing slow-paced pre-requisites, for example), while making others more complicated (like the 2-hour roundtrip to the community college for Spanish classes, and the difficulty of finding or making lab equipment at home).

How do I help my students to navigate the fine lines that they walk, too, because of being gifted?

I’m not sure which “fine lines” she is referring to here.  There are many challenges associated with being a gifted teen, but the challenges are not greater than those facing non-gifted teens.  Different perhaps, but a lot of the worst pressures on teens are from schools with unhealthy cultures, so simply by home-schooling and allowing him to form his own associations based on shared interests (with kids in his theater classes, for example) rather than the forced proximity of schools reduces the number of “fine lines” he has to walk.

How do I help the parents of my students find that balance between letting their children “run” and not pushing them?

This is indeed a challenge, though I am not opposed to a gentle push now and again, to get him over a barrier (see above about getting him to try things he believes he is not good at) or to help him manage his time more productively.  Like his mother and me, he generally has more things to do than he has time for, and suffers occasionally from being overwhelmed by everything that needs to be done. Deadlines help prioritize the tasks and a gentle push to get him started is sometimes needed.  (I need someone to help me that way sometimes.)

2012 January 31

Contacting home-schooling parents and parents of gifted kids

Filed under: home school — gasstationwithoutpumps @ 10:14
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On Mark Guzdial’s Computing Ed blog, I commented

The ‘gifted children’ mailing lists are full of parents looking for computer science courses (on-line, textbook, summer camp, … ) for their kids. So are the home school mailing lists. There is a large under-served market—the best known player is iD tech camps, and their material tends to be rather light on content and unsatisfying to the brighter students.

Someone asked me where to find these lists and how to market to them.  I responded there, but I thought that the information was useful enough to put it here on my blog, and not just buried in a comment elsewhere.

The best lists I’ve found for parents of gifted kids are the “tag” lists at but marketing is prohibited on the lists.

The best clearinghouse for info about gifted students is Hoagies (and they will take advertising, I think, though most of their material is non-commercial). They have a pretty good list of on-line communities. Listing resources at Hoagies is a great way to reach a lot of parents and teachers of gifted kids, as it is the most commonly referred to resource site. (So far as I know, listing stuff at Hoagies is free—they are interested in being as inclusive as possible of resources.)  The resource lists cover a lot of different subjects (books, toys, games, courses, support groups, training materials for educators, conferences, jokes, schools, psychologists, testing, … ).

One of the three home-school lists I’m on is tagmax (one of the lists)—the other two are small local lists and not appropriate to point to here. There is a lot of discussion of curricula and on-line courses, and endorsements of particular classes are ok (as long as they are real endorsements by people on the list whose kids have taken the courses—advertisers are quickly banned).

I have found quite a few useful pointers on the mailing lists, but traffic on some of the lists is overwhelming.  I generally divert the list traffic to separate files, and only look at the messages once or twice a day.  Some of the lists have many readers—I often get a big spike in readership on this blog when I mention one of my posts there.  (I try to do that sparingly, with only the posts that are really of wide interest to the readership of the mailing lists.)

Another mailing list that I’ve found useful, but overwhelming, is the ap-bio mailing list for teachers of AP Bio classes (mentioned on College Board’s teacher’s corner page).  I’m not an AP bio teacher, but I’m working to get bioinformatics into AP bio classes—a group of grad students and I tested one lesson last week at Pacific Collegiate with 3 AP bio classes and will test another in about 2 weeks.  We’ll be releasing them as soon as we get feedback and clean up any rough spots.

I’ve just joined the AP Physics teachers mailing list, since I find myself needing advice about low-cost lab setups for the home-schooled physics classes fairly often (and I’d like to share some of the labs I’ve posted in this blog).

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