Inspiring Math -- Help me think this through?

[Jenny in Florida]

So, we got our 10-year-old son's ITBS/CogAT scores back today. No big surprises, but some interesting information that seems to be trying to gel in my brain with some other thoughts I've been having lately.

 

This is the kid whom I've always assumed was more math and science oriented. However, we've noticed over the last couple of years that he consistently tests considerably higher in language and reading. He still scores quite high on the conceptual/problem solving math tests, but his computational skills are distinctly lagging by comparison.

 

He has also begun to say he doesn't like math, that it's boring.

 

So, a couple of weeks ago, I started turning over this idea in my head: "Real" mathematicians, as I understand it, don't sit around making up and solving equations. They are actually much more involved in figuring out how to apply theories and ideas to solve complex problems, right? I mean, I'm sure they're really, really good at arithmetic, but for the kinds of problem solving they do, they probably mostly use computers and calculators to do the actual "work."

 

Now, when my kids were learning to read, I did not restrict them to taking in only material they could read independently. In other words, I did not allow their limited skills with the mechanics of reading to keep them from hearing bigger, more complex, more interesting, more challenging stories or ideas. I read aloud to them. They listened to audio books. I read aloud to them some more.

 

My son is taking piano lessons, but we don't limit him to hearing only the music he is capable of producing. We enrich his environment with lots of great music, played by excellent musicans, and we talk about what he hears, and he learns about the lives of the composers and the stories of the operas, and he happily hums along .

 

And the same thing is true for pretty much any other subject I can think of . . . except math. In math, all he gets to do is trudge along from day to day working mechanically through one problem after another, for no particular reason other than that we tell him he has to.

 

Now, I know "real" math people love math, think it's beautiful and exciting. But that's just not a factor in any math curriculum I've ever seen.

 

So, I'm absolutely determined to figure out how to start communicating that to my son, to give him some reason to care about the mechanical, boring, daily stuff he "has to" do.

 

But I have no idea how to do it.

 

Just to give you an idea of where we are: My son has already finished the Florida Virtual School middle school math sequence with very good grades and is currently working through the UCCP open access Algebra 1 course. He started it in February and finished about the first third of it before we knocked off for the summer. He likes it reasonably well, and he's doing fine with it, but it's not by any means inspiring. And sticking with that exclusively won't do a thing to help reinforce or improve his computational skills.

 

So, I'd like to add something fun or jazzy alongside it for next year. We should have time, since the current plan is to spread out the remaining two-thirds of the class over the full academic year.

 

I've spent quite a bit of time looking at the book lists at ww.livingmath.net, but haven't seen too much that looks like it will fit the bill. Many of the books recommended are things we're either already using (although I consider them part of our science curriculum, not math) or that I've already turned down because they are too simplistic or too boring.

 

I really will try to stop babbling now and just ask: Does anyone have any brilliant ideas or suggestions? Web sites to use for research? Great, math-y books you or your kids have just loved? Anything?

 

I mean, I'd love to find something like the Composer's Specials, but with math, but I haven't found any trace of such a thing yet . . .

[Melinda]

I will have to look, but I have a book that teaches you how to do mental math and make it fun. Supposedly, it will teach you to do the problem faster than someone can input it into a calculator.

[Anne/Ankara]

Jenny, have you checked out math competitons? They are just great for kids who need to see the point in all those equations/calculations. We have done several for many years and recommend them all. Here are some to check out: Math Counts, Math Olympiads (Elementary & Middle School), Academic League Math Competition, AMC 8, 10, Purple Comet Math Contest. Each of these have websites for further information. He's at the perfect age for all that stuff.

 

Also, I can't remember if he likes the Teaching Company series-- they have a new one on the History of Math http://www.teach12.com/ttcx/coursedesclong2.aspx?cid=1434&pc=HomePageFeature which we haven't seen, but their Joy of Thinking was great, and we just bought their Number Theory one to watch soon. Maybe those would interest him?

 

Lastly, if he likes the "camraderie" of working with other kids, I highly recommend the Art of Problem Solving math courses, http://www.artofproblemsolving.com/Classes/AoPS_C_About.php because here the student is with other kids and can be motivated by his fellow students. We took the Number Theory class last semester and really enjoyed it... perhaps he could try one out?

[Guest odette]

Texas Instruments sponsors a program with math activities from all areas of mathematics. It's tied to a drama on CBS that you may or may not find to adult-themed ( mathematician uses math to solve crimes for the FBI), but you needn't watch the show to understand most of the work. It's free and the activities are well-organized so you can try a few different things and see if you can't catch his interest.

 

www.weallusematheveryday.com/

[merylvdm]

Could you post the website for Math Olympiads? I know about all the other ones you mentioned.

Thanks

Meryl

[Anne/Ankara]

Could you post the website for Math Olympiads? I know about all the other ones you mentioned.

Thanks

Meryl

 

Math Olympiads was one of the first competitons we ever did, and really did enjoy them. Here is their website, http://www.moems.org/. They are geared for grades 4-8, I believe (Elementary school and then Middle School divisions). There are five competition dates through the school year (Nov, Dec, Jan, Feb, March I believe) and the student gets five questions on the test. You can see samples on the website.

 

They have a nice book with past exams and answers, which is helpful to have.http://www.moems.org/Books.htm

 

If I remember correctly, there is something like an $80 fee to register, so we always got a group of 4 or 5 families together to split the costs. You can administer the test yourself, and homeschoolers are permitted, so that was easy enough...

 

It was fun! And the kids definitely learned a lot.

[Capt_Uhura]

Anne/PA: have you seen the MOEMS grade 4-8 books? I'm wondering if the 4th graders are actually advanced 4th graders such that the books would be over the head an advanced rising 3rd grader?

[Storm Bay]

Is he ready for Algebra? If he likes theory, Gelfand's Algebra is a lot more fun because it shows proofs for a number of axioms, and all the answers have been posted by Charon. For my dd, the problems were too long for her patience at 11, but she loves it now. Perhaps that will be different for you.

 

Also, you might have him read a history of mathematics, such as the one by Boyer. The Teaching Company has a conceptual Calculus teaching set he might find interesting, among others.

 

My dd and I love the theory part more than anything else (but I didn't major in math because no one showed me all the really fun stuff when I was in ps plus other stuff they did that turned me off.)

[Anne/Ankara]

Anne/PA: have you seen the MOEMS grade 4-8 books? I'm wondering if the 4th graders are actually advanced 4th graders such that the books would be over the head an advanced rising 3rd grader?

 

I *do* have and have extensively used the contest problem book by George Lenchner, called Math Olympiad CONTEST PROBLEMS for Elementary and Middle Schools, Revised Expanded Edition. It is great, and well worth it, even if you don't do the competition formally. It includes past tests, and the solutions. I see that they now offer an additional volume of more tests, which could be helpful if you've gone through the first volume.

 

Of course it's always hard to tell if a book is the right level for a particular student, but by all means I would definitely recommend this one for an advanced third grader. We started about at that age, and in the beginning, we could only correctly solve one or two problems out of the five, but, like anything else, the more you do, the more you learn, and by 4th grade, you could definitely successfully work many problems. If you look at the website, I believe they give examples...http://www.moems.org/sample.htm

 

And if the student routinely does this sort of problem solving, by 8th grade or so this type of thinking is second nature, and VERY helpful to SAT math and other higher level math. And it is fun!

 

Why not, indeed!

[Myrtle]

 

So, a couple of weeks ago, I started turning over this idea in my head: "Real" mathematicians, as I understand it, don't sit around making up and solving equations. They are actually much more involved in figuring out how to apply theories and ideas to solve complex problems, right? I mean, I'm sure they're really, really good at arithmetic, but for the kinds of problem solving they do, they probably mostly use computers and calculators to do the actual "work."

Now, I know "real" math people love math, think it's beautiful and exciting...

 

Physicists, programmers, engineers, and accountants may use computers and calculators to solve physics problems, engineering problems, etc, but real mathematicians still prove theorems using paper and pencil. For more details see page 30 of Krantz's article here.

 

The math that is taught in K12 is not "real" math. It might be more accurate to say that it's training in the math methods used by physicists, accountants, etc. It's about career training more so than learning about the field of math. A mathematical problem deals with a problem in math, such as the Poincare Conjecture and Fermat's last theorem. A real math problem would not be "how many bags of fertilizer are needed if 3/4 of a bag is used per 7/9 of a row and 15 rows need to be fertilized" ( I don't know if that's what you were trying to get at):tongue_smilie:

 

Both my husband, who has an advanced degree in math, and my father in law, who was a math professor, communicate that math is interesting to the kids but they don't do that by giving them books or lectures, they do that because they both love math and love talking about and can't resist thinking about questions that come up. It's like veganism, sports, or music, if the parents are doing it and sincerely excited, the kids will catch on. (Books and lectures are used for teaching how to calculate bags of fertilizers, an important skill, to be sure, but nobody cares how much the kids like doing that sort of thing. They are obliged to learn it whether they like it or not)

 

 

They don't tend to apply theories so much as invent theories and prove that it's true, if that makes any sense---like nosey, curious mechanics trying to figure out how some novel machine works by taking it apart with logic. Then if you say you think that it works one way, they lawyer you to death to show that you must be wrong or you get the ultimate reward which is having your clever argument acknowledged. In order to survive these brutal cross examinations you develop airtight arguments to support your beliefs.

 

As an aside, I once brought up the idea to them that anyone that likes to debate law would love to debate math but they debated me on that one too.

 

There really isn't a whole lot out there for kids still in arithmetic. We use Singapore because it encourages children to think creatively and gives challenging problems that they can't get without hard thinking and also Singapore's Intensive Practice. In general, we want mastery of basic algorithms and facts but do not judge mastery by absolute speed, but rather by the kid's ability to use the properties of numbers to solve problems he's never seen before.

 

I have another book that teaches geometric constructions to the 4,5,6th grade range... lots of neat designs result and you can talk about the principles informally. I've used a lot of origami ideas and projects. I've also used Number Theory by Art of Problem Solving and in algebra (6th grade) we are using Gelfand's Algebra to supplement. Dmitri Fomin's Mathematical Circles doesn't teach math but it has some awesome and interesting problems in it once you can do a little algebra.

[abbeyej]

I'll second the recommendation for Math Olympiad. Ds did Math Olympiad for the first time this past year, and the problems they offer are just marvelous. It helped that the dad coaching our team was a wonderful, kind guy with a strong math/engineering background himself. It would have been even better on a team with other really strong math students (ds was an 8yo 4th grader and he got the trophy for best individual score on his team -- I actually found that frustrating), but the problems were just great. You can buy books of Math Olympiad problems (and they include strategies for approaching the problems -- often several strategies -- so that after the kids have worked for a while, you can discuss various approaches), and they're great, but being on a great team would be even more motivating...

 

I'm sure you've probably explored most of the other materials we've gotten to use so far at our house... Challenge Math, Real World Algebra and other titles by Zaccaro. "Mathematicians Are People Too". Number Devil (book and software). Penrose (possibly below your son's level). Sir Cumference books. (Cute, picture book things, but with math concepts that might still be challenging.) Tall-Tale Math books.

 

And I have to say that 5 minutes daily of easy drill (start with the super-easy and add either more problems or more complexity step-by-step) every single day shave off far more time than that in time doing "real" math work. I can tell a huge difference between times when ds is doing daily drill (in addition to conceptual math) and when he isn't -- it may seem like a chore, but 5 minutes of mild unpleasantness keeps those computational muscles in great shape and means there's less huffing and puffing about the computation in problems that are otherwise much more interesting and challenging.

[Donna]

"The Art of Mathematics" by Jerry P.King. If your son loves to read and reads at an advanced level, he may find it interesting. Otherwise, you might find it an interesting read and relate the information to him.

[Nancy in NH]

I just ordered this for my ds (11) who is bored with math. It teaches math in the context of music, and infuses physics and some history, too (mostly ancient history, I believe). It is a software program geared towards grades 7-12, covering higher-level math concepts. I went through the online samples and thought it seemed to be just what I was looking for and then had my ds do the same. My ds is a talented pianist and has enjoyed making the connections of music to other subjects. He loved it. I'm not sure how bogged down he'll get with all the higher level concepts, but he made it through the online sample (which includes a quiz at the end). My goal is to have him work through it at his own speed.

 

Here's the link:

http://www.wildridge.com/index.html

 

They also offer another product, called Math and the Cosmos, which looks appealing, too. Maybe something like this will motivate your child.

Nancy in NH