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Showing posts from April, 2008

Points on math education

I found something really nice at Mathmom's. She has written an excellent piece about problems in math education in elementary grades. Her point of view is of classroom instruction, but it is still really relevant even for homeschoolers.

Some excerpts follow.

On calculators:

But to be honest, as much as I hate calculator use in school, in this age of calculators and computers, efficiency at hand computation is not, IMO, the most critical math skill for kids to learn. I am NOT saying that it should be ignored, or that kids should be allowed to skip it, and just use calculators in class (see rant linked above). But it is not, IMO, the be all and end all of math education, nor is it a prerequisite, IMO, for studying anything else.

What I consider even more important is a strong sense of number. I want kids who know immediately when the answer they got (either by hand computation or with a calculator) is way off. I want kids who have an instinctive understanding of the distributive law …

High school geometry - a review

It's done! Finally! Took me some time to finish this review, perhaps because it involved three products:
The book Geometry: A Guided Inquiry. As the name suggests, this book is based on letting students learn about theorems and their proofs in the setting of "guided inquiries" or interesting problems. It is quite unique in its approach.
A Home Study Companion which includes solutions and about 300 interactive demonstrations
Geometer's Sketchpad - dynamic geometry software.
This review isn't just what you typically find on the web; someone called it an "exquisite in-depth review". It's fairly long... with sample pages and other pictures, examples, and more.

I encourage you to read it even if you don't need a high school geometry book right now... because you'll get valuable insight just HOW GOOD geometry instruction can be, how the book handles proof, or what to think about an axiomatic vs. discovery based geometry text.

Review of Geometry: A Guide…

Free math videos...

...for this week only!

MathTV.com is letting us test-drive (public beta) their new website for FREE for one week only:

http://www2.mathtv.com/

Hundreds of videos on pre-algebra, algebra, trig, and calculus topics. Even in Spanish.

Brain rules

This was an interesting website, and can give you some insight into how our brains work -- which is always a good thing to know, to enhance learning!

It is based on a book, which explores the 12 brain rules in detail. These rules or principles have to do for example with exercise, sleep, stress, how our memories work, and so on.

On the website you can read and watch little videos about each. Warning: the video about "attention" is illustrated by an immoral "attention getter". But you will glean some good ideas and learn pretty interesting stuff in the others; I enjoyed most of it:

Brainrules.net/the-rules

It's been quiet...

Image
at my blog lately and I'm sorry for that. But, I have something in the works.

I'm working on a review of a "three-combo" geometry curriculum for high school geometry:

The textbook Geometry: A Guided Inquiry
Geometer's Sketchpad - a dynamic geometry software
A Home Study Companion to accompany the book, which includes solutions and dynamic illustrations with Sketchpad
I enjoy doing geometry. This book has problems that "evolve" from one to the next, leading to important conclusions. Then it has really interesting projects, and many of them can naturally be constructed with Geometer's Sketchpad, which is lots of fun - for me anyway.

The problem is, I cannot afford to take the time to study and solve all these projects and interesting problems, but just to pick and choose one here, another there.

Anyhow, I hope to complete this review within a week.

Backwards math

This is just a really cute story of a 3rd grader who on her own figured out a way to do "backwards math"...

Backwards math

Kindergarten math

People occasionally ask me about kindergarten math, and if I'm going to write kindergarten level books for the Math Mammoth series. The answer is no, I don't feel there's any need for me to write books, because there already exist plenty of good materials for these very basic and easy concepts.

BUT I did write a comprehensive article about what you can do in kindergarten math, including many games you can play, and what basic concepts should be covered in order to prepare for 1st grade.

Problem solving & math as an art

Continuing on a litlte bit more with my thoughts concerning Lochart's Lament.

Lockhart starts out his lament with a comparison: WHAT IF music teaching only consisted of learning to write music, write notes on paper, and only after high school level would students be allowed to actually hear and make music? WHAT IT art instruction would consist of "paint by numbers" until high school, which is when they'd actually start applying paint...

Lockhart remarks that if he wanted to destroy a child's natural curiosity and love of pattern-making, "...I simply wouldn't have the imagination to come up with the kind of senseless, soul-crushing ideas that constitute contemporary mathematics education."

He calls school mathematics "pseudo-mathematics", where emphasis is on the accurate yet mindless manipulation of symbols.

These are, of course, very strong words. I don't fully agree... I don't feel all that's done at school would be pseudo-math…

Carnival of Homeschooling - the April fool's day edition

Carnival of Homeschooling is up at Why Homeschool. This one is the April fool's day edition, and Henry has sprinkled the carnival with juicy stories of past April fool's day jokes from BBC or others.

Check also Denise's entry for subtracting mixed numbers.

Kindergarten question

How to teach subtraction in the kindergarten with the tens place values and in horizontal sequence, for eg, 20-5=? They know to count their fingers, from the smaller number to the bigger number, but when the fingers are not enough to count, then what?

I'm not sure kindergartners are necessary ready for this. I would ONLY do these types of problems with concrete help.

Get a 100-bead abacus. Instruct them to first "make" 20 or show 20 on the abacus, and then move 5 away. Then "see" how many are left.

This online abacus is also really good for illustrating such.

Once they've done 20 - 5 and many other problems, you can ask if they notice a similarity in these problems:

10 - 5

20 - 5

50 - 5

70 - 5

etc.

But if some don't, wait till 1st grade. Practicing problems that "cross the ten" without manipulatives, such as 23 - 5 or 71 - 9, can wait even till 2nd. I realize kids might be able to do them by counting down, but to learn effective strategies for solving t…