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Showing posts from November, 2005

Fibonacci numbers

The solution to the little thinking exercise of previous week is here:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...
-> Add two consecutive numbers from the sequence to get the next one following them

This sequence is called Fibonacci numbers. And it isn't just any ole sequence of any ole numbers... it has some amazing properties, plus it's found in nature in many places.

For example, Fibonacci numbers are found in

* Petals on flowers
* Seed heads
* Pine cones
* Leaf arrangements
* Vegetables and Fruit

The links go to a magnificent site about Fibonacci numbers with tons of information and pictures. Go click the links and see for yourself! It's very informative and well done, plus I don't have those photos.

Then come back. I have a question for you:

Should your child or student learn about this? Is this important to know? Well, you think about it - in the next post we will study just a tiny bit more about Fibonacci numbers.

Too busy for a friend

I'm sorry this is pretty much off topic (though it mentions a math teacher!) but I just got it this morning in my email and it is a good story about something important.


One day a teacher asked her students to list the names of the other students in the room on two sheets of paper, leaving a space between each name.

Then she told them to think of the nicest thing they could say about each of their classmates and write it down.

It took the remainder of the class period to finish their assignment, and as the students left the room, each one handed in the papers.

That Saturday, the teacher wrote down the name of each student on a separate sheet of paper, and listed what everyone else had said about that individual.

On Monday she gave each student his or her list. Before long, the entire class was smiling. "Really?" she heard whispered "I never knew that I meant anything to anyone!" and, "I didn't know others liked me so much." were most of the comments…

US students lag behind in math

Well this is not real uplifting, nor is it really news (we knew it before), but here is another study showing how US students score way below average among industralized nations
.
NEW STUDY FINDS U.S. MATH STUDENTS CONSISTENTLY BEHIND THEIR PEERS AROUND THE WORLD - FINDINGS CHALLENGE CONVENTIONAL WISDOM ABOUT U.S. MATH SUCCESS IN EARLY GRADES.

Continue this sequence of numbers!

Okay, teachers and homeschoolers and other readers, I want you to think:
How does this continue:

0, 1, 1, 2, 3, 5, 8, 13, ...

Answer will be here next week.

If you already know, stay tuned anyway; I have a point to make besides the math.

Fun math and math appreciation

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Some of us are math enthusiastics: we love math, think it is full of beauty, logic, and patterns; we think it can be fun, exciting, amusing even. (I include myself in this category.)

And then some of us don't care for math, didn't like it in school, didn't do well in it, don't want anything to do with it anymore. And I'm sure there are people in between these extremes, too.

As a teacher, you would like your students to belong to the first category, of course.

Now, I sincerely think that the biggest factor in whether student ends up liking or hating math is what kind of math teacher and teaching he/she gets. Parents' attitudes play a role too, but teacher's attitude to math and the way math is taught are the weightiest factors, I feel.

But books such as The Adventures of Penrose The Mathematical Cat by Theoni Pappas can help too. It is intended for fun reading, exploring exciting mathematical topics in an easy-to-understand way.

The storyline includes Penrose …

Adding in the kitchen

I like to try make it a habit asking my daughter math questions here and there. Today, while working in the kitchen, I said we're doing "plus one" questions. I asked, what is one plus one, which was easy for her. Then she told me a question. I did another one, six plus one. After that we dealt with one plus six and how to make it easy.

She suddenly said eight and six makes two. Well I should have dug deeper into why she thought that way but this time we just did it with tiny rocks on the carpet. I put the rocks out and asked could that make two. She agreed it couldn't and counted the answer.

After that she said 1 + 2 = 4. Well I asked her to make it with rocks again and then she came up with the right answer.

Then she wondered herself what is 3 + 1, and found the answer.

Then, one more time I got to hear the wrong math: while eating her soup, he announced 2 + 2 = 5. This time I asked her to use her fingers to get it straight.

We've done similar things with plasti…

Number sense

I recently found a
nice article at Apples4theTeacher.com that summarizes 10 research findings as to what teaching practices and methods are the most effective. For example,

8) Teaching mathematics with a focus on number sense encourages students to become problem solvers in a wide variety of situations and to view mathematics as a discipline in which thinking is important.

What is number sense? It's something where the child is comfortable with numbers, knows what numbers mean, can do mental calculations, can connect numbers and real world situations, and can make comparisons.

Kids with number sense have built a 'mental number line'. They can tell that 11 is more distance away from 15 than what 14 is.

How can you help develop it?

Think how can children get to be FAMILIAR with numbers. It's when they have lots of opportunities to use them and to play with them.

Games are good. Observing how parents use numbers in daily life is good. Doing lots of calculations ('dr…

Math wars: is it "drill and kill" or "discovery learning"?

Today, Barry Garelick sent me an article of his which explores the topic of MATH WARS.

You may have heard of them. Math wars refer to the debate or controversy about how math should be taught in school. There have been two main camps: those who emphasize discovery learning and calculators, de-emphasizing algorithms and memorization - and those who claim kids need to learn and memorize basic facts and algorithms such as long division.

Mathematicians have been fiercely opposing the math education reforms that are based on the discovery learning postulate.

In my opinion, I think kids surely need to memorize their basic facts, and learn the basic algorithms. Learning by discovering is a fine teaching method, but it shouldn't replace teacher telling or explaining how things work.

I guess what I feel is that learning by discovery (or explorations) can be great but you need to use it right and not let it 'rule'. It is an instructional method or a tool - not a goal in itself.

A…

Study order of the ebooks

Posted a short article about in which order to study the ebooks to answer questions from customers.

What's going on at Homeschoolmath.net

Today I got done moving the preview lessons from Division 1 ebook to the 'teaching tips' section (in the menu at the bottom of page, under multiplication/division lessons), and then extracting a few example pages from the ebook itself to be shown on the Division 1 ebook contents page.

I still have two more ebooks to go, and do similar changes.

I've also received a few books in the mail that I will be writing about later, after I get some time to read them.

One was like a 'bible' of school math - reference book for teacher. One is math history book titled "Mathematics The Science of Patterns" (which is an excellent title), and two are kind of fun math books where a cat is exploring things. Stay tuned.

Calculator in elementary grades?

There is controversy over how much elementary school kids should be allowed to use the calculator. Some say it's a no-no altogether, some think it should be used almost all the time - and some think it should be balanced.

In my opinion, one should severely restrict the calculator use in early grades - until the student has mastered the basic math facts and can quickly do basic mental calculations. Until then, calculator should be used only for some special projects or illustrations.

Why? Because not knowing those facts by heart is a big hindrance when learning fractions, factoring, etc. And because it helps children develop NUMBER SENSE - to be familiar with our number system.

Also kids need to learn to do multiplication and long division by hand - it is needed later when those same procedures are used in algebra.

Read more at this link: Using calculator in elementary math teaching.

More on focus

I wanted to clarify something about my earlier post on focus and math teaching.

Focusing doesn't mean that you would focus on, say, addition only for a year, and then subtraction for a year, then multiplication for a year etc. No. Mathematical concepts connect together and so you need to study closely connected concepts fairly close to each other.

The idea is to focus on a few topics or themes.

For example, for 1st grade, the focus topics could be concept of addition, concept of subtraction, place value, and memorizing basic addition/subtraction facts.

Several of them connect together too: for example, subtraction/addition have a close connection. So do understanding tens/ones and concept of addition.

Measuring and geometry are needed, to some extent. The less important topics could be fractions and data analysis (if any).

When you are focusing on some topics, you should have a goal: you want the student to MASTER something. After that, you can move on to something else.

Maybe you …

Mathematics is all about... ?

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In elementary school, I was under the impression that math was all about NUMBERS. Before 7th grade, I was thinking that there couldn't be much more math since we seemed to be doing the same things over again (spiraling curriculum).

After that, the math I was learning seemed to be all LETTERS: x's, y's, a's, b's, f's etc. And soon it was Greek letters too!

But math is actually neither. Math is all about PATTERNS.

The whole structure of our base-10 number system is a certain pattern. Multiplication, division, etc. are full of patterns to notice. Functions and relations are all about making general rules for patterns.

When first learning about sine in right triangle, it may seem to students like a disjointed piece of information - but if they could get past the initial stage and see the sine curve! Patterns!


But I especially wanted to mention trees, ferns, coastlines, snowflakes, and such. Because they have a pattern too, and mathematicians have unveiled the ma…

Education and entertainment - children don't differentiate

Like I said, people send me links. This time it was www.Time4Learning.com. They say they're "children’s educational and entertainment online subscription service for ages 3 to 9".

I went and looked at the site and some of their free examples - and it seems like a quality service. It has learning activities and games and worksheets for K-5 language arts and math.

Like I read in a news article recently, children don't differentiate between entertainment and education - they learn and absorb whether they are watching a violent cartoon movie or an educational clip. I would definitely opt for the latter.

So I posted the link at my site's educational links page.

Elementary math ebooks on a CD now

The elementary math ebooks that I've written are also available on a CD now, for the price of $34.50 + shipping. That is 18 ebooks covering all four basic operations, geometry, fractions, and an introduction to decimals.

You can also buy them individually, prices ranging from $1.25 till $4 per ebook. Or, buy the whole set for $27.50 if you download them.

Click here for more info on the ebooks - or
go order (from Kagi store - my reseller).

It's easy when it's Bear Math

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Recently we bought this great book in a yard sale, it's called Bears! Bears! Bears! by Scholastic. It comes with a handful of small cute plastic bears.

My 3-year old is fascinated by the bears (plays with them all the time) AND by the book, which teaches some early math concepts. For example, it tells to put equal amounts of bears into two balloons (see pic above). Or, set bears sitting facing each other - is one left over - so she can observe even/odd numbers. Or, you can measure by bears since each one is exactly one inch.

A great concept, unfortunately the book is not available much anywhere. Originally it was only distributed via school market. But, some folks sell it used at Amazon (probably the bears will not be included in these used versions, is my guess...).

Anyway, you know it but it's good to be reminded: when it's fun, learning is easy.