Showing posts from August, 2006

Remember the Goals

Seven (?) Habits of Highly Effective Math Teaching:

Habit 2: Remember the Goals

What are the goals of your math teaching?

Are they
* to finish the book by the end of school year
* make sure the kids pass the test

or do you have goals such as
* My student can add, simplify, and multiply fractions
* My student can divide by 10, 100, and 1000.

These are all just "subgoals". But what is the ultimate goal of learning school mathematics?

Don't we want our students to be able to navigate their lives in this ever-so-complex modern world?

This involves dealing with taxes, loans, credit cards, purchases, budgeting, shopping. Our youngsters need to be able to handle money wisely.

All that requires good understanding of parts, proportions, and percents.

Another very important goal of mathematics education as a whole is to enable the students to understand information aroud us. In today's world, this includes quite a bit of scientific information. Being able to read through it and make sen…

Let It Make Sense

I've seen homeschooling blogs lately filled with seven habits of highly effective school year... so I thought of doing something similar, basically just by myself, about math teaching. You know, Seven (?) Habits of Highly Effective Math Teaching.

And I'm going to take these one by one so you have better chance to think about these. And I'm not even sure if I'll get to seven! Anyway...

Habit 1: Let It Make Sense

Let us strive to teach for understanding of mathematical concepts and procedures, the "why" something works, and not only the "how".

This understanding, as I'm sure you realize, doesn't always come immediately. It may take even several years to grasp a concept. For example, place value is something kids understand partially at first, and then that deepens over a few years.

This is why many math curricula use spiraling: they come back to a concept the next year, and the next. And this can be very good if not done excessively (like for 5-6…

Math is old and new

Today we're going to consider two math websites.

1) Interested in learning mathematics with an abacus? While you can buy this age-old device about anywhere, at the website you can find workbooks that teach arithmetic with abacus.

From the website:
"In Japan, educators maintain that the abacus helps children develop powers of mental calculation. It enables children to:

* understand the base-ten number system and place values,
* understand concepts of carrying and borrowing in arithmetic, and
* visualize close relations between numbers and numerals."

2) is a website hard to classify. The author says, "This site is for teachers, parents and students who seek engaging mathematics. "

Indeed, the Cut The Knot is full of engaging mathematical facts, lots of puzzles and thinking exercises, some proofs, games, paradoxes, mathematical facts illustrated with Java applets, mathematical droodles, and Miscellaneous! How about Eye Open…

Amazon has new stores for affiliates

Just found out about this today... Amazon lets their affiliates create their own customized "stores" with recommended products. So I went in and tinkered and played... It's very easy to set up. Here are the results for the curious:

Following the state standards?

As you're probably aware, each state has learning standards for various school subjects and grades.

What many don't know, though, is that the MAJORITY of the math standards are poorly written.

This is what Thomas B. Fordham Foundation has found in its research. They have published the findings in their State of State Math Standards 2005.

They gave state math standards grades - and 29 of the states get Ds or Fs! Only three states - California, Indiana, and Massachusetts - received grade A!

So why is that? The executive summary (makes for excellent reading) lists nine major, widespread problems within most states' standards:

1. Calculators

Typically state standards emphasize the use of calculators.

"But for elementary students, the main goal of math education is to get them to think about numbers and to learn arithmetic. Calculators defeat that purpose."

2. Memorization of Basic Number Facts

Many states don't require that students memorize basic facts. But that is th…


Just a reminder... there is still one week time to enter the giveaways drawing, and we're wishing for more participants... you have an excellent chance to win!

A parallel world

I hope you enjoy this (mathematically) inspirational piece that Alexander Givental sent to me. It relates to the discussion about the need of answer keys and a certain Russian geometry book.

Dear Homeschoolers,

I'd like to thank Maria Miller for initiating the discussion on answer keys and passing some of my remarks on to you. Yet I feel the need to communicate something directly.

The question emerged in connection with "Kiselev's Geometry" which happens to come in a very "unusual" form: with no teachers' scripts, parents' guides, workbooks, answer keys, solution manuals.

In fact, I don't see anything wrong with answer keys. While for the most of 600 problems in "Kiselev's Geometry", there is no any answer, as those problems ask to prove or construct something, there are also several dozens of computation problems there, and when I have a spare
day I might post a page with answers to such problems on the web. However, the whole discu…

Coupon codes for math curricula...

I've received not one, but TWO, coupon codes for math curricula to post on my blog and tell people about. They happen to be non-competing, so I put both here.

1) Carnegie Learning gives 10% off for new customers with the code LAUNCH10.

Carnegie Learning is a newcomer on homeschool market; they have pre-algebra, algebra 1, algebra 2, geometry, and integrated math products - in other words, grades 8-11.

These are unique in the sense that the product consists of both textbook AND a sophisticated software (Cognitive Tutor) that goes with it. (And you can buy the software separately, too, to supplement your existing book.)

The software allows students to work at their own pace, identifies student's weaknesses, and customizes instruction to focus on areas where the student is struggling. The system is built on cognitive models, which represent the knowledge a student might possess about a given subject. The software assesses the prior mathematical knowledge of students on a step-by-ste…

It's carnival time

Homeschooling Carnival is up at Common Room. Lots to choose from as usual. I picked a post for you, too: a nice write up Math Without Tears.

My entry was Math Giveaways - don't forget that! There is still plenty of time to participate!

Homeschool Math Blog Giveaways - win a membership to The Math Forum Problem of the Week service, or math ebooks!

I talked recently how solving challenging problems is the only way to be a good problem solver. And, one way to accomplish that is to take part in a Problem of the Week activity.

So... I'm very pleased to announce that The Math Forum wants to give away 2 memberships to their Problem of the Week service:

1) One INDIVIDUAL MEMBERSHIP(Gives access to the current problems and ability to submit solutions, get answer checks, and receive free mentoring when it's available.)
2) One CLASS MEMBERSHIP - the GRAND PRIZE! (Includes an account to monitor multiple student submissions and the possibility of mentoring students using the interactive system of emails/messages. Also gives access to some parts of the Active Problem Library.)

Here you can learn more how this problem of the week thing works.

And... that is not all, folks! I will also be giving away some ebooks as runner-up prizes for 10 people. It will be your choice of either Place Value 1, Multiplication 1, or Geometry ebook!

So this …

Blog updates.... less often?

No, I don't mean I'm planning to blog less, but I've thought about this often, and want to give THOSE OF YOU WHO GET THE FEEDBLITZ EMAILS an option to not receive emails from me so often.

Currently, if you've subscribed to the blog via email, you get an email a day after I blog something... generally about three times a week.

Maybe that's too often for some. So I've decided to start a traditional newsletter that comes out just monthly. The stuff I'm planning to put it in will be taken from whatever I've blogged about - anything concerning math teaching. Obviously that newsletter, since it's only one thing per month, cannot include all that I might blog about, but I'll try to pick and choose the most interesting things, maybe include links to the blogposts for people to read more, etc.

Here's the subscription form for the newsletter. I hope to send it between 15th and 20th of each month.

Subscribe me to
- math teaching…

Homeschooling Carnival

The Homeschooling Carnival is online as of today, at Sprittibee's. She's organized it all around the theme "The Wild, Wild West!" My entry was about Life without answer keys.

Challenging problems in math education and "Problems of the Week"

This post kind of follows the earlier line of thought about "Life without answer keys"... Also I want to tell you I'm going to have a blog contest with giveaways real soon! Stay tuned...

I've mentioned the importance of challenging problems before. You know, just learning concepts and practicing procedures all the time is not going to make your child a good problem solver in math.

Have you ever wondered how a tailor or a car mechanic or a hairdresser got so skillful at what he/she is doing? Some of it may be talent and natural abilities, but a lot of it is due to EXPERIENCE or we could call it PRACTICE.

And, have you ever wondered how some people get to be good problem solvers in math? I will tell you the same thing: some of it may be natural talent, but a lot of it is due to PRACTICE. Those folks have solved many problems!

And I don't mean just simple calculation problems, but true problems that require the student to think a little

All math curricula supposedly &…

More submissions wanted

Sprittibee sent me this sparkly hat and said I've earned it and that now I'm schooling in style! Thanks!

She'd like to have more blogpost submissions to this week's homeschooling carnival (with western theme). Deadline is 6PM (PST) Monday July 7th.

Logic course for the gifted

Some of you might be interested:

Recently I've had the pleasure to review a logic course by IMACS - Institute of Mathematics and Computer Science. This course is meant for the mathematically precocious middle/high schoolers. It truly is not for everyone - there is even an aptitude test before entering the course.

The logic course I reviewed is the first course in the Elements of Mathematics series for gifted secondary school students. Top universities are keen on recruiting students who have studied this math curriculum.

Read the review here: Introduction to Logic course (Propositional Logic) by IMACS.

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Homeschooling Carnival, week 31

Homeschooling Carnival is up again. This time the theme is "Galactic Adventures". My entry was about Kepler's laws and discoveries of planets. Enjoy!