Final Fantasy Papercraft - Cactuar

Oi paperkraft netizens, here's another Final Fantasy paper model, this green cactus-looking character is the Cactuar (also known as Cactuer, Qactuar, Cactrot, and Sabotender). It's main features are two black dot-eyes, an oblong shape mouth, three red quills on the top of their head, and their trademark pose, stiff arms and legs. On the Final Fantasy video games (FF VIII) they are best known for their 1,000 Needles (Defensive attack), which deals exactly 1,000 hit points of damage to an oponent, regardless of defenses. There was also a Jumbo Cactuar that had the 10,000 Needles attack, which was kinda like an instant-death attack since prior to FF X the maximum number of hit points for a character in FF is limited to 9999. If you noticed that my Cactuar is of a different color (blueish top, green legs) and not solid green, don't panic, it's because mine is of a different breed, it's a color-shifting Cactuar (also known as Printerus Hasno Inkus). This paper model stands about 6" tall and 4" wide and comes with a stand (not shown).

Final Fantasy Papercraft - Cactuar [via mediafire]

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 years is probably excessive).

However, spiraling also has its own pitfalls: if your child doesn't get a concept, don't blindly "trust" the spiraling and think, "Well, she gets it the next year when the book comes back around to it."

The next year's schoolbook won't necessarily present the concept at the same level - the presentation might be too difficult. If a child doesn't "get it", they might need a very basic instruction for the concept again.

The "how" something works is often called procedural understanding: the child knows how to work long division, or the procedure of fraction addition or fraction division, for example. It is often possible to learn the "how" mechanically without understanding why it works. Procedures learned this way are often forgotten very easily.

The relationship between the "how" and the "why" - or between procedures and concepts - is complex. One doesn't always come totally before the other, and it also varies from child to child.

You can try alternating the instruction: teach how to add fractions, and let the student practice. Explain why it works. Go back to some practice. Back and forth. Sooner or later it should 'stick' - but it might be next year instead of this one, or after 6 months instead of in this month.

As a rule of thumb, don't totally leave a topic until the student both knows how, and understands the 'why'.

Tip: you can often test a student's understanding of a topic by asking HIM to produce an example, preferably with a picture or other illustration: "Tell me an example of multiplying fractions by whole numbers, and draw a picture." Whatever gets produced can tell the teacher a lot about what has been understood.

---

See also
7 (?) Habits of Highly Effective Math Teaching:
Part 2: Remember the Goals
Part 3: Know Your Tools
Part 4: Living and Loving Math

Tags: math, teaching

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 years is probably excessive).

However, spiraling also has its own pitfalls: if your child doesn't get a concept, don't blindly "trust" the spiraling and think, "Well, she gets it the next year when the book comes back around to it."

The next year's schoolbook won't necessarily present the concept at the same level - the presentation might be too difficult. If a child doesn't "get it", they might need a very basic instruction for the concept again.

The "how" something works is often called procedural understanding: the child knows how to work long division, or the procedure of fraction addition or fraction division, for example. It is often possible to learn the "how" mechanically without understanding why it works. Procedures learned this way are often forgotten very easily.

The relationship between the "how" and the "why" - or between procedures and concepts - is complex. One doesn't always come totally before the other, and it also varies from child to child.

You can try alternating the instruction: teach how to add fractions, and let the student practice. Explain why it works. Go back to some practice. Back and forth. Sooner or later it should 'stick' - but it might be next year instead of this one, or after 6 months instead of in this month.

As a rule of thumb, don't totally leave a topic until the student both knows how, and understands the 'why'.

Tip: you can often test a student's understanding of a topic by asking HIM to produce an example, preferably with a picture or other illustration: "Tell me an example of multiplying fractions by whole numbers, and draw a picture." Whatever gets produced can tell the teacher a lot about what has been understood.

---

See also
7 (?) Habits of Highly Effective Math Teaching:
Part 2: Remember the Goals
Part 3: Know Your Tools
Part 4: Living and Loving Math

Tags: math, teaching

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 NurtureMinds.com 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) Cut-the-Knot.org 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 Opener Series? And that is not all.

Anyway, most of Cut The Knot is enjoyable for those who have studied high school math, and maybe even beyond. It's definitely like candy for anyone who loves mathematics in all its aspects, full of little puzzles and interesting facts. Go visit the home page to find links to the interactive puzzles.

I want to feature one page from the site, for all of you who think mathematics stops at high school calculus, or for you who see 'black hole' when you think about all the mathematics beyond high school.

No, I'm not meaning for you to study it all, but just check this page: DID YOU KNOW?

It's good to be aware of the fact that mathematics is an advancing science, and that typical school mathematics covers mathematical knowledge only up to about early 17th century (that is, if you take calculus).

3) Well this third one isn't a website. Just a reminder; you can still participate in the giveaways drawing.

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 NurtureMinds.com 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) Cut-the-Knot.org 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 Opener Series? And that is not all.

Anyway, most of Cut The Knot is enjoyable for those who have studied high school math, and maybe even beyond. It's definitely like candy for anyone who loves mathematics in all its aspects, full of little puzzles and interesting facts. Go visit the home page to find links to the interactive puzzles.

I want to feature one page from the site, for all of you who think mathematics stops at high school calculus, or for you who see 'black hole' when you think about all the mathematics beyond high school.

No, I'm not meaning for you to study it all, but just check this page: DID YOU KNOW?

It's good to be aware of the fact that mathematics is an advancing science, and that typical school mathematics covers mathematical knowledge only up to about early 17th century (that is, if you take calculus).

3) Well this third one isn't a website. Just a reminder; you can still participate in the giveaways drawing.

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:

http://astore.amazon.com/homeschoolmat-20

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:

http://astore.amazon.com/homeschoolmat-20

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 the only way to truly progres in mathematics studies, because when they are memorized, it
"...frees up working memory to master the arithmetic algorithms and tackle math applications. Students who do not memorize the basic number facts will founder as more complex operations are required, and their progress will likely grind to a halt by the end of elementary school."


3. The Standard Algorithms

Most states don't require that students know the standard algoritms for addition, subtraction, multiplication, and division!

"...They are guaranteed to work for all problems of the type for which they were designed. Knowing the standard algorithms, in the sense of being able to use them and understanding how and why they work, is the most sophisticated mathematics that an elementary school student is likely to grasp, and it is a foundational skill."

4. Fraction Development

Again, typically the standards don't pay too much attention to fractions. At high school level, studying rational functions relies heavily upon student's understanding of fraction arithmetic.

5. Patterns

Are they really that important?

"The attention given to patterns in state standards verges on the obsessive. In a typical document, students are asked, across many grade levels, to create, identify, examine, describe, extend, and find "the rule" for repeating, growing, and shrinking patterns, where the patterns may be found in numbers, shapes, tables, and graphs. "

6. Manipulatives

Typically the standards, again, place too much emphasis on the usage of manipulatives.

"...too much use of them runs the risk that students will focus on the manipulatives more than the math, and even come to depend on them."

7. Estimation

Too much emphasis on estimation skills as opposed to finding the exact result.

8. Probability and Statistics

Are these topics really needed in kindergarten through 6th grade?

"...sound math standards delay the introduction of probability until middle school, then proceed quickly by building on students' knowledge of fractions and ratios. Many states also include data collection standards that are excessive. Statistics and probability requirements often crowd out important topics in algebra and geometry."

9. Mathematical Reasoning and Problem-Solving

Typically the standards don't include much in the way of problem solving.

"Children should solve single-step word problems in the earliest grades and deal with increasingly more challenging, multi-step problems as they progress. "

---

So for the most part, beware of following state standards. Remember also that textbooks (at least those written for public schools) often follow state standards. But unfortunately, that won't necessarily make for good learning.

Tags: math, mathematics, standards

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 the only way to truly progres in mathematics studies, because when they are memorized, it
"...frees up working memory to master the arithmetic algorithms and tackle math applications. Students who do not memorize the basic number facts will founder as more complex operations are required, and their progress will likely grind to a halt by the end of elementary school."


3. The Standard Algorithms

Most states don't require that students know the standard algoritms for addition, subtraction, multiplication, and division!

"...They are guaranteed to work for all problems of the type for which they were designed. Knowing the standard algorithms, in the sense of being able to use them and understanding how and why they work, is the most sophisticated mathematics that an elementary school student is likely to grasp, and it is a foundational skill."

4. Fraction Development

Again, typically the standards don't pay too much attention to fractions. At high school level, studying rational functions relies heavily upon student's understanding of fraction arithmetic.

5. Patterns

Are they really that important?

"The attention given to patterns in state standards verges on the obsessive. In a typical document, students are asked, across many grade levels, to create, identify, examine, describe, extend, and find "the rule" for repeating, growing, and shrinking patterns, where the patterns may be found in numbers, shapes, tables, and graphs. "

6. Manipulatives

Typically the standards, again, place too much emphasis on the usage of manipulatives.

"...too much use of them runs the risk that students will focus on the manipulatives more than the math, and even come to depend on them."

7. Estimation

Too much emphasis on estimation skills as opposed to finding the exact result.

8. Probability and Statistics

Are these topics really needed in kindergarten through 6th grade?

"...sound math standards delay the introduction of probability until middle school, then proceed quickly by building on students' knowledge of fractions and ratios. Many states also include data collection standards that are excessive. Statistics and probability requirements often crowd out important topics in algebra and geometry."

9. Mathematical Reasoning and Problem-Solving

Typically the standards don't include much in the way of problem solving.

"Children should solve single-step word problems in the earliest grades and deal with increasingly more challenging, multi-step problems as they progress. "

---

So for the most part, beware of following state standards. Remember also that textbooks (at least those written for public schools) often follow state standards. But unfortunately, that won't necessarily make for good learning.

Tags: math, mathematics, standards

Giveaways

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!

Giveaways

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 discussion of the need and use of answer keys misses a key point, and I am writing to let you hear it.

The point is: there is a parallel world out there. In that world, people use the same words like math, geometry, textbooks, problems, etc. but these words have different meaning. You may judge for yourself how different it is.

In that world, a half of all children say they prefer math over languages and humanities (quote-unquote) *because in math you don't need to memorize anything*. In that world, the question "What can be done to make high school geometry less of a pain?" that HomeschoolMath experts are wrestling with, sounds an extreme form of absurd, because most students there refer to their geometry course as the most enjoyable learning experience. Authors of modern textbooks in that world warn their readers (I am quoting from memory): "even if you have not been good in math so far this may very well change because geometry is a different kind of math where your imagination and creativity matter most." Neither the authors nor their readers have ever heard of such oxymorons as "two-column proofs", "formal proofs", "informal proofs." Likewise, they cannot imagine that mathematics can be taught "without proofs". For, in that world math seeks deep, hidden relationships between seemingly unrelated matters, and, being a science, it is also concerned with *why* these relationships hold true.

Respectively, textbooks in that parallel world are not 700-pages long, 5 pound heavy, watery monsters prescribing daily diets for SAT-fitness, but ordinary books easy to read and carry around whose primary goal is to expose the subject (e.g. a math theory) as clearly and concisely as possible. "Teacher's editions" there are identical to student's ones, and the idea that for reading one book one may need another one that explains how to read the first one, would pass for a "postmaster" joke.

People in that world are not terrified with "word problems" and cannot imagine why anyone would be, as mathematics for them makes sense, and is a tool to make complicated matters simple, and not the other way around. Their teachers there understand the difference between concepts
and mere terms, and their students are embarrassed to answer questions, asking for mere rephrasing of definitions. The euphemism "strategies" for mechanical routines is not in use by the "parallel" people. They do prefer however the real problems which require thinking (not "a little" of it, but just as much as needed to find out what is true and why).

The question "How long are you ready to ponder over a math problem?" is replaced in that parallel world with "How little time may a math problem take to be worth your attention?" As a lower estimate, consider that getting into a college includes a written math test with 4 hours given for 5 problems. Respectively, it is not unusual - in that world - to spend the whole evening trying to solve 2-3 homework problems, or to fall asleep at midnight attempting the last one of them, and to wake up in the morning with a ready solution.

This picture of two parallel worlds may seem to you as surreal as Harry Potter's worlds of muggles and wizards, but there are two essential differences. One is that this parallel world is real, and exists not only in Eastern Europe, Russia, China, and in some past, but also to some extent here and now. The second difference is that you and your children *are welcome* in this parallel world. Those who choose to try moving there will get help; some will learn to fly (no broomsticks!), but most will at least learn how to walk without crutches.

However, if you plan to try yourself in the parallel world, you should be ready to live by its rules. The requests for teachers' scripts, parents' guides, solution manuals, and other crutches are understandable, but they may not be granted. Your children need to learn how to learn from ordinary books which expose scientific theories.

There is nothing inherently wrong with solution books to collections of math problems, they are found in the parallel world when needed, and people there know when and how to use them. "Kiselev's Geometry" has been in active use without such a solution book for over a century, which proves that in the parallel world the solution book for it is not needed. However in order to see this for yourself you need to read the book and solve the 600 problems. The choice whether to do this or not is of course yours.

Sincerely,

Alexander Givental



Tags: math, mathematics, teaching, geometry, philosophy

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 discussion of the need and use of answer keys misses a key point, and I am writing to let you hear it.

The point is: there is a parallel world out there. In that world, people use the same words like math, geometry, textbooks, problems, etc. but these words have different meaning. You may judge for yourself how different it is.

In that world, a half of all children say they prefer math over languages and humanities (quote-unquote) *because in math you don't need to memorize anything*. In that world, the question "What can be done to make high school geometry less of a pain?" that HomeschoolMath experts are wrestling with, sounds an extreme form of absurd, because most students there refer to their geometry course as the most enjoyable learning experience. Authors of modern textbooks in that world warn their readers (I am quoting from memory): "even if you have not been good in math so far this may very well change because geometry is a different kind of math where your imagination and creativity matter most." Neither the authors nor their readers have ever heard of such oxymorons as "two-column proofs", "formal proofs", "informal proofs." Likewise, they cannot imagine that mathematics can be taught "without proofs". For, in that world math seeks deep, hidden relationships between seemingly unrelated matters, and, being a science, it is also concerned with *why* these relationships hold true.

Respectively, textbooks in that parallel world are not 700-pages long, 5 pound heavy, watery monsters prescribing daily diets for SAT-fitness, but ordinary books easy to read and carry around whose primary goal is to expose the subject (e.g. a math theory) as clearly and concisely as possible. "Teacher's editions" there are identical to student's ones, and the idea that for reading one book one may need another one that explains how to read the first one, would pass for a "postmaster" joke.

People in that world are not terrified with "word problems" and cannot imagine why anyone would be, as mathematics for them makes sense, and is a tool to make complicated matters simple, and not the other way around. Their teachers there understand the difference between concepts
and mere terms, and their students are embarrassed to answer questions, asking for mere rephrasing of definitions. The euphemism "strategies" for mechanical routines is not in use by the "parallel" people. They do prefer however the real problems which require thinking (not "a little" of it, but just as much as needed to find out what is true and why).

The question "How long are you ready to ponder over a math problem?" is replaced in that parallel world with "How little time may a math problem take to be worth your attention?" As a lower estimate, consider that getting into a college includes a written math test with 4 hours given for 5 problems. Respectively, it is not unusual - in that world - to spend the whole evening trying to solve 2-3 homework problems, or to fall asleep at midnight attempting the last one of them, and to wake up in the morning with a ready solution.

This picture of two parallel worlds may seem to you as surreal as Harry Potter's worlds of muggles and wizards, but there are two essential differences. One is that this parallel world is real, and exists not only in Eastern Europe, Russia, China, and in some past, but also to some extent here and now. The second difference is that you and your children *are welcome* in this parallel world. Those who choose to try moving there will get help; some will learn to fly (no broomsticks!), but most will at least learn how to walk without crutches.

However, if you plan to try yourself in the parallel world, you should be ready to live by its rules. The requests for teachers' scripts, parents' guides, solution manuals, and other crutches are understandable, but they may not be granted. Your children need to learn how to learn from ordinary books which expose scientific theories.

There is nothing inherently wrong with solution books to collections of math problems, they are found in the parallel world when needed, and people there know when and how to use them. "Kiselev's Geometry" has been in active use without such a solution book for over a century, which proves that in the parallel world the solution book for it is not needed. However in order to see this for yourself you need to read the book and solve the 600 problems. The choice whether to do this or not is of course yours.

Sincerely,

Alexander Givental



Tags: math, mathematics, teaching, geometry, philosophy

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-step basis and presents curricula tailored to their individual skill levels.

Website: Store.CarnegieLearning.com. Normal prices (per course): $99 (software, textbook, install guide), $85 software only, $21 student text only. But you get 10% off with the coupon.


2) You get 20% off of any of the RightStart Math products at Ladybug Homeschool Supplies with the coupon code: Homeschoolmathdiscount. Order before Sept. 30, 2006.

RightStart Math is a manipulative based elementary program that teaches math facts with games. Their geometry program is for middle school, and is excellent beyond words; I've written a review of it, too.

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-step basis and presents curricula tailored to their individual skill levels.

Website: Store.CarnegieLearning.com. Normal prices (per course): $99 (software, textbook, install guide), $85 software only, $21 student text only. But you get 10% off with the coupon.


2) You get 20% off of any of the RightStart Math products at Ladybug Homeschool Supplies with the coupon code: Homeschoolmathdiscount. Order before Sept. 30, 2006.

RightStart Math is a manipulative based elementary program that teaches math facts with games. Their geometry program is for middle school, and is excellent beyond words; I've written a review of it, too.

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!

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 'contest' will have a total of 12 prizes - in a random drawing!

How to participate

To appreciate the generousness of the folks at The Math Forum AND also because I feel it is a great and valuable service and learning opportunity, we wish to spread the word about their Problem of the Week (PoW) activities.

So... the way to take part in the contest is if you spread the word about the contest and about the PoW service! I'll have a random drawing for the prizes after Friday, August 25th.

You can either

• Post on your blog, if you have one.


• Post on a message board, if you frequent one so that the people are already used to you posting something. This has to be a message board whose readers would be likely to be interested in The Math Forum PoW - preferably a homeschooling OR an educational message board.


• Email some of your friends about it - 3 at least. Please only email people who you feel would be interested. Send me a cc (carbon copy) of the email.


• If you have a different idea about how to spread the word, check with me first.

And don't forget to let me know. Leave a comment here, or email me at .

Whatever you write, include

• a clickable link to this blogpost (so people can find out about the contest). The address is http://homeschoolmath.blogspot.com/2006/08/homeschool-math-blog-giveaways-win.html
  


• and a link to The Math Forum Problem of the Week webpage
  http://mathforum.org/pow/pow.html


• Also, include this paragraph of text:

  The Math Forum's mission is to provide interactive learning services and a library of resources from the online mathematics community that enrich and support teaching and learning in an increasingly technological world.

If you feel your friends or readers would like this article, you're welcome to link to it too: Challenging problems in math and how to use a "Problem of the Week" activity (optional).

The drawing will be random, and performed after Friday, August 25th.

That's all folks! Happy contest time!

---

Disclaimer: The Math Forum provided the prize for the drawing to Maria Miller and HomeSchoolMath.net and has no other responsibility for the drawing, rules or promotion of the contest.


Tags: math, contest, giveaways

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 'contest' will have a total of 12 prizes - in a random drawing!

How to participate

To appreciate the generousness of the folks at The Math Forum AND also because I feel it is a great and valuable service and learning opportunity, we wish to spread the word about their Problem of the Week (PoW) activities.

So... the way to take part in the contest is if you spread the word about the contest and about the PoW service! I'll have a random drawing for the prizes after Friday, August 25th.

You can either

• Post on your blog, if you have one.


• Post on a message board, if you frequent one so that the people are already used to you posting something. This has to be a message board whose readers would be likely to be interested in The Math Forum PoW - preferably a homeschooling OR an educational message board.


• Email some of your friends about it - 3 at least. Please only email people who you feel would be interested. Send me a cc (carbon copy) of the email.


• If you have a different idea about how to spread the word, check with me first.

And don't forget to let me know. Leave a comment here, or email me at .

Whatever you write, include

• a clickable link to this blogpost (so people can find out about the contest). The address is http://homeschoolmath.blogspot.com/2006/08/homeschool-math-blog-giveaways-win.html
  


• and a link to The Math Forum Problem of the Week webpage
  http://mathforum.org/pow/pow.html


• Also, include this paragraph of text:

  The Math Forum's mission is to provide interactive learning services and a library of resources from the online mathematics community that enrich and support teaching and learning in an increasingly technological world.

If you feel your friends or readers would like this article, you're welcome to link to it too: Challenging problems in math and how to use a "Problem of the Week" activity (optional).

The drawing will be random, and performed after Friday, August 25th.

That's all folks! Happy contest time!

---

Disclaimer: The Math Forum provided the prize for the drawing to Maria Miller and HomeSchoolMath.net and has no other responsibility for the drawing, rules or promotion of the contest.


Tags: math, contest, giveaways

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
HOMESCHOOL MATH NEWSLETTER
- math teaching tips and news delivered monthly


remove
subscribe




Email List Management by Ezine Director

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
HOMESCHOOL MATH NEWSLETTER
- math teaching tips and news delivered monthly


remove
subscribe




Email List Management by Ezine Director

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.

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 "emphasize problem solving". They have charts about problem solving strategies. They have lessons which concentrate on a certain strategy. But, does that sort of thing really help the students a lot? If you know what strategy you're supposed to use on a problem, then the problems are easy. Sure, it helps to see examples of problem situations. But that is just "mild exercise" - it won't yet get your student to be a proficient problem solver in math.

And kids' minds NEED 'exercise' to grow, to develop. You need to feed the mind, and you need to provide good exercise. Most of the problems in a typical math book are to help the student learn concepts and procedures. Then some are 'applications' or word problems of some sort.

Often, lamentably, the word problems are in the end of a lesson and are solved using the same operation that is studied in the lesson. This just about leaves word problems with the status "last and least".

If you're like me, you wish something more for your students.

One way to add challenging problems to math education is using a Problem of the Week activity.

Those problems are more challenging, sometimes open-ended. The student can't just check an answer key but has to use that brain, struggle a little.

→ And this is where the soon upcoming BLOG CONTEST will come in! The Math Forum is going to donate some free memberships to their Problem of the Week service. I will post the details of this contest later (hopefully this coming Sunday), so stay tuned!

The Math Forum PoW service is truly of a professional quality. Some of the main features of the Math Forum PoWs are:

• The Math Forum PoWs come in four different flavors: Math Fundamentals (grades 3-5), Pre-algebra (grades 6-8), Algebra, and (high school) Geometry. Also available are special problem libraries for Discrete Math and Trig/Calculus.


• A student can revise his solution unlimited number of times (a fantastic feature!)


• Mentoring is available.
  (There are two kinds of mentoring offered: you can either pay an extra fee for it, or receive free mentoring which is subject to availability.)

As Suzanne Alejandre, Educational Resource & Service Developer from The Math Forum, says,

"Our research has shown that a student's mathematical thinking and their communication skills really improve if they are encouraged to revise. ... It's really a mindset -- it's that idea that you treat problem solving as you would the writing process.
You have a draft, you reflect, you talk with peers or someone (like the teacher) who has read your first draft, you write a second draft, you reflect, etc."

I've written more about this topic so please continue reading: Challenging problems and how to use a "Problem of the Week" activity in homeschooling.



Tags: math, mathematics

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 "emphasize problem solving". They have charts about problem solving strategies. They have lessons which concentrate on a certain strategy. But, does that sort of thing really help the students a lot? If you know what strategy you're supposed to use on a problem, then the problems are easy. Sure, it helps to see examples of problem situations. But that is just "mild exercise" - it won't yet get your student to be a proficient problem solver in math.

And kids' minds NEED 'exercise' to grow, to develop. You need to feed the mind, and you need to provide good exercise. Most of the problems in a typical math book are to help the student learn concepts and procedures. Then some are 'applications' or word problems of some sort.

Often, lamentably, the word problems are in the end of a lesson and are solved using the same operation that is studied in the lesson. This just about leaves word problems with the status "last and least".

If you're like me, you wish something more for your students.

One way to add challenging problems to math education is using a Problem of the Week activity.

Those problems are more challenging, sometimes open-ended. The student can't just check an answer key but has to use that brain, struggle a little.

→ And this is where the soon upcoming BLOG CONTEST will come in! The Math Forum is going to donate some free memberships to their Problem of the Week service. I will post the details of this contest later (hopefully this coming Sunday), so stay tuned!

The Math Forum PoW service is truly of a professional quality. Some of the main features of the Math Forum PoWs are:

• The Math Forum PoWs come in four different flavors: Math Fundamentals (grades 3-5), Pre-algebra (grades 6-8), Algebra, and (high school) Geometry. Also available are special problem libraries for Discrete Math and Trig/Calculus.


• A student can revise his solution unlimited number of times (a fantastic feature!)


• Mentoring is available.
  (There are two kinds of mentoring offered: you can either pay an extra fee for it, or receive free mentoring which is subject to availability.)

As Suzanne Alejandre, Educational Resource & Service Developer from The Math Forum, says,

"Our research has shown that a student's mathematical thinking and their communication skills really improve if they are encouraged to revise. ... It's really a mindset -- it's that idea that you treat problem solving as you would the writing process.
You have a draft, you reflect, you talk with peers or someone (like the teacher) who has read your first draft, you write a second draft, you reflect, etc."

I've written more about this topic so please continue reading: Challenging problems and how to use a "Problem of the Week" activity in homeschooling.



Tags: math, mathematics

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.

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.

Moogle Papercraft

One of the most loveable characters to come out of the Final Fantasy series is the Moogle (Moguri, Japanese), they are small, good-natured creatures that are usually white or tan in color and has a protruding antenna from its head with a small red, orange, or yellow ball at the end called a "pompom". They have either red or purple wings with ears shaped like a cat or rabbit. You'll know it's a moogle when you hear or see the word "kupo" which is their trademark sound. Next to Chocobos, the Moogles are often considered mascots for the Final Fantasy series. They first appeared on Final Fantasy III for the Famicom (Eurasia) and as Final Fantasy VI for the SNES is North America. Square Enix is going to bring an enhanced remake of Final Fantasy III, updated with 3D visuals to the Nintendo DS by November 2006. Of course Japan will have it first by 08.06 then Europe by 09.06, then finally NA. This moogle paper model was hosted by Takuya, but their site is down so I hope they won't mind if I host it in rapidshare. Enjoy!

Moogle Papercraft [via mediafire]

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.

Tags: math, logic, gifted

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.

Tags: math, logic, gifted

Update - 08.01.06

I've been receiving a lot of email with regards to Ryo's paper models changing address all the time, I haven't had the time to ask him why, so I've decided to put them up in a bundle (zipped) for easy downloading, I only included those paper models that I've already done and posted on this site, if you want to see or download Ryo's other works then head on to his site.

Ryo Tokisato - Web Site

Catbus (Nekobasu)

Here's the Catbus paper model from the movie "My Neighbor Totoro" (Tonari no Totoro), which was created by the famous anime film maker, Hayao Miyazaki. This paper model is pretty basic, cut-score-fold-glue. There are two types of format for you to choose from, one is in JPG and the other is PDF. The finished paper model is quite small, about 8cm L x 2cm W x 4cm H. Now you have a new Ghibli paper model to go along with Totoro.

Catbus PDF - Download

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!

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!

Life without answer keys?

Recently I've been exchanging emails with Alexander Givental, who has translated the famous Russian book Kiselev's Geometry into English.

He's raised some interesting points regarding answer keys. I will just quote him directly from his emails to me. The discussion concerns geometry problems (please see the earlier post for examples).

"What is actually accomplished by supplying any solution at all? Ideally a student should be able not only to find a solution himself, but also be able to check that his solution is correct. With the aid of a written colution, the exercise is rendered useless for both purposes. Furthermore, a beginning student who finds a more complex solution (or may be even the same solution but eplained differently) may decide - incorrectly! - that his solution was wrong.

So, comparing your solution with your classmate's, teacher's, or parent's one makes sense, but with the one written in a silent book - very little. That's why, I think, no one bothered to write solutions for "Kiselev".

There is one general problem with solution books: there are many ways to describe the same solution to a problem, and there may be many solutions to the same problem; so it requires just as much expertise from a reader to figure out if his own solution is correct by reading somebody else's solution as it would without it. That is why collections of problems *with* solutions (which do exist in geometry), typically deal with higher range of difficulty than Kiselev's problems, are written in a very concise style and intended for highly experienced readers. BTW, for more than a hundred years of systematic use of Kiselev's book in Russia, it didn't occur to anyone to publish a solution manual. This should tell you something.

Teacher's guides are intended to save a teacher, clueless about the subject he teaches, from the embarassment in front of the class. They don't make him less clueless for, if they did, then teacher's guides would be used in place of textbooks. With or without teacher's guides,
a clueless instructor - teacher or parent - is of little help to the student. Conclusion: teacher's guides are obstructions to learning - for the instructor, and therefore for the student."

I agree with some things here. Being able to check that your solution is right is indeed desirable. After all, real life situations won't come with an answer key either. You need to be pretty sure about your solution then.

But, I'm sure answer keys save many homeschooling families many frustration tears.

Maybe it would work if every parent had someone to turn to in moments of problems - support. It could be another person, or internet message board.

Maybe the existence of answer keys reflects the culture and the times: we want everything fast and easy. Even answers to math problems. No one wants to ponder on a math problem for more than ___ (fill in) minutes.

What do you think?

See also Challenging problems in math education

Life without answer keys?

Recently I've been exchanging emails with Alexander Givental, who has translated the famous Russian book Kiselev's Geometry into English.

He's raised some interesting points regarding answer keys. I will just quote him directly from his emails to me. The discussion concerns geometry problems (please see the earlier post for examples).

"What is actually accomplished by supplying any solution at all? Ideally a student should be able not only to find a solution himself, but also be able to check that his solution is correct. With the aid of a written colution, the exercise is rendered useless for both purposes. Furthermore, a beginning student who finds a more complex solution (or may be even the same solution but eplained differently) may decide - incorrectly! - that his solution was wrong.

So, comparing your solution with your classmate's, teacher's, or parent's one makes sense, but with the one written in a silent book - very little. That's why, I think, no one bothered to write solutions for "Kiselev".

There is one general problem with solution books: there are many ways to describe the same solution to a problem, and there may be many solutions to the same problem; so it requires just as much expertise from a reader to figure out if his own solution is correct by reading somebody else's solution as it would without it. That is why collections of problems *with* solutions (which do exist in geometry), typically deal with higher range of difficulty than Kiselev's problems, are written in a very concise style and intended for highly experienced readers. BTW, for more than a hundred years of systematic use of Kiselev's book in Russia, it didn't occur to anyone to publish a solution manual. This should tell you something.

Teacher's guides are intended to save a teacher, clueless about the subject he teaches, from the embarassment in front of the class. They don't make him less clueless for, if they did, then teacher's guides would be used in place of textbooks. With or without teacher's guides,
a clueless instructor - teacher or parent - is of little help to the student. Conclusion: teacher's guides are obstructions to learning - for the instructor, and therefore for the student."

I agree with some things here. Being able to check that your solution is right is indeed desirable. After all, real life situations won't come with an answer key either. You need to be pretty sure about your solution then.

But, I'm sure answer keys save many homeschooling families many frustration tears.

Maybe it would work if every parent had someone to turn to in moments of problems - support. It could be another person, or internet message board.

Maybe the existence of answer keys reflects the culture and the times: we want everything fast and easy. Even answers to math problems. No one wants to ponder on a math problem for more than ___ (fill in) minutes.

What do you think?

See also Challenging problems in math education