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.
Tuesday, November 29, 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.
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.
Sunday, November 27, 2005
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.
No one ever mentioned those papers in class again. She never knew if they discussed them after class or with their parents, but it didn't matter. The exercise had accomplished its purpose. The students were happy with themselves and one another. That group of students moved on.
Several years later, one of the students was killed in Viet Nam and his teacher attended the funeral of that special student. She had never seen a serviceman in a military coffin before. He looked so handsome, so mature.
The church was packed with his friends. One by one those who loved him took a last walk by the coffin. The teacher was the last one to bless the coffin.
As she stood there, one of the soldiers who acted as pallbearer came up to her. "Were you Mark's math teacher?" he asked. She nodded: "yes." Then he said: "Mark talked about you a lot."
After the funeral, most of Mark's former classmates went together to a luncheon. Mark's mother and father were there, obviously waiting to speak with his teacher.
"We want to show you something," his father said, taking a wallet out of his pocket. "They found this on Mark when he was killed. We thought you might recognize it."
Opening the billfold, he carefully removed two worn pieces of notebook paper that had obviously been taped, folded and refolded many times. The teacher knew without looking that the papers were the ones on which she had listed all the good things each of Mark's classmates had said about him.
"Thank you so much for doing that," Mark's mother said. "As you can see, Mark treasured it."
All of Mark's former classmates started to gather around. Charlie smiled rather sheepishly and said, "I still have my list. It's in the top drawer of my desk at home."
Chuck's wife said, "Chuck asked me to put his in our wedding album."
"I have mine too," Marilyn said. "It's in my diary."
Then Vicki, another classmate, reached into her pocketbook, took out her wallet and showed her worn and frazzled list to the group. "I carry this with me at all times," Vicki said and without batting an eyelash, she continued: "I think we all saved our lists."
That's when the teacher finally sat down and cried. She cried for Mark and for all his friends who would never see him again.
The density of people in society is so thick that we forget that life will end one day. And we don't know when that one day will be.
So please, tell the people you love and care for, that they are special and important. Tell them, before it is too late.
And One Way To Accomplish This Is: Forward this message on. If you do not send it, you will have, once again passed up the wonderful opportunity to do something nice and beautiful.
If you've received this, it is because someone cares for you and it means there is probably at least someone for whom you care.
If you're "too busy" to take those few minutes right now to forward this message on, would this be the VERY first time you didn't do that little thing that would make a difference in your relationships?
The more people that you send this to, the better you'll be at reaching out to those you care about.
Remember, you reap what you sow. What you put into the lives of others comes back into your own.
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.
No one ever mentioned those papers in class again. She never knew if they discussed them after class or with their parents, but it didn't matter. The exercise had accomplished its purpose. The students were happy with themselves and one another. That group of students moved on.
Several years later, one of the students was killed in Viet Nam and his teacher attended the funeral of that special student. She had never seen a serviceman in a military coffin before. He looked so handsome, so mature.
The church was packed with his friends. One by one those who loved him took a last walk by the coffin. The teacher was the last one to bless the coffin.
As she stood there, one of the soldiers who acted as pallbearer came up to her. "Were you Mark's math teacher?" he asked. She nodded: "yes." Then he said: "Mark talked about you a lot."
After the funeral, most of Mark's former classmates went together to a luncheon. Mark's mother and father were there, obviously waiting to speak with his teacher.
"We want to show you something," his father said, taking a wallet out of his pocket. "They found this on Mark when he was killed. We thought you might recognize it."
Opening the billfold, he carefully removed two worn pieces of notebook paper that had obviously been taped, folded and refolded many times. The teacher knew without looking that the papers were the ones on which she had listed all the good things each of Mark's classmates had said about him.
"Thank you so much for doing that," Mark's mother said. "As you can see, Mark treasured it."
All of Mark's former classmates started to gather around. Charlie smiled rather sheepishly and said, "I still have my list. It's in the top drawer of my desk at home."
Chuck's wife said, "Chuck asked me to put his in our wedding album."
"I have mine too," Marilyn said. "It's in my diary."
Then Vicki, another classmate, reached into her pocketbook, took out her wallet and showed her worn and frazzled list to the group. "I carry this with me at all times," Vicki said and without batting an eyelash, she continued: "I think we all saved our lists."
That's when the teacher finally sat down and cried. She cried for Mark and for all his friends who would never see him again.
The density of people in society is so thick that we forget that life will end one day. And we don't know when that one day will be.
So please, tell the people you love and care for, that they are special and important. Tell them, before it is too late.
And One Way To Accomplish This Is: Forward this message on. If you do not send it, you will have, once again passed up the wonderful opportunity to do something nice and beautiful.
If you've received this, it is because someone cares for you and it means there is probably at least someone for whom you care.
If you're "too busy" to take those few minutes right now to forward this message on, would this be the VERY first time you didn't do that little thing that would make a difference in your relationships?
The more people that you send this to, the better you'll be at reaching out to those you care about.
Remember, you reap what you sow. What you put into the lives of others comes back into your own.
May Your Day Be Blessed As Special As You Are
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.
No one ever mentioned those papers in class again. She never knew if they discussed them after class or with their parents, but it didn't matter. The exercise had accomplished its purpose. The students were happy with themselves and one another. That group of students moved on.
Several years later, one of the students was killed in Viet Nam and his teacher attended the funeral of that special student. She had never seen a serviceman in a military coffin before. He looked so handsome, so mature.
The church was packed with his friends. One by one those who loved him took a last walk by the coffin. The teacher was the last one to bless the coffin.
As she stood there, one of the soldiers who acted as pallbearer came up to her. "Were you Mark's math teacher?" he asked. She nodded: "yes." Then he said: "Mark talked about you a lot."
After the funeral, most of Mark's former classmates went together to a luncheon. Mark's mother and father were there, obviously waiting to speak with his teacher.
"We want to show you something," his father said, taking a wallet out of his pocket. "They found this on Mark when he was killed. We thought you might recognize it."
Opening the billfold, he carefully removed two worn pieces of notebook paper that had obviously been taped, folded and refolded many times. The teacher knew without looking that the papers were the ones on which she had listed all the good things each of Mark's classmates had said about him.
"Thank you so much for doing that," Mark's mother said. "As you can see, Mark treasured it."
All of Mark's former classmates started to gather around. Charlie smiled rather sheepishly and said, "I still have my list. It's in the top drawer of my desk at home."
Chuck's wife said, "Chuck asked me to put his in our wedding album."
"I have mine too," Marilyn said. "It's in my diary."
Then Vicki, another classmate, reached into her pocketbook, took out her wallet and showed her worn and frazzled list to the group. "I carry this with me at all times," Vicki said and without batting an eyelash, she continued: "I think we all saved our lists."
That's when the teacher finally sat down and cried. She cried for Mark and for all his friends who would never see him again.
The density of people in society is so thick that we forget that life will end one day. And we don't know when that one day will be.
So please, tell the people you love and care for, that they are special and important. Tell them, before it is too late.
And One Way To Accomplish This Is: Forward this message on. If you do not send it, you will have, once again passed up the wonderful opportunity to do something nice and beautiful.
If you've received this, it is because someone cares for you and it means there is probably at least someone for whom you care.
If you're "too busy" to take those few minutes right now to forward this message on, would this be the VERY first time you didn't do that little thing that would make a difference in your relationships?
The more people that you send this to, the better you'll be at reaching out to those you care about.
Remember, you reap what you sow. What you put into the lives of others comes back into your own.
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.
No one ever mentioned those papers in class again. She never knew if they discussed them after class or with their parents, but it didn't matter. The exercise had accomplished its purpose. The students were happy with themselves and one another. That group of students moved on.
Several years later, one of the students was killed in Viet Nam and his teacher attended the funeral of that special student. She had never seen a serviceman in a military coffin before. He looked so handsome, so mature.
The church was packed with his friends. One by one those who loved him took a last walk by the coffin. The teacher was the last one to bless the coffin.
As she stood there, one of the soldiers who acted as pallbearer came up to her. "Were you Mark's math teacher?" he asked. She nodded: "yes." Then he said: "Mark talked about you a lot."
After the funeral, most of Mark's former classmates went together to a luncheon. Mark's mother and father were there, obviously waiting to speak with his teacher.
"We want to show you something," his father said, taking a wallet out of his pocket. "They found this on Mark when he was killed. We thought you might recognize it."
Opening the billfold, he carefully removed two worn pieces of notebook paper that had obviously been taped, folded and refolded many times. The teacher knew without looking that the papers were the ones on which she had listed all the good things each of Mark's classmates had said about him.
"Thank you so much for doing that," Mark's mother said. "As you can see, Mark treasured it."
All of Mark's former classmates started to gather around. Charlie smiled rather sheepishly and said, "I still have my list. It's in the top drawer of my desk at home."
Chuck's wife said, "Chuck asked me to put his in our wedding album."
"I have mine too," Marilyn said. "It's in my diary."
Then Vicki, another classmate, reached into her pocketbook, took out her wallet and showed her worn and frazzled list to the group. "I carry this with me at all times," Vicki said and without batting an eyelash, she continued: "I think we all saved our lists."
That's when the teacher finally sat down and cried. She cried for Mark and for all his friends who would never see him again.
The density of people in society is so thick that we forget that life will end one day. And we don't know when that one day will be.
So please, tell the people you love and care for, that they are special and important. Tell them, before it is too late.
And One Way To Accomplish This Is: Forward this message on. If you do not send it, you will have, once again passed up the wonderful opportunity to do something nice and beautiful.
If you've received this, it is because someone cares for you and it means there is probably at least someone for whom you care.
If you're "too busy" to take those few minutes right now to forward this message on, would this be the VERY first time you didn't do that little thing that would make a difference in your relationships?
The more people that you send this to, the better you'll be at reaching out to those you care about.
Remember, you reap what you sow. What you put into the lives of others comes back into your own.
May Your Day Be Blessed As Special As You Are
Saturday, November 26, 2005
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.
.
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.
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.
.
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.
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.
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.
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.
Wednesday, November 23, 2005
Fun math and math appreciation
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 the mathematical cat who seems pretty lazy but often gets interested in her mistress' math papers and thus ends up learning about this and that in math.
For example, you get to encounter 0s and 1s (binary numbers), fractals, infinity, Mobious strip, Pascal triangle, golden rectangles, paperfolding, tessellations, abacus, magic squares, tangrams, nanoworld... For math geeks, these are familiar topics. They show some of the beautiful or fun or intriguing aspects of math.
You could almost say this book is about "Math appreciation". We are told to teach our kids art appreciation, to teach them to appreciate fine arts, paintings, sculptures. In my opinion, learning about these fascinating math topics can go a long way towards teaching children to appreciate math.
Read the complete review here.
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 the mathematical cat who seems pretty lazy but often gets interested in her mistress' math papers and thus ends up learning about this and that in math.
For example, you get to encounter 0s and 1s (binary numbers), fractals, infinity, Mobious strip, Pascal triangle, golden rectangles, paperfolding, tessellations, abacus, magic squares, tangrams, nanoworld... For math geeks, these are familiar topics. They show some of the beautiful or fun or intriguing aspects of math.You could almost say this book is about "Math appreciation
". We are told to teach our kids art appreciation, to teach them to appreciate fine arts, paintings, sculptures. In my opinion, learning about these fascinating math topics can go a long way towards teaching children to appreciate math.Read the complete review here.
Fun math and math appreciation
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 the mathematical cat who seems pretty lazy but often gets interested in her mistress' math papers and thus ends up learning about this and that in math.
For example, you get to encounter 0s and 1s (binary numbers), fractals, infinity, Mobious strip, Pascal triangle, golden rectangles, paperfolding, tessellations, abacus, magic squares, tangrams, nanoworld... For math geeks, these are familiar topics. They show some of the beautiful or fun or intriguing aspects of math.
You could almost say this book is about "Math appreciation". We are told to teach our kids art appreciation, to teach them to appreciate fine arts, paintings, sculptures. In my opinion, learning about these fascinating math topics can go a long way towards teaching children to appreciate math.
Read the complete review here.
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 the mathematical cat who seems pretty lazy but often gets interested in her mistress' math papers and thus ends up learning about this and that in math.
For example, you get to encounter 0s and 1s (binary numbers), fractals, infinity, Mobious strip, Pascal triangle, golden rectangles, paperfolding, tessellations, abacus, magic squares, tangrams, nanoworld... For math geeks, these are familiar topics. They show some of the beautiful or fun or intriguing aspects of math.You could almost say this book is about "Math appreciation
". We are told to teach our kids art appreciation, to teach them to appreciate fine arts, paintings, sculptures. In my opinion, learning about these fascinating math topics can go a long way towards teaching children to appreciate math.Read the complete review here.
Tuesday, November 22, 2005
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 plastic bears and blocks too.
I do love the fact that she's interested, and is doing it on her own even.
And I'm sure most kids do the same - we educators just should try not to kill the little child's enthusiasm as school years go on.
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 plastic bears and blocks too.
I do love the fact that she's interested, and is doing it on her own even.
And I'm sure most kids do the same - we educators just should try not to kill the little child's enthusiasm as school years go on.
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 plastic bears and blocks too.
I do love the fact that she's interested, and is doing it on her own even.
And I'm sure most kids do the same - we educators just should try not to kill the little child's enthusiasm as school years go on.
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 plastic bears and blocks too.
I do love the fact that she's interested, and is doing it on her own even.
And I'm sure most kids do the same - we educators just should try not to kill the little child's enthusiasm as school years go on.
Thursday, November 17, 2005
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 ('drill') helps too. And why not have the kids draw number lines. I'm sure you can think of other ideas (welcome to comment!).
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 ('drill') helps too. And why not have the kids draw number lines. I'm sure you can think of other ideas (welcome to comment!).
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 ('drill') helps too. And why not have the kids draw number lines. I'm sure you can think of other ideas (welcome to comment!).
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 ('drill') helps too. And why not have the kids draw number lines. I'm sure you can think of other ideas (welcome to comment!).
Tuesday, November 15, 2005
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.
Anyway, if you are lacking in this topic, Barry's article summarizes nicely how math wars and fuzzy math began, what has been going on, and how the wars are now (unfortunately) turning into politics instead of being purely an academic debate.
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.
Anyway, if you are lacking in this topic, Barry's article summarizes nicely how math wars and fuzzy math began, what has been going on, and how the wars are now (unfortunately) turning into politics instead of being purely an academic debate.
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.
Anyway, if you are lacking in this topic, Barry's article summarizes nicely how math wars and fuzzy math began, what has been going on, and how the wars are now (unfortunately) turning into politics instead of being purely an academic debate.
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.
Anyway, if you are lacking in this topic, Barry's article summarizes nicely how math wars and fuzzy math began, what has been going on, and how the wars are now (unfortunately) turning into politics instead of being purely an academic debate.
Study order of the ebooks
Posted a short article about in which order to study the ebooks to answer questions from customers.
Study order of the ebooks
Posted a short article about in which order to study the ebooks to answer questions from customers.
Sunday, November 13, 2005
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.
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.
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.
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.
Wednesday, November 9, 2005
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.
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.
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.
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 have a goal for the first grade (or first part of first grade) that the student understands certain things about addition and subtraction, understands tens and ones, and knows by heart certain basic addition facts. You want mastery in those topics, so you concentrate on them.
Then, the next goals could be hundreds/tens/ones, and adding and subtracting two and three-digit numbers.
Then could come concept of multiplication, and memorizing the times tables.
You may have more or deeper goals -- you should check your state standards what they say also; these are just examples. I am NOT saying you should teach exactly this way or in this order. It depends on the child, on various standards, on the curriculum. For example I know some people introduce multiplication concept in first grade along with the other operations.
But focusing on a few closely connected topics, with the goal of mastery, is the idea.
Hope this helps.
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 have a goal for the first grade (or first part of first grade) that the student understands certain things about addition and subtraction, understands tens and ones, and knows by heart certain basic addition facts. You want mastery in those topics, so you concentrate on them.
Then, the next goals could be hundreds/tens/ones, and adding and subtracting two and three-digit numbers.
Then could come concept of multiplication, and memorizing the times tables.
You may have more or deeper goals -- you should check your state standards what they say also; these are just examples. I am NOT saying you should teach exactly this way or in this order. It depends on the child, on various standards, on the curriculum. For example I know some people introduce multiplication concept in first grade along with the other operations.
But focusing on a few closely connected topics, with the goal of mastery, is the idea.
Hope this helps.
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 have a goal for the first grade (or first part of first grade) that the student understands certain things about addition and subtraction, understands tens and ones, and knows by heart certain basic addition facts. You want mastery in those topics, so you concentrate on them.
Then, the next goals could be hundreds/tens/ones, and adding and subtracting two and three-digit numbers.
Then could come concept of multiplication, and memorizing the times tables.
You may have more or deeper goals -- you should check your state standards what they say also; these are just examples. I am NOT saying you should teach exactly this way or in this order. It depends on the child, on various standards, on the curriculum. For example I know some people introduce multiplication concept in first grade along with the other operations.
But focusing on a few closely connected topics, with the goal of mastery, is the idea.
Hope this helps.
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 have a goal for the first grade (or first part of first grade) that the student understands certain things about addition and subtraction, understands tens and ones, and knows by heart certain basic addition facts. You want mastery in those topics, so you concentrate on them.
Then, the next goals could be hundreds/tens/ones, and adding and subtracting two and three-digit numbers.
Then could come concept of multiplication, and memorizing the times tables.
You may have more or deeper goals -- you should check your state standards what they say also; these are just examples. I am NOT saying you should teach exactly this way or in this order. It depends on the child, on various standards, on the curriculum. For example I know some people introduce multiplication concept in first grade along with the other operations.
But focusing on a few closely connected topics, with the goal of mastery, is the idea.
Hope this helps.
Monday, November 7, 2005
Mathematics is all about... ?
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 mathematical laws governing them. Those nature objects are fractal-like.
Check this introduction to fractals or fractal lessons for middle school to learn a little bit. Then go check some nature fractals.
I love it when natural beauty and mathematics connect.
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 mathematical laws governing them. Those nature objects are fractal-like.
Check this introduction to fractals or fractal lessons for middle school to learn a little bit. Then go check some nature fractals.
I love it when natural beauty and mathematics connect.
Mathematics is all about... ?
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 mathematical laws governing them. Those nature objects are fractal-like.
Check this introduction to fractals or fractal lessons for middle school to learn a little bit. Then go check some nature fractals.
I love it when natural beauty and mathematics connect.
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 mathematical laws governing them. Those nature objects are fractal-like.
Check this introduction to fractals or fractal lessons for middle school to learn a little bit. Then go check some nature fractals.
I love it when natural beauty and mathematics connect.
Friday, November 4, 2005
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.
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.
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.
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.
Thursday, November 3, 2005
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).
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).
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).
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).
Wednesday, November 2, 2005
It's easy when it's Bear Math
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.
It's easy when it's Bear Math
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.
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