This is a very interesting piece of research, and I personally believe in this "effect": that a teacher's attitude towards math can easily be passed on to his/her students.
In this case, all the teachers studied were elementary and female. I figure the same could happen with male teachers too, affecting boys, if the teacher feared and/or disliked math. It's just a lot less likely because most elementary teachers are female, and also because math anxiety is more common among females.
Girls may learn math anxiety from female teachers
The article also points to the best solution: the elementary teachers need trained much better in math so they can teach it confidently, including teaching the concepts and the 'why's of math.
Elsewhere:
Girls inheriting math anxiety from female teachers? at Casting Out Nines
Showing posts with label attitudes towards math. Show all posts
Showing posts with label attitudes towards math. Show all posts
Wednesday, January 27, 2010
Female teachers pass math anxiety to girls
This is a very interesting piece of research, and I personally believe in this "effect": that a teacher's attitude towards math can easily be passed on to his/her students.
In this case, all the teachers studied were elementary and female. I figure the same could happen with male teachers too, affecting boys, if the teacher feared and/or disliked math. It's just a lot less likely because most elementary teachers are female, and also because math anxiety is more common among females.
Girls may learn math anxiety from female teachers
The article also points to the best solution: the elementary teachers need trained much better in math so they can teach it confidently, including teaching the concepts and the 'why's of math.
Elsewhere:
Girls inheriting math anxiety from female teachers? at Casting Out Nines
In this case, all the teachers studied were elementary and female. I figure the same could happen with male teachers too, affecting boys, if the teacher feared and/or disliked math. It's just a lot less likely because most elementary teachers are female, and also because math anxiety is more common among females.
Girls may learn math anxiety from female teachers
The article also points to the best solution: the elementary teachers need trained much better in math so they can teach it confidently, including teaching the concepts and the 'why's of math.
Elsewhere:
Girls inheriting math anxiety from female teachers? at Casting Out Nines
Saturday, June 14, 2008
High school math after algebra, geometry, and consumer math?
Question:
"I am a homeschooling mom, with two children still at home. We use Switched On Schoolhouse almost exclusively. My son will be a senior this fall. He took Algebra 1 and geometry but was against taking trig. I had him take Consumer Math this year and I am trying to find him something for his senior year. He is not leaning towards college, but perhaps a tech school. ANY advice you can give will be greatly appreciated! Thanks!"
Well, if you don't want to do trig or algebra 2, consider the book Mathematics, a Human Endeavor: A Textbook for Those Who Think They Don't Like the Subject
.
This book by Harold Jacobs covers a wide range of mathematical topics, aiming to show students how interesting math can be. The topics include for example number tricks, inductive reasoning, deductive reasoning, number sequences, functions and their graphs, large numbers and logarithms, polygons and symmetry, mathematical curves, probability, and topology.
Jacobs always gives you problems where you have to investigate and find out patterns. He aims to minimize the usage of formulas, shows all kinds of interesting ideas and tricks, and thus lets the student fall in love with mathematics.
More info:
Harold Jacobs Mathematics Human Endeavor Curriculum
Review by TOS
Review of Harold Jacobs books by Susan Richman.
Mathematics, a Human Endeavor at Amazon.
"I am a homeschooling mom, with two children still at home. We use Switched On Schoolhouse almost exclusively. My son will be a senior this fall. He took Algebra 1 and geometry but was against taking trig. I had him take Consumer Math this year and I am trying to find him something for his senior year. He is not leaning towards college, but perhaps a tech school. ANY advice you can give will be greatly appreciated! Thanks!"
Well, if you don't want to do trig or algebra 2, consider the book Mathematics, a Human Endeavor: A Textbook for Those Who Think They Don't Like the Subject
.This book by Harold Jacobs covers a wide range of mathematical topics, aiming to show students how interesting math can be. The topics include for example number tricks, inductive reasoning, deductive reasoning, number sequences, functions and their graphs, large numbers and logarithms, polygons and symmetry, mathematical curves, probability, and topology.
Jacobs always gives you problems where you have to investigate and find out patterns. He aims to minimize the usage of formulas, shows all kinds of interesting ideas and tricks, and thus lets the student fall in love with mathematics.
More info:
Harold Jacobs Mathematics Human Endeavor Curriculum
Review by TOS
Review of Harold Jacobs books by Susan Richman.
Mathematics, a Human Endeavor at Amazon
.
High school math after algebra, geometry, and consumer math?
Question:
"I am a homeschooling mom, with two children still at home. We use Switched On Schoolhouse almost exclusively. My son will be a senior this fall. He took Algebra 1 and geometry but was against taking trig. I had him take Consumer Math this year and I am trying to find him something for his senior year. He is not leaning towards college, but perhaps a tech school. ANY advice you can give will be greatly appreciated! Thanks!"
Well, if you don't want to do trig or algebra 2, consider the book Mathematics, a Human Endeavor: A Textbook for Those Who Think They Don't Like the Subject.
This book by Harold Jacobs covers a wide range of mathematical topics, aiming to show students how interesting math can be. The topics include for example number tricks, inductive reasoning, deductive reasoning, number sequences, functions and their graphs, large numbers and logarithms, polygons and symmetry, mathematical curves, probability, and topology.
Jacobs always gives you problems where you have to investigate and find out patterns. He aims to minimize the usage of formulas, shows all kinds of interesting ideas and tricks, and thus lets the student fall in love with mathematics.
More info:
Harold Jacobs Mathematics Human Endeavor Curriculum
Review by TOS
Review of Harold Jacobs books by Susan Richman.
Mathematics, a Human Endeavor at Amazon.
"I am a homeschooling mom, with two children still at home. We use Switched On Schoolhouse almost exclusively. My son will be a senior this fall. He took Algebra 1 and geometry but was against taking trig. I had him take Consumer Math this year and I am trying to find him something for his senior year. He is not leaning towards college, but perhaps a tech school. ANY advice you can give will be greatly appreciated! Thanks!"
Well, if you don't want to do trig or algebra 2, consider the book Mathematics, a Human Endeavor: A Textbook for Those Who Think They Don't Like the Subject
.This book by Harold Jacobs covers a wide range of mathematical topics, aiming to show students how interesting math can be. The topics include for example number tricks, inductive reasoning, deductive reasoning, number sequences, functions and their graphs, large numbers and logarithms, polygons and symmetry, mathematical curves, probability, and topology.
Jacobs always gives you problems where you have to investigate and find out patterns. He aims to minimize the usage of formulas, shows all kinds of interesting ideas and tricks, and thus lets the student fall in love with mathematics.
More info:
Harold Jacobs Mathematics Human Endeavor Curriculum
Review by TOS
Review of Harold Jacobs books by Susan Richman.
Mathematics, a Human Endeavor at Amazon
.
Monday, March 19, 2007
Developing positive attitude
What are the incentives needed in order to develop a positive attitude in children and other students towards mathematics?
I am not sure if (special) incentives is the main factor in developing a positive attitude towards mathematics.
I feel it is probably sufficient to get a few of the basics right, and then that alone will take care of most of it, and students can like math just fine.
Disliking math is not something that is inherent in us or in our kids. Little kids don't dislike math or numbers. They're just fine with math. As we know, this "I hate math" or "I don't like math" attitude seems to develop during school years.
Now, I also don't think that children are disliking reasoning, because they're happy to do puzzles and go through games where you have to think.
And, students' negative attitude towards math also is NOT due to (school) math being difficult. The math we learn in school is not difficult. You don't have to be a math whiz to understand it.
If you can learn to read and to use computer software, surely you can learn basic math. It's not that complex.
So... here are the two main factors that I feel contribute most to what attitude children develop towards math:
1) The teacher's attitude.
If you love math and are enthusiastic about it, it is seen in your teaching, and your attitude will be somewhat contagious.
It's true the other way around as well: if you don't like math and are teaching it, students will sense it. (I've written about the teacher's attitude in this article.)
2) How the math is being taught.
Children can end up not liking math when it is taught in such a way that they don't end up understanding it.
When they don't understand it, then they don't like studying more of it.
The teacher is obviously hugely influental in how the math is taught, but curriculum or the math book also plays a role.
So if we as teachers can get these two things straightened out and thus have the basics covered, then some special incentives and other extra "math goodies" won't hurt either.
See also:
Four habits of highly effective math teaching
Is your math curriculum coherent?
How to motivate and prevent math anxiety
Developing positive attitude
What are the incentives needed in order to develop a positive attitude in children and other students towards mathematics?
I am not sure if (special) incentives is the main factor in developing a positive attitude towards mathematics.
I feel it is probably sufficient to get a few of the basics right, and then that alone will take care of most of it, and students can like math just fine.
Disliking math is not something that is inherent in us or in our kids. Little kids don't dislike math or numbers. They're just fine with math. As we know, this "I hate math" or "I don't like math" attitude seems to develop during school years.
Now, I also don't think that children are disliking reasoning, because they're happy to do puzzles and go through games where you have to think.
And, students' negative attitude towards math also is NOT due to (school) math being difficult. The math we learn in school is not difficult. You don't have to be a math whiz to understand it.
If you can learn to read and to use computer software, surely you can learn basic math. It's not that complex.
So... here are the two main factors that I feel contribute most to what attitude children develop towards math:
1) The teacher's attitude.
If you love math and are enthusiastic about it, it is seen in your teaching, and your attitude will be somewhat contagious.
It's true the other way around as well: if you don't like math and are teaching it, students will sense it. (I've written about the teacher's attitude in this article.)
2) How the math is being taught.
Children can end up not liking math when it is taught in such a way that they don't end up understanding it.
When they don't understand it, then they don't like studying more of it.
The teacher is obviously hugely influental in how the math is taught, but curriculum or the math book also plays a role.
So if we as teachers can get these two things straightened out and thus have the basics covered, then some special incentives and other extra "math goodies" won't hurt either.
See also:
Four habits of highly effective math teaching
Is your math curriculum coherent?
How to motivate and prevent math anxiety
Friday, September 8, 2006
Living and Loving Math
X (however many) Habits of Highly Effective Math Teaching:
You are the teacher. You show the way - also with your attitudes, your way of life.
Do you use math often in your daily life? Is using mathematical reasoning, numbers, measurements, etc. a natural thing to you every day?
And then: do you like math? Love it? Are you happy to teach it? Enthusiastic?
Both of these tend to show up in how you teach, but especially so in a homeschooling enviroment, because at home you're teaching your kids a way of life, and if math is a natural part of it or not.
Math is not a drudgery, nor something just confined to math lessons.
Some ideas:
I've talked about all this before, so I really don't want to go into repeating myself too much. But I did want to include this principle in my "mini-series" of effective habits of math teaching.
Part 4: Living and Loving Math
You are the teacher. You show the way - also with your attitudes, your way of life.
Do you use math often in your daily life? Is using mathematical reasoning, numbers, measurements, etc. a natural thing to you every day?
And then: do you like math? Love it? Are you happy to teach it? Enthusiastic?
Both of these tend to show up in how you teach, but especially so in a homeschooling enviroment, because at home you're teaching your kids a way of life, and if math is a natural part of it or not.
Math is not a drudgery, nor something just confined to math lessons.
Some ideas:
- Let it make sense. This alone can usually make math quite a difference and kids will stay interested.
- Read through some fun math books, such as Theoni Pappas books, or puzzle-type books. Get to know some interesting math topics besides just schoolbook arithmetic. And, there are even story books to teach math concepts - see a list here.
- Try including a bit about math history. This might work best in a homeschooling environment where there is no horrible rush to get through the thick book before the year is over. Julie at LivingMath.net has suggestions for math history books to buy.
- When you use math in your daily life, explain how you're doing it, and include the children if possible. Figure it out together.
I've talked about all this before, so I really don't want to go into repeating myself too much. But I did want to include this principle in my "mini-series" of effective habits of math teaching.
Living and Loving Math
X (however many) Habits of Highly Effective Math Teaching:
You are the teacher. You show the way - also with your attitudes, your way of life.
Do you use math often in your daily life? Is using mathematical reasoning, numbers, measurements, etc. a natural thing to you every day?
And then: do you like math? Love it? Are you happy to teach it? Enthusiastic?
Both of these tend to show up in how you teach, but especially so in a homeschooling enviroment, because at home you're teaching your kids a way of life, and if math is a natural part of it or not.
Math is not a drudgery, nor something just confined to math lessons.
Some ideas:
I've talked about all this before, so I really don't want to go into repeating myself too much. But I did want to include this principle in my "mini-series" of effective habits of math teaching.
Part 4: Living and Loving Math
You are the teacher. You show the way - also with your attitudes, your way of life.
Do you use math often in your daily life? Is using mathematical reasoning, numbers, measurements, etc. a natural thing to you every day?
And then: do you like math? Love it? Are you happy to teach it? Enthusiastic?
Both of these tend to show up in how you teach, but especially so in a homeschooling enviroment, because at home you're teaching your kids a way of life, and if math is a natural part of it or not.
Math is not a drudgery, nor something just confined to math lessons.
Some ideas:
- Let it make sense. This alone can usually make math quite a difference and kids will stay interested.
- Read through some fun math books, such as Theoni Pappas books, or puzzle-type books. Get to know some interesting math topics besides just schoolbook arithmetic. And, there are even story books to teach math concepts - see a list here.
- Try including a bit about math history. This might work best in a homeschooling environment where there is no horrible rush to get through the thick book before the year is over. Julie at LivingMath.net has suggestions for math history books to buy.
- When you use math in your daily life, explain how you're doing it, and include the children if possible. Figure it out together.
I've talked about all this before, so I really don't want to go into repeating myself too much. But I did want to include this principle in my "mini-series" of effective habits of math teaching.
Wednesday, May 10, 2006
I hate math but don't want to anymore...
I want to blog again on Julie's great Living Math website. You can really get help there if you're one of those who don't care for math, or even hate math, but want to get rid of that feeling.
She has suggestions on how to start teaching "living math" - teaching math in a way that makes connections to real life, takes away the dryness of it, takes away the 'kill' from "drill and kill" (note that drill in itself doesn't have to be always bad - drill is a tool amongst many), etc.
On this page, Julie has book suggestions to many different situations... Consider finding one or a few (from library or bookstore). Reading a math book that's not a school book can do SO much good! For your kids too!
As you probably know, I wish everyone would get to know some of the interesting, fascinating, fun, curious aspects of mathematics. Or, get to know a bit of math history. You don't get those in school books. Or, finally learn why things work.
These things CAN change your attitude towards math, and then you can relay it to your children.
Julie has already done the work of listing these books; I'm glad for that. Does any of the following apply to you? She says:
Now just go jot down a few of those books, run to library (or bookstore), and get started:
Living Math: Starting out suggestions
Tags: math, mathematics, teaching
She has suggestions on how to start teaching "living math" - teaching math in a way that makes connections to real life, takes away the dryness of it, takes away the 'kill' from "drill and kill" (note that drill in itself doesn't have to be always bad - drill is a tool amongst many), etc.
On this page, Julie has book suggestions to many different situations... Consider finding one or a few (from library or bookstore). Reading a math book that's not a school book can do SO much good! For your kids too!
As you probably know, I wish everyone would get to know some of the interesting, fascinating, fun, curious aspects of mathematics. Or, get to know a bit of math history. You don't get those in school books. Or, finally learn why things work.
These things CAN change your attitude towards math, and then you can relay it to your children.
Julie has already done the work of listing these books; I'm glad for that. Does any of the following apply to you? She says:
QUOTE
Are you a parent wanting to increase your understanding of *why* math is important?
Do you need understanding to increase your own enthusiasm, creativity and motivation?
Are you a parent wanting to understand why mathematics can seem difficult, wanting to gain reassurance that the "math gene" didn't skip your family?
Are you wanting to be convinced that mathematics can be a readable, living, subject?
Are you wanting to introduce mathematics to your children and adolescents in a vibrant, visual way, expanding the understanding of what mathematics is beyond arithmetic
~~ allowing them to *hear* the "music" they might play some day?
Are you a parent with a child that is "burned out" and needs a math reading break?
Now just go jot down a few of those books, run to library (or bookstore), and get started:
Living Math: Starting out suggestions
Tags: math, mathematics, teaching
I hate math but don't want to anymore...
I want to blog again on Julie's great Living Math website. You can really get help there if you're one of those who don't care for math, or even hate math, but want to get rid of that feeling.
She has suggestions on how to start teaching "living math" - teaching math in a way that makes connections to real life, takes away the dryness of it, takes away the 'kill' from "drill and kill" (note that drill in itself doesn't have to be always bad - drill is a tool amongst many), etc.
On this page, Julie has book suggestions to many different situations... Consider finding one or a few (from library or bookstore). Reading a math book that's not a school book can do SO much good! For your kids too!
As you probably know, I wish everyone would get to know some of the interesting, fascinating, fun, curious aspects of mathematics. Or, get to know a bit of math history. You don't get those in school books. Or, finally learn why things work.
These things CAN change your attitude towards math, and then you can relay it to your children.
Julie has already done the work of listing these books; I'm glad for that. Does any of the following apply to you? She says:
Now just go jot down a few of those books, run to library (or bookstore), and get started:
Living Math: Starting out suggestions
Tags: math, mathematics, teaching
She has suggestions on how to start teaching "living math" - teaching math in a way that makes connections to real life, takes away the dryness of it, takes away the 'kill' from "drill and kill" (note that drill in itself doesn't have to be always bad - drill is a tool amongst many), etc.
On this page, Julie has book suggestions to many different situations... Consider finding one or a few (from library or bookstore). Reading a math book that's not a school book can do SO much good! For your kids too!
As you probably know, I wish everyone would get to know some of the interesting, fascinating, fun, curious aspects of mathematics. Or, get to know a bit of math history. You don't get those in school books. Or, finally learn why things work.
These things CAN change your attitude towards math, and then you can relay it to your children.
Julie has already done the work of listing these books; I'm glad for that. Does any of the following apply to you? She says:
QUOTE
Are you a parent wanting to increase your understanding of *why* math is important?
Do you need understanding to increase your own enthusiasm, creativity and motivation?
Are you a parent wanting to understand why mathematics can seem difficult, wanting to gain reassurance that the "math gene" didn't skip your family?
Are you wanting to be convinced that mathematics can be a readable, living, subject?
Are you wanting to introduce mathematics to your children and adolescents in a vibrant, visual way, expanding the understanding of what mathematics is beyond arithmetic
~~ allowing them to *hear* the "music" they might play some day?
Are you a parent with a child that is "burned out" and needs a math reading break?
Now just go jot down a few of those books, run to library (or bookstore), and get started:
Living Math: Starting out suggestions
Tags: math, mathematics, teaching
Saturday, May 6, 2006
How far you can go when you're REALLY motivated
Just found this... decided that it's good reading for all. When you have lots of motivation, like these kids did, you can learn and will learn - math or anything else. It may not be easy at all times, but the motivation will make you persistent so you will eventually learn.
A certain arithmetic class at Sudbury Valley School
A certain arithmetic class at Sudbury Valley School
QUOTE
"Because everyone knows," he answered, "that the subject matter itself isn't that hard. What's hard, virtually impossible, is beating it into the heads of youngsters who hate every step. The only way we have a ghost of a chance is to hammer away at the stuff bit by bit every day for years. Even then it does not work. Most of the sixth graders are mathematical illiterates. Give me a kid who wants to learn the stuff -- well, twenty hours or so makes sense."
How far you can go when you're REALLY motivated
Just found this... decided that it's good reading for all. When you have lots of motivation, like these kids did, you can learn and will learn - math or anything else. It may not be easy at all times, but the motivation will make you persistent so you will eventually learn.
A certain arithmetic class at Sudbury Valley School
A certain arithmetic class at Sudbury Valley School
QUOTE
"Because everyone knows," he answered, "that the subject matter itself isn't that hard. What's hard, virtually impossible, is beating it into the heads of youngsters who hate every step. The only way we have a ghost of a chance is to hammer away at the stuff bit by bit every day for years. Even then it does not work. Most of the sixth graders are mathematical illiterates. Give me a kid who wants to learn the stuff -- well, twenty hours or so makes sense."
Friday, April 21, 2006
Living math
I've been looking over the website LivingMath.net recently. Lots of good stuff there.
What is 'living math'? How do you make math "come to life"?
Well, I guess we could ask that when did math become 'dead' and who killed it?
Some people feel that it is worksheets, tests, drill, and 'scope and sequence' that killed it. But I don't feel it's that simple. Those things are tools you can use, and they don't necessarily make math 'all dead'.
There are many ways to make math 'living'. One important way, I feel, is to show your kids when you do use math in your daily life. I've written about it before.
When YOU use math, it conveys the idea that math and numbers are things we use, not some obscure school subject that one does for half an hour five times a week, and then tries to forget the rest of the time.
I have never understood mothers who say they didn't like math, hated it, etc. Don't say that! That attitude will be absorbed by the little 'sponges' around you...
When kids are little, play counting games with them - show them math is part of life, part of the fun. Point out 'math' situations in life, such as: here are two plates, and then two more. Or, here's six toy cars but see, two of them drive away. Oh, look: three bikes, each of them has two wheels. Have measuring tapes, rulers, scales, calendars around your house.
When they're older and you go shopping, try 'think aloud' how you figure out comparing prices, or how you mentally calculate discounts, or do your taxes etc.
You don't have to be an 'unschooler' to use some of these ideas. Just go visit the LivingMath.net site for some more: Julie has made a page with lots of simple ideas how to make math LIVING!
Tags: math, lessons
What is 'living math'? How do you make math "come to life"?
Well, I guess we could ask that when did math become 'dead' and who killed it?
Some people feel that it is worksheets, tests, drill, and 'scope and sequence' that killed it. But I don't feel it's that simple. Those things are tools you can use, and they don't necessarily make math 'all dead'.
There are many ways to make math 'living'. One important way, I feel, is to show your kids when you do use math in your daily life. I've written about it before.
When YOU use math, it conveys the idea that math and numbers are things we use, not some obscure school subject that one does for half an hour five times a week, and then tries to forget the rest of the time.
I have never understood mothers who say they didn't like math, hated it, etc. Don't say that! That attitude will be absorbed by the little 'sponges' around you...
When kids are little, play counting games with them - show them math is part of life, part of the fun. Point out 'math' situations in life, such as: here are two plates, and then two more. Or, here's six toy cars but see, two of them drive away. Oh, look: three bikes, each of them has two wheels. Have measuring tapes, rulers, scales, calendars around your house.
When they're older and you go shopping, try 'think aloud' how you figure out comparing prices, or how you mentally calculate discounts, or do your taxes etc.
You don't have to be an 'unschooler' to use some of these ideas. Just go visit the LivingMath.net site for some more: Julie has made a page with lots of simple ideas how to make math LIVING!
Tags: math, lessons
Living math
I've been looking over the website LivingMath.net recently. Lots of good stuff there.
What is 'living math'? How do you make math "come to life"?
Well, I guess we could ask that when did math become 'dead' and who killed it?
Some people feel that it is worksheets, tests, drill, and 'scope and sequence' that killed it. But I don't feel it's that simple. Those things are tools you can use, and they don't necessarily make math 'all dead'.
There are many ways to make math 'living'. One important way, I feel, is to show your kids when you do use math in your daily life. I've written about it before.
When YOU use math, it conveys the idea that math and numbers are things we use, not some obscure school subject that one does for half an hour five times a week, and then tries to forget the rest of the time.
I have never understood mothers who say they didn't like math, hated it, etc. Don't say that! That attitude will be absorbed by the little 'sponges' around you...
When kids are little, play counting games with them - show them math is part of life, part of the fun. Point out 'math' situations in life, such as: here are two plates, and then two more. Or, here's six toy cars but see, two of them drive away. Oh, look: three bikes, each of them has two wheels. Have measuring tapes, rulers, scales, calendars around your house.
When they're older and you go shopping, try 'think aloud' how you figure out comparing prices, or how you mentally calculate discounts, or do your taxes etc.
You don't have to be an 'unschooler' to use some of these ideas. Just go visit the LivingMath.net site for some more: Julie has made a page with lots of simple ideas how to make math LIVING!
Tags: math, lessons
What is 'living math'? How do you make math "come to life"?
Well, I guess we could ask that when did math become 'dead' and who killed it?
Some people feel that it is worksheets, tests, drill, and 'scope and sequence' that killed it. But I don't feel it's that simple. Those things are tools you can use, and they don't necessarily make math 'all dead'.
There are many ways to make math 'living'. One important way, I feel, is to show your kids when you do use math in your daily life. I've written about it before.
When YOU use math, it conveys the idea that math and numbers are things we use, not some obscure school subject that one does for half an hour five times a week, and then tries to forget the rest of the time.
I have never understood mothers who say they didn't like math, hated it, etc. Don't say that! That attitude will be absorbed by the little 'sponges' around you...
When kids are little, play counting games with them - show them math is part of life, part of the fun. Point out 'math' situations in life, such as: here are two plates, and then two more. Or, here's six toy cars but see, two of them drive away. Oh, look: three bikes, each of them has two wheels. Have measuring tapes, rulers, scales, calendars around your house.
When they're older and you go shopping, try 'think aloud' how you figure out comparing prices, or how you mentally calculate discounts, or do your taxes etc.
You don't have to be an 'unschooler' to use some of these ideas. Just go visit the LivingMath.net site for some more: Julie has made a page with lots of simple ideas how to make math LIVING!
Tags: math, lessons
Monday, March 27, 2006
Challenging / open-ended math problems
I just read a very inspirational article Teenager or Tyke, Students Learn Best by Tackling Challenging Math (PDF) (html).
It tells about two teachers who frequently employ open-ended problem-solving sessions in their teaching - and the students (almost all) like it well and are very motivated.
In math education, OPEN-ENDED problem usually means it doesn't have a specific step-by-step solution. You can solve it in many different ways. Or, it may have more than one solution.
The problems these teachers use are often from real life, and not quick to solve. Instead it can take some time and struggling to get anywhere. (Hey, that's how problems in real life often are, too!)
But, struggling can be valuable. One of the teachers featured in the article, Heidi Ewer, says:
There's even some value in trying impossible problems! Douglas Twitchell says in The Value of 'Impossible' Problems, "...if you have students who are interested in trying, think of the mathematics they might learn in the process of attempting these! [some very difficult problems]"
I realize dealing with open-ended problems is not easy to do if you're not an experienced math teacher - and not even then. Like the other teacher from the article, Judith Carter, says, a problem-solving activity is not something she can fit into every day, or even every week.
But, parents organize field trips in other subjects. Maybe an occasional afternoon dedicated to a challenging open-ended math problem can serve as a 'mathematical field trip'!
Find out more:
Teenager or Tyke, Students Learn Best by Tackling Challenging Math (PDF)
Teenager or Tyke, Students Learn Best by Tackling Challenging Math (html)
The article is from a publication "Northwest Teacher". Their volumes seem to have interesting titles.
If you're ready to give some challenging problems for your student(s), check out these:
Open-Ended Math Problems from The Franklin Institute Online (middle school level). Check also the links in my previous post.
And, by the way, there's nothing wrong in working together. If you as the homeschooling parent don't yet know the answer, you can work the problems together with your child.
Tags: math, mathematics, teaching
It tells about two teachers who frequently employ open-ended problem-solving sessions in their teaching - and the students (almost all) like it well and are very motivated.
In math education, OPEN-ENDED problem usually means it doesn't have a specific step-by-step solution. You can solve it in many different ways. Or, it may have more than one solution.
The problems these teachers use are often from real life, and not quick to solve. Instead it can take some time and struggling to get anywhere. (Hey, that's how problems in real life often are, too!)
But, struggling can be valuable. One of the teachers featured in the article, Heidi Ewer, says:
"Struggling helps them see this as an investment of their own time and energy. It makes them more willing to learn," Ewer says. "Struggling to solve problems requires students to use their intuitive skills to investigate concepts, she explains,
and, in this way, they gain a deeper and more lasting understanding of the mathematics."
There's even some value in trying impossible problems! Douglas Twitchell says in The Value of 'Impossible' Problems, "...if you have students who are interested in trying, think of the mathematics they might learn in the process of attempting these! [some very difficult problems]"
I realize dealing with open-ended problems is not easy to do if you're not an experienced math teacher - and not even then. Like the other teacher from the article, Judith Carter, says, a problem-solving activity is not something she can fit into every day, or even every week.
But, parents organize field trips in other subjects. Maybe an occasional afternoon dedicated to a challenging open-ended math problem can serve as a 'mathematical field trip'!
Find out more:
Teenager or Tyke, Students Learn Best by Tackling Challenging Math (PDF)
Teenager or Tyke, Students Learn Best by Tackling Challenging Math (html)
The article is from a publication "Northwest Teacher". Their volumes seem to have interesting titles.
If you're ready to give some challenging problems for your student(s), check out these:
Open-Ended Math Problems from The Franklin Institute Online (middle school level). Check also the links in my previous post.
And, by the way, there's nothing wrong in working together. If you as the homeschooling parent don't yet know the answer, you can work the problems together with your child.
Tags: math, mathematics, teaching
Challenging / open-ended math problems
I just read a very inspirational article Teenager or Tyke, Students Learn Best by Tackling Challenging Math (PDF) (html).
It tells about two teachers who frequently employ open-ended problem-solving sessions in their teaching - and the students (almost all) like it well and are very motivated.
In math education, OPEN-ENDED problem usually means it doesn't have a specific step-by-step solution. You can solve it in many different ways. Or, it may have more than one solution.
The problems these teachers use are often from real life, and not quick to solve. Instead it can take some time and struggling to get anywhere. (Hey, that's how problems in real life often are, too!)
But, struggling can be valuable. One of the teachers featured in the article, Heidi Ewer, says:
There's even some value in trying impossible problems! Douglas Twitchell says in The Value of 'Impossible' Problems, "...if you have students who are interested in trying, think of the mathematics they might learn in the process of attempting these! [some very difficult problems]"
I realize dealing with open-ended problems is not easy to do if you're not an experienced math teacher - and not even then. Like the other teacher from the article, Judith Carter, says, a problem-solving activity is not something she can fit into every day, or even every week.
But, parents organize field trips in other subjects. Maybe an occasional afternoon dedicated to a challenging open-ended math problem can serve as a 'mathematical field trip'!
Find out more:
Teenager or Tyke, Students Learn Best by Tackling Challenging Math (PDF)
Teenager or Tyke, Students Learn Best by Tackling Challenging Math (html)
The article is from a publication "Northwest Teacher". Their volumes seem to have interesting titles.
If you're ready to give some challenging problems for your student(s), check out these:
Open-Ended Math Problems from The Franklin Institute Online (middle school level). Check also the links in my previous post.
And, by the way, there's nothing wrong in working together. If you as the homeschooling parent don't yet know the answer, you can work the problems together with your child.
Tags: math, mathematics, teaching
It tells about two teachers who frequently employ open-ended problem-solving sessions in their teaching - and the students (almost all) like it well and are very motivated.
In math education, OPEN-ENDED problem usually means it doesn't have a specific step-by-step solution. You can solve it in many different ways. Or, it may have more than one solution.
The problems these teachers use are often from real life, and not quick to solve. Instead it can take some time and struggling to get anywhere. (Hey, that's how problems in real life often are, too!)
But, struggling can be valuable. One of the teachers featured in the article, Heidi Ewer, says:
"Struggling helps them see this as an investment of their own time and energy. It makes them more willing to learn," Ewer says. "Struggling to solve problems requires students to use their intuitive skills to investigate concepts, she explains,
and, in this way, they gain a deeper and more lasting understanding of the mathematics."
There's even some value in trying impossible problems! Douglas Twitchell says in The Value of 'Impossible' Problems, "...if you have students who are interested in trying, think of the mathematics they might learn in the process of attempting these! [some very difficult problems]"
I realize dealing with open-ended problems is not easy to do if you're not an experienced math teacher - and not even then. Like the other teacher from the article, Judith Carter, says, a problem-solving activity is not something she can fit into every day, or even every week.
But, parents organize field trips in other subjects. Maybe an occasional afternoon dedicated to a challenging open-ended math problem can serve as a 'mathematical field trip'!
Find out more:
Teenager or Tyke, Students Learn Best by Tackling Challenging Math (PDF)
Teenager or Tyke, Students Learn Best by Tackling Challenging Math (html)
The article is from a publication "Northwest Teacher". Their volumes seem to have interesting titles.
If you're ready to give some challenging problems for your student(s), check out these:
Open-Ended Math Problems from The Franklin Institute Online (middle school level). Check also the links in my previous post.
And, by the way, there's nothing wrong in working together. If you as the homeschooling parent don't yet know the answer, you can work the problems together with your child.
Tags: math, mathematics, teaching
Monday, March 6, 2006
What to do when math gets dry
Have you ever felt like your child needed something different for math than whatever you were currently doing? Like your math program didn't work anymore: your child didn't learn, or was bored? What to do?
Here a little while back I received a question along those lines. We exchanged a few emails and I got permission to post her situation here on this blog. I think it is a good example of what many times happens in home school.
I then suggested to her a change in curriculum, perhaps to Singapore or Math-U-See. Or, giving him more responsibility in completing his lessons. I also suggested RightStart Geometry since he seemed to like geometry, and Developmental Math workbooks, or Key To... workbooks.
She responded back:
Then, as of last week, she said, "...we've had a bit of a break and been experimenting with some software and online resources. We have not settled on any one thing yet."
THE MORALE... Sometimes a change in approach or material is beneficial. Or even just a break from math. I've written along these lines before, in my article How to choose a homeschool math curriculum.
You don't always need to hunt for a new curriculum, though. Internet is full of all sorts of math tutorials, as you can imagine. And learning games.
Remember the principle of "variable learning": use various materials or resources to teach the same thing. When the child encounters the same topic several times with slightly different wordings, it helps to solidify his knowledge.
How about using some software or interactive online math curriculum to supplement the existing curriculum? The child could get instruction from those lessons, then read the corresponding material in the existing textbook and do SOME practice problems found in there.
Parents don't always realize this, but math textbooks include lots of practice problems to accommodate all kinds of learners. You certainly don't have to have your child do all of them.
Here a little while back I received a question along those lines. We exchanged a few emails and I got permission to post her situation here on this blog. I think it is a good example of what many times happens in home school.
"We have 4 children; boy-12, girl-8, girl-5 and boy-3. With oldest we have used the gamut of curricula for math and eventually settled out with Abeka for the past 3 years.
However, the material seemed to not sufficiently explain new material, but run old material in the ground until the grinding sensation was numbing. That in itself seems to be contradictory, but my son was really not getting much better at the basics, mainly I think because he was bored with the repetition.
I narrowed his assignments down to every other one and if I found he missed a problem, he had to do the complete set of that type of problem. He was terribly slow in doing his assignments and spacing out everytime I looked over toward him.
I found your e-books somehow during a search for explaining some concept in decimals. He needed better
explanation than what his text was offering and I could only put it so many
ways.
The samples seemed promising and the price was worthwhile so we ordered the Decimal book. His interest, comprehension and speed picked up noticeably. I ordered the Multiplication one for my daughter then.
Now we are nearly finished with the Geometry one we ordered when he finished the decimals book. He really likes the Geometry book and I wish there were more to go on to such as Pre-Algebra and further.
His ability to do basic math seems to be fine, it was just he wasn't focusing or interested and making silly mistakes all the time. The break away and into the two books we did from you was what he needed!
Sonya
I then suggested to her a change in curriculum, perhaps to Singapore or Math-U-See. Or, giving him more responsibility in completing his lessons. I also suggested RightStart Geometry since he seemed to like geometry, and Developmental Math workbooks, or Key To... workbooks.
She responded back:
We've pretty much done the gamut of approaches. He is responsible for his lessons, but math is the one thing that zones him out. We've done Singapore and he did like it, but I didn't think it was complete and took too long to get to certain concepts that are typically achieved at a certain level here.
The first math curriculum we tried was Math-U-See and we use it to introduce math and reinforce certain concepts like place value. I still had the same complaint with it as I did the Singapore.
I look forward to looking into the curriculum you sent a link to [meaning RightStart Geometry]. I am not really looking for a new curriculum though, but rather something more like your individual books covering, and covering well, the individual concept levels. I was given some math software awhile ago and looked into its approach this morning. It may be helpful for now. Thanks for answering my questions and trying to help, its appreciated! Sonya
Then, as of last week, she said, "...we've had a bit of a break and been experimenting with some software and online resources. We have not settled on any one thing yet."
THE MORALE... Sometimes a change in approach or material is beneficial. Or even just a break from math. I've written along these lines before, in my article How to choose a homeschool math curriculum.
You don't always need to hunt for a new curriculum, though. Internet is full of all sorts of math tutorials, as you can imagine. And learning games.
Remember the principle of "variable learning": use various materials or resources to teach the same thing. When the child encounters the same topic several times with slightly different wordings, it helps to solidify his knowledge.
How about using some software or interactive online math curriculum to supplement the existing curriculum? The child could get instruction from those lessons, then read the corresponding material in the existing textbook and do SOME practice problems found in there.
Parents don't always realize this, but math textbooks include lots of practice problems to accommodate all kinds of learners. You certainly don't have to have your child do all of them.
What to do when math gets dry
Have you ever felt like your child needed something different for math than whatever you were currently doing? Like your math program didn't work anymore: your child didn't learn, or was bored? What to do?
Here a little while back I received a question along those lines. We exchanged a few emails and I got permission to post her situation here on this blog. I think it is a good example of what many times happens in home school.
I then suggested to her a change in curriculum, perhaps to Singapore or Math-U-See. Or, giving him more responsibility in completing his lessons. I also suggested RightStart Geometry since he seemed to like geometry, and Developmental Math workbooks, or Key To... workbooks.
She responded back:
Then, as of last week, she said, "...we've had a bit of a break and been experimenting with some software and online resources. We have not settled on any one thing yet."
THE MORALE... Sometimes a change in approach or material is beneficial. Or even just a break from math. I've written along these lines before, in my article How to choose a homeschool math curriculum.
You don't always need to hunt for a new curriculum, though. Internet is full of all sorts of math tutorials, as you can imagine. And learning games.
Remember the principle of "variable learning": use various materials or resources to teach the same thing. When the child encounters the same topic several times with slightly different wordings, it helps to solidify his knowledge.
How about using some software or interactive online math curriculum to supplement the existing curriculum? The child could get instruction from those lessons, then read the corresponding material in the existing textbook and do SOME practice problems found in there.
Parents don't always realize this, but math textbooks include lots of practice problems to accommodate all kinds of learners. You certainly don't have to have your child do all of them.
Here a little while back I received a question along those lines. We exchanged a few emails and I got permission to post her situation here on this blog. I think it is a good example of what many times happens in home school.
"We have 4 children; boy-12, girl-8, girl-5 and boy-3. With oldest we have used the gamut of curricula for math and eventually settled out with Abeka for the past 3 years.
However, the material seemed to not sufficiently explain new material, but run old material in the ground until the grinding sensation was numbing. That in itself seems to be contradictory, but my son was really not getting much better at the basics, mainly I think because he was bored with the repetition.
I narrowed his assignments down to every other one and if I found he missed a problem, he had to do the complete set of that type of problem. He was terribly slow in doing his assignments and spacing out everytime I looked over toward him.
I found your e-books somehow during a search for explaining some concept in decimals. He needed better
explanation than what his text was offering and I could only put it so many
ways.
The samples seemed promising and the price was worthwhile so we ordered the Decimal book. His interest, comprehension and speed picked up noticeably. I ordered the Multiplication one for my daughter then.
Now we are nearly finished with the Geometry one we ordered when he finished the decimals book. He really likes the Geometry book and I wish there were more to go on to such as Pre-Algebra and further.
His ability to do basic math seems to be fine, it was just he wasn't focusing or interested and making silly mistakes all the time. The break away and into the two books we did from you was what he needed!
Sonya
I then suggested to her a change in curriculum, perhaps to Singapore or Math-U-See. Or, giving him more responsibility in completing his lessons. I also suggested RightStart Geometry since he seemed to like geometry, and Developmental Math workbooks, or Key To... workbooks.
She responded back:
We've pretty much done the gamut of approaches. He is responsible for his lessons, but math is the one thing that zones him out. We've done Singapore and he did like it, but I didn't think it was complete and took too long to get to certain concepts that are typically achieved at a certain level here.
The first math curriculum we tried was Math-U-See and we use it to introduce math and reinforce certain concepts like place value. I still had the same complaint with it as I did the Singapore.
I look forward to looking into the curriculum you sent a link to [meaning RightStart Geometry]. I am not really looking for a new curriculum though, but rather something more like your individual books covering, and covering well, the individual concept levels. I was given some math software awhile ago and looked into its approach this morning. It may be helpful for now. Thanks for answering my questions and trying to help, its appreciated! Sonya
Then, as of last week, she said, "...we've had a bit of a break and been experimenting with some software and online resources. We have not settled on any one thing yet."
THE MORALE... Sometimes a change in approach or material is beneficial. Or even just a break from math. I've written along these lines before, in my article How to choose a homeschool math curriculum.
You don't always need to hunt for a new curriculum, though. Internet is full of all sorts of math tutorials, as you can imagine. And learning games.
Remember the principle of "variable learning": use various materials or resources to teach the same thing. When the child encounters the same topic several times with slightly different wordings, it helps to solidify his knowledge.
How about using some software or interactive online math curriculum to supplement the existing curriculum? The child could get instruction from those lessons, then read the corresponding material in the existing textbook and do SOME practice problems found in there.
Parents don't always realize this, but math textbooks include lots of practice problems to accommodate all kinds of learners. You certainly don't have to have your child do all of them.
Saturday, January 14, 2006
Can girls do math? A paper folding story.
This story is cute, and even though it happened several years ago, it was new to me, and I really want to share it with you.
Maybe you've heard that it's impossible to fold paper more than 7 or 8 times, no matter how hard you try?
Well, that turned out to be a myth. Then high-schooler, Britney Gallivan tackled the challenge of folding paper 12 times and succeeded (in 2002). She experimented and thought about it, and found out what exactly limits the folding process. She discovered an equation linking the minimum length of paper needed, thickness of paper, and number of foldings.
Then, she calculated she needed paper about 4000 feet long to do 12 foldings! Britney found one special toilet paper roll that would do, went to a mall with her parents and started folding... It took 7 hours for her and her parents to do it, mostly on hands and knees.
Don't you ever think or leave that impression that girls can't do math - even if you're a female yourself and weren't good in math. Remember, your students will be affected by your attitudes.
Read more and see a picture of Britney and the paper:
Champion paper-folder and Paper folding at Mathworld and Folding paper in half 12 times.
P.S.
If you wanted to do 13 foldings, you'd need about 6000 feet of paper (if it was 0.002 inches thick).
Maybe you've heard that it's impossible to fold paper more than 7 or 8 times, no matter how hard you try?
Well, that turned out to be a myth. Then high-schooler, Britney Gallivan tackled the challenge of folding paper 12 times and succeeded (in 2002). She experimented and thought about it, and found out what exactly limits the folding process. She discovered an equation linking the minimum length of paper needed, thickness of paper, and number of foldings.
Then, she calculated she needed paper about 4000 feet long to do 12 foldings! Britney found one special toilet paper roll that would do, went to a mall with her parents and started folding... It took 7 hours for her and her parents to do it, mostly on hands and knees.
Don't you ever think or leave that impression that girls can't do math - even if you're a female yourself and weren't good in math. Remember, your students will be affected by your attitudes.
Read more and see a picture of Britney and the paper:
Champion paper-folder and Paper folding at Mathworld and Folding paper in half 12 times.
P.S.
If you wanted to do 13 foldings, you'd need about 6000 feet of paper (if it was 0.002 inches thick).
Can girls do math? A paper folding story.
This story is cute, and even though it happened several years ago, it was new to me, and I really want to share it with you.
Maybe you've heard that it's impossible to fold paper more than 7 or 8 times, no matter how hard you try?
Well, that turned out to be a myth. Then high-schooler, Britney Gallivan tackled the challenge of folding paper 12 times and succeeded (in 2002). She experimented and thought about it, and found out what exactly limits the folding process. She discovered an equation linking the minimum length of paper needed, thickness of paper, and number of foldings.
Then, she calculated she needed paper about 4000 feet long to do 12 foldings! Britney found one special toilet paper roll that would do, went to a mall with her parents and started folding... It took 7 hours for her and her parents to do it, mostly on hands and knees.
Don't you ever think or leave that impression that girls can't do math - even if you're a female yourself and weren't good in math. Remember, your students will be affected by your attitudes.
Read more and see a picture of Britney and the paper:
Champion paper-folder and Paper folding at Mathworld and Folding paper in half 12 times.
P.S.
If you wanted to do 13 foldings, you'd need about 6000 feet of paper (if it was 0.002 inches thick).
Maybe you've heard that it's impossible to fold paper more than 7 or 8 times, no matter how hard you try?
Well, that turned out to be a myth. Then high-schooler, Britney Gallivan tackled the challenge of folding paper 12 times and succeeded (in 2002). She experimented and thought about it, and found out what exactly limits the folding process. She discovered an equation linking the minimum length of paper needed, thickness of paper, and number of foldings.
Then, she calculated she needed paper about 4000 feet long to do 12 foldings! Britney found one special toilet paper roll that would do, went to a mall with her parents and started folding... It took 7 hours for her and her parents to do it, mostly on hands and knees.
Don't you ever think or leave that impression that girls can't do math - even if you're a female yourself and weren't good in math. Remember, your students will be affected by your attitudes.
Read more and see a picture of Britney and the paper:
Champion paper-folder and Paper folding at Mathworld and Folding paper in half 12 times.
P.S.
If you wanted to do 13 foldings, you'd need about 6000 feet of paper (if it was 0.002 inches thick).
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