Some may find this interesting...
Pupils 'are urged to drop maths' in the UK.
"Pupils are being discouraged from taking A-level maths as schools in England chase higher places in the league tables, scientists have claimed."
If the school performance is measured in students' grades or exam results, then this sounds like an obvious tactic.
Kamis, 26 April 2007
Kamis, 19 April 2007
News... WinterPromise and Math Mammoth
What I am about to explain you might have already found out... but this is the first time I'm announcing it on my blog.
It has been BIG NEWS to me... and lots of work! (And that hasn't ended... I'm still working on this.)
Namely...
Starting in June 2007, WinterPromise will carry a Math Mammoth complete curriculum for grades 1-3!
These new books constitute a complete mathematics curriculum for grades 1, 2, and 3, and will be offered exclusively via WinterPromise during year 2007 (not even sold on my website for that period).
Each grade level will be offered as a printed textbook and a CD, or a CD alone. The entirety of the textbook is on the CD, and can be printed for use within a family for unlimited use.
The CD will also contain answer keys, tests, and an easy access to script-made free worksheets.
The new products
Math Mammoth Grade 1-A and 1-B complete worktexts
These two books focus on addition and subtraction concept and basic facts within 0-10, place value with 2-digit numbers, and some adding and subtracting within 0-100. Also covered are some geometry topics, measuring, clock, and counting coins.
Pricing: CD only $32; textbook and CD $52
Sample pages for 1-A (PDF)
Sample pages for 1-B (PDF)
Math Mammoth Grade 2-A and 2-B complete worktexts
These two books focus on memorizing the basic addition and subtraction facts with single-digit numbers, developing fluency with multidigit addition and subtraction, and place value with 3-digit numbers. Also included is introduction to multiplication concept, measuring and geometry topics, clock reading and money.
Pricing: CD only $32; textbook and CD $52
Math Mammoth Grade 3-A and 3-B complete worktexts
These two books focus on multiplication concept, memorizing multiplication tables, division concept and facts, adding and subtracting 4-6 digit numbers, and using addition and subtraction to solve problems. Also covered are time, money, measuring, and geometry topics, and introduction to fractions.
Pricing: CD only $32; textbook and CD $52
Here is the link to the Math Mammoth books at WinterPromise website.
As a "side effect", I will also have two new workbooks to sell as part of the Blue Series: one about clock, and the other about measuring and early geometry concepts.
So that's all going to be in June... and I'm in a big hurry to get it all ready!
It has been BIG NEWS to me... and lots of work! (And that hasn't ended... I'm still working on this.)
Namely...
Starting in June 2007, WinterPromise will carry a Math Mammoth complete curriculum for grades 1-3!
These new books constitute a complete mathematics curriculum for grades 1, 2, and 3, and will be offered exclusively via WinterPromise during year 2007 (not even sold on my website for that period).Each grade level will be offered as a printed textbook and a CD, or a CD alone. The entirety of the textbook is on the CD, and can be printed for use within a family for unlimited use.
The CD will also contain answer keys, tests, and an easy access to script-made free worksheets.
The new products
Math Mammoth Grade 1-A and 1-B complete worktexts
These two books focus on addition and subtraction concept and basic facts within 0-10, place value with 2-digit numbers, and some adding and subtracting within 0-100. Also covered are some geometry topics, measuring, clock, and counting coins.
Pricing: CD only $32; textbook and CD $52
Sample pages for 1-A (PDF)
Sample pages for 1-B (PDF)
Math Mammoth Grade 2-A and 2-B complete worktexts
These two books focus on memorizing the basic addition and subtraction facts with single-digit numbers, developing fluency with multidigit addition and subtraction, and place value with 3-digit numbers. Also included is introduction to multiplication concept, measuring and geometry topics, clock reading and money.
Pricing: CD only $32; textbook and CD $52
Math Mammoth Grade 3-A and 3-B complete worktexts
These two books focus on multiplication concept, memorizing multiplication tables, division concept and facts, adding and subtracting 4-6 digit numbers, and using addition and subtraction to solve problems. Also covered are time, money, measuring, and geometry topics, and introduction to fractions.
Pricing: CD only $32; textbook and CD $52
Here is the link to the Math Mammoth books at WinterPromise website.
As a "side effect", I will also have two new workbooks to sell as part of the Blue Series: one about clock, and the other about measuring and early geometry concepts.
So that's all going to be in June... and I'm in a big hurry to get it all ready!
Rabu, 18 April 2007
Math in books (not math books!)
I just recieved an email from a publishing company. They want to send me a few books to review and then list on my site.
I've written reviews before, a whole bunch. I started my "reviewer career"... well, in school of course. We wrote book reviews, as I'm sure you did too. I don't think mine were that special. But somehow the role of reviewer has fallen to my lap nowadays.
For example, recently I just finished the review of YourTeacher and MathScore.
The new books that this email was about are
I haven't seen these yet. The reason I put them in this blogpost is because it sounds like these books are examples of math in a somewhat entertaining or interesting context, aimed at high school or middle-school level.
You know, to so many people math remains a "dull" school subject only. And that is so far from truth. It is some of those same people, I'm sure, who confess to the "I'm bad at math and that's okay" attitude as mentioned in the previous blogpost.
I, for sure, intend for my kids to learn the beauty of math, to learn about some of these interesting subjects such as basic cryptography, to learn even of math history.
There exist lots more books like those above, "living math" books - books where mathematical concepts are at the centerpiece of the story.
I encourage you to do something similar. Don't just use the curriculum. Go to the library, and find some of these kind of books (or buy them). It shows kids so much more about math, inspires them about math, and gets rid of these silly attitudes of math being boring or not worth learning.
Because all in all, we can then appreciate mathematics so much more (and its Creator). People are awed by the animal kingdom and appreciate the beauty of this Earth and its plants, its geography, the planets, space etc. But the same applies to math.
I've written reviews before, a whole bunch. I started my "reviewer career"... well, in school of course. We wrote book reviews, as I'm sure you did too. I don't think mine were that special. But somehow the role of reviewer has fallen to my lap nowadays.
For example, recently I just finished the review of YourTeacher and MathScore.
The new books that this email was about are
- Crimes and Mathdemeanors
A collection of short detective stories for young adults who are interested in applying high school level mathematics and physics to solve mysteries. - The Cryptoclub: Using Mathematics to Make and Break Secret Codes.
Join the Cryptokids as they apply basic mathematics to make and break secret codes. This book has many hands-on activities that have been tested in both classrooms and informal settings.
I haven't seen these yet. The reason I put them in this blogpost is because it sounds like these books are examples of math in a somewhat entertaining or interesting context, aimed at high school or middle-school level.
You know, to so many people math remains a "dull" school subject only. And that is so far from truth. It is some of those same people, I'm sure, who confess to the "I'm bad at math and that's okay" attitude as mentioned in the previous blogpost.
I, for sure, intend for my kids to learn the beauty of math, to learn about some of these interesting subjects such as basic cryptography, to learn even of math history.
There exist lots more books like those above, "living math" books - books where mathematical concepts are at the centerpiece of the story.
I encourage you to do something similar. Don't just use the curriculum. Go to the library, and find some of these kind of books (or buy them). It shows kids so much more about math, inspires them about math, and gets rid of these silly attitudes of math being boring or not worth learning.
Because all in all, we can then appreciate mathematics so much more (and its Creator). People are awed by the animal kingdom and appreciate the beauty of this Earth and its plants, its geography, the planets, space etc. But the same applies to math.
I'm bad at math... and fine with that!
I just received a nice article from Jim Stone, a math teacher at Global Institute of Mathematics.
I enjoyed it; I thought you might too. I've seen this issue raised and talked about elsewhere as well.
Namely, that it seems to be socially acceptable to admit how bad you're at math... while no one would comfortably admit that they can't read.
So here goes:
I'm bad at math and I’m okay with it!
By Jim Stone
For the past eighteen years I’ve been reading articles and editorials lamenting the mathematical performance of America’s school children. It has become an annual ritual for politicians and educators alike to bemoan the results of the latest tests showing American kids falling behind their international counterparts.
What is the problem? More importantly, what is the solution?
The answer to the first question is almost always laid at the doorstep of our system of education. Blaming the system is safe. No one person represents the system. No one person is held accountable. Everyone can look outside themselves for accountability.
Attempts at fixing the system have largely focused on three areas: overhauling mathematical curriculum, changing the methodology of teaching that curriculum and the implementation of standardized tests to measure what kids know.
But here is the problem. The performance of American students has remained stagnant. Despite the implementation of integrated curricula, the establishment of benchmarks and a seemingly never ending battery of standardized tests, American students still lag behind students beyond our borders.
Perhaps we are missing the boat. Perhaps the problem isn’t really the system with its traditional curriculum. Perhaps the problem isn’t with a traditional lesson beginning with going over homework from the previous day, an introduction to a new topic followed by time working on a new homework assignment. Perhaps the problem is more societal. Perhaps the problem lies with us all.
Since becoming a high school mathematics teacher I have been struck by the seemingly countless times I have heard parents and other adults, well educated or not, utter statements such as, “math was my worse subject” or “I can’t do math.”
I have never once heard a person say, “I can’t read.” Why, then, is it so acceptable to publicly declare, without the slightest bit of embarrassment, one’s inability to do mathematics? In our society one would be shamed and embarrassed to admit their inability to read. The point is it is perfectly acceptable to be poor at mathematics in this country. We are an anomaly compared to most of the rest of the world when it comes to our comfortable attitude that it is acceptable to be poor at math. Is there any doubt that our children haven’t learned this lesson?
Or have they? While American adults casually admit to their mathematical ignorance, American children appear to overestimate their mathematical ability. In a 2003 study, 84% of American 8th graders agreed with the statement, “I usually do well in mathematics.” Of their counterparts in Singapore, 64% agreed with the same statement. Confidence often, especially in America, is considered as a positive personality trait. However, it is ironic that of the same group of 8th graders, the least confident students in Singapore, on average, outscored the most confident American students on an international math test.
If the results of the 2003 study are accurate, then our young students are overconfident. If my informal observations over the years are accurate, they ultimately learn of their shortcomings and then shrug them off with a cavalier attitude of acceptable incompetence. If so, then new curriculum, changes in pedagogy and an implementation of standardized tests are not addressing the real problem and, therefore, doom us to perpetual mediocrity.
Perhaps we all share the responsibility for the dismal mathematical performance of our children. If so, it begs a difficult and frightening question: What can be done about it?
Jim Stone, a math and physics teacher for more than 18 years, teaches at Global Institute of Mathematics.
I enjoyed it; I thought you might too. I've seen this issue raised and talked about elsewhere as well.
Namely, that it seems to be socially acceptable to admit how bad you're at math... while no one would comfortably admit that they can't read.
So here goes:
I'm bad at math and I’m okay with it!
By Jim Stone
For the past eighteen years I’ve been reading articles and editorials lamenting the mathematical performance of America’s school children. It has become an annual ritual for politicians and educators alike to bemoan the results of the latest tests showing American kids falling behind their international counterparts.
What is the problem? More importantly, what is the solution?
The answer to the first question is almost always laid at the doorstep of our system of education. Blaming the system is safe. No one person represents the system. No one person is held accountable. Everyone can look outside themselves for accountability.
Attempts at fixing the system have largely focused on three areas: overhauling mathematical curriculum, changing the methodology of teaching that curriculum and the implementation of standardized tests to measure what kids know.
But here is the problem. The performance of American students has remained stagnant. Despite the implementation of integrated curricula, the establishment of benchmarks and a seemingly never ending battery of standardized tests, American students still lag behind students beyond our borders.
Perhaps we are missing the boat. Perhaps the problem isn’t really the system with its traditional curriculum. Perhaps the problem isn’t with a traditional lesson beginning with going over homework from the previous day, an introduction to a new topic followed by time working on a new homework assignment. Perhaps the problem is more societal. Perhaps the problem lies with us all.
Since becoming a high school mathematics teacher I have been struck by the seemingly countless times I have heard parents and other adults, well educated or not, utter statements such as, “math was my worse subject” or “I can’t do math.”
I have never once heard a person say, “I can’t read.” Why, then, is it so acceptable to publicly declare, without the slightest bit of embarrassment, one’s inability to do mathematics? In our society one would be shamed and embarrassed to admit their inability to read. The point is it is perfectly acceptable to be poor at mathematics in this country. We are an anomaly compared to most of the rest of the world when it comes to our comfortable attitude that it is acceptable to be poor at math. Is there any doubt that our children haven’t learned this lesson?
Or have they? While American adults casually admit to their mathematical ignorance, American children appear to overestimate their mathematical ability. In a 2003 study, 84% of American 8th graders agreed with the statement, “I usually do well in mathematics.” Of their counterparts in Singapore, 64% agreed with the same statement. Confidence often, especially in America, is considered as a positive personality trait. However, it is ironic that of the same group of 8th graders, the least confident students in Singapore, on average, outscored the most confident American students on an international math test.
If the results of the 2003 study are accurate, then our young students are overconfident. If my informal observations over the years are accurate, they ultimately learn of their shortcomings and then shrug them off with a cavalier attitude of acceptable incompetence. If so, then new curriculum, changes in pedagogy and an implementation of standardized tests are not addressing the real problem and, therefore, doom us to perpetual mediocrity.
Perhaps we all share the responsibility for the dismal mathematical performance of our children. If so, it begs a difficult and frightening question: What can be done about it?
Jim Stone, a math and physics teacher for more than 18 years, teaches at Global Institute of Mathematics.
Senin, 16 April 2007
I get these questions a lot...
I've recently embarked on something new... I let people request a package of over 100 free worksheets and over 180 sample pages from the Math Mammoth books and worksheet collections.
In it, I included one question along with the name & email that people can fill in: "What is your most pressing math teaching question?"
I did that because I saw some other people had done something similar, and I thought that's a great idea - I would get to know what kind of math teaching related problems people have.
I also wanted to give people a chance to communicate a little with me... You know, we all go visit these multitudes of websites, and we show up as numbers on the website statistics program. It all can seem so impersonal, so "machinistic" sometimes.
But the reality is, behind every website are people. On school days, over 10,000 people visit HomeschoolMath.net. Over 1,000 people visit MathMammoth.com. I never hear from most.
If I had a physical store, I would see those people, talk to many. With a website, I still want some COMMUNICATION with my visitors and customers.
So that's what that little box with the question is about. Communication.
In this blogpost I want to answer TWO popular questions or themes that people keep writing into that little question box.
Interestingly - though not surprisingly - these two most popular themes correspond to the two best-sellers of my Blue Series books.
The two themes are:
1) Multiplication tables and
2) Fractions.
****************************************************
1) I've gotten questions such as (copied and pasted here verbatim):
"multiplication & division of one and two-digit numbers"
"How can i get my students to learn all of the multiplication tables?"
"What is the easiest way to teach the times tables?"
"It is very tough for me to learn tables. Please help me"
I believe in the methods I've put into my book Math Mammoth Multiplication 1:
****************************************************
* First teach the concept of multiplication well down pat.
* Then the tables in a specific order, with a systematic drill approach and 12x12 grid.
****************************************************
Let me explain a little more.
* First teach the concept of multiplication well down pat.
In the book, I have written not 1 or 2, but all these lessons about multiplication concept itself, to be studied BEFORE the drills:
Multiplication is Repeated Addition ............ 6
Multiplication as an Array ..................... 11
Multiplication on a Number Line ................ 14
Multiplication in Two Ways ..................... 17
Multiplying by Zero ............................ 22
Understanding Word Problems .................... 25
Order of Operations ............................ 27
Understanding Word Problems, Part 2 ............ 30
There are total of 28 lesson and practice pages in the book before the drills.
Studying the concept super well helps children to understand, become very familiar and at ease with multiplication.
While they study through these, they will probably memorize a few facts already - AND they will start seeing the need of having an effective and quick way to multiply (which is of course, knowing the facts by heart).
* Then the tables in a specific order, with a systematic drill approach and 12x12 grid.
The tables in my book are studied in this order:
table of 2
table of 4
table of 10
table of 5
[More Practice and Review]
table of 3
table of 6
table of 9
table of 11
[More Practice and Review]
table of 7
table of 8
table of 12
So it's the easiest first. Not only that, but in each lesson the student fills in a 12x12 grid to those facts he already knows. The "blacked out" unknown facts territory gets smaller really fast - and they can SEE it!
AND... that's not all. I feel it is VERY important kids learn their tables "both ways" - so they not only know that 5 x 6 is 30, but that they also know that 30 IS in the tables of 5 and 6.
To that end, I include specific instructions how you can "drill" or help the memorization of first the ANSWERS (skip-counting list), then associating each answer with a problem.
(This guide to oral drill is available online.)
All this multiplication info and practice is yours for only $4.50 :
=> Math Mammoth Multiplication 1
****************************************************
Well, this got to be long. I better save the fractions questions for another post.
Maria
P.S. If you go ahead and request that package of free worksheets, don't then be too surprised to get this blogpost as an email as well... I'm sorry but I just have to use what I write in multiple places, let many people read it. You know, sometimes I put my blogposts to an article to the website, I always pull my newsletter content from my blogposts - this time one of my email series emails ended up to be a blogpost.
In it, I included one question along with the name & email that people can fill in: "What is your most pressing math teaching question?"
I did that because I saw some other people had done something similar, and I thought that's a great idea - I would get to know what kind of math teaching related problems people have.
I also wanted to give people a chance to communicate a little with me... You know, we all go visit these multitudes of websites, and we show up as numbers on the website statistics program. It all can seem so impersonal, so "machinistic" sometimes.
But the reality is, behind every website are people. On school days, over 10,000 people visit HomeschoolMath.net. Over 1,000 people visit MathMammoth.com. I never hear from most.
If I had a physical store, I would see those people, talk to many. With a website, I still want some COMMUNICATION with my visitors and customers.
So that's what that little box with the question is about. Communication.
In this blogpost I want to answer TWO popular questions or themes that people keep writing into that little question box.
Interestingly - though not surprisingly - these two most popular themes correspond to the two best-sellers of my Blue Series books.
The two themes are:
1) Multiplication tables and
2) Fractions.
****************************************************
1) I've gotten questions such as (copied and pasted here verbatim):
"multiplication & division of one and two-digit numbers"
"How can i get my students to learn all of the multiplication tables?"
"What is the easiest way to teach the times tables?"
"It is very tough for me to learn tables. Please help me"
I believe in the methods I've put into my book Math Mammoth Multiplication 1:
****************************************************
* First teach the concept of multiplication well down pat.
* Then the tables in a specific order, with a systematic drill approach and 12x12 grid.
****************************************************
Let me explain a little more.
* First teach the concept of multiplication well down pat.
In the book, I have written not 1 or 2, but all these lessons about multiplication concept itself, to be studied BEFORE the drills:
Multiplication is Repeated Addition ............ 6
Multiplication as an Array ..................... 11
Multiplication on a Number Line ................ 14
Multiplication in Two Ways ..................... 17
Multiplying by Zero ............................ 22
Understanding Word Problems .................... 25
Order of Operations ............................ 27
Understanding Word Problems, Part 2 ............ 30
There are total of 28 lesson and practice pages in the book before the drills.
Studying the concept super well helps children to understand, become very familiar and at ease with multiplication.
While they study through these, they will probably memorize a few facts already - AND they will start seeing the need of having an effective and quick way to multiply (which is of course, knowing the facts by heart).
* Then the tables in a specific order, with a systematic drill approach and 12x12 grid.
The tables in my book are studied in this order:
table of 2
table of 4
table of 10
table of 5
[More Practice and Review]
table of 3
table of 6
table of 9
table of 11
[More Practice and Review]
table of 7
table of 8
table of 12
So it's the easiest first. Not only that, but in each lesson the student fills in a 12x12 grid to those facts he already knows. The "blacked out" unknown facts territory gets smaller really fast - and they can SEE it!
AND... that's not all. I feel it is VERY important kids learn their tables "both ways" - so they not only know that 5 x 6 is 30, but that they also know that 30 IS in the tables of 5 and 6.
To that end, I include specific instructions how you can "drill" or help the memorization of first the ANSWERS (skip-counting list), then associating each answer with a problem.
(This guide to oral drill is available online.)
All this multiplication info and practice is yours for only $4.50 :
=> Math Mammoth Multiplication 1
****************************************************
Well, this got to be long. I better save the fractions questions for another post.
Maria
P.S. If you go ahead and request that package of free worksheets, don't then be too surprised to get this blogpost as an email as well... I'm sorry but I just have to use what I write in multiple places, let many people read it. You know, sometimes I put my blogposts to an article to the website, I always pull my newsletter content from my blogposts - this time one of my email series emails ended up to be a blogpost.
Sabtu, 14 April 2007
You have to see this cartoon...
The numbers i and Pi got into an argument...
(Remember i is the imaginary unit and does not belong to the set of real numbers; Pi is an irrational number.)
(Remember i is the imaginary unit and does not belong to the set of real numbers; Pi is an irrational number.)
Rabu, 11 April 2007
Homeschool Blog Awards prizes
Due to a very unfortunate illness, the Homeschool Blog Awards website may not be able to post the prizes that the winners will get.
Since I am one of those that have promised prizes, I will just go ahead and post what I'll give here on my blog, to help out a little.
1) For the winners in categoriesBest Thrifty Homeschooler,
Best SUPER-HOMESCHOOLER,
Best Unschooling or Eclectic Homeschooling Blog,
Best Crafts, Plans & Projects Blog
- Math Mammoth All Inclusive CD (value $80)
2) For the winners in all the rest of the categories
- Math Mammoth Blue Series package as a download (value $40)To learn more, please follow these links:
Math Mammoth books
Math Mammoth packages and CD products
And... you can also request a FREE sample package that contains over 100 worksheets from the Math Mammoth Golden Series collections and over 170 other sample pages from the Blue Series books.
Go vote!
Senin, 09 April 2007
Homeschool blog awards
Voting has begun at the Homeschool Blog Awards web site, for the belated 2006 Homeschool Blog Awards. You can vote till Friday.
(I am actually one of the companies offering prizes.)
(I am actually one of the companies offering prizes.)
Jumat, 06 April 2007
Some new reviews...
I have recently completed not one, but TWO new reviews for the site. They are
1) YourTeacher.com - online math lessons that consist of video and audio clips, practice problems, solutions to those, "Deep Thought" question, and a quiz.
The list of lessons is long - and thus the amount of material is huge. It covers all topics from prealgebra through algebra 2.
I found the lessons to be very good. Read the review, or visit the website and see their sample lesson.
2) MathScore.com - online math practice environment. This is an intelligent system which catches the student's mistakes and adapts the practice accordingly.
For each topic there are several levels of difficulty, and the student is motivated to compete against him/herself to attain higher levels.
MathScore covers a ton of math topics from grade 2 to algebra 1. MathSCore is NOT only for math facts or basic computation, but includes all sorts of geometry topics, word problems, fractions, proportions, algebra ... all kinds of basic problems that you'd need to practice.
Read my review, or visit MathScore.com and check out their free instant trial.
1) YourTeacher.com - online math lessons that consist of video and audio clips, practice problems, solutions to those, "Deep Thought" question, and a quiz.
The list of lessons is long - and thus the amount of material is huge. It covers all topics from prealgebra through algebra 2.
I found the lessons to be very good. Read the review, or visit the website and see their sample lesson.
2) MathScore.com - online math practice environment. This is an intelligent system which catches the student's mistakes and adapts the practice accordingly.
For each topic there are several levels of difficulty, and the student is motivated to compete against him/herself to attain higher levels.
MathScore covers a ton of math topics from grade 2 to algebra 1. MathSCore is NOT only for math facts or basic computation, but includes all sorts of geometry topics, word problems, fractions, proportions, algebra ... all kinds of basic problems that you'd need to practice.
Read my review, or visit MathScore.com and check out their free instant trial.
Rabu, 04 April 2007
Calculator activitity for 2nd grade
I would like to know a simple activity that i could do with a grade 2 student, which involves using the calculator.
Here are a few ideas. Hopefully they are of help.
Add or subtract the same number repeated times.
For example, start with 10, subtract 1 repeated times and see how it goes to the negative numbers.
Start with any 2-digit number and add 100 repeated times. Or start with a 3-digit number and subtract 50 or 100 repeated times.
Here's a game: Player 1 chooses a 2-digit number. Player 2 predicts how many times you can subtract 10 before the number becomes negative. Then this is checked with calculator. If player 2 was right, he gets a point. Play till a predetermined amount of points.
Or, use adding. Player 1 chooses a three-digit number, and player 2 has to predict how many times you can add 100 to it before the result is more than 1000. Then check with calculator.
Readers, feel free to submit more ideas in the comments.
Senin, 02 April 2007
Teaching elementary mathematics - don't skip stages
I received recently a book called "Arithmetic for Parents. A book for Grownups about Children's Mathematics" by Ron Aharoni.
I want to tell you a little bit about this book, because I think it is exceptionally good, and a very worthwhile book to read if you're a teacher OR a parent.
Ron Aharoni was like many: he thought he could easily teach elementary school math because he knew college level math and beyond (he was teaching math in a university).
But... he was in for a big surprise when he entered the fourth, fifth, and first grade classes in a backward town in northern Israel, in 2000.
One surprise he had was that...
- ...he did not know how to teach elementary mathematics.
For example, during his first lessons he took children outside to measure shadows of trees, buildings, and the children themselves. The idea was to use the ratio of a child's shadow to his height to find the height of a tree or a building.
He took children outside to draw circles on the pavement and measure diameters, and compare them.
But as he admits in the introduction to his book, his first lessons were just a mess and confusion, with little meaningful teaching going on.
He wanted to do "hands-on experimentations" with children. But he didn't know how to integrate the hands-on experiences into the learning process, how to be systematic.
He lacked the idea of building concepts upon many small elements, one upon another, and the idea that you cannot skip any of these steps.
But he found out all that, and wrote an excellent book about how to teach elementary math.
...and the other big surprise was that
- During his teaching career in the elementary school he actually learned a LOT of mathematics... not new facts, but subtleties: how that concepts we adults think are easy, are actually built upon other simpler concepts and notions, and how children need to be explained ALL those little steps.
For example, Aharoni learned that he couldn't just present first graders a question such as
"Donna has 4 pencils more than Joseph. How many pencils does Donna have, if Joseph has 5 pencils?"
He had skipped stages. Children couldn't do it. They needed first to learn the concept of there being a certain number more than another number.
You can read how he handled the lesson from that on, and many other things.
The last part of the book goes through all important concepts in elementary mathematics from grade 1 to grade 6, and explains these subtleties and little steps that you should teach.
I highly recommend this book. It costs $19.95, you can find it at www.sumizdat.org.
Please note, I'm not affiliated with this; I'm not getting a penny for promoting the book. I just truly feel that reading it is a MUST for each and every teacher and parent who's teaching elementary math.
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