Becoming a Teacher

"How did you decide to become a teacher?"  I asked this question for many years of my students and of the experienced teachers that I had contact with.  One of the more prevalent answers was because "I had this exceptionally (good or bad) teacher in school."  Students grade teachers as much as teachers grade students.  I can remember in my high school days having both an  outstanding (for me) teacher and a teacher that was just this side of terrible.  Strangely enough the terrible teacher was very popular with most of my high school peers.  I guess I just didn't fit in with his teaching styles. 

So based on those meager experiences I thought to myself that given what I had seen of teachers I could become one.  I liked people.  The pay was low but it was steady.  All I had to do was get into college and learn how to teach.  No sweat.  No problem.  Remembering all this makes me embarrassed today.  How arrogant I was in my youth.  I suppose idealistic in my thinking.

But that same answer was given to me by scores of entering education students at my university.  "I wanted to be like my fourth grade teacher" or "my high school coach really turned me around" or "I had this horrible civic teacher and I knew I could do better."

For me my arrogance or idealism was brought to reality the summer of my sophomore year in college.  I returned home to the New York suburbs to be with my folks.  And of course I looked for a summer job to help with the finances.  I remember applying to the local city recreation department but was turned down. They had a full slate of playground supervisors.  "But we can use some volunteers during the summer."  I signed up.

It was a day or two later that phone rang and a lady asked if I would be will to accompany some children to the Bronx zoo the next day.  Yes, of course. I'd be delighted.

We met at the recreation headquarters and the adults that were volunteering were introduced--there were a number of us.  And a number of busses and hordes  of over excited kids. We loaded the busses and headed for the Bronx zoo.  Upon arriving, each adult was given about ten children and told be back at the busses by a certain time.  That was it.  And off I went with my ten kids.

They were good kids and excited.  Age ranged from about seven to maybe thirteen.  I got all boys.  I found out later that if you got half boys and half girls in your group you had an easier time of it.....but what was I to know.  All I remember is that we started out and keeping the kids in a group was my main challenge.  Also finding the rest rooms was important.  It seemed that everyone in my group was on a different schedule for this activity.  But we scampered from this exhibition to the next....  The kids and I were having a good time.

At noon I found a grassy area and we had our lunch and then back to seeing EVERYTHING!  By early afternoon, some of my little kids, the seven year olds were getting tired.  So I picked the first one up and put him on my shoulders....and on we went.   Soon I put him down and picked up the next small child.  

Somewhere along our meanderings we saw a child crying--I remember one of the bigger kids recognized him as being with our busses.  He was lost and I said, not to worry, come with us.  Shortly afterwards another lost one was spotted and told to get into line. My kids from the original group were somewhat smug that we hadn't lost anyone.....yet.  Soon after we spotted another crying and lost child from our recreation tour group.  "Come along, you belong to us now."  And I was getting tired--really beat.  Hauling a kid on your shoulders for much of the afternoon was tiring.  But it also gave my group a way of always knowing where I was--just look into the crowd and see someone on someone's shoulders--that would be our group.

I do think we visited just about every exhibit at the zoo.....and just about every rest room.  I was concerned as we headed back to the bus area.  The kids were dragging their tail ends and had slowed down considerably.  I was dragging as well but concerned that we would make the busses late.  

Around the corner and into the bus area.  There were our busses and there was a bunch of concerned adults.  It turns out that I had the answer to their concern--the missing three kids.  Everybody was happy.  And I felt good.  I had successfully herded ten plus kids around a zoo and no one got hurt or lost.  And I was  bushed.  

The next day there was a phone call from the recreation office.  Would I please come down and fill out some papers.  They had a job for me.  I was to be the recreation supervisor (with an assistant) for a city playground.  Cool.

But I instinctively knew that teaching would not be as easy as I first thought.  I had good success with the playground and I gained much confidence.  I learned that I didn't have to know everything but respecting the kids was important.  I could see in myself the growth of understanding that first summer working with the kids on the playground.  And I could see the same growth of understanding in my student teachers as they began their career in teaching.

Teaching is a complex and demanding profession that is not meant for everyone.  Most teachers could do other jobs and a few do leave the teaching profession (more about this in another blog).  But most HAVE to teach.  Low pay and long hours does not deter those that need to be a teacher.  

[A sidebar]  Recently on local and national news a high school student from the east side of the Lake Washington was given the assignment to find and look at different types of human cells.  This high school girl had been quite ill, hurting at times.  She obtained cells from her intestines  from her doctor and while looking at the slides discovered the cause of her illness which the medical labs had not seen.  She is well now and plans to become a medical doctor--thanks to her science teacher.

I'm glad I went into teaching and I thank all those kids who taught me much at the Bronx zoo that one day long ago.  Don't forget to thank a teacher for helping  you.

$125,000 salary for some teachers

It has been in the news, on the web and on television--a report about eight teachers being selected to teach at a charter school in New York.  They were selected from all over the country and will be paid $125,000 dollars per year.

Two of you have written and asked that I comment about this story.  I have several thoughts that have been raging through my mind in the last few days.  Let's first look at the obvious.  These teachers can't fail.  They are all good.....already.  A puzzlement in my mind is why did the CEO of this project go all over the country.  I suspect one could find just as good teachers in the New York area.   But that is the theme of this blog--that teachers in general are pretty terrific people.  Most could do many other jobs but prefer to teach.

Here is something else to consider.  These selected teachers will be teaching at a charter schools.  Charter schools are ones that get a little extra attention.  The administration will talk up their charter schools--like souping up a car or giving a restaurant four stars.  What does this do then?  Parents hear about this and want their children to go to that school.  Right there we have a variable that is important for success--parental involvement. Any time you can get the parents to come to your school, interact with the teacher, even help out in the classroom, then you will have a successful school.  Consider private secular schools that charge large tuitions.  Already you have de-selected your students.  You have students who already know that they will be successful.  I suspect that is why so many parents want to place their children in a private school if they can afford it.  Bill Gates and Paul Allen graduated from private schools.

I'm not knocking private schools--most are very very good.  And they have great teachers. What they don't have are students with single parents and students who come from a stressful environment.  What they do have is a homogenous student body.....that thinks alike.  I saw this in Norway schools--very few minorities.  And the parents were involved with the school.

I do give this project higher scores in one area.  They will hold a raffle to see what students will be admitted.  But given the fact that the parents will have had to fill out forms and submit them to the project already means a certain type of parent.  I see success written all over this school already. 

Also given the fact that this is a charter school with well paid teachers I suspect there are some other factors coming into play.  I suspect they will have enough textbooks for everyone, enough desks (and the proper size) for each child, and that the physical plant, the school building itself will be in good shape.  But I wonder--will they have blackboards or white boards or the new technology, Smart Boards (Smarttech.com).  I also figure they will have enough computers for all the children.  Why pay large salaries for a number of teachers and not give them the necessary tools to accomplish the task.  So it is not just large salaries that will make a difference--but it will promote a better environment for learning.

I do have another concern however.  The articles reporting about these teachers do not mention other teachers--how are they going to be paid?  Studies have been done in which a few teachers were paid a larger salary and interaction between the better paid and the lower paid teachers decreased.  If I were one of the lower paid and wanted to get a pay raise why would I share my ideas of teaching the kids with other teachers?  It just doesn't compute in my mind.

If I were a principal today, I would want my faculty to be a team--not individual stars.  

So I am delighted to see eight teachers getting a decent salary.  I wish we could do that for all the teachers in this country.  But I hope at the end of the first year we try to compare this charter school against other schools in the area.  We will be comparing apples and lemons...and you can't do that.

If you've read all this and are pondering what your education might have been with higher paid teachers, be sure to thank a teacher because you are doing the thinking that they wanted you to do.

Television and learning

I don't know what most teachers think about television--I suspect that they resemble much of this country and have mixed emotions about the so-called boob tube.  I happened to grow up with this new medium so that it and I seem comfortable with each other.  When I see something that I am not interested in I either switch channels or turn it off.  In recent years I have become quite happy with the ability to set up my computer or my television to record programs that I can view at a latter date.  Cool!

But I read on the web and in some newspapers that there are those who are concerned about the use of television and children's learning.  Some researchers suggest that it retards the learning of children's speech--some authors even suggest that no television will improve SAT scores.  I can hear a number of parents applauding now across this continent.   However I suspect even in those homes of cheering parents one would find at least one if not more television sets.  It is a medium that is hard to ignore.

I once had a graduate assistant who said in a class one day that her family did not have a television.  Here she was in an instructional technology course learning about media and she did not have a television set.  Amazing!  On closer questioning from me she did admit that her family (husband, wife and two kids of school age) did have a television but it was under the bed that she and her husband used.  So I asked, is it then just stored there?  "Oh no, it is hooked up and useable but it is kept under the bed."  Not sure where this was going I asked if her husband watched football on the television?  "Yes, on Sunday's he watches the Seahawks."  So I asked, do you bring it out and set it up in the room somewhere?  "No, he lies on the floor and watches the game."  "In fact when ever someone needs to watch something, they turn on the tv and lie on the floor watching under our bed."  To this day I'm not sure I understand their use of the television in their family.

Still, the TV is a part of our society.  I'm always fascinated with the public television and its relationship to the children.  From Kermit the Frog to reruns of being Welcomed to my neighborhood children have learned.  But someone has to make sure those channels are on and that the children have to watch.  Actually, they have to learn to watch......

Let me switch subjects just for a moment.  How do children learned to read?  Optimally, Mom or Dad sits down with their child and says let me read you a story and then proceeds to read a simple story to their child pointing out the pictures and turning the page.  "Turning the Page!"  That is how children learn to use a book.  Then we read them another book and pretty soon they begin to see a relationship between those strange markings on the bottom of the page and what the parent is saying.  And as they become familiar with the story the child may ask to please read the story again.  There isn't a parent today that hasn't been bored with a child's beloved story being read to them for the nth time.  Indeed, some parents have reported changing the story and having their child say, "No, that is not what you read last night!"  "Read it like you did before."  Oh Happy Days.

But how many of you parents have helped your children to "learn" television.  How to watch and how to listen.  Very few I suspect.  In the early seventies, I found some parents who would work with me and their children.  I'd have them put in a tape (before DVDs), then tell the child what the tape was about (mostly Disney's short films).  Getting a sense of what is to come is important to children's learning, sorta like setting goals.  Then the parent and the child watch....together.  In fact the parent needs to say things like, "that is funny" or "Oh no, he's going to be caught."  Reacting to the TV is good.

After the tape or DVD is over, the parent needs to ask questions like--"who was your favorite person, animal, whatever, in the show?" " What was the best part?"  "Did you know what was going to happen?"  Questions like this help the child learn to interpret the television signal much like learning to decipher those strange marks on a page of a book.  

Now a warning to parents who do this with their children.  Those kids will want to watch that show over and over.  And they will want to tell you what is coming in the next scene.  Boredom city for the parent but a delight for a child.  They even begin to memorize the lines in the movie.  Which indeed is learning to speak in longer sentences as they grow older.  It is a learning situation.

Parents can't always watch with their children.  But after initial watching of some shows, parents can set up a movie and then proceed to get dinner ready, e-mails answered and so on.  When the child is finished with the tape, Mom or Dad need to sit down for a short moment and ask, "what was the show about?  "Did it have good parts that you enjoyed?"  "Would you like to watch it sometime again?"  All of these types of questions leads the child to watching with more intensity and not just being a passive receiver of the message.  

Hey Teachers-you too can help in "teaching" television.  When showing a movie (I use tape, DVD, film, movie and shows interchangeable in this type of writing) teachers ought to put special words on the blackboard, ask the students to look for certain activities or findings.  In essence, get the students to look actively for something rather then passively watching and trying to recall.  In the movie "Hemo, the Magnificent" I learned to put scientific words on the board early in the day and the kids could either look them up or just think about them.  When they were said in the film, hands would go up.  This is important--it made them successful in watching a movie.

I have one more major point I want to make about using television in your home or school but it will wait until next time.  I use to do this with my kids.  Show them a movie about a kid breaking the glass on a greenhouse and just as he is about to be caught turn off the TV.  Tell them they can see it tomorrow.....after they write me an ending.  Writing an ending for TV?  What a thought.  I got some of my best writing from the kids doing this trick.  Learning English and Television.  My oh my.

So what do you think this major point will be?  Any idea?  If you do have some thoughts, write me.....OR go thank a teacher who taught you to anticipate.

Strange problems that teachers face

There are times when problems arise in a class that the college of education   have not prepared you for.  What should a teacher do when a kid gets sick in class--all over his desk!  Or the parent that comes mid morning to take his boy for a haircut.  Really.  Little problems like this are just not discussed in college classes on how to teach.  Behavior problems, yes, we do a good job of behavior modification training and we can teach reading to just about anyone.  But sometimes you get a problem that just wasn't in the books.

I had a fifth grade--a really nice bunch of kids.  Pretty evenly divided between boys and girls.  That's always nice as it seems to keep the goofiness index low.  I had my room arranged with the individual student's desk in rows but we did move them around.  I found that I would change the desk arrangements about every six weeks.  It seemed to help the kids from getting into cliques or groups that would then exclude someone.  I wanted a friendly class.  Sometimes I would put the desks into groups of four or five.  Interestingly enough I found this to assist the kids to help each other and learning increased.

But as I said, at the moment I had the desks and chairs in rows by and large.  I always kept my desk in the back of the room--hardly every used it but it was a good place to send a kid who was behaving poorly to do his/her school work at my desk.  In the parlance of today's kids, "it was cool to work at Mr. Blackwell's desk."

I remember walking into my class one morning before school started and walking around.  I always like to have ten minutes or so just to look at my classroom and get a feel for it.  Sometimes I'd see a desk that needed cleaning (inside) or someone had left a lunch pail somewheres and I would want to remind that student to take it home.  However on this morning as I walked around I seem to smell an oder  that didn't see quite right.  I sniffed here and there but couldn't quite put my finger....or nose on it.

But life goes on in a classroom and we got through the day.  The next morning I went through my usual procedure and going around the room and still I smelled something not quite right.  I remember opening the coat closet doors and sniffing in there.  There were always an extra jacket or two.  One day I remembered a dress hanging in there as well.  How and why?  I have no idea.  The dress was probably to be taken home from one girl's house to another.   Best for me not to go there.

The next day the smell was a bit stronger.  I remember asking the janitor if he was using a new cleaning agent but he said he wasn't.  However, he hadn't noticed anything yet.  He keep his eyes open or nose.......

On Friday of that week the problem was getting to me.  I could smell something but I could not place it.  So doing the day when we were between this subject and that, I told the class that we were going to clean out our desks.  Always an exciting time for the kids and too much noise for me.  Some of the boys would actually pick up their desks and dump the contents onto the floor.  But most students just took everything out and placed it on the top of the desks.  I had rags available for them to wipe out their desks and then they could put back things in some sort of neatness however they would like.  It was always amazing what the kids would find in their desks.  Always a permission slip that was suppose to be turned it weeks earlier, lunch bags that were never taken  home, someone else's textbook that had been missing and of course at least four or five overdue library books.  

As I walked around the room guiding the kids and looking at what they were doing, I noticed one boy who had four milk cartons that he appeared to be saving.  As I got closer to his desk the smell was stronger.  Aha! I had found the source of the strange smell.  It was in Samuel's desk.  Now Samuel was a good student--very bright and somewhat popular.  Not athletic and he didn't run around with any one peer.  But the kids liked him and he was a happy kid.  I enjoyed having him in class and he was always asking interesting questions.  I suspect he would have won the award for being sent to the encyclopedia  the most to look something up--he enjoyed that activity.

So I asked Samuel--"What are those milk cartons for?"  "Oh, Mr. Blackwell, this is my wormatorium.  I am growing worms."  And then he proceeded to tell me how many worms he had and where he had gotten them.  He also mentioned that they didn't need sunlight so it was good to keep them in his desk.  But as I leaned closer to his "wormatorium" I recognize the smell--old milk.  Only milk can make that smell.  Ugh!  He had not rinsed his lunch milk cartons out before putting in some dirt from the playground and finding some worms to keep him company.

I found Samuel a brown bag and had him take home his wormatorium with the promise that I would ask him to tell the class how things went.  That suited him well and he remained happy.  And the room had a much better.....and normal smell to it after that. 

If you had a happy classroom and the room smelled nice when you were growing up, be sure to thank a teacher for taking time to make sure that happened for you.

A Teacher's innovation

I've been reading a lot about autism lately.  What a challenging problem for parents...and for teaches.  How do we teach these children?  Before World War II, most challenged children were kept at home.  If the parents were financially secure, they could hire a private teacher or tutor.  But the lower the economic level of the family the less likely that would happen.

After World War II,  a division of the public schools elected to take on the challenge of dealing with children with different learning and behavior styles. This division is now called "Special Education."   Note that I did not write that these were mentally challenged children, rather they have a style of learning for which we have yet to gain some knowledge.  Before anyone writes me to challenge my knowledge of such children (which indeed is limited and I admit that fact) let me state that one of my family is....different.  But let me also state that she is a lovely lady and is smart in her own way.  She has taught me much over the years and I love her dearly.  She knows that she is different from others but she refuses to let that bother her or change her course of direction in life.  She gets up each day and looks forward to helping and taking care of others.  She has increased my knowledge of what is "smartness."

However my main focus today was to write about a special education teacher I met one time in a local high school.  Although I had some student teachers in the school at that time, I became aware of a special education teacher who was using technology to help his children learn.  I asked if I could watch and he agreed.

Robert Gibbs (not real names as usual) had a special education class of about eight or nine students of high school age but of primary grade aptitude.  The kids also had some behavior problems as well.  It must have been a challenging class for Robert.  But he was an innovating teacher and managed to use an early Radio Shack computer to help him with his students.

One objective for these students was number recognition.  They weren't ready to add or subtract yet--merely knowing that the number was a "1" or an "8" was what Robert wanted his kids to achieve.  So Robert on his own learned "Basic", a early programming language for the computer.  He spent nights practicing on a computer at home and soon developed a simple program that was perfect for his use.

He would sit one of his students at the computer and load the program.  The program's first activity was to ask what was the student's name using a speaking program that was available at that time.  Robert's student would type in their name and the program would say to them, "Welcome Tom" or Jim or whoever it might be in the class.  Robert said that his students were so delighted with the computer saying their name that they wanted to go back and back and back......  Robert rewrote the program so that the students could hear it over and over and Robert reported to me that he became slightly dazed after hearing "Welcome Tom" over a hundred times one morning.  So he added ear phones for his own sanity.  Smart teacher...

Once the student got by the name recognition segment, the program would place numbers between zero and nine on the screen in different locations. Then the program would ask "Tom" where is the number "six?"  Tom was suppose to place the curser on the number six and click return.  Then the computer would redo the screen with new numbers and ask for the curser to be placed on a new number.  If Tom did not select "six" the program would say, "No, find six."  It would continue this answer until Tom would eventually find six.

However Robert's students quickly realized that if they did everything right, the program would end but if they made mistakes the program would continue.  So I watched Tom place his curser on every number on the screen except the one requested until there were none left for him to pick except the correct number.  They he would look up at me and smile a big smile.  He had learned his number recognition and a little bit more.

Robert told me that he wasn't upset with this behavior that indeed the deliberate picking of the wrong numbers was actually good practice for his students.  It was like, "I am fooling this computer."  

Robert's computer program on number recognition was one of the more innovating ways of teaching special education children that I saw.  However, it was the beginning of my notion that the interaction between students (no matter what their age) and the computer had a decidedly valuable contribution to education.  The kids of today navigating the web are light years ahead of children who grew up in the fifties, sixties and seventies.  (Hi Moms and Dads of that era.  Makes you feel old, doesn't it?)  Like Louis Armstrong sang in his popular song, "It's a Small, Small World," the children of today know more then we did back then.  And that's good.

If you know how, why not write an e-mail thanking a teacher for all they do....  Or get your child to help you..

The mathematics debate continues

There is an advantage to being old(er).  In this case I have seen this math argument several times during my teaching career.  Back in the seventies, there was the push in my school district to use something called SMSG Mathematics.  It had rods, and lesson plans that were designed to help students "discover" the relationships between numbers.  SMSG stood for "School Mathematics Study Group" although many of us called it "Some math, some garbage."   I am amused to see that some of the SMSG learning materials on now housed at the archives of American Mathematics at the University of Texas.  Now that does make me feel old.  Some of my students really liked it--others sort of blew it off.

I note in my local newspaper (The Bellingham Herald. 5/18/09)an article that reports that the local school district has been using a sub-standard mathematics in the schools.  I'm not sure what sub-standard means as it was not fully explained in the article.  I suspect the school district will return to the more direct and rote method of instructions in mathematics.  I have mixed emotions however.  I suspect somewhere in the research and other articles that students in other lands are scoring higher then our children in mathematics.  It is a pretty standard commentary that is made from time to time.

The problem that I see is that, at least in my local town, we were teaching the children how to discover mathematics and then we test for straight learning of numbers.  You teach the children to do one thing but you test for another.  And then you get upset because the kids don't do well on your test.  

I want to digress for a moment.  I taught for thirty two years at my university....my field of study and research was Instructional Technology.  Basically it was how to use technology in the teaching/learning situations.  This was at a time when computers were just coming into prominence in education.  

I had students of all types who were interested on how to use computers in teaching....both undergraduate students and graduate students wanted to know more about how to use computers.  Not only did I have both undergraduates and graduates in class, I also had students from foreign countries.....India, Canada, Lithuania, and Indonesia and a few countries I have forgotten.  Let me say at the onset that Canada has an excellent educational system.  They train their teachers well.  And those teachers do a good job.  In some areas they do a better job of teaching then we do in the United States....but then I think we do better in a few areas as well.  It's a mixed bag.   

But excluding Canada, it is my opinion that the foreign students that I had were very bright, intelligent and wonderful people but they did not work well on problem solving.  If I gave an assignment, they wanted to know each step of the way.  I did more "hand holding" with foreign students then with American students.  The American student was able to think through the steps to the solution of the assignment and carry them out.  Most of my foreign students could not.

For example.....in one class I wanted students to make color lift transparencies for use in teaching a class.  I had several Indian grad students who wanted to know what they were going to teach, which overhead transparencies they would need and how to start.  I remember telling them to pick something they would be teaching and this left them in a quandry.  Their ability to imagine themselves teaching a subject was very difficult.

My Indonesian students were even more of a problem to teach.  They were so use to working in a group that they could not study a subject and bring a report to class to share with the others.  They had to do it all together.  Now I am not unhappy with my Indonesian students--it was a cultural style of learning an I had to adjust my assignments so they could work together.  Margaret Mead, the great sociologist and anthropologist would have loved to study this differences.

My Indian students were very, very bright.  They could memorize entire pages of information.  With multiple choice and fill in the blanks, they would beat the American students time after time.  But when I asked on a test of how they would use something in an educational setting, they couldn't do it.  

Returning to my original theme, American students are much better at analyzing the situation, deciding upon some action and then completing the task.  Many foreign students are not up to this type of learning.

So when we compare our American students in mathematics with foreign students one has to know what the test are testing.  Rote knowledge or problem solving?   It is my gut feeling that our students can hold their own quite well in Mathematics.....they might not score well, but they will understand what the goal is and how to get there.

The mathematical argument goes on.  If your checkbook is close to coming out correct, be sure to thank your math teacher in your prayers. 

The Mathematics conundrum...

As I write the Seattle School Board is debating on how they will address mathematics in their schools for the coming year.  The television news have reported on it and I suspect if I check we would find that the newspaper and the blogs have also made comments as to what is happening.  But before you think you are on top of all this, let me explain that this problem of how to present mathematics to our students has been around since slightly after world war II.  And we still haven't solved the issue.

I hope you remembered my simplistic explanation of the three philosophies of education some blogs back, the one involving circles.  Let me explain the math problem from that point of view.  There are two basic methods in teaching mathematic.  One is from top down--the idealistic method.  You start by explaining what numbers are and how to manipulate those numbers.  You work from the simple to the complex, from adding of small numbers to the big bang theory and quantum physics.  It is primarily a rote method of instruction. 

The other method (note that I did not say the second method as that might imply the 1st being better then the 2nd--see how numbers can be viewed?) is the realistic method of teaching where the students have a problem to solve and use numbers in a way to "discover" or "own" the solution to the problem.  They may actually use something else besides the numbering system we now use but in essence they then understanding "numbers" as well as the solution to their problem.  

So what we have then is the "rote" method vs. the "ownership" method.  Which is best?  In spite of studying the mathematics curriculum problem for most of forty years, I still haven't the foggiest idea which method is right.  And if you think "politics" or "religion" are super sensitive subjects, try asking the Mathematics Department at your university as to which is best and watch the fur fly.  A hot question to ask any math prof is...."How much mathematics does a K-12 teacher need to know to be able to teach?"  And....."how should they teach mathematics?"  This is one of the more perplexing problems of the educational system.

I have a sense after teaching all these years that the answer to this question of learning mathematics is in our genes.  Some children seem to understand the abstraction of numbers and enjoy manipulating them.  Other children see no fascination in arithmetic and are bored with the subject.  It seems to last throughout one's lifetime.  But I have no proof (pun intended).  

I wonder what the Seattle School Board decided?  [blogger's update]  Seattle decided last night to forego the discovery approach to mathematics and by a 4 to 3 vote picked a more top down approach.  Many reasons for the change, many people unhappy.  You can read Seattle P.I. article about it at:  http://www.seattlepi.com/local/405961_math07.html  [May 7, 2009]

Do you know how to count and make change?  Remember to thank a teacher for that skill.