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.

A mixed bag of thinking...

There is so much happening in education that I'm somewhat confused as to where I should begin.  The absolutely sad news is that so many of our state teachers have been given either pink slips meaning they will not be hired again next year or letters indicating that there is a strong possibility that they will not be rehired.  

Amidst all this downturn, the New York Times has an article detailing news about the National Assessment of Educational Progress, a federal test designed to check long range progress of mathematics and reading achievement of our kids.  They report pretty much that it has been flat with little progress for a number of years.  Yes, you guess it--there are those after reading the results of this testing suggest strongly that we need educational reform.  You know what?  Maybe we don't need reform but rather we need to de-clutter our educational system.  Throw out all sorts of curricula that is out dated.  Maybe like a good Bonsai artist, we need some pruning of the curriculum.  Just an idea.

Another idea is to sit down and define some terms.  What do we mean by "science?"  Is science a subject or a way of thinking.  There are those who say we need more science....and I suspect they mean more chemistry, more biology, more botony, more astronomy, etc.  They are enamored with the subjects.  But science can be a way of thinking too.

Okay, for those parents and a few teachers that are willing to try some science--here is a project for you.  You will need an old turntable (for those who are young, it is a device to play 33 and a 3rd records (records were a way to play music.....)).  The turntable doesn't need the arm if yours is broken.  You'll need some playclay, three grow pots, six inch size will do and some string bean seeds.  Plant the seeds in the pots, water them and let them sit in the sun.  After a day or two, place the pots on the turntable with the playclay holding the pots on.  With me so far?  Put the turntable on a table near a sunny window and each day turn the turntable on and forget about it until evening.  Water the pots every so often to keep a damp soil.  If you have intermediate or upper grade level children, they should do all this work.

Then sit back a watch.  And ask questions--that is what science is all about.  Asking questions.  Will the seeds germinate?  If so, will they grow straight up?  Will they be twisted?  Have your kids write down their predictions--you too.  Be an example.  Write on a tablet what you think the string bean plants will do if they are moving around on the turn table.   In about three months, maybe sooner, you'll have your answer.  Write to me and tell me what happened.  

This is science.  I did this experiment in a fifth grade class.  Every student had to write and predict what they thought would happen.  When we had some results of what the plants were doing I asked why this phenomenon was happening.  We had more discussions in class about this then I needed.  I had parents come visit to see what was going on.  A few duplicated the experiment at home.  This was science, a way of thinking and trying out our thoughts.  And it was fun.  The best part was that the kids in my class "owned" their learning from this.  Then when I read to them about Galileo and his telescopes, they saw the similarities of what they were doing and what he was doing.

So don't forget, tell me how your experiment turned out.

Mathematics is another long term problem in education.  The lower grades do well but as we approach middle school and secondary school our math instruction seems to get stuck in the mud.  College and university math professors have been telling K-12 teachers what they should be teaching for some time with mixed results.  This kaleidoscope of suggestions has resulted with much confusion both of teaching and of objectives.  I don't have an answer--but we teachers are trying to do right by the mathematics goals.  Who should say what our kids ought to learn?  The mathematics scholars?  Industry?  The parents?  Maybe it's time for teachers to step in and make some suggestions.

We'll continue this discussion in the coming weeks.  Meanwhile be sure you thank a teacher for helping you learn about numbers.