Wednesday, November 28, 2012

Elementary Education majors practice Engineering

Up until recently it was called Design Technology, the art of using our scientific knowledge to solve problems and create solutions. Today, thanks in large part to the Boston Museum of Science it is now called Engineering. Yesterday, in my math and science education class I challenged my elementary education majors to support a small washer as high as they could using two copies of the Defender, the student newspaper. I made sure the students spent a few minutes first reading the paper so that we could genuinely recycle it through the engineering activity.

In science the questions and curiosity arise from the natural world; How do seeds grow? What is magnetism? What are genes? In engineering the questions and curiosity arise from the ways we can use our scientific knowledge to overcome problems or improve our lives. Building a better mousetrap is probably the epitome of an engineering project. Just about everything we use in our lives owes its existence to the application of some type of engineering.

There are other differences between science and engineering that we need to be aware of when we are teaching students. The skills we want children to learn in science class include observation, classifying, measuring, predicting and communicating. In engineering we want children to learn all about researching, designing, constructing, testing, adapting and improving and presenting. Engineering provides students with authentic situations of problem solving and creativity. And it is incredible fun too so students are highly motivated to succeed.  

Saturday, November 17, 2012

The Math of Aging

The older I get the faster time seems to pass. I've always felt this and have heard many others make this observation. There is, of course, a mathematical explanation since each successive year in one's life is a smaller fraction of one's lived life so far. At age 6 a year is a whole sixth of one's life whereas at 60 it is a sixtieth.

The speed of life also tends to slow down with the passing of the years. Athletes lose a yard, reaction time increases and and tasks around the house that used to take half an hour now need two hours to complete.

There also seems to be an inverse correlation between the accumulation of wisdom and one's ability to recall facts, names and fundamental relationships. I've always thought that wisdom is the ability to use one's knowledge and understanding in a beneficial way within a social context. I think it  would be difficult to be wise in the forest, so to speak, in the same sense that if one were not there, the falling tree would make no sound.

The finances of aging also take on a different character and dimension. The things one buys change since one has accumulated most of life's essential material things. One learns to do with less, want less, and wish there was less sometimes.

Geometrically life seems to take on a downhill slope having passed over a crest of some sort. When you look back you start looking uphill instead of downhill all the way back to one's birth. I find myself sneaking a look around the crest or the hump to see things way back in the past. The geometric shape of the individual years also seems to have changed. It's flatter and has fewer peaks and valleys; summer tends to resemble a wide valley while winter looks like a plateau. Spring and fall don't seem to count in the shape of the year any more.

The frequency of doing mindless things seems to increase too. I poured a can of dry dog food into the garbage can the other day instead of putting it in the dog's food bowl. A week ago I mislaid the potato peeler and finally found it in the draw under the computer table.

The geometry of one's physical shape also seems to change but I don't think I'll go there. The dog did eventually get fed by the way.

Wednesday, November 14, 2012

Zero is an Even Number

There was a neat, short article in the NYT this past Monday (thanks VBJ) about the dilemma posed by whether 0 was an odd or even number. It was a high stakes decision because it determined when you could get gas during the gas rationing imposed in the wake of hurricane Sandy. After consulting a number of mathematicians Mayor Bloomberg correctly called it as an even number so that owners of cars with license plates ending in 0 knew exactly when to fill up. The article also went on to describe how the French police in Paris just ignored the issue during a smog alert in 1977. While odds and evens drove on alternate days 0s could drive whenever they wanted to.

I grew up calling 0 nought and played the game noughts and crosses which seems a much more logical name than the tic-tac-toe used in the US. The name has 3 parts yet there are only two options - very illogical. The name also gave rise to the early (2000 - 2004) and late (2005 - 2009) noughties in the UK. The word also features frequently in British history, literature and lore while Zero for me, growing up, was the name of a Japanese fighter plane.

The recent inclusion of 0 as the starting number in teaching counting in elementary school math is, however, a serious issue. When we teach children to count these days we teach them to begin with zero. The reason for this is that researchers have discovered that it makes fractions much easier to teach, and for student to learn,  if students realize that there is a space on, say, a number line, between 0 and 1. Fractions are introduced as parts of a whole using a variety of different models. One of these models is a linear model such as a ruler. This is really useful because rulers are usually marked with fractional parts beginning at the 0 or origin.

This idea of counting from 0 also helps young chidlren learn about measurement. Life begins at 0 as does time, distance, weight, volume, capacity and angles. Since all measurement is the repetition of the referent unit it is important for children to realize what that referent unit is; what is the one or the whole of the referents being counted.

The really interesting thing, though,  about the numbers on the license plates is that they weren't even being used as counting numbers but as naming numbers so it didn't matter at all if it was odd or even in a cardinal or counting sense. The fact that it was called an even number just made everything tidy and mathematically correct. 

Monday, November 12, 2012

Geography; the Most Important Science

If you want to be licensed as an elementary school teacher in Vermont, and in many other States too, you have to have a second academic major in addition to your education major. This requirement came into effect in the late 1980s and I remember well being part of the team of HE teacher education folks and  VTDOE staffers who met for several days to work out a rationale and how the requirements would fit. The primary idea behind the regulation was that an in-depth knowledge of something other than how to teach would bring scholarship to the teaching profession and help teachers become subject leaders in their schools. It would give them an academic passion to go along with their passion for teaching. I thought, and still do, that this was a great step forward, not least, because I had gone through this process some 10 - 15 years earlier in the UK.

My academic major was geography which complimented my teacher education studies so well. I remember learning all about geomorphology, a little geology, human geography, some social geography as well as physical geography. I learned about probablism v possiblism, Gondwanaland, drumlins, eskers, eratics and Monadnocks. So much of what I learned is still with me (there's a great eratic in the middle of the Bolton golf course) because I loved learning it so much and I used what I knew with passion when I was a fourth grade teacher. It wasn't that I didn't enjoy teaching math, language, reading and science but geography was just something else.

I remember teaching an eight week unit on the canals of England in which the students read and wrote about just about everything related to canal construction, canal life, influences on commerce and on and on. The student even brought in old pots and plates and cups which they then decorated in the traditional roses and castles artwork of those who lived on the canals. So when Richard Kujawa, the geographer extraordinaire at SMC, put this link on his FB page it brought a little sadness into my life to know that Geography was no longer a top ten favorite discipline in British high schools. I was glad to know, however, that I was in good company with my love of geography as the author of the article was none other than Michael Palin, president of the Royal Geographical Society.

Friday, November 9, 2012

British Government bans Calculators

Here's a remarkably backward step by the British Government concerning the use of calculators in primary school maths (elementary school math). They are banning calculators from the test taken by 11 year-old students.  It's almost inconceivable to believe that a group  of educated people could consign young children to the laborious task of nineteenth century pencil and paper computations. It's like not allowing people to use word processing technology to write.

This is such a bad idea. First, it is guaranteed to do nothing to help children develop more positive attitudes toward math. There are so many more wonderful things to learn about in math class than the unbelievable drudgery of doing algorithms by hand.

Secondly, the incredible amount of time wasted in schools teaching children how to complete laborious algorithms could so much better be spent teaching them how to solve problems. According to Thomas Carpenter, there are 22 different types of simple mathematical constructs involving joining, separating, part-part-whole, comparison, equal groups, area and so on that can be solved through the application of the addition subtraction, multiplication and division operations. We need to spend our precious time we have teaching children how to identify the nature of a particular math problem so they can then know which button to press on the calculator in order to solve the problem.

We cannot, of course, allow calculators to replace mental math. We now teach children from a young age all about the intricacies of our number system and how to use number mentally. Wonderful math programs such as Bridges focus extensively on numeracy or quantitative literacy as it is sometimes called.

It's interesting to note the use of the word "sums" in the BBC article. In the UK a sum is any one of the four operations, not just addition as an Harry Potter fan knows.

Thursday, November 8, 2012

Vi Hart's Revolutionary Mathematics

For years now I've believed that Mathematics has an aesthetic, creative, and joyful component to it that is sadly ignored for the most part in the way we teach it; especially at the high school level. I have also believed that one of the main reasons why students at the K - 12 level, as well as the 13 - 16 level, dislike it so much is that it is seen, and taught for the most part, as a functional, objective discipline with little intrinsic value.

In math education there tends to be no equivalent of  poetry, creative writing, literature or anything that really helps children develop a sense of enjoyment or creativity. Imagine if reading and writing were taught from a totally functional perspective? One of the most remarkable things is the number of times students will ask of a particular math skill or concept "when am I ever going to need this" compared with the number of times a student will ask the same question of something related to creative writing.

One person who is doing something about this is Vi Hart, a self proclaimed mathmusician. She could also be called a mathartist or a mathologist as what she does flings wide the boundaries of  what we traditionally think of when we hear the word 'math'. You can also now see her videos on the Kahn Academy site which is a place many people go if they are having a difficulty understanding a particular mathematical idea.

Tuesday, November 6, 2012

Voting for the First Time

My son Andrew was able to vote today for the first time in his life. He was very excited and wanted to make sure he voted for the right people. It's a neat experience voting for the first time. It's almost like a rite of passage and it suddenly gives you a sense of responsibility and a sense that you really matter; at least that's how I felt both times I voted for the first time.

The first time I voted for the first time was in the UK in 1965. It was different there, as it still is, from how we vote in the US. In the UK you vote for your local candidate for one of the political parties. In each of the wards throughout the country individuals who represent the entire spectrum of political viewpoints, and usually a political party, "stand" for the House of Commons and  try to win your vote. The political party that has the most candidates elected to the House by a certain margin wins the election with the prime minister coming from that political party.

The second time I voted for the first time was in 1986 after becoming a US citizen in 1985. It was the same level of excitement all over again even though it was quite a different system. It has always seemed strange voting for a single person, a President, but in retrospect voting for a political party in England was probably the same thing because you always knew before you voted who the Prime Minister would be if a certain political party ended up being elected.

So, I'm off to vote.

Monday, November 5, 2012

Bonfire Night

Oh how I miss Bonfire Night and everything that went with it on November 5th. The incredible anticipation or waiting for my dad to get home from work with boxes of fireworks when I was but a lad. It was one of the annual rituals of growing up in England and, as a celebration, rivaled Christmas and birthdays for the sheer excitement of it all.

It is, of course, the annual celebration of the discovery of a plot to blow up the houses of Parliament in London by Guy Fawkes and his band of anarchists.

              "Remember, remember the fifth of November, the Gunpowder treason and plot
                    I know of no reason why the Gunpowder treason should ever be forgot"

The full verse is much longer but this s all we ever had to remember. For weeks leading up to Bonfire Night, every school boy and girl would be collecting combustible material to build the largest bonfire they could manage in their back yard. It was tended with loving care as the days grew shorter. Guy effigies would be made by stuffing old clothes with whatever was available to make them as life-like as possible. The Guy was always topped off with an evil looking mask. As the day approached praying in earnest would begin that it would not rain, for rain was the absolute scourge of everything related to bonfire night. The fire would not burn and the damp fireworks would not light, and this in a country renowned for its rain.   

The fireworks were the highlight of the night and only my dad was allowed to light them, at least until by brother and I were old enough, around 12 or so, to be given the lighting honor. Catherine wheels were always pinned to the same tree and jumping jacks always terrified me. The rockets were spectacular but I was always worried that the burning embers would start a fire somewhere. They never did, of course. Later, when we were teenagers we were only interested in "bangers" which were virtually small charges of gunpowder that made the most incredible bang.

Friday, November 2, 2012

Memory Pegs are Great

A light year ago in another life I was teaching a class of pre-service teachers all about problem solving in science. Today it's called engineering but back then it was called design technology. I was happily telling the students that they could get help completing the activity by asking their uncle, brother, father, son, or grandfather when Cathy, at the back of the room slammed her hand down on the desk and said "you can't say that". Somewhat stunned I asked "Why not?" and before she answered I realized just how gender biased I had been. It had never occurred to me before but from that moment on I resolved to rid myself of any gender biased language, disposition, intention or anything else that would discriminate on the basis of gender. What it took to raise the issue to my awareness was a shock that shook me out of my usual behavior; something that caused me to change. I am forever indebted to Cathy who I see at conferences from time to time.

So, mindful of the trauma of that moment I resolved to help pre-service teachers change their habits in less traumatic ways. Such a strategy is the 'memory tag' or "reminder" that a student can use to raise her consciousness concerning something about her teaching behavior she wants to change. For the past two weeks I have been working with Natalie, one of my student teachers, to slow her rate of speech when she is teaching. She's doing an outstanding job in the classroom but I felt she would get less tired and frazzled if she slowed down a little. To do this I suggested she put a Bandaid on one finger so that when she felt it it would remind her about her rate of speech.

Today when I observed her I couldn't believe the difference. She was speaking at exactly the right speed and everything about her  was calmness. The fourth grade students were also noticeably less frenetic and so after I had observed the lesson I complimented her on her new found skills and asked her if she had tried the Bandaid idea. She held up her hand to reveal the largest costume jewelry ring I have ever seen. She said that every time she felt the ring she remembered to slow down. Isn't that neat!