Math is in Everything

As any of my students will tell you my favorite words of encouragement are "well done". In fact, it has beeen known in years past for students to have informal competitions to see how many 'well done's they can get on one paper.

So a hearty 'well done' to all the graduate students in my Teaching Mathematics in the K - 8 Classroom course this semeester for the wonderful eNotebooks they have all completed. I don't think I have ever had such a variety of topics before as the list below illustrates.

Brewing and Math - Scott  Football and Math - Ira Curling and Math - Pat Origami and Math - Gretchen Comic Books and Math - Steven Burlingtonian Math - Micky Art, Nature and Math - Claire Knitting and Math - Kris Motorcycles and Math - June The Roman Empire and Math - Joe Lax and Math - Kevin Three Course Meal and Math - Stephanie Theatre and Math - Marcy
Arthurian Lore and Math - Karyn Math in the Garden - Aurelia Math and Yoga - Kate
The Math of Jane Austen - Julie

The assignment is designed to help students see how math is a part of the world in which we live in all it's wondrous diversity and not just for "balancing a checkbook". It is my hope that children will also see how math is an everyday part of their lives so that they never have to ask the question "when am I ever going to need this?". Most of the things we learn in school are not really needed in the strictest sense of the word; they just make our lives better, richer and more worth while.

Teaching What you Cannot Do!

Many years ago when I was teaching fourth grade in England I used to teach gymnastics in the after-school gymnastics club twice a week. It was an after-school  program sponsored by BAGA, the British Gymnastics Association. I was pretty good at it too; the teaching that is and not the gymnastics. I could, in fact, barely do a handstand but I could teach 10/11 year-olds how to do front and back flips and even a twisting back flip from a standing start. I read extensively about each individual move, the muscle control, the vital suppport points and the required techniques. Several of my students even went on to win regional prizes and may well have gone on to greater accomplishments after I emigrated. The key to success was being able to describe to the students what was required and to give the students the confidence to know that when they were risking something for the first time I was there to support them.

Fast forward forty years to tonight's graduate math ed class in which I have to teach probablity and proportional reasoning. Both are fairly abstract concepts althought they can be made concrete through the use of inquiry-based activities such as tossing coins and drawing. There are, however, some tricky abstract concepts one of which eluded my understanding for several hours today. For some reason I could just not understand, perhaps remember is more accurate, the difference between additive and multiplicative comparisons. I read extensively and figured some problem examples but it just was not working for me and I could feel the panic and fear rising. I even read about how some people cannot think proportionally but I knew this did not apply to me. I finally saw the light, so to speak, when I completed a problem in which a runner starts 6 laps before the second runner starts. If they are both running at the same speed the first runner will always be six laps ahead (Additive comparison) at all times. If the two runners started at the same time and one had completed 9 laps while the other had completed only 3 laps this would be multiplicative comparison. Ahaaaa, sigh of relief!

Why should lack of understanding invoke such panic when the inability to do something such as a back flip is taken for granted as quite normal? Therein lies one of the cornerstones of my beliefs about teaching.  

It's Got Its Problems!

Sometimes it’s really important to use a word purely for its sound or the way it’s written. It’s not necessarily the way it’s used or the sounds its letters make. Sometimes it’s just the interest its use generates within certain circles where its correct or incorrect use might cause its avoidance in the written form. 

The use of ‘its’ or it’s” in oral conversation, of course, has no effect on which form of ‘its’ is used.  Whether it’s ‘its’ or it's it’s’ really doesn’t matter since each ‘its’ or ‘it’s’ in this pair of homophones cannot be distinguished from the other by its sound. On occasion, it’s necessary to think even more carefully when one has a plural possessive but, of course, we all know that it’s not correct to place an apostrophe after ‘its’ to make 'its’'.

It's often occurred to me that it would be good to simplify our English language to make such errors obsolete but I doubt it's ever going to happen, at least not in my lifetime. So for all those who, like me, occasionally miscue with its', or it's' use here's a page that defines it's or its use with great clarity.  

The Three RRRs

At least the new 3Rs are grammatically correct in that they are all Rs. The old 3Rs, of course, were really only 1R plus 1W and 1A or, readin', 'ritin', and 'rithmetic to our forefathers in the nineteenth century when all this began. Education has always been characterized by the "pendulum swing", to make a link with my last post, whereby the dominant theories and practices tend to swing from one extreme to the other, often in harmony with the dominant political persuasions of the day. No Child Left Behind and the recent crisis of test score tampering in Atlanta suggest we are currently in a more formal, traditional and accountable interpretation of the process of Education. Standards are clearly defined and yearly growth rates have to be met if schools are not to be defined as failing. The recent Atlantic schools crisis most likely came about because the school system was doing the unthinkable, tying salary bonuses for teachers to student test scores.

One of the less well known outcomes of this more conservative, accountable approach to Education is that if something is not tested it is most likely not taught. Science, for example, is only tested at 4th, 8th and 12th grade and so is less likely to be included in the daily curriculum than the 3"R"s which are tested in all grades from 3rd grade in the New England Common Assessment (NECAP). No testing is required in social studies or engineering, or music, or PE.

The last time science education really had its day was in the last century when the "alphabet" inquiry centered  science programs were developed in response to Sputnik. Programs such as ESS and SCIS through the 70s and 80s could be found in every elementary school classroom when the pendulum was swinging the other way. It's interesting to consider how the pendulum is going to swing in the coming years as change occurs at an increasingly speedier rate. An old friend, Lee Goldsberry, recently suggested to me that spelling is to the 20th century as black-smithing was to the 19th century. As popular written communication is reduced to 140 character tweets , one wonders if he might not be onto something. Heresy, indeed!

ps I don't mean to imply that the ability to write, to communicate one's thoughts effectively,  is not important:.

 

Science or Engineering and a Pendulum

Today was the second class in my Teaching Elementary School Science and Math course. Last week we explored what it means to think and act like a scientist by using our science process skills to explore surface tension and the properties of water drops. Today we briefly explored the content of the elementary school science curriculum and then looked at the difference between science and engineering. The perfect way to do this is to explore the properties of a pendulum. We explored three variables to see  which of them affected the speed of the pendulum; the length, the weight or the release position. After some exploration the students decided only the length affected the time of the swing. They also discovered that if there is more weight and the release  position is higher the pendulum will swing for a longer time.

With this new-found scientific knowledge I then challenged the students to make a pendulum clock that swung exactly 15 times in 15 seconds. The activity had segued into an engineering activity because they were now using their scientific knowledge to solve a problem. In science the questions arise from the natural world; in engineering they arise from how we use our knowledge of science to answer questions of our adaptation to the natural world, or how to invent things or solve problems.

Here is the most amazing pendulum video I have ever seen; from harmony to chaos and back again, over and over, just like life.

Interactive Sierpinski Triangle Fractal

After Lydia, one of my undergraduate students, completed her Math eNotebook on pennies I decided to use one of the ideas she had included as an interactive activitiy on the wall outside my office. The Sierpinski Triangle is an example of a fractal where each element is an exact copy of the whole, or vice versa.

Fractals are a wonderful example of how math is the science of pattern and how once you see the pattern the learning becomes much easier. The extra pennies on the left are for people to add to as they get to know the pattern and can predict where to place the additional pennies. Theoretically, this pattern could go on for ever although in reality it will probably stop when we either run out of room, or pennies. Here are some fractals in nature and here are some 'far-out' Mandlebrot fractals and MC Escher fractals.

You can also create your  simple fractal with this NCTM fractal tool or your own incredible fractal with this Nova interactive activity. 

Maths is Everywhere

One of the fundamental cornerstones of my teaching is to help my students see how math has real world applications in just about everything we can possibly experience. I am always surprised, and a little dismayed, when students list the main reasons for learning math as "balancing their checkbook", "doing taxes" or "making change". It would be like saying the only reason to learn to read would be to read instructions in manuals or read streetsigns. So to help my students come to this woderful realization I have them complete a Math eNotebook using some form of technology such as Powerpoint, Prezzie, or a blog. The students can choose any topic in which they have an interest and then gather 12 interesting  math-related things in their presentation.

This year my undergraduate students presented a wonderful diversity of topics. Here they all are;

Soccer and Math- Aris
Fibonacci Math- Emily
New York and Math- Helen
Music and Math - Jenn
Chocolate Cake and Math - Katherine
Maple Sugaring and Math - Kathryn
Monkeys and Math - Leanna
Pennies and Math - Lydia
Wedding Math - SaraJapan and Math - Zach

Here are all the archived math enotebooks .

April fools in the Classroom

Many years ago when I taught fourth grade (UK third year) students at Sefton Park Primary School in England April first was always a day of great fun, especially before noon. April fools day, a time for harmless fun and a chance to help children develop their sense of humour.

There were the usual attempts at tricks such as "there's a spider crawling up you shirt" but every so often there was a wonderfully creative one. The last class I taught before emigrating in 1977 pulled one of the best. As I entered the classroom on that particular morning the students were all sitting very quietly at their desks; a sure sign that something was afoot. I sat down at my desk and went to open the draw to pull out the class register but there was no drawer there; in fact there were no drawers visible anywhere.The students had turned my desk around so that the drawers were on the other side. Having turned the desk back the right way and managed to open the drawer I then discover the drawers had been topped up with rice. Hmmm, how to get my own back?

After an hour or so of the usual routine I told the students we were going to learn about spaghetti as part of our project on Europe. I then proceeded to fill the blackboard with information all about how spaghetti grows on trees and how it is harvested (similar to the above recreation). The students dutifully copied the information from the board into their notebooks for 30 minutes and just as the last students were finishing I said "Oh, there's one more thing I've forgotten to write" and I wrote "April fools" at then foot of the board. At first the students were quite shocked and couldn't quite believe what I had written; but then we all laughed together, all 35 of us.

I learned two things from this experience. One, it is important to laugh with your students at least once a day; and two, it's really important to be sure of what you teach children as they will believe almost anything you tell them.