School League Tables?

Growing up in England I was an avid soccer fan and would check the league tables every Sunday after the Saturday soccer games to see where my team, Bristol City, stood in the league.They were usually in the Second Division, one of four divisions, at that time. I'm still a soccer fan and frequently watch Premier League games on the Fox soccer channel. I also still avidly check the League tables although they have changed somewhat since the latter part of the last century.

The football league tables, however, have now been joined  by the England school league tables. Remarkably, schools are ranked in tables according to the success of the students on a number of different criteria all of which seem to involve exam results of some sort. There are different tables for primary (elementary) schools and secondary (high) schools.  In the Primary League Tables, the equivalent of US elementary schools, success is measured by student performance in just two areas of the curriculum, Maths and English. This makes one wonder just what type of incentive there is for teachers to spend time teaching science, social studies, music and art. I'm sure these subjects are probably taught but since they play no part in the measurement of a school's success one must wonder about the enthusiasm with which resources and time are devoted to learning in these subjects.

In the US we have No Child Left behind and Race to the Top which, although suspect in their motives and application don't seem anywhere near quite as demeaning as reducing a child's  education to the instant self-gratification of seeing where one's school is in a league table. 

Global Differences in Math: an Example

Since this blog seems to be read in over 30 different countries from time to time I thought I would see if anyone would like to share how they complete simple arithmetic activities.

For example, the image on the left shows two different ways of doing a simple subtraction activity. The one to the left is labeled the equal addition method while the one on the right, the one currently used as a "standard algorithm" in US schools, is labeled the decomposition method. (The use of the term "borrow" in this one is an error as we will see) If you are familiar with the one on the right and still use the term "borrow" you might have wondered why the "borrowed one" was never paid back.

The "borrow" language actually originated with the method on the left which was used in the US prior to the 1950s. This method is still used in Bosnia and many other countries. The way it works is like this; 9 from 5 you can't so borrow 1(1 ten) to make the 5 into 15. Since you "borrowed" 1 from the tens you have to "pay it back" by putting a 1 next to the 3 (or changing the 3 into a 4 in this example). You now take 9 from 15 to get 6 and 4 from 6 to get 2 (actually 40 from 60 to get 20). It was called the equal addition method because you added ten ones to the top number (5 +10 = 15) and one ten to the bottom number (3 tens + 1 ten = 4 tens). The word "borrow" just stuck even though it didn't really make any sense.

In the method used in the US today, the one on the right, we decompose (or regroup) 65 into 50 plus 15. This is still frequently and erroneously referred to as "borrowing 1". In the decomposition method there is no "payback" so it really should be "steal 1".

To use the word "borrow" today is to use it as a metaphor. The correct conceptually-based language is "regroup 65 into 50 and 15". I learned the equal addition method of subtraction growing up in England and still use it today, but only for my personal math calculations, and only when no-one is around. Let me knowif you do something different.  

Student Teaching; an Ending and a Beginning

For my student teachers this semester, the experience marks an end to their college life and a beginning to their careers as elementary school teachers. It's a time of great growth and development, a time to take risks and also a time to finally find out if teaching is the right choice of career. For the vast majority of students the student teaching experience affirms this choice and is a culmination of all the hard work of the previous semesters. For a very, very small number, perhaps less than 1% it is a time of great anguish and soul searching for everyone involved when the prospect of failure looms large. Thankfully I have been involved in very few such situations but when it does happen it takes a long time to recover both mentally and emotionally because one cares so deeply about one's students' success.

No such problems this semester. All four of my student teachers are off to a great start and already there are some great stories of things children say or do. Things like the third grader  who ignored what the teacher was asking about how balls bounced during a science lesson because he thought she had said Beyonce and couldn't understand why she would say that.

The same student teacher also relayed a story about students thinking about how they could make the world a better place. One student said they could help animals while another student said they should help the elderly. Together they decided that they would help "old people's animals".

I observe my student teachers every week for the first 4 or 5 weeks of the semester so I can act as a resource for them as they develop their whole class teaching skills and come to terms with the myriad demands of running a class of twenty-something students. The most rewarding part of the job is seeing the joy on a student teacher's face when everything goes to plan and the students learn. 

Three Men in a Classroom

With apologies to Jerome K. Jerome.

For the first time in my professional life, at least since I started supervising student teachers in 1977, I am supervising a male student teacher in a classroom with a male cooperating teacher. Since less than 10% of elementary school teachers are male the likelihood of this happening again is pretty slim. At least three of the elementary schools where we place student teachers have only one male teacher and I have a sense that most of the elementary schools in Chittenden County where we place most of our students for classroom experiences have fewer than the national average of 9%. I have one male student in my two teacher education classes this semester. Why are there so few men in the nation's elementary schools and teacher education programs?

My first teaching job was as a 4th grade teacher in a Primary (Elementary) school in my native England. I was part of about 40%
of all primary teachers in England in the  1970s who were male. During the past twenty or so years there has been a similar decline in the percentage of male teachers in UK primary schools as in the US elementary schools  as this Daily Telegraph article illustrates.

One of the reasons for the original difference in male teacher percentage between the two nations can, perhaps be traced  to the origin of public education in the two nations. In the UK public education, part of which was primary education grew out of the "Public" schools such as Harrow and Eton, Sunday Schools and the industrial revolution. At this time all teachers in all types of schools were men. In the US, public education developed, especially at the elementary level from the one-room school house where the teacher was always a young lady, unmarried and of great virtue (or so history tells us). So there could be a cultural reason for this original imbalance.

The topic is a popular one for the national press and a quick Google search will bring up many newspaper articles with associated blogs through which writers share a myriad of reasons as to why elementary school teaching does not appeal to men. Women are more nurturing, men cannot cope with the demands, children only really play in the elementary school, it's just like babysitting - not a "man's" job and so on..

More serious research projects and articles, however, begin to highlight some of the real reasons why men do not choose to become elementary school teachers. Here's an interesting perspective about male teachers in early childhood education : an Austrlian perspective and a research proposal with a great list of references.
It would appear that the issue is far more complex than one might expect but one that should probably be addressed. The question is how?

Yes, There Are Fun Math Tests

The first day of class in a new semester is always a time of great excitement and nervousness for the students and especially, for me. No matter how many times I teach a class I am always nervous with anticipation during the first class.

As part of the ice-breaking process I give the students a fun math test to complete while I am setting out the math materials. It has a serious side to it too because I want the students to begin the semester with the sense that math really has dynamic, creative, and aesthetic qualities as well as being a "useful" subject. Math is also the "science of pattern", a theme we celebrate and develop throughout the semester.

Now here's the fun math test we did. The letters stand for words that are related to the numbers. For example the first one is "Wheel on a Unicycle".

1 = W on a U ………………………………………………..

3 = B M (S H T R)…………………………………………..

4 = Q in a G………………………………………………….

5 = D in a Z C………………………………………………..

7 = W of the W………………………………………………

8 = S on a S S…………………………………………………

9 = P in the S S……………………………………………….

11 = P on a F T ………………………………………………

12 = S of the Z……………………………………………….

13 = S on the A F…………………………………………….

16 = O in a P…………………………………………………

18 = H on a G C …………………………………………….

24 = H in a D…………………………………………………

26 = L of the A……………………………………………….

27 = C F in a C Y…………………………………………….

29 = D in F in a L Y………………………………………….

32 = D F at which W F………………………………………

52 = W  in a Y……………………………………………….

54 = C in a D ( with the Js)………………………………….

57 = H V …………………………………………………….

64 = S on a C B………………………………………………

88 = P K …………………………………………………….

90 = D in a R A……………………………………………..

200 = D for P G in M……………………………………….

212 = D F at which W B……………………………………

1000 = W that a P is W…………………………………….

1001 = A N ………………………………………………..

Let me know if you need help.

By the way, one of the students in class yesterday suggested that the perfect way to pour a bottle of Heinz 57 sauce is at 57 degrees! 

Kindergarten Blog

One of the wonderful things about about having my students complete their student teaching experience at the Williston schools is the level of technology used by the teachers and students at the two schools. From their very first days in kindergarten students get to learn how different forms of technology can be used to improve both the quality of education and of life itself.

Jen Canfield, an amazing kindergarten teacher at Allen Brook school, keeps a wonderful blog about life in her kindergarten class. Just imagine what it must be like as a parent of one of Jen's students to be able to see what goes on in your child's classroom from day to day. The picture is of my student teacher, Ali McHenry who is completing her student teaching experience in Jen's classroom this semester.

In the last couple of years of the last century I was employed as the Science Education Professional Development specialist at the two Williston schools, Central and Allen Brook. I loved every minute I was there and it's always a neat experience for me when I return to work with my former colleagues.

It's Triad Time

A triad, according to the dictionary is 1) a set of three, 2) a musical chord, 3) an atom with valence of 3, 4) a U.S. strategic missile force, or 5) a Welsh literary form. In the world of teacher education it is the meeting, held three times a semester, between the student teacher, cooperating teacher and college supervisor during the student teaching semester. Since I have four student teachers to supervise in local area schools I have four "Initial Triad Meetings" during the first two weeks of the semester.

I always find the first meetings a time of great hope and excitement as the student teacher looks forward to putting into practice all the things she/he has learned in the courses they have taken in previous semesters. We talk about the expectations for the semester, the lesson plans and instructional unit  the student will need to complete, their commitment to student teaching as a full-time activity for the semester, the expertise the cooperating teacher will share them, and the need to make sure that they let the students they are working with know they care about them.

My four student teacher span the elementary grades from kindergarten to fourth grade this semester which is a wonderful experience for me. I often think it would be neat if public school teachers got to share this wonderful experience I have of working in so many different classrooms with so many inspirational teachers.

A triad in music is an "implied harmony". I can't think of a better metaphor for the student teaching experience.  

Math Must Be Believable

Many thanks to my colleague Aostre Johnson for this wonderful cartoon. It does make you stop and think just what was on people's minds thousands of years ago There must have been people with senses of humor back then just as there are now. Perhaps Stonehenge was a practical joke by some wealthy stonemason. What will they make of Carhenge in the year 4012?.

There has been a depressing math story circulating in the media for the past several days that describes how a group of Georgia teachers used the topic of slavery to write math problems for third grade students. As worrisome as the content of the math problems is I find the math involved in the problem just as disturbing.

The problem reads " Each tree has 56 oranges. If 8 slaves pick them equally, then how much would each slave pick?" One of the most important things to consider when writing math problems for children to solve is to make the problem as realistic, meaningful, relevant and grammatically accurate as possible. This particular problem fails in every way.

How could "each tree" have 56 oranges. I'm not a biologist but I would imagine it would be an unbelievable coincidence if each tree in an orange grove had 56 oranges. Why "each tree"? There's an implicit number of trees but it is, somewhat confusingly,  not stated. Why not say "An orange tree"? None of the orange trees that I have seen would be big enough for 8 people to pick oranges at the same time. Would each picker have his/her own ladder or picking tool or would they each take it in turns to pick their oranges? Wouldn't it be one, or maybe 2, pickers per tree? Why would they all pick the same number? If there were 9 oranges close together would one picker pick 7 and then call on another to pick the other two?  Finally, the use of the word "much" is grammatically and mathematically incorrect. Much refers to a continuous variable and not a discrete variable which oranges are. It should be " How many oranges did each person pick?".

Aaarrrrgggghhhhhhh!

Knowing and Caring

The field of Education probably has more meaningful sayings and quotations than just about any other area of human endeavor. "Everything I ever learned worth learning I learned in kindergarten" is one that has been around for years while the "Give me a fish and I will eat for a day; teach me to fish and I will eat for a lifetime" is another.

But sometimes you come across one that is so startling in its simplicity and so wonderfully inspirational that it just makes you stop and think; and then think some more. I recently visited on of the local elementary school websites and there on the Principal's page was "Children don't care what you know until they know you care". I've been unable to find the source of this pearl of wisdom but it is true no matter what level or age the student is.

The disposition of caring  is, perhaps, more true today than ever for those engaged in the art of teaching college students. In a world in which the future is less certain than it has been there is now a greater need to care about the students we work with on a daily basis. As they grapple with the demands of balancing their course work, jobs, relationships, and aspirations, we must show that we care about them as learners, academics, and most of all as individuals.

I have always found St. Michael's College to be a truly caring place to work where every individual is a valued and appreciated member of the community.
         

Reflecting on Reflecting

Deborah Meier, author of The Power of Their Ideas and many other wonderful educational writings, believes that teaching must be an intellectual process if teachers are to be truly effective in what they do. I have always believed this too.

The act of teaching requires the processing of a vast number of different things often simultaneously and often without a lot of time to think too much. On the other hand there are times when there is time to think; time to process the what we have learned from experience, what we are  learning about the students we are currently working with, as well as information from the currency of the ever changing world in which we live. In teacher education we call this reflective thinking; the ability to process all kinds of information so that our practices are improved through the disposition of  lifelong learning.

My student teachers started their Spring student teaching experience this past week and one of the most critical things they need to do is to think reflectively. They need to be able to use all the knowledge and understandings they have gained from their coursework and synergystically combine this with the new knowedge they are gaining of the students and classrooms in which they find themselves. The act of thinking reflectively helps them develop the teaching strategies, classroom management styles and a "teacher voice" that will form the basis for what type of teacher they will become. Throughout the semester I will read their weekly journals through which they will share their challenges and successes in the form of reflective thinking. It's one of the most exciting and rewarding parts of my job.     

Today's Number is 5

This is a remarkably informative website, Numbers: Facts, Figures, and Fiction, by Richard Phillips that tells all about the number of the day's date. The breadth and depth of the information included with each number is stunning and quite amazing in some instances. Just click on a number when you get to the web-site and it will tell you all about it.

For some reason I only go to the number that is today's date; it would seem like cheating to go to another number! For example, apart from being a prime number and a fibonnaci number did you know, for example, that 5 was the lucky number of superstitious French fashion designed Gabrielle "Coco" Chanel who, in 1921, chose the fifth day of the fifth month to introduce her new brand of perfume called Chanel No. 5. 

5 also occurs in nature all over the place, in addition to the 5 digits we have on each hand or foot, such as in petals on many flowers and the 5-pointed star in the middle of an apple cut the "wrong" way.

When children learn to count, develop a sense of numeracy and the cardinality of number we can begin to embellish their basic understanding and knowledge of numbers by looking at the way each number relates to our lives. This brings numbers to life by giving them meaning, magnitude, and an individual identity that lifts them out of the sequence in which they always seem to exist.  5 becomes 5 for its own sake and not simply because it separates 4 and 6  or comes after one and before the other. It takes on a scientific, historical,   social or geographic quality that makes it so wonderfully interesting. 

What's Math Got To Do With It?

I don't smoke and I'm not overweight so for my New Year's resolution I have decided to read more books about math. Not the kind that one meets in school such as textbooks or workbooks but the type written by kindred souls who see the joy and beauty of math in the real world.

The first one I'm going to read is Why Do Buses Come in Threes? by Eastaway, Wyndam and Rice. It's been on my bookshelf for a year and I remember first seeing the title with a sense of disbelief. Growing up in England I took public transport buses everywhere before I had a car. I spent the daily  45 minute journey to and from high school on the top deck of a green Bristol double decker. You wouldn't believe the times you'd wait for ages for a bus and 2 or 3 would all come together. 

The second book I want to read is What's Math Got To Do With It? by Jo Boaler. I want to read this book because I've been following the career of the author ever since I read a definitive piece of research she conducted many years ago that demonstrated how much better it was for children to learn mathematics conceptually with understanding than it was to learn it by rote memorization. In her study she demonstrated how children, at the end of elementary school, might do better on traditional recall tests when taught to learn math by rote memorization, but later, in high school, children who had been taught conceptually were light years ahead of the "rote memorizers".

The third book on my list, to be read by Easter, is The Number Sense by Stanislas Dehaene. I've read parts of this book but not from cover to cover. Dehaene was the one who introduced us to the idea of numeracy and the idea of subitizing. This is where you can recognize how many things are in a group by not actually counting them. Believe it or not, crows can do this when checking the eggs in their nests!
    

Science or Art?

Nothing has dimmed the line between art and science quite like the study of fractals. The study of this remarkable phenomenon has been around for many years but recent research in the application of fractal geometry to explaining the apparent randomness of the natural word  is changing everything. One of the most creative uses of fractals in in the field of prediction, from predicting natural disasters to nervous breakdowns.

Is it an art or a science? Today this is probably a false dichotomy even though we persist in using the terms in specific instances. Can politics really be a science as in political science or should it be political studies as one of my colleagues suggests? Thankfully, the new Environmental Studies major at St. Mike's was not called the Environmental Science major so that courses focussing on the more humanistic and philosophical aspects of this study could  be included in the major 

Many years ago I remember having rich and interesting discussions with fellow graduate students about whether teaching is a science or an art. Everyone, including me, always seemed to argue from a certain point of view or disposition based on what they had studied and experienced. I always firmly believed it was an art.  I don't recall any of us identifyng which componenets of teaching were scientfically or artistically defined.

There is now so much research available on how children learn that is scientifically derived that the art of teaching has to have a scientific component that informs our practice. The artistic creativity with which the best teachers approach their jobs probably has to include, in some way, the results of the best that is thought and said by their scientist colleagues.

Have a wonderful 2012.