Counting from 2010

Learning to count in English is fraught with difficulty and non-intuitive sequences. The way our English counting words are constructed is probably one of the most significnt reasons why young children in English speaking countries tend to lag behind those, especially in Asian countries, in terms of early learning in Math. The counting systems in most Asian languages follow a very logical sequence, especially through 20, sequences such as ten and one, ten and two, ten and three where the confusing words of eleven, twelve and thirteen are used in the English language.

Once we get to twenty a logical sequence steps in where the sigle digits (1 - 9) are repeated  in each decade up to 100. Counting from 20 - 100 all seemed quite logical to me until yesterday when I suddenly realised we have been creating yet another dilemma for young children learning to count. One of the common errors young children make when they first learn to count in the decades is to say, for example,  "twenty-seven, twenty-eight, twenty-nine, twenty-ten (instead of thirty). In the past this has easily been corrected as it did not make any sense to say "twenty-ten". The problem is that the terms twenty-ten, twenty-eleven, and twenty-twelve have become legitimate terms of usage when refering to the date of the year. These terms seem to have replaced the more mathematically correct, for example, "two thousand twelve" (with or without the "and').

This is similar to the double use of the word "third", for example, as an ordinal number as in "I am third in line" and as a fractional number such as "I have a third of a cup of orange juice".

Happy Holidays

Merry Christmas and seasons greetings everyone, and may you find peace and happiness in 2012. 

The Cycle of the Semesters

I couldn't imagine having a job that didn't have semesters; a job that continued endlessly week after week, year after year, without an end in sight.

The end of each semester provides a time for renewal, a chance to take a deep breath and reflect, an opportunity to bring a close and consider another beginning, to say goodbye to some and anticipate saying hello to others.

At the end of every semester I think deeply about the courses I have taught and the students I have met. No  course is ever the same from one semester to the next. This is partly because things in the world of education change quickly these days one has to change to keep up; things such as the Core Curriculum that needs to be included in my Math/Science Ed course in the future. My courses also change in response to the student feedback I receive both informally throughout the semester and formally through the course evaluations at the end of the semester. This has been particularly true this semester when the college changed to a 4 x 4 curriculum (four 4-credit course each semester instead of five 3-credit courses).

Courses also change because one thinks of better ways of doing things based on how they went the last time. For example, the Learning Communities I set up in Schools and Society based on the five tables in the room seem to really work well. Perhaps I'll establish Learning Communities in my other courses next semester.

Then there are the students who change from one semester to the next. Each class is unique in that it is made up of unique individuals with their unique forms of interaction. This is just the same as the classes of students one finds in  public schools classrooms. Sometimes, teaching strategies that work with one group need to be modified for another group so that learning is optimized. This is why I have always felt that teaching is primarily an art form as opposed to a science.

Teaching is Sowing Seeds

Planting seeds, or bulbs, or beans is always an exciting thing to do because you have the growth of the plant to look forward to as well as the harvesting of the fruit. This doesn't happen by accident though. The plant has to be cared for and nurtured with the right amount of water, food and sunlight. We can provide the conditions to optimize the growth of the plant but it is, ultimately,  up to the plant whether it thrives or not.

I often think teaching is a bit like this. As teachers we can plant the seeds of knowledge and understanding and provide the student with a stimulating, creative, and supportive learning environment. We can share our passion for what we teach, and we can care deeply about the students we teach but, ultimately, it is up to the student whether she/he thrives within the educational context.

As teachers, we can teach but it is always the student who does the learning.

At the end of each semester the students in my Elementary Math and Science class plant a selection of beans that were part of the 15 Bean Soup project we completed in the penultimate class of the semester. The project involves exploring different ways we can use 15 Bean Soup to teach a variety of topics in math, science, language and art. Here's a school where the students do similar activities.

Many of the students, like Kerry and Carleen who sent me these pics, really look after their beans and are able to grow them to the point where they can actually harvest the beans.

One of the incredible rewards of teaching is seeing the successes of one's students. Kerry and Carlene have clearly learned something about the educational value of this particular activity. Well done indeed.

   

Professing by the Numbers

Perhaps I shouldn't have done this but I have just discovered that I have read at least 576 student papers this semester. The papers have ranged from one-page journal entries to 12 page philosophy of teaching assignments with just about every length in between represented.
I have also made around 75 visits to local area schools, requiring  600 miles and around 30 hours of driving, to observe my 4 student teachers and arrange field placements for the 38 students in my Schools and Society and Teaching Math and Science courses. My student teachers averaged about 40 hours a week in their classrooms while my sophomores and juniors spent 2 hours a week in public school classrooms. I have given  45 class sessions for a total of 225 hours, spent countless hours in meetings, and I love every minute of it all.

I have also presented papers at 2 conferences, one in Massachusetts (MDSC) and one in Rhode Island (ATMNE), and have read about 40 journal article  and 3 new books on educational theory. The emails I have read and written number around 5000. And yes, I have loved every minute of it except for driving on the Massachusetts turnpike and the spam emails. 

I "borrowed" the picture from my good friend Karyn Vogel's wonderful math blog. Karyn is a Graduate of the St. Mike's Graduate Education program and was a member of my graduate math ed. course several years ago. She is now a Math Coach for the Flynn and C.P. Smith elementary schools in Burlington, VT. Her blog is going to be required reading of my math ed. students next semester.
  

A New Windshield; Improved Vision!

I had a new windshield installed in my van yesterday to replace the one that suddenly cracked almost all the way across on my way home last Friday. The new windshield is remarkable for both its clarity and lack of pits, scratches and cracks accumulated during the 219,000 miles it has travelled.

This new clarity of vision occurred as a result of a fairly intense experience during which I didn't know if I would be showered with glass or whether I would be hit by a sudden  inrush of cold air if the glass should shatter.  None of these things happened and it was, in fact,  just a gentle event the result of which is increased clarity with everything I see as I'm driving.

Sometimes, the experiences we have in life cause us to see things with a similar new clarity. In fact, I sometimes think that one of life's main goals should be to obtain a certain clarity of vision. I remember the year I spent working with teachers in an inner city school and how it added significantly to my clarity of vision of what math education should be all about; it had never occurred to me before that there was such global diversity in mathematics. My students also gain great clarity of vision when they first experience what it's like to teach.

Today, I read my first teacher licensure portfolio. The portfolio is an extensive piece of work students are required to complete as part of their teacher education program at St. Mike's leading to teacher licensure in the State of Vermont, and elsewhere. The portfolio, completed at the end of the student teaching semester, is assessed according to an extensive set of criteria which must be met by the student. In reality though, while I'm checking the boxes next to each criterion, I'm also trying to determine the student's clarity of vision concerning her/his teaching experience at this point in their teaching career.

     

I Want to be a Teacher

During exam week I always meet individually with the students in my Schools and Society course to see how their plans of becoming a teacher are going. It's a chance for me to give the students some individual feedback as well as an opportunity for them to ask questions and give me ideas.

The course is the first in the sequence of  courses they need for either elementary of secondary teacher licensure and is an opportunity for them to get their first teaching experience as well as begin to develop their ideas about what type of teacher they want to become.

For some, it is an exploration of whether they really do want to teach. Sometimes, growing up through our teen years we hear so many times "how good we are with young children"  or how we have a  "knack for remembering dates; you should teach history" that we think our chosen livelihood must be to teach.  For some they have always loved math or art and want to share their passion, while for others it is the thought of being part of the wonderful developmental phases of childhood that draws them on.

This semester the course has been filled with  a truly remarkable group of young men and women all with a  genuine passion for life whether it be teaching or, as in one case, journalism. There isn't a single student in the course who, I think, should reconsider their choice of career. In fact, there have been many students who I think will make a meaningful contribution to the teaching preofession in years to come.

The most important characteristic the students seem to share is that none of them see the task of becoming a teacher as a "spectator sport". They have all been actively engaged in their learning through the learning communities we set up in the class as well as their participation in the field placements. The cooperating teachers' evaluations of the students were wonderful.

In the current economic uncertainty it has been a pleasure and a privilege to work with a group of students with such a genuinely positive outlook on life.

Learning and the Brain

In teacher education programs like the one at St. Mike's, we talk a lot about how the brain works. It's important for future teachers to have a sense of the role the brain plays in learning. Howard Gardner, for example describes seven different types of intelligences in his Multiple Intelligence Theory. Eric Jensen also describes ways in which the brain works in his series of books, Teaching with the Brain in Mind.


But in all the years I've been teaching I have never come across a piece of research quite like this. In London (UK), taxi cab drivers are required to learn "The Knowledge" and pass rigorous tests before they can operate a taxi-cab. Researchers have discovered that adult brains still retain some of the plasticity more commonly associated with young chidlren.

This is good news indeed for those of us beginning to wonder if we are getting too old to learn new things. 

A Calling, Perhaps, But So Much More

'Tis the time of year for reading students' philosophy of teaching papers in my ED231 Schools and Society class. The thought of reading twenty 10 - 15 page papers is always more than a little daunting but once I start I realize why it is such a great experience. For this assignment the students have to write a single paragraph identifying the major contributions to the field of Education of 25 of the Great Eudcators included on the Great Educator webpage. Several years ago I asked all 13 of my colleagues in the Education Department who the greatest influences were on their approach to Education; hence the men and women who appear here from the past 150 years.The students are then required to select the five they most identify with a write their first philosophy of teaching based on these five Great Educators. (The students help me construct this webpage every semester by finding the links)

In each student's paper there is at least one pearl of wisdom or, perhaps, tweetable statement, and often many more, that makes me think about learning and teaching differently; a new perspective, a new idea, a new phrase, something that causes me to think and learn. In one of the papers I read today, the student introduces very eloquently a series of events and thoughts that set him on the path to being a teacher. I described this, in the comments I wrote on the paper, as his "calling" and suggested that now the rest is up to him.

Over the years, teaching, like nursing, has been identified as a calling, a vocation, even something one 'has been born' to do. It may be any of these but it is so much more. We have read some pretty great writings   about teaching this semester including To Teach, a book by William Ayers who, as one of the students pointed out, was once on the FBI's Most Wanted list. What is so interesting about Ayers' still somewhat radical  ideas about teaching (there should be an element of "creative insubordination" in all teachers) is that he is, in a way, confirming our cultural belief that teaching is, in fact, a calling in its purest sense.

Once one has been "called" however, there is so much to do, so much to know, so much to understand and so many opportunities to be seized. This is where the pre-service teacher, the college student, can really become an active participant in the process of becomeing a teacher; a caring and passionate student of the art of teaching. 

Be an Internet Connoisseur

One of the wonderful things the Internet has allowed us to do in the world of Education is to easily access all sorts of things that enhance a student's learning especially at the elementary school level. This only works, however, if we truly understand what we are trying to teach and how  the resources available on the internet can effectively enhance learning.

Take, for example, the seemingly simple idea of teaching students about angles like the one in the picture.

One of the common misconceptions children can develop is that angles are measures of distance. Students will focus on the distance between the two rays of the angle when describing it. If angles were measures of distance how could we possibly conceptualize that there are 180 degrees in a straight line? Or how could we explain how the distance between the rays increases as we get further from the origin of the angle. If, however, we teach angles as degrees of rotation things become much easier to understand.We can do this by using a circular protractor like this one which actually shows angles as the rotation of a line about a point.


We can also be connoisseurs of what is available on the Internet. Banana Hunt is an incredible activity that demonstrates the idea of rotation perfectly and is fun to play too. Here's another one, The Angles Game,  that on the face of it, looks interesting and fun but has virtually no educational value at all.

Knowing what to look for in terms of Internet resources is a significant component of the teacher education programs at St. Mike's. Future teachers need to be Internet connoisseurs.