## Thursday, December 29, 2011

### 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".

## Sunday, December 25, 2011

### Happy Holidays

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

## Tuesday, December 20, 2011

### 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.

## Friday, December 16, 2011

### 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.

## Thursday, December 15, 2011

### 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.

## Tuesday, December 13, 2011

### 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.

## Monday, December 12, 2011

### 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.

## Thursday, December 8, 2011

### 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.

## Wednesday, December 7, 2011

### 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.

## Thursday, December 1, 2011

### 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.

## Wednesday, November 30, 2011

### College is for Life

I received news yesterday that the 2012 reunion at St. Matthias College in England where I did my undergraduate studies will be the last to be held at the college. Although the College closed as a teacher education institution in the late 1970s  the campus became part of the University of the West of England(UWE) where academic departments were housed and classes were held. Now, UWE  has decided to close the campus next summer. This raises the real possibility that the beautiful old buildings with all their ghosts and memories may well be razed to make room for housing, offices or worst of all, perhaps a shopping mall.

On several of my trips back to the "auld sod" I have visted the college and strolled the hallowed hallways and pretended to play croquet on the lawn or field hockey on the sports field, or even listen to my favorite lecturer in one of the lecture rooms. It always seemed so permanent, one of life's anchors that would always be there. There is always something undemanding and unconditional about the role physical structures play in our life voyages. It's almost impossible to imagine it not being there.

On the other hand, the personal connections one makes at college can change with the times, are much more maleable and flexible, and, perhaps, a lot more valuable in the long run. My memories of my college-friends live on through Facebook contacts and a wonderful web-site, Old Lags,  run by Ade George, one of my good college friends. It's been one of life's treasures to watch the lives of one's friends unfold from afar. Some have stayed close to home and others, like me, have flown far to new worlds and cultures in which they have made their homes and lived out their lives.

Our college days are to be treasured for what they are but they can also be seen as the acorns to the oak trees of our lives and nurtured and valued over a lifetime through both their physical structures and the wonderful friendships we made.

## Monday, November 21, 2011

### Schema; the Blueprints of Teaching and Learning

One of the things we talk about in Teacher  Education is the idea of schema or the way children  put ideas, facts, feelings, attitudes and information together so that they make sense. In fact, we probably all use schema, in one way or another, in just about everything we do. It's a way of making sense of the world, of looking at the relationships between things, of making decisions or operationaliziing our ideas.

When I am supervising my student teachers in their student teaching experience I use Frances Fuller's Stages of Concerns Model as a means of determining where my students are in their development as teachers. The model has three basic stages through which students pass, quite naturally,  from the moment they first set foot in their classrooms. The first stage comprises a set of survival concerns; (Can I do this? Do I look the part? Will I last 16 weeks?) The second stage of concerns is all about their ability to teach; (Am I using the technology properly? Am I planning my lessons effectively? Is my classroom management working?) Finally, and this is the exciting part, their concerns focus on the students; (Are they learning? Are they engaged in what they're doing? Are they constructing meaning?)

This series of concerns is actually played out over and over again each time the student has a new classroom experience from their very first one in Schools and Society to the last, the student teaching experience. It even happens again when they get their first job as a licensed teacher. I remember my first week teaching my first 4th grade class as if it were yesterday especially after my Headmaster said to me "Do you realize that if those 34 4th graders you're about to meet all decide to sit there and ignore you there's not a thing you can do about it?" That advice assured the length of my survival concerns was the absolute minimum.

## Thursday, November 10, 2011

### A Busy, Busy, Busy Time.

It's been a busy few weeks with stacks of papers to read, student teachers to observe in their solo weeks and conference presentations to make. It's also been a busy week for the St. Michael's Teaching Gardens where a new, large stone was installed faced on one side with a chalkboard. It looks like the first person to take advantage of this chalky mode of expression was a math person (although maybe not as members of the SMC Math Department have assured us that the expressions don't make a whole lot of sense). It's fun to write on a chalkboard again as they finally disappeared from school classrooms with the advent of computers which are allergic to chalk dust.

The conferences I presented at were quite different but there was a common theme of mathematics education. The first was the annual Massachusetts Down Syndrome Congress in Worcester, Mass. on November 3, where I presented a paper on teaching math to students with Down Syndrome.  The presentation comprised four parts; some theory, some math, some Andrew and some applications. These four aspects of teaching are based on the idea that you have to make connections between your theoretical  understanding of math, your knowledge of the student you are working with, and the available applications for helping the student interact with the math.

The second presentation was yesterday at the annual ATMNE (Association of Teachers of Mathematics in New England) conference and focused on the application of the idea of the referent unit in elementary school math. It's something we often don't think about but has a significant impact on the way children develop their ideas of quantitative literacy. For example, in 1/2 x 1/2 = 1/4, what is the 1 (the referent unit)  of each fraction if  we are asking what is half of the first half of a football game? No wonder operations with fractions is so difficult.

## Friday, November 4, 2011

### Remember, Remember the 5th November

When I was a child growing up in England one of the poems I learned by heart in school was;

Remember, remember the 5th November
the gunpowder treason and plot
I see no reason the gunpowder treason
should ever be forgot.
Guy Fawkes, Guy Fawkes,
t'was his intent
to blow up the King and the Parliament
Three score barrels of powder below
Poor old England to overthrow
By God's providence he was catch'd
With a dark lantern and burning match
Halloa boys, halloa boys make the bells ring
Halloa boys, halloa boys, God save the King
Hip, hip, hoorah.

The poem commemorates the deeds of Guy Fawkes who tried to blow up the Houses of Parliament during a ceremonial opening by King James I in 1605. Every year on November 5th children and their families light bonfires, topped with a stuffed effigy of Guy made from old clothes, in their back yards and let off fireworks. Such was the excitement of it all that the word "fifth" now can mean nothing else to me, and probably every other British person, than November 5th,

This is a wonderful example of how out cultures are ingrained with numbers. Not only our cultures but our subcultures and our individual lives. 89 can mean nothing else to me than I89, the Interstate road that I drive on twice a day to and from St. Mike's. 217 is important to me because it is my house number while 19 has a special place because it is the day I was born on. What numbers are important in your culture and  in your life? These significant numbers are important to children as they learn math in school and see its relevance in their daily lives.

Students in my ED325 Teaching Math and Science course will soon be completing their Math eNotebook assignment in which they have to find the math in their favorite past-time or activity. Hopefully, graduates from my course will be able to help children see just how relevant math is in their lives in not only a utilitarian sense but in an aesthetic sense as well.

## Monday, October 31, 2011

### Incredible Math Night

Last Thursday evening I attended the Math Night at Flynn Elementary School in Burlington and what an incredible experience it was. Over 300 parents and children took part in the event in which they experienced a variety of neat math activities put together from the Bridges Math Program as well as some culturally diverse math activities from different countries represented at the school.

The evening was planned by Karyn Vogel, the school math specialist, and a recent graduate from the SMC Graduate Education Program, and Rebekah Thomas, the school ELL teacher . There were over 25 tables set out with math activities including the Hungry Caterpillar, the Sierpinski triangle, and Tangrams to name a few. Each table was staffed by one of the Flynn school teachers, a student from Burlington High School or a Flynn school parent such as Kyendamina Cleophace Mukeba who shared a popular game from the Congo called Kisoro.

Judging by the enthusiasm with which the parents took part, the happy buzz that emanated from the cafeteria where the event took place, and the excitement in the children's voices as they taught their parents how to participate in the activities the event was a major success.

We now know, from definitive research, that adults' attitudes toward math have a direct effect on the way students learn math whether they be teachers, parents, or older siblings. Anything we can do to demystify math, to make it more user friendly, and to help people see the aesthetic side of math, the more effective our teaching will be and the more complete will our students' learning be. The Flynn school Math Night was a huge step in the right direction,.

## Friday, October 28, 2011

### Teaching Is All About Students

Whether we teach young kindergarten children, older graduate students or anyone in between, teaching is all about the students. My sophomore level Schools and Society students have been spending two hours a week in a public school classroom for the past six weeks. For most of them this has been their first formal experience on the other side of the desk, so to speak. Each week, they have been journaling about their experiences based on a journal prompt I have given them. This week, I asked them to bring to mind six of the students they have been working with (K - 8th grade), codify the students' names and then write a few comments next to each student that describes each student as they see them.

I haven't read their journals yet but my hunch is that close to 99% of their comments will be in what we call the affective/social area of learning. In other words the comments will identify the students attitudes, values, and social attributes. Very few will describe the students' cognitive (thinking/knowledge) attributes or their  psychomotor (physical skill) development. This is quite natural because when we first interact with other individuals the first thing we are aware of are these types of characteristics especially when individuals are observed in a social context.

But the primary goal of teaching is to help students learn in the cognitive domain of learning. Of course, learning in the social/affective and psychomotor domains are important but it is the development of a student's knowledge and understanding, for the most part, that is the primary goal of teaching. So on Monday when I meet with the students, we'll go over their student observations and talk about how they can change their perceptions of their students through changing the way they observe and interact with them. The more they can learn how to find out what their students know and understand the better teachers they'll be.

And the  more I'll know about how my students think  in the context of becoming a teacher too.

## Tuesday, October 25, 2011

### Elementary Education is not so Elementary

Many, many years ago someone asked me which 3-credit course she needed to take at College to become an elementary school teacher. When I told her that she needed a Bachelor's degree with a double major in Elementary Education and a liberal arts major she was stunned. Such is the public perception sometimes of what it takes to become an elementary school teacher. No longer is the elementary school teacher the unmarried, virtuous maiden required of the local community to staff the one-room school house of two centuries ago.

Today, elementary school teachers are knowledgable about everything, skilled at dealing with every possible type of human interaction, and familiar with just about every research-based teaching strategy known to the profession. Well, maybe not quite that much, but the demands we place on those who teach our under-eleven offspring are pretty significant in a fast-changing and complex world such as the one we live in.
The epistemology or elementary education comprises three broad areas; knowledge of child development, pedagogical content knowledge, and the teaching strategy skills that act synergistically between these two areas of knowledge. Knowledge of child development means understanding how neuro-typical children develop as well as the unique characteristics of children with special needs. It means having a sense of what students from other cultures might need to adapt to US classrooms as well as the customs of their families that might impact their child's education.

Pedagogical content knowledge is knowing and understanding the content of the elementary school curriculum at a developmentally appropriate level. For example, the science that kindergartners learn is very different from that in fifth grade. The reading skills we teach in first grade are also quite different from  the reading skills we might expect a fourth grade student to learn.

The third piece of the puzzle is knowledge of, and the ability to operationalize, the actual teaching skills that help students learn in an orderly and motivating classroom environment. These skills range from the ability to write an effective lesson plan to the way one uses one's voice during interactions with students in the classroom.

The Elementary Education program at St. Mike's helps students progressively develop their knowledge and skills in each of these three cornerstones that make being an elementary school teacher one of the best, most rewarding occupations on the planet.

The picture, by the way, is of a group of students from the Lawrence Barnes Sustainability Academy in Burlington who are taking part in the Vermont Community Garden Project.

## Monday, October 24, 2011

### The Albert Hall....How Many Holes Fill It?

Many years ago The Beatles assumed we all knew how many holes it takes to fill the Albert Hall. To be absolutely sure we'd need to know both the size of the Albert Hall as well as the size of the holes they were filling it with. We'd also need to know whether the holes were pressed together with no gaps or overlaps.

More recently, an article on the MSNBC website described the extent of Ted Turner's ranch as "just shy of three Rhode Islands". Since most of us have no idea how big Rhode Island is, beyond the fact that it is quite small as States go, we can only assume Mr. Turner's ranch is rather large.

The Beatles' "holes" and Turner's "Rhode Islands" are examples of referent units, things we use to give us a sense of the size of something.  As useful referents these two example are not terribly useful but there are literally millions of referents that are. In fact, mathematics in the elementary school, as well as our lives in general, would be pretty bleak and meaningless if we were not familiar with a good number of these referents. Just about every noun you can think can be a referent. A referent can be an orange, a house, a universe, a plant, a person, a feeling, a hope or a penny.

There are also things made up specifically to act as referents. A "byte", for example, is a referent as is a foot, a pound, a dollar, a gallon or a  degree Fahrenheit. There are also referents that are culturally defined such as a gram, liter,  or centimeter. How wide is the span between your thumb and little finger in inches? How far in centimeters?

This ability, or inability, to think in terms of referents is what we can call quantitative literacy and is a key component of the elementary school math curriculum where we need to try to avoid the use of "naked numbers" or numbers without referents. The use of a referent changes a numeral, a grapheme, into a number and gives it magnitude. For young children this is an important part in learning how to use mathematics in everyday life as well as learning the joys and wonders of mathematics.

I once asked a group of kindergartners what was the biggest number they could think of.  After most had strung together a bunch of jumbled, familiar number names one little girl responded "One Universe".

## Thursday, October 20, 2011

### John Dewey; a Vermont Legend

There was a wonderful article on John Dewey in the Burlington Free Press this weekend. Dewey is a native son of Vermont and was born and raised in Burlington where he taught at the University of Vermont for some years. His greatest gifts to the field of Education were probably his steadfast beliefs that students should be taught to think for themselves and to learn through discovering the true meaning of knowledge. Labeled a progressive and a pragmatist, he wrote many books about education and was a strong advocate of education for democracy and the role of discovery learning.

He also developed theories about thinking focused on the ideas of deductive and inductive logic. In How We Think, he relates two stories about the ferries that ply Lake Champlain between Burlington and New York State 13 miles away. In one story he describes how, standing on the car deck of the ferry, he notices what looks like a crane derrick, a 20 foot pole,  jutting out from the wheelhouse at a 45 degree angle. He notices that is had no rope attached to it so it couldn't be a crane. He then notices that it has a ball on the end and is the same height as the pilot in the wheelhouse. Being a ferry, there is no pointed bow, just a flat place where the cars drive on and off. From all these observations he deduces that the pole is in fact a false bow that allows the pilot some accuracy when steering the ferry across the lake. The ferry captain can line up the ball with something on the shore. I remember standing in the identical spot on the same ferry when I first moved to Vermont and looking at the pole in the same way Dewey had done..

In the second story he describes a strange sight of sparrows flying down and landing in front of cars parked waiting to board the ferry. As soon as the birds land they disappear up inside the engines of the cars only to reappear moments later with something in their beaks. Knowing that cars have radiators at the front and that all kinds of bugs get caught in the radiators as the car is moving he deduces that the sparrows have somehow learned that there is a veritable cooked feast waiting for them in every car that shows up at the ferry dock.
I have seen sparrows doing this too at the ferry dock. I wonder what they would do with an old VW Beetle with the engine in the back and no radiator.

Dewey's ideas are alive and well in the Teacher Education Programs at St. Michael's. His ideas of "Inspired Vision" and "Executive Means" are illustrated and exemplified in senior student licensure portfolios where they share their philosophical beliefs about teaching, their inspired visions,  and the teaching skills they craft in classrooms in local area schools, their executive means.

## Sunday, October 16, 2011

### Math Is For Everyone

I've just finished putting together my presentation for the Massachusettes Down Syndrome Congress conference this coming November. I've always believed that the math we teach to children with special needs is the same as the math we teach to all students. The difference lies in the way we teach it and how we adjust our expectations. In order to make these adaptations special education professionals need to have a deep understanding of the math they are expecting their students to learn.

So my presentation will have 4 parts; some theory, some math, some Andrew, and some applications. The theory part will address the way we can think of math as composed of both procedural and conceptual knowledge. This distinction can be illustrated by the idea that math is composed of symbols, rules and methods (procedural knowledge) and ideas, concepts and schema (conceptual knowledge). 3 + 4 = 7 is a piece of procedural knowledge comprising 5 symbols and a syntactic rule. It could be used for solving a joining, separating, combining or part-part-whole problem, the conceptual knowledge. This example also included some of the math I will be presenting.

The Andrew part will include pictures of my son Andrew in a variety of activities in which he has the opportinuty to develop his math skills while the final part of the presentation will include a selection of instructional strategies and applications of math I have used with Andrew; things like the iPAD2, the Wii system, his Hotwheel car collection,  the daily calendar he uses, clocks and board games to name just a few.

The interesting thing I have found working with Andrew, who has Down Syndrome, in math is that he finds it difficult to make the cognitive connections between procedural and conceptual knowledge. For this reason we have focused almost exclusively on the development of his conceptual knowledge. It is almost certain that he will not pursue a career involving higher mathematics so the most important thing for him is that he develops his quantitative literacy skills so that he can use the math in his life that he needs to use and can appreciate the numerical and quantitative relationships he encounters.

That's Andrew at 4,800 feet on top of Mt Mansfield, Vermont's highest peak, earlier this summer.

## Thursday, October 13, 2011

### There's More to 2+2=4 Than....

I observed a great math lesson this morning with one of my student teachers. She was introducing her first grade students to the idea of the horizontal  number line such as the one in the picture on the left (3 + 4 = 7).
Traditionally we have used language like "three plus four makes seven" or "three and four are seven". We now know that both these forms of language actually develop in children a misconception about what is happening in this piece of procedural knowledge. Children tend to think that the equals sign makes things happen. This can cause untold problems when they come to do serious algebra in middle and high school.

The key to later success in math, and algebra in particular, is to develop the equals sign as a sign of equality by helping children develop the appropriate concept-based language as they are learning the meaning of this number sentence. This key to later success is helping the children associate the equals sign with the idea, "is the same as". Three plus four is really just another way of writing seven. So is 2 + 5, and  1 + 6.

The student, assisted by the cooperating teacher and school math specialist, then went on to ask if it was OK to write 7 = 3 + 4. As I would have predicted, the children had a really difficult time with this. Almost all of them decided that you could not write the sentence this way; "this is just wrong" as one student said. The teachers then did several activities  using small cubes in which they showed the children that it really didn't matter which way round they wrote it; it still meant the same thing.

It's attention to small details like this when teaching young children that make a profound difference years later when students learn more complex math ideas.

## Wednesday, October 12, 2011

### SMC Teacher Ed. Programs Shine

For the past four days the Teacher Education programs at St. Mike's have been undergoing intense scrutiny by a team of educators appointed by the VT State Department of Education Standards Board. The purpose of the assessment is to make sure that all the SMC teacher licensure programs comply with the VT State DOE regulations and standards for teacher licensure. At the exit interview this morning we learned that not only were all the programs approved, we also received four commendations which is highly unusual.

The commendations described how our students are encouraged to excel in all they do, they are well-versed in working with students from diverse populations, they are committed to inclusive education and they use the assessment of student work to drive instruction.

For the past several years we have been assembling a 67 page self study which formed the basis for their assessment. In addition, they spent time talking with graduates, visiting local schools to talk with teachers and administrators, visiting college classrooms and reviewing course materials

We also assembled a Presentation of our programs to introduce the team to the teacher licensure programs at St. Mike's.

Many thanks to everyone who took part in the assessment; the graduates, undergraduates, graduate students, faculty, staff, administration, local area teachers, administrators, public school students and to those who were part of the DOE team.

## Friday, October 7, 2011

### Is it the 1970s again?

When I was an undergraduate in the late 60s and early 70s there always seemed to be some cause to join. Hardly a month seemed to pass without a sit-in for this, or a march for that, or gathering for the other. I remember one sit-in in the "Junior Common Room" (student bar) that lasted several days because the college would not let the students install a cigarette machine (I kid you not). Usually, however, the cause was much more celebrated such as supporting a miner's strike or going on a "ban the bomb" march. They were always peaceful and always had some positive effect on public opinion, or so we thought.

This week on the St. Mike's campus little signs have been appearing on walls and doors declaring "We are the 99%" and other topical slogans. I'm sure they are connected with the current Wall Street "sit-in" and I think it is wonderful. I don't want to use my blog as a political soapbox but I think this passion for an issue that the students are showing is great, as long as it remains peaceful and is focused on the issues. I remember the wonderful sense of hope and involvement our support for various causes invoked in us back in the middle of the last century. There's nothing quite like it to take one beyond one's own little niche in the world.

By the way, that Peace Sign, or Ban The Bomb sign as we used to call it, in the picture is on the back of my VW van. It's called a Peacewheel. It's my way of staying connected with the causes of my youth.

## Tuesday, October 4, 2011

In my last blog entry I mentioned how I was going to withhold the letter grades when I returned the weekly journals to the students in my Schools and Society class. It turned out to be a really interesting and worthwhile activity because it raised all kinds of thoughts and questions in the students' minds regarding the purposes and roles of grading in the world or K - 16 education.

As I gave the papers back, the students looked immediately for the small grade slip stapled to the backs of the papers. After a minute or so I asked them to talk in their groups about how they felt and what they thought about not getting a letter grade.

We concluded by deciding that since the State Dept. of Education requires a B grade average in order for students to be licensed to teach it was really important to have a grading system. However, none of us were convinced that there is a clear link between a grade and what has been learned, all the time.

Tomorrow, were going to be exploring issues of assessment especially the role of what one knows about the topic in the assessment of a student's work. Why is the picture above so strange? Or is it? What do you need to know to make that decision?

## Saturday, October 1, 2011

This past week, my Schools and Society students have been reading about different points of view regarding assessment. Each week, each student sends me two journal entries. One is a focused response to the chapter they read in the Educational Foundations text we are reading and the other is a response to a question about their two-hour weekly public school classroom experience. The journals are great and give me a good insight into how the students are thinking about the profession of teaching.

Most of the readings in the book present quite a radical view of teaching and education because in the Education Department at St. Mike's we believe the teachers who graduate from our teacher education programs should be thinkers and intellectuals in addition to caring about children's learning and welfare and having a passion for teaching. Two of the readings on assessment this week are by Alfie Kohn and William Ayers; two of the great writers and thinkers about issues in education.

To make the discussion more interesting I am going to leave off the small grade sheet I attach to the students' journals when I return them at the beginning of class. They will only get to read the copious comments I write on their papers. How do you think they will react? I have a feeling they will want to know what grade they got before the end of class.

My grading system is a bit tougher than the one above; a few points more are required for each letter grade.

## Thursday, September 29, 2011

### SMARTboard Expertise

One of my student teachers, Erika Kirslis is completing her student teaching in Julie Roger's first grade class at Allenbrook School in Williston. For several years, Julie has been an expert in, and advocate for, the use of SMARTboards in public school classrooms. Julie can now develop her own applications though the use of Studio 10 software for use on the SMARTboard which means she can use it to teach whatever she feels the students need to learn and she needs to teach using this incredible piece of technology.

So far, I have observed Erika incorporating the SMARTboard into her instruction for two math lessons she has taught and she has done it brilliantly. Today she was teaching the students the concept of sequencing using coins. She had prepared a repeating pattern using quarters, dimes and nickels and was asking the student to continue the pattern. One of the wonderful things about the SMARTboard is the ease with which things can be done, even by first grade students. In order to continue the sequence all the first grader needs to do is place her finger on the appropriate coin and drag (a copy) to the next place in the sequence.

After the students had completed two sets of three iterations of a pattern Julie suggestions they say the coin sequence chorally as a rhythm. At that point I couldn't help but suggest that what they were doing in the first example was musically 3/4 time since there were 3 coins repeated in the pattern. In the second example there were four coins in the pattern so it was in 4/4 time. There are so many connections between music and math.

Once again this is a wonderful example of the incredible quality of the public school teachers who host our student teachers as well as those students in field placements in other courses. We are all at St. Mike's very grateful to have such great role models.

## Wednesday, September 28, 2011

### A Different Perspective

Last week I observed one of my student teachers teaching a lesson using the Fundations reading and writing program. It was a first grade classroom and the students were learning how to say and form letters of the alphabet. Now I'm not an expert in the area of reading and language arts so I tend to see these type of activities through the lens of a math/science person.

The lesson involved using four horizontal lines to help children form their letters. At the top was the "sky line" where the tall letter start or end. Next was the "plane line", the upper limit of letters like a,e, c and so on. Next came the "grass" line, the line upon which all letters rest, and finally the "worm line" or the lowest line where letter like g and p finish their tails.

Each line is represented by a picture; the "sky line" by a cloud, the "plane line" by a Boeing 757, the grass line and worm line by grass and a worm respectively. The more I looked at the image of the four lines and associated pictures projected on the screen in the classroom the more confused I became. Every large plane I've ever traveled on has flown above the clouds as in the picture above. I would imagine many of the students in the class have flown and marvelled at all the fluffy white clouds as they look down on them through the window. I wonder if they were thinking about this? Probably not, but it's an interesting example of how the things we spend our time working with bring a specific perspective to how we see the world.

All the Elementary Education majors at St. Mike's are required by the Vermont State Department of Education to take a second major. I wonder if the types of second major the students are studying affects the way they see teaching and education? Maybe I'll ask them.

## Monday, September 26, 2011

### The Teaching Gardens at St. Mike's

In my Schools and Society course this week the readings focused on a part of the book that describes good schools; schools such as Summerhill in England, the Central Park East Schools in New York, the Met in Rhode Island and the HiPass schools. In Addition to having a focus on the individual student and the establishment

of authentic learning communities the guiding tenets of these schools also include the belief that genuine learning must occur outside the classroom as well as within and that there has to be a connection between the two.

The Teaching Gardens at St. Mike's are a wonderful example of the way the classroom can be taken outdoors. This weekend another feature was added to the Gardens that enhances their value as part of an extended learning community.

A series of signs has been added to the Gardens that help people

The signs are the work of Professor Valerie Bang-Jensen and senior SMC elementary education major Courtney Smith.

Courtney, a double elementary education and religious studies major designed the signs during the summer with a VPAA summer research grant. She designed the five signs using visual and verbal text (symbols and words) to help educate visitors

to the gardens about the purpose of each garden. In addition to being visited by SMC students and staff, the gardens are becoming
a destination for classes of students from many local area schools.

In fact, many of the groups of children who visit the gardens are accompanied by SMC education majors who are completing their student teaching experience in public school classrooms.

Many SMC faculty also hold their classes in the Teaching Gardens when the weather permits.

The Teaching Gardens are also a central theme in an integrated First Year seminar co-taught by Professors Valerie Bang-Jensen (Education) and Mark Lubkowitz (Biology).

When we reach out beyond the classroom walls both teaching and learning become more real and relevant to the lives of everyone involved.

## Friday, September 23, 2011

### Sierpinski and the Joys of Learning Math

Many years ago I used to conduct regular Math Nights at local area schools to help parents develop an understanding of the new math program their children were using in schools and the type of math their daughters and sons were likely to bring home in K - 6th grade. They were nearly always lively events with teachers running parents through the math activities their children did in class and me finishing the evening with a Q&A session.

Earlier this week I was at Flynn school where I have two student teachers and as I walked the hallways to their classrooms I noticed some eye catching posters advertising the upcoming Math Night in October to which everyone in the school community was invited. What caught my eye was the Sierpinski triangle, a fractal, as shown in the picture, displayed on many of the posters.. There were also some posters with Escher-like tessellations all designed to catch the eye of the passer-by. Fractals (PBS- Nova), once thought of as a curiosity or an extreme art form, are now being used as mathematical models to explain all kinds of things in the natural world.

But there was more to these posters than just announcements. The work of Karyn Vogel, the Flynn and C.P.Smith schools math professional development coordinator, they were also communicating the aesthetic component of math, a critically important element if we are ever going to help students enjoy math for what it is, the science of pattern. Imagine learning to read and write without poetry, fiction, literature and creative writing? Imagine if the only thing we learned in language arts was the ability to read directions and write formal descriptions? Imagine if reading and writing were reduced to a purely utilitarian function?

I spent the day today at a conference on teaching math to children who struggle to learn math. The presenter was excellent but he made the points that "math ain't easy" and that "math learning has no ceiling". Learning to read is extremely difficult for many children, so is learning science or social studies. In fact, everything can be difficult in some way for some children. I also cannot think of a subject that has a "ceiling". One can study for a PhD, and beyond, in almost anything. If math was made as motivating to learn and as interesting as language life would be very different.

## Tuesday, September 20, 2011

### First Classroom Experiences

In addition to supervising student teachers I also place my Schools and Society students in a classroom experience as part of their first Education course. Today, I spent four hours reading their journals of their first experiences as a teacher; for most of them, their first experience in a public school classroom not as a public school student. It's almost like the other bookend from student teaching and I can't wait to supervise my first student teachers who were also in my Schools and Society class.

Their journal entries are full of wonderful events, experiences and first impressions. One student shared how she wanted to raise her hand when the teacher asked the students a questions. Many students described how "terrified" they were driving to the school (they travel in groups so I can imagine the conversations in their cars!) until they reached their classrooms and the teachers and students welcomed them with open arms.

In their journals I asked them to respond to their first feelings about their first steps on the road to becoming teachers. Their responses were quite varied but for the most part it was an exciting and exhilarating experience for them. I reassured them that their nerves and worries were quite normal because this was something they wanted so much. It's so interesting how they mostly follow Fuller's Stages of Concerns model of socialization into the teaching profession. The first stage is one of survival, which is what they almost all go through during their first visit. It's the same in student teaching. They then become concerned about whether they are acting like a teacher, teaching properly and generally performing well. The final stage is their concern for the outcomes of what they are doing; are the students learning from them? Are they making a positive difference in children's lives?

The picture is of Matt Hadjun who came through our program at St. Mikes several years ago and is now teaching in a local elementary school and is one of our cooperating teachers. Life has come full circle for Matt.

## Thursday, September 15, 2011

### Student Teaching is the Best

Part of my job as a professor of teacher education is to supervise students during their senior student teaching experience. This involves visiting each student in her classroom eight times during the semester. During each visit I observe the student working with children as they learn what it really means to be a classroom teacher. It's the time when they get to put into practice all the things they have learned during the courses that comprise their teacher education program at St. Mike's. Last year, because of other course load commitments, I wasn't able to do this. Only now, when I am once again supervising students in classrooms, do I realise just how much I missed this part of my job.

I now have confirmation of what I always thought; not only is it a critical part of our students' education it's also a critical part of my ongoing education as a teacher educator. I now realise that for a whole year, the first time in my professional life, I was cut off from the public school classroom. Looking back, I can see what I missed; no new stories about things children do; no new learning about the things teachers use in their day to day interactions with children. For example, I learned this morning that teachers at one of the schools where two of my students are, Allenbrook school in Williston, now have access to an IPAD2 cart that allows them to integrate this wonderful piece of technology into their teaching. I plan to use the iPAD2 in one of my courses this semester but I wasn't sure until this morning whether this was a realistic expectation for prospective teachers to develop their skills in. I also learned that we can no longer assume that children know how to use a traditional telephone. One of the first grade students had no idea how to hang-up an old press-button 'phone.

My weekly visits to classrooms keep me grounded in the day to day activities of teachers; the way students in K - 5 classrooms learn and behave. Being in schools on a weekly basis is a way of keeping me honest in the things I teach about in my other courses. I have three student teachers in first grade classrooms and one in a fourth grade classroom and they are all doing really well. The cooperating teacher we use in public schools are wonderful; skilled not only in working with their students but also in the challenges of helping their St. Mike's interns develop their teaching skills.

## Friday, September 9, 2011

### 9/11 in the Classroom

For the last 15 minutes of my Schools and Society class today I thought I would give the students a group assignment of thinking about how they would handle the 10-year anniversary of 9/11 in a public school classroom. Each group chose a grade level spread of 3 - 5, 6 - 8 or 9 - 12. The goal of the activity was for them to think about how they would access resources and then identify the things they would talk about. Within a couple of minutes I realized that they all wanted to talk about their own experiences At the time, in 2001, they were all in fifth grade and so had a remarkable variety of experiences to share; a much better activity than the one I had originally thought of.

Some of the things they described were; how their teachers left the classroom and returned without saying anything; how some of them were asked to shepherd the kindergarten students from the school without telling them anything; how some of them were told nothing and knew nothing until they got home. Since they were all fifth graders at the time they were old enough to process what occurred that day. We ended the discussion by sharing thoughts about how to use Internet resources to help students in classrooms today to understand what happened that day in 2001 and how to process some of the terrifying images and videos they will see during the coming days.

Perhaps, a little too late, I made a September 11 web-page which includes many of the useful on-line resources that teachers have access to as they attempt to make the event part of the history and social studies curriculum. The event is still not specifically included in State standards and in very few textbooks.

On a personal note, I had my own "attack" in the form of a heart attack on 9/13 that required four bi-passes to keep me going. I was told at the time there was a dramatic increase in the number of bi-pass surgeries conducted in the week following 9/11. Such was the impact of the event that anyone anywhere close to having a cardio event was going to have it during that week. I've made a full recovery but remember so clearly the days following 9/11.

## Wednesday, September 7, 2011

### Knowledge is a Wonderful Thing

So is this a map of the United Kingdom, Great Britain or the British Isles? A passing comment by Professor Jeffrey Ayers started a couple of us thinking about the question of whether the three terms are synonyms or whether there are geographical or political differences between them. It is, actually, a map of the British Isles which, interestingly, includes Ireland, as well as the islands of Guernsey and Jersey off the coast of France and about 6000 other small islands (according to Wiki). The United Kingdom includes England, Wales, Scotland and Northern Ireland while Great Britain includes just England, Wales and Scotland, the three countries joined together, as illustrated on this informative website.

There's a tendency in our current skills-based culture to trivialize the role and importance of personal knowledge in our lives and in the field of Education in general. When computers and technology were first integrated into school classrooms there was a sense among many educators that this instant access to knowledge would mean that students no longer would need to know or remember things. They could simply "look it up". The same happened fifty years ago when calculators began to appear. It was thought students would no longer need to remember their addition, subtraction or multiplication facts. How wrong they were.

Instant, independent access to knowledge is one of the things that makes an educated person. It's a great feeling to know things just because one does. The things we know, along with our thinking skills, are the tools we use to solve problems, conduct conversations, write, and generally be human. Knowing things we have taken the time to remember also helps develop our memory skills which in turn help us remember even more things with which to think..

Of course, not everything we are required to remember in school is useful, helpful, or even desirable. I remember learning the following when I was an undergraduate student; Arun, Ouse, Rother, Stour, Medway, Darnet, Mole and Wey. I memorized them so well for an exam that I can still rattle them off without even thinking about them. I even still remember what they are!