Wednesday, October 31, 2012

Tommy Sands is coming to St. Michael's

Tommy Sands is coming to Saint Michael's College in March for the next Concert for Saint Patrick. Probably best known for his incredible antiwar song Roses, Tommy Sands has been a voice for peace and justice for as long as I can remember. I have sung many of his songs with my band, the Highland Weavers, over the years so to meet him in March is something incredible to look forward to through the long, dark winter months.

Here's more about the legendary Tommy Sands. 

The concert will once again be a fund raiser for the Sustic Fund for Families of Children with Cancer.

Tuesday, October 30, 2012

Clocks Fall Back

I am determined not to miss the clocks "falling backwards" this year.  It's already happened in the UK so I have been warned. It's been so warm and un-fall-like recently that it's easy to miss the event. I completely missed the "Springing forward" because it was such a dark and dismal time of the year this year.

The changing of the clocks in Spring and Fall is one of the most difficult concepts to teach young children. It's such an abstract thing and yet it affects everyone. Time, in hours and minutes, is a man-made construct. It's really the daily rotation of the Earth on its axis that gives us day and night. The two things are related but not "glued" together, so to speak. We can "slide" the hours and minutes construct/scale back and forth on the Earth-related time scale to optimize the daylight time available to us. Here's a neat web-site that shows day and night as it's actually happening as well as the time anywhere in the world. Put a small piece of "post-it" on your monitor screen next to the line that shows night-time and leave the website up for half an hour or so. When you return to the screen you'll see how much it has changed.

Here's another web-site that shows you the time instantly anywhere in the world. It's very difficult for children to grasp the idea that it can actually be tomorrow or yesterday at this very moment somewhere else in the world. In fact, a fourth grade student once asked me if he went to Australia and watched a horse race and flew home could he bet on the winner he had seen win the race and win the bet because he had watched it yesterday which was really now!

The Moment you Know you can Teach

The mid-term of student teaching is a time of great anticipation in the lives of everyone involved in the student teaching experience. There are probably as many definitions of what constitutes a good teacher as there are teachers. In fact, there are probably as many definitions of what a good teacher is as there are teachers, parents and legislators combined. Just about everyone has experienced a teacher of some sort in their life so just about everyone "knows" what a "good" teacher is.

Regardless of what constitutes a good teacher there are signs to look for when you are learning how to teach that let you know that you can actually teach, in the institutional sense, that is. These are not things that other people tell you you are doing but things that come from within. There's something quite unique about teaching; it's the only job where you are face to face, within one room, and in control of up to 30 other people for around 180 days a year. This is what sets teaching, in the institutional sense, apart from all other human endeavors. So knowing, for yourself, that you can do it is a huge milestone on one's life. This "knowing" usually occurs in an instance, in a trice, momentarily; it's not something that creeps up on most people.

I knew I could teach when I was called from my class one day to deal with an urgent issue to find, when I returned, some 7 minutes later, all 34 fourth graders were still happily working on their individual assignments. Last semester I finally saw it happen with Teal, one of my student teachers when she stopped during a class and said quietly  "you're all being so good". Yes, I know that teaching is infinitely more than classroom management but that institutional sense of teaching comes primarily from that threshold of confidence across which all successful teachers step at some point.

Then begins the life  journey of learning how to teach in the pedagogical sense where the learning of each individual student in your class becomes the number one priority and your knowledge and understanding of the subject matter enables you to optimize the learning of each of these  individual students. OK, so this is how I define good teaching!

Friday, October 26, 2012

Outstanding Teacher Recognized

It's not every day that someone you know gets a $25,000 award and incredible recognition  for being the best there is. This is what happened to Matt Hadjun, a St. Mike's grad., current graduate student, cooperating teacher, fifth grade teacher, and all around great person. On the morning of Monday October 15 Matt was presented with a Milken Family Foundation National Educator award. Each year the award is presented to forty teachers nationwide in a surprise ceremony in which only a handful of people are privy to before the event. This creates one of the most exciting momentary situations one can imagine.

In a school assembly at Champlain school where Matt teaches fifth grade, all the students, teachers, a selection of local dignitaries, and past Milken award winners gathered under the pretense of listening to a presentation given by the Vermont Commissioner of Education. Commissioner Vilaseca started to speak but quickly turned the proceedings over to the Milken representative who then skilfully led the audience on a journey of what it means to be a great teacher until she finally identified Matt as the winner of the Milken Family Foundation award in Vermont. Sheer joy and pandemonium broke out as a battery of TV cameras rolled to capture the moment. Some of Matt's fifth grade students even had tears of joy rolling down their cheeks as he stepped forward to receive the giant check.

I have known Matt for several years and had the pleasure of working with him last Spring when he hosted one of our student teachers. His classroom is a remarkable  place of learning. With the subdued lights, intimate places for students to learn, and Matt's ever present gentle demeanor and sincere caring for his students and the subject matter he teaches, it is not difficult to imagine how wonderful it must be to be a student in his class at a time when the wonders of the world are just beginning to raise curiosity and a passion for learning.

Well done, Matt, you are an inspiration to all our students who want to be elementary school teachers.

Thursday, October 25, 2012

Place Value and Reader's Theatre

In a previous life and many years ago I taught a language arts and social studies course as part of a teacher education program. My favorite part of the language arts part of the course was Reader's Theatre (and I intentionally put the r before the e). I think I enjoyed it so much because it was an opportunity for students to come to terms with the most incredible teaching tool we all have, our voices. I used to tell them that they had to imagine they were performing a play on the radio so no-one could see any of their actions or facial expressions; everything had to be communicated through the voice.

Yesterday evening I spent half an hour with Stephanie, a graduate education student to help her develop her project which was to teach place value through reader's theatre. Since I believe math should always have an aesthetic component this seemed like a wonderful way of developing the fundamental concepts of place value in an artistic and motivating context.

We talked primarily about place value, how it is groups of tens of tens and how we have ten numerals with which to make every conceivable number possible. We also talked about the misconceptions caused by phrases such as "0 is a place holder" and how 0 really means "none of". For example, in 103 the 0 means there are no tens. We also talked about the reason for putting a comma every three digits to help us read large numbers. Most people remember being taught this but few people ever remember being taught why. If you think about a large number such as 21,487,439 the first 3 digits from the right, 439 refer to ones, the next 3 digits, 487,  refer to thousands while the 21 refers to millions. Between each set of commas, from right to left are ones, tens and hundreds. 439 is ones, tens and hundreds of ones. 487 is ones, tens and hundreds of thousands and 21 is ones and tens of millions. This pattern of ones, tens and hundreds repeats itself between each comma for ever.

Tuesday, October 23, 2012

Teaching and Learning Abroad

It's advising week this week which means I get to share in my advisees plans and goals for their lives. I spend 15-20 minutes with each student as they share their excitement about their courses, professional goals and their work with children. Every so often a student is really excited about a program they have experienced and they want other students to know about it. So when Elizabeth Watts shared her excitement about her participation in Projects Abroad this past summer I had to add a link to the Education Department  webpage.

We frequently hear negative things in the news about study or work abroad programs so it is really good to hear about one that really works well. Elizabeth went to Ghana through Projects Abroad and was really impressed with both the educational component of the program as well as its administration. It's a volunteer program but everything is really well organized and coordinated. She says she always felt she was well looked after and knew exactly where she was supposed to be.

Another great overseas program is the Advanced Studies in England program which is a more formal educational experience but with a significant field placement in a public school classroom. One of my advisees, Sara Denton is currently studying with ASE in Bath, England. You can read all about her experiences in her SMC blog.  

Tuesday, October 16, 2012

Inspirational Teacher Voices

In one of the undergraduate courses I took when I was learning to be an elementary school teacher in the late '60s/early 70s the instructor would have us all periodically lie on the floor and project our voices up to the ceiling. Sophie Williams was her name and she taught Theatre courses as well as Education courses. The idea behind this was to help us develop our teacher voices so that we could be heard and understood without shouting. She taught us how to project our voices from our diaphragms as opposed to our chests. She taught us all about voice intonation, pitch and volume. These, she assured us, were the tools of our trade. They would help us use our voices in a survivable and effective way; something we would need for a lifetime of some 45 years of teaching.

Since that time, I have treasured Sophie's words and come to realize the wisdom in what she said as I try to help my student teachers master the infinite qualities of their voices. I have added to Sophie's advice by reassuring my students that they will get much more enjoyment from their teaching if they see it as a "theatrical art" form in which they can play the part by using their voices effectively and enjoyably.

For example, I tell them to sound curious and genuinely interested when they are asking a question; soften the voice or use falling or rising intonation so that is sounds like a genuine stimulus for thought or search for an answer. I tell them when they want student to follow specific directions to say what they mean and mean what they say. It doesn't really work very well if you want to let children know you are not terribly happy with their behavior if you say it with a big smile on your face.

So although I want my students to develop their teacher voices the idea is a long way from what is traditionally known as a "teacher voice". This is something left over from a Dickensian classroom. Effective teacher voices are inspiring, encouraging, enlightening, motivating, sensitive and theatrical. If they are this, they never need to be "teacher voices".

Saturday, October 13, 2012

Presidential Debate Numbers

The last presidential debate was really interesting from the perspective of the numbers used by the two candidates. Both candidates started off with small numbers then went to big numbers and finally finished up with specific numbers.

By this I mean the numbers used by the candidates when they are trying to score points. At the beginning of the debate the numbers were mostly single digit with Obama using 4,5,2 and 46 while Romney used 4,3,5,1,2,3,4,5,4, 30 and 4. This went on for some 5 to 8  minutes or so and then they got into the big numbers such as millions, billions and trillions such as 2 million, 3.5 trillion and so on. Then came the specific numbers like 4,300, 3,600 and so on. The rest of the debate was a mixture of all sorts of numbers with the large numbers being the most frequently referred to.

The other interesting way of analyzing the debate numerically is the type of numbers they used; were they cardinal, nominal, or ordinal numbers? For the most part they were cardinal or counting numbers but Romney did use quite a few nominal numbers in referring to his 5-point plan. There is yet a third way of looking at the numbers which involves identifying whether the candidates use a referent or not when using a number. For the most part the referents are not included especially when the number is in the mill-, bill-, or trillion (e.g. "the national debt is at 3.5 trillion").

After you've heard these big numbers over and over again they begin to lose their intended meaning because they are not intentionally connected to referents. It's much easier to throw around numbers rather than use logical, reasoned arguments to make a point in a discussion. In the end, though, the numbers will just become hollow words without any real meaning.

Here are some even bigger numbers the candidates could use to further their arguments. They've used up to several trillion. They could go on to use quadrillion, sextillion, nonillion or, to really make a splash, they could use septendicillion or the very apt novemdecillion (this would be 1 followed by 60 zeros).

It's fun to note the numbers people use when you are in a meeting. Keep a note of the numbers  and develop a PNP, a personal numerical profile, for each person.

Tuesday, October 9, 2012

A Student Teacher's Words

Sometimes the words of a student are far more eloquent that those of the professor.

An Excerpt from a Student Teaching Journal

"I really enjoyed teaching the students the game “An Hour or Bust” this morning. I was a little nervous giving the directions since I was not sure if the students were understanding the concept of the game but once we started playing I could tell that they were getting the hang of it. In this “me vs. you” game as we like to call them I played against the entire class. Each team could spin up to five times on a spinner that had six different increments of time on it ranging from 5 to 20 minutes. The goal is to get as close as possible to 60 minutes in five spins without going over. The team that gets the closest is the winner, and both teams can choose to stop spinning at any point in time. The students followed along with me as I filled out the game sheet on the overhead, coloring in the increments of time that were being spun on the clocks and writing down each increment. The students were really engaged in the game and I could feel the effects of this engagement on their behavior. When I asked for students to show me they were ready to move to the next spin by putting their materials down they really followed through with that signal and we were able to have a good pace throughout the lesson. Students were not playing with their crayons or having side conversations and they were really excited about the game.
            I think students were so engaged in the lesson today because I really had a good understanding of the math concept that was being taught and I was excited to share my knowledge with them.  Students could tell that I was excited about playing this game and as a result they were really giving me their attention. The game was so much fun for me to teach because of how visual it was for the students. It was fantastic to show them how to count by 5’s around the clock and be able to shade in increments of time on the clock. At one point we had half of a clock shaded in and I asked the students how many minutes were shaded in. S___ raised her hand and shared with the class that we had half an hour shaded in on the clock, or thirty minutes. When I asked S____ how she knew this she was able to tell me that she could see half of the clock was shaded in which must mean 30 minutes since half of 60 is 30. Having the shaded in clock as a visual to refer to was so helpful for so many students today.  Near the end of the game the students had 50 minutes shaded in on their clock and I asked M____, one of our students who struggles with math how many minutes the students needed to reach 60. I pointed out to her the empty space that had not been shaded in and she was able to tell me that the students needed 10 more minutes to reach 60. I explained to the class that instead of counting all the way around the clock up to 50 minutes they could figure out that they have 10 minutes until 60 by thinking about 60 as a whole and knowing that they are missing a part that is equal to 10 minutes. I could have gone on all morning about subtraction, addition, fractions, and probability using this simple game.
 It was fantastic to see the students feeding off of my excitement about number corner this morning and having them so engaged and on task was a great feeling. Towards the end of the game when the class had to make a decision about whether or not to take their final spin because they were close to 60 minutes the students were on the edge of their seats with excitement. Our math enrichment students were at this point late for their enrichment class and I had to almost kick them out of the room with promises that we would fill them in later on the results of the game. It’s a credit to the Bridges program to have the students so engaged in an activity and utilizing visuals to make concepts concrete for students. I hope that I can carry over the good vibes from today into future lessons and keep in mind that enthusiasm is contagious."

This is why I love what I do. 

Saturday, October 6, 2012

Ambition, Distraction, Uglification and Derision

In my math ed class this week I talked about ambition and distraction and uglification and derision but no-one knew what they were so I asked who had read Alice in Wonderland and could remember the Mock Turtle. Perhaps three students out of the eighteen raised their hands. I was initially somewhat alarmed by this but then I started thinking that what is termed a classic piece of literature  probably changes over time. But I'm not an expert in this area so I'll just wonder about it.

Something else we did pursue in class through a really interesting discussion is  whether the incredible amount of time we spend teaching algorithmic procedures  such as 54   is still
worth it given the culture in which we live. Is the use of endless tedious practice exercises really worth it given the extent of the work we now do on numeracy skills as well as the technology-based tools available for computing. Shouldn't we be spending our valuable time teaching children to compute simple problems mentally and more complex problems using some sort of calculator? Shouldn't we be spending our time teaching children the meanings of the operations such as recognizing joining, separating, comparing, part-part-whole, groupings, Cartesian products and multiplicative comparisons?  The essence of solving a math problem is deciding which operation to use. Once this has been done the problem becomes simple arithmetic which can be solved either mentally of through the use of a calculator. In the discussion with the students I was playing devil's advocate; well maybe!

There are very few places in more advanced mathematics where the use of paper and pencil algorithms is required over mental or technology based computations.

Friday, October 5, 2012


As I mentioned in a recent post I am involved in the development of a STEM Academy at one of the local elementary schools. At the first meeting someone raised the idea that it should be a STEAM Academy. We kind of joked about it for a few minutes, wound up the meeting and all went home. Yesterday, one of my colleagues, Professor Jonathan Silverman, an art ed. professor extraordinaire and instrumental part of the Integrated Arts Academy elementary school in Burlington sent me a link to a site advocating for STEAM Academies.

The idea behind STEAM is the integration of creativity and the arts into what has traditionally been called STEM. As I said, when we first heard this we treated it somewhat humorously but as this video, STEM to STEAM shows this is far from a cute acronym or humorous matter. My initial concern was that if we are going to integrate the arts then why not language, reading, social studies and so on which would basically lead us back to a school with an integrated curriculum; just like the great innovative schools of the 1970s and '80s.

But, I keep thinking about this and the more I think about it the more sense it seems to make sense because what it really does is to take us out of our traditional interpretations of what math, in particular, is all about especially in the elementary school where it tends to be somewhat destroyed by the dominance of arithmetic. Combining math and art is what Vi Hart is all about. It is what the Bridges math program  is hinting at; it is what I have believed for many years we should be doing in math; looking at the aesthetics of math, the pattern of number and the joys of probability and geometric shapes.

Science, engineering and technology have for many years been blessed with a strong creative/artistic component but never math. Perhaps this is the real opportunity for the salvation of math at the elementary school  level.


Tuesday, October 2, 2012

Classrooms Around the World

One of the significant elements of my research into how English Language Learners learn math in US classrooms is the nature of the schools and classrooms the students experience before ariving on US shores. For several years I taught a graduate course for a week at a school in Monterrey, Mexico and was alsways impressed by the way adults treated children as children and celebrated childhood. Children were not seen as mini or potential adults as we often tend to do in the US.

Valerie Bang Jensen, one of my colleagues, recently sent me a link to an interesting website that shows the diversity of classrooms around the world. The website, Brain Pickings is the work of Maria Popova, a self confessed  "interestingness hunter-gatherer and curious mind at large".

By looking carefully at each picture you can get a sense, to a small degree, of what education might be like in that particular school. One of the things that strikes me is the incredible diversity between each classroom and the almost total lack of diversity in some of the classrooms. There are classrooms where all the students are either male or female and there are classrooms where all the students are wearing identical clothes.

Perhaps the most remarkable lack of diversity is in the facial expreessions of all the students. Not a single student in any of the pictures is laughing, smiling broadly or even smiling at all. The pictures are clearly posed for the camera but I wonder why no-one said the usual "say cheese" or whatever it is in the appropriate language. The author describes how the students have to concentrate during the photoshoot but why do they have to all look so glum?

Is school really like that? Perhaps Sir Ken Robinson is right!