The other afternoon I was watching the John Adams series on DVD and became obsessed with Thomas Jefferson's character in the story.  I couldn't get past how silent he was during the Continental Congress.  I always assumed that Thomas Jefferson was an eloquent speaker considering how well written the Declaration of Independence was.  When I asked my stepfather about this point he responded quickly, "No, Jefferson wasn't much of an orator." 

This raised some questions about how people can be pigeon holed into a particular type of expression or even mode of learning.  People obviously have different ways of learning and expressing themselves as reported in the studies of Howard Gardner and his research on Multiple Intelligences.  In the early primary grades educators use multiple intelligences to drive their instruction.  In some quality pre-k programs this is the sole means for curriculum integration.  The problem that I have observed is that as the school years progress we move further away from how students learn as we begin to focus on "standardization" and minimizing the amount of effort we put into presenting information.

Everywhere you turn in the world of education the word "standard" is more and more embedded itself into the educational vernacular.  Ironically there really is nothing less standard than the way in which people receive, process, and disclose information.  The other evening over dinner I was discussing this observation with some friends and we found ourselves discussing how we all processed the same piece of information.  Out of the four of us, we found that we all process and store information in four very different ways.  Now try to imagine a classroom full of about 27 and try wrap your head around what is going on inside of the minds of the class as a whole as a new piece of information is presented.  

This stresses the importance of getting to know how each student in a classroom processes information, and how an educator would require them to present what they have learned.  I plan on offering multiple options for each student to exhibit their learning to help aid in their personal expression, because what would have happened if we had asked Thomas Jefferson to stand in front of a room and express his ideas orally about what truths we hold to be self-evident?   

Over the years my stepfather has created one of the most beautiful and well stocked libraries that I have ever witnessed in some one's home.  It is comprised of all historical nonfiction, organized very diligently  in chronological order.  He begins with the Bible (Genesis) and then moves all the way up through Egyptian history, The American Revolution, The War Between the States, and so on.  While glancing through the different units that I will be discussing with my class this year I took note and shared the curriculum with him over coffee one morning.  He took me into his library to show me where each of the units fell on the shelves pointing out some of his favorite books, and of course taking time to share some of the most interesting stories from each.  I couldn't help but get even more excited about the year to come and the invaluable resource that I have located just 42 steps from my front door.

Over the last 5 years I have always seen math as being a very concrete theme that my students were able to see.  We were constantly joining different sets together (addition) and comparing or removing items from a set (subtraction).  Now that I am moving on to the 4th grade I have been studying the math curriculum this summer and trying to remember how I learned to multiply.  For the most part I remember putting two numbers together as a pair (i.e. 2 and 3) and then I always associated a third number that went with that pair, in this case "6".  This was not a very visual model from what I remember, and I was always a very visual person so as you could guess memorizing my multiplication tables wasn't that easy.   

So as I began to imagine multiplication as a visual process I was brought back to a book that I read a year ago titled "Born on a Blue Day" by Daniel Tammet.  Daniel Tammet is an autistic savant who was able to write his own memoir that allowed people a window into how his mind worked.  I have always been fascinated with how savants "see" numbers, and in his book Tammet does a wonderful job describing his relationship with numbers.  One of the ways that he describes how he "sees" multiplication in his mind is where the shape that occupies the space between the two shapes of the factors being multiplied is the product of the two numbers.  I know that this can sound confusing, but if you refer to the diagram I included from the book it makes it easier.

As I was reading through some of the  teacher's manuals I came upon a strategy used in Investigations (yes everyone, don't forget I am one of the lone teachers who saw the eloquence in the "new" math curriculum) described as Quick Images.  The concept for Quick Images is for the teacher to flash an image on the board and then ask the students how many dots they saw.  The students do not have time to count all of the dots so they must use other strategies to derive their answers.  This is an interesting strategy for teaching students how to visualize multiplication.  Sure it isn't as flashy as the way Tammet saw his numbers, but it is an excellent strategy for creating metacognitive strategies for visualizing multiplication.