Lincoln Portrait Penny Mosaic

Happy New Year everyone; time to start putting pen to paper again, metaphorically speaking, sine I haven't for some time.

So I have decided to complete the Lincoln penny mosaic that one of my students, Lydia, began the past summer. She is currently student teaching so has little time for things like this. The mosaic in 51 pennies wide and 61 pennies deep so it's just a cse of using coordinates to get the righ shade of penny in the right place; at least that is the plan. Each penny can be located by using a grid coordinate system, the fist number will be the column and the second will be the row. The key to success will be keeping things vertical and horizontal.

There will be 3111 pennies altogether and it looks like I will need an addition 2500 to finish what Lydia has started. Any penny donations will be gratefully accepted.

I was observing one of my student teachers in a kindergarten class this morning when one of the kindergartners said "I subitized" when asked ow she knew how many dots there were. This is the first time I've ever heard a child use this intriguing term.

A Custom Built Text

I did something this week that I've never done before; I designed my own custom textbook for my Teaching Elementary School Math and Science course. I have used a wonderful textbook by John Van de Walle in the course for many years but I wasn't using all of it. The book costs an amazing $158 and so didn't want my students to spend all that money on a book  I only partially used. The part I didn't use was pedagogy or how-to of teaching math. For this part of the course I use the Bridges program which is used extensively in school throughout Vermont and the US.

What I did want to use was the pedagogical content knowledge or 'what to teach' section of the book as I feel very strongly that my students need to understand the math they are teaching even if it is something as basic as subitizing.

So after several emails with the very helpful Pearson rep I now have a custom made book that includes only the pieces I need and with a really neat Matisse painting on the cover. You can even see some numbers in the picture if you look carefully; math and art are so interrelated. The book will only cost my students $123 and will be completely up to date with Common Core info, unlike the used copies of previous editions that are available on-line. They can also get it conveniently at the college book store.

Subitizing, by the way is one of the "basics" of math. It is the ability to look at a number of objects and quantify them without having to count them. Many animals can do this, with crows being quite spectacularly good at it. Most people can subitize up to 5 to 7 objects randomly placed although it takes significantly longer to subitize quantities after 3. We arrange dots on dice and dominoes into patterns so that they are easier to recognize (or, perhaps, subitize). Double 6 dominoes are familiar but try looking at a set of double 12s; the 7 and 8 and 11 arrangements are quite a challenge.

Rekenrek: State of the Art Instruction at SMC

I was observing one of my student teachers in a kindergarten class today during math time and ended up having my first experience with Rekenrek math. This is one of the wonderful things about supervising student teachers; I get to work with incredible teachers in public schools using state of the art instructional materials. I have known about this incredible approach to teaching young children about number but this is the first time I have seen it in action in a Vermont classroom. Developed in the Netherlands it is now promoted by many math organizations as well as the Math Learning Center, publisher of the Bridges Math program used in many of the elementary school in Vermont.

Looking a bit like a simple abacus, the math behind the simple beaded counting frame is just incredibly good math.  There are many different activities that can be done with this simple device but the one I watched this morning went like this. Two students each  draw a card from a pile of cards with numbers 1 - 19 written on them. They then make that number using the beads; but in a very specific way. If they draw 8, they move 8 beads on the top line to the right with "one finger push". This simple little command makes the student subitize as opposed to counting one by one. This helps students develop the idea of numeracy, the essential element of quantitative literacy. If students are allowed to push each individual bead across they will develop an over-reliance on counting and not develop good numeracy skills, the idea, for example of "eightness". If 17 was the number drawn, the top 10 beads would be moved to the right  and then 7 from the second row for a total of 17.

Once the number of beads has been slid across the frame  students take turns to roll a die with the words 'more' or 'less' on each face. If "less" comes up the student with the smaller number takes both number cards. This simple activity develops the difficult comparative concept of more and less. They then continue until all the cards have been used and a winner is declared. Jen Canfield, whose class I was observing in this morning uses the game aspect of the activity as an opportunity to teach children how to be good winners and losers. At the end of each game the two students look each other in the eye, shake hands, and the loser congratulates the winner. Isn't that cool.