Aaah, Multiplication Facts

There are few things mathematical guaranteed to stir the emotions more than the multiplication facts. Over the centuries just about everything has been tried to help students, round about the age of ten, memorize or remember their multiplication facts. Traditionally, they have been presented in the format in the image to the left. For example for the 'fives' the 5s came first followed by x1,x2,x3,x4 etc. This format is still frequently used which is really unfortunate because it would be so much more efficient if the 1x,  2x, 3x, 4x, etc came first (as in 1 x 5 = 5). This would allow students to use the repeated addition concept of multiplication to learn the sequence of the multiples of 5 more efficiently and effectively as in one 5 is 5, two 5s are 10, 3 5s are 15 and so on. Here an additional 5 is being added each time; something that does not work when the 5 is presented before the x1, x2 etc.

More recently, we have started using the multiplication square as a way of learning and remembering the facts. This method has the added advantage that each fact makes an array (rectangle or square)which helps the student visualize the fact as they are learning it. For example 5 x 4 can be visualized as a rectangle with side 5 and 4. Square numbers can also be idenfied as squares such as 36 or 6 x 6. Prime numbers make only one array (e.g. 13 only makes 1 x 13) but that's another story.

Today, in my Teaching Math to ELL students class we interviewed students from different countries around the world to find out about the way they learned math. Interestingly, most learned their multiplication facts to 9 x 9 while some learned to 10 x 10 and one student from Saudi Arabia learned up to 19 x 19. No-one seemed to learn to 12 x 12.

10 x 10 is the usual limit for remembering the facts but I always have wondered why it was, traditionally, 12 x 12. Perhaps it was because 12 figures so large in our Western culture (12 Apostles, 12 months in a year, 12 hours in a day, 12 in a dozen, twelfth day of Christmas, 12 inches in a foot etc). Perhaps there is a more logical reason? I can't find an answer on Google, yet.

Math and English Language Learners

I started teaching a new course today, GED611 Teaching Mathematics to English Language Learners in the K - 8 Classroom . The topic of the course, a new requirement in the TESOL Program at St. Mike's, is the focus of my research during the past six years and is something for  which I have great enthusiasm and endless stories to tell,  as the student will tell you.

When I teach a math course I always have manipulative materials on the tables so that students have something to "doodle" with. It's not at all distracting and gives the students an opportunity to learn the characteristics of the math tools we use. Today, when I went to get my box of some 500 Unifix cubes (see picture) I found someone had put all the same colors together in rows of 15 or so. I was quite amazed by this since they are always just jumbled in the box the way they are in the picture. So, a little miffed, I gave lengths of  blues to some students, red to others and greens and so on until all 6 students had several colored rows in front of them.

After class I relayed the strange situation to a couple of my colleagues one of whom was able to shed light on the mystery. Apparently, a student in an earlier summer course needed something to do during class and so had methodically organized the Unifix cubes into colored lines. It must have taken several hours of class time to do this with so many cubes.

The class, just one graduate credit, got off to a great start and I'm very much looking forward to working with the students for the rest of the week. 

Science Understanding Takes Time

"American children do much better identifying the correct answers to simple scientific tasks than using evidence from their experiments to answer those questions". So begins a review of the NAEP report, the Nations Report Card on public education. The review, in the local paper, concludes with "Teachers have moved towards teaching more knowledge, as opposed to the  understanding behind the knowledge".

If you plant carrot seeds you will get carrots and if you design widgets you will get widgets. Our whole education system, under the pressures of  NCLB, is designed to measure, and subsequently value, student retention of knowledge as opposed to their understanding of that knowledge. There's such a vast difference between knowing that the sun "rises" in the east to understanding what that means.

 The financial pressures associated with being a "failing school" as measured by tests in language and mathematics mean there is little time for the type of activities required to develop deep understanding in science as opposed to simple recall as measured on spurious multiple choice questions.

In the early 1960s the US was devastated by the Russian Sputnik triumph. The next two decades were characterized by feverish investment in hands-on (now known as minds-on, hands-on) science in an effort to produce a nation of scientifically literate students. Programs such as ESS and SCIS (known as alphabet science programs because they all had acronyms) proliferated and science education had its golden era. Today, we struggle to get even a couple of hours a week of science education in most elementary school classrooms so it is no wonder that we are producing a nation of scientifically illiterate students.

Professor Bang-Jensen receives Governor's Award

It's been a quiet few weeks at St. Mike's, apart, of course from the construction work going on for the new Student Center and dorm. I've been busy getting ready for my new Teaching math to English Language Learners course that begins next week.

One of the really neat things that happened recently is that one of my colleagues, Professor Valerie Bang-Jensen received a Governor's Award for Outstanding Community Service - Service Learning category, for the work her students have been doing at the COTS Main Street Family Shelter in Burlington, Vermont for the past two years. Valerie received the award from Peter Shumlin, Vermont State Governor at the Vermont State House in Montpelier. With Valerie, is Nicole Marshall, a St. Mike's graduate ('09) who nominated Valerie for the award. Nicole took Valerie's Children's Lit course a few years ago while a student at St. Mike's and is now the Development Assistant and Volunteer Coordinator at COTS.

St. Mike's is well known for the Service learning activities of its students such as inner city renewal projects and Habitat for Humanity. Many courses are also designated as having a service learning component. But there is something special about being recognised for service to the community when the activity is set up with the goal of providing everyone involved with a positive and worthwhile experience.

The "Book Buddies" program that Valerie connected with is a way of providing the St. Mike's students with a great learning experience while at the same time bringing the richness of children's literature into the lives of young children who find themsleves in less fortunate circumstances. The Children's Literature Class is one example of how the  Education Programs at St. Mike's are incorporating more and more non-traditional education settings into student experiences as thjey pursue their teacher licensure.

Math Leaders Unite

There's nothing quite like having the opportunity to talk about something you really enjoy doing with other people who really like doing the same thing.
Last Friday, 20 or so of us got together to talk about what it means to be a K-6 school-based math leader.

One of the first things we discovered was just how many different ways the job of "math coach" could be defined not to mention the variety of different job titles that are used by school districts.

Regardless of all the differences the one common theme that everyone agreed upon is that working with teachers in their classrooms is the most effective way to improve the quality of math instruction students receive. Being a "guide on the side" so to speak is probably the most effective way of helping teachers develop their mathematical understanding as well as improving their pedagogical skills. There is, however, no clear model that works better than any other. It would appear that whichever model is used the key to success is time. In other words, the implementation of a math coach within the structure of a school takes time for it to be effective as described in this study  by Campbell and Malkus.

The study is one of the resources included on the new Math Leadership webpage I have created to be used as a resource by school-based math leaders