My Math Explorations

Today as we settled back into our routines after Spring Break, I took a little time to share with my math group about some math related explorations I did over break. For the first part of the break I took time off entirely: time to play with my granddaughters, time to watch the Final Four, time to hike and look for wildflowers. But the last few days of break I began to look through some math materials and think more about math and the rest of the year.

Math Solutions has a new book that looks interesting, Faster Isn't Smarter. Several chapters of the book are available online (http://www.mathsolutions.com/index.cfm?page=wp18&contentid=994&crid=294&mcrid=107) and that gave me a chance to read through them and mull them over. I shared with my students the name of the book and the idea that sometimes thinking deeper and taking time to process yields a broader understanding than coming up with a quick answer. Being fast in math doesn't necessarily mean you are smarter than others who take more time. I told my students that what is important is to learn what strategies work for you.

I also shared an activity from the latest edition of Teaching Children Mathematics, published by the National Council of Teachers of Mathematics. The activity I read about was for kindergarten students so I upgraded it some for my students. It involved tossing some 2 sided counters (red and white) and recording how many of each color turned up. Students were asked how they figured the totals (recognized the number, counted, knew the number fact, grouped the counters in their mind, etc.) They got practice in explaining their math strategies to the group or to a partner. Some students took on the additional challenge of explaining what they heard another student share as a strategy. We will do this activity again soon, working with a different total number of counters.

Visualizing Numbers

One thing math teachers learn is that it is important for children to be able to represent and visualize numbers in different ways. Last spring when I went to the conference for the National Council of Teachers of Mathematics, I heard a lot about visualizing numbers in a variety of sessions, including one on Singapore math and ones presented by Marilyn Burns and others from Math Solutions. (For more about my thoughts on the NCTM conference see http://skyclassjoanmath.blogspot.com/2009/04/nctm-meeting-in-washington-dc.html and http://skyclassjoanmath.blogspot.com/2009/04/marilyn-burns-and-more.html )

Lisa Rogers from Math Solutions presented a session I enjoyed on developing number sense. One model she shared for visualizing numbers is using ten-frames. It's a model that helps students regroup numbers within our base 10 number system. I have done several mini-lessons with my math group using the overhead projector to introduce them to ten-frames. I have drawn ideas from Susan Scharton's book, Teaching Number Sense- Grade 2. The children have responded with enthusiasm and have been becoming more articulate in describing how they see and manipulate numbers with ten-frames.