September 20th, 2011
We continue our math quick tip series with another idea from Jessica Shumway’s recent book Number Sense Routines. Counting the days in school is a routine that Jessica uses at the end of the day to help separate it from the calendar routine, after she and fellow teachers realized that students were confused about counting the days of the month and the days spent in school at the same time. Read more about this routine here and then head over to the Stenhouse site where you can still preview Jessica’s book in its entirety!
Counting and keeping track of the days in school is an especially beneficial routine for kindergarten and first-grade students. This routine lends itself to talking about numbers, thinking about patterns, and seeing amounts. It provides an opportunity for these young students to count every day, see and experience an increasing amount, and think about numbers beyond 100. For second and third graders, there are a variety of reasons and ways to keep track of the days in school, from organizing a growing amount to developing sophisticated strategies for comparing two sets of numbers (days in school versus days on the calendar).
As a mathematics coach at Bailey’s Elementary, I worked with a team of kindergarten teachers who described a problem they came across with keeping track of the days in school. They realized that students were getting very confused between how many days are in a month and how many dayswe had been in school during that month. “What are we counting?” became a common question. Teachers were not asking students to compare the days in a month versus the number of days students had been in school. The problem was that there were too many different numbers (day of the month and the number of days in school) for them to keep track of, especially early on in the year.
One of the kindergarten teachers and I decided to use this routine of Counting the Days in School at the end of the school day as a way to remedy the confusion. That way, the calendar routines, which students worked on during morning meeting or at the beginning of the math lesson, were separate from the Counting the Days in School routine. We used Counting the Days in School as a check-off system: “We are finishing the ninth day of school. Let’s add 9 to our counting tape and move our circle on the number grid from 8 to 9. Wow, you’ve just finished up another day of kindergarten. You are nine days smarter!”
I have seen many different ways to keep track of the days of school. Many teachers use a place-value pocket chart, with each pocket labeled from left to right as Hundreds, Tens, and Ones. They add a straw to the Ones pocket for each day they are in school. Every tenth day of school, students bundle the straws into a ten and place the bundle in the Tens pocket on the chart.
Although this routine is effective in third-grade classrooms, it does not seem to be very effective for kindergarten and first grade. Students at this age are in the process of constructing early ideas of number sense and are not yet near understanding why you bundle straws every tenth day of school. This routine requires students to have an understanding of unitizing—counting ten straws as one bundle of straws or one ten. Students in kindergarten and first grade are grappling with early ideas of how we count objects and represent the count with symbols. Counting ten objects as “one” is difficult when you are still constructing the early ideas of counting, one-to-one correspondence, cardinality, and hierarchical inclusion. Understanding unitizing is a huge leap.
Many teachers believe that the straws routine for keeping track of the days in school is planting the seed for strong place-value understanding as students move into second and third grade. I used to believe that, too; however, I have seen time and again that these young kindergarten and firstgrade students are more focused on what that quantity means and what it looks like. Using cubes instead of bundling straws seems to be an easier way for students to construct early ideas of unitizing and of the importance and efficiency of ten. Opportunities to see ten ones being connected to one ten (without the exchange that takes place with bundles of straws or base ten blocks) will help these younger students construct the ideas of “ten-ness.”
The idea of ten as a group is at the core of unitizing. Early on, though, many children are learning that 1 means one item. It is too confusing to bring in the idea that 1 can also mean one group of ten. That will come later. It is more important for very young children (kindergarten and first grade) to build visual images of the amounts rather than focus on unitizing. Collecting items (like rocks or cubes) for each day of school and counting by ones seems to be a more authentic and age-appropriate task for students who are still figuring out what twenty looks like, how to count twenty efficiently, and how to represent that number. The place-value chart does not yet make sense. Let’s shift the focus for these young learners and instead create routines that will help them see amounts, learn the counting sequence, construct a sense of quantities, and recognize patterns.