A POWERFUL, POWERFUL tool! I cannot say it enough...
In the past, many second grade teachers taught the traditional algorithm for addition and subtraction. A HUGE shift in focus has come with the Common Core Standards for Mathematics--and even without the Common Core, I believe this to be essential at this level. The primary focus should be in helping students develop a strong sense of number and exposing them to strategies for addition and subtraction that are strongly rooted in their understanding of place value.
With all of this known, if not the traditional algorithm for addition and subtraction, then WHAT?
My personal experience with second graders, in helping them develop a strong foundation in place value, has taught me how powerful and capable their young minds are. From day one of second grade, students have been immersed in making sense of the WHY, not simply the HOW. I believe one of the most POWERFUL tools in helping do this has been the introduction, instruction, and application of the open number line.
I began to use the open number line with my students after coming across an INVALUABLE resources titled, The Number Line: Learning to Think Mathematically with the Number Line (A Resource for Teachers, A Tool for Young Children) by Jeff Frykholm, Ph.D. This resource concisely explains the theory and rationale for using an open number line with young children and provides a series of lessons that can be followed in sequence. Differentiation options are included as well. All I really needed was this resource to get started, that's it! It is available at Thinking Mathematically for $21 (hard copy) or $15 (download).
So our journey with the open number line began...
The concept of the open number line was introduced to students the first week of school. They immediately began to explore its use with a "life-sized" number line constructed with Command hooks, clothesline, number cards, and clothes pins. Students interacted with the life-sized number line as various numbers were place on the line and justifications were given for their placement.
I also used various lessons in the text and supplemented with additional lessons modeled after those presented. This provided practice for students and began to build their understanding of the tool.
Now, after extended use of the tool, I truly feel that it has been internalized as one of various strategies for approaching and making sense of problem situations. I have tried to pinpoint when students became so proficient with its use (not all of them at the same time, of course), but I have not been able to do so. I think it was magic! Ha!
A student created "situation" and her solution... :0)
If you haven't already, I STRONGLY suggest you introduce this tool to your students. No frills, no catchy phrases, no cute graphics, no bells and whistles--just cheap and conceptually sound! Put the POWER in your students' hands--furthermore, their minds!