I've been teaching middle school mathematics now for a little over 8 years. I take pride in the fact that I've never taught the same lesson in exactly the same way from year to year. I'm always tinkering with approaches to content delivery, whether it be direct instruction, inquiry learning, or any other of the related teaching strategies that I have picked up throughout my career. I like to think that my approach to teaching and student learning has gotten better every year, maybe even from day to day.
However, even with all this reflection, experimentation, and trial and error, I have always had this nagging feeling in the back of my mind that I wasn't adequately meeting the needs of my lowest math students. Each year, I have both the advanced seventh grade students (pre-algebra) and those students that struggle (math 7) with grade level skills and concepts. I couldn't wrap my head around the major difference(s) between these two groups and their proficiency with "doing mathematics."
Last spring (April 2012), I was lucky enough to attend the national conference of the National Council of Teachers of Mathematics in Philadelphia, PA. Going in to the conference, my focus was to be on the Common Core State Standards for Mathematics and its implementation into our district's curriculum. The sessions I attended pretty much were all similar in regard to the CCSSM, so I decided to branch out into other areas of presentations. By chance, I overheard another attendee talking very highly of this presenter that he just "had to hear." So I stalkingly followed him to a session that was presented by Dan Meyer. Dan's session was amazing, and eye-opening, but the biggest benefit I received was introduction to the math edutwitterblogosphere. This in turn led me other great math teachers who were collaboratively working via digital means to make math teaching better. Twitter. Blogs. Online professional development meetings (Global Math Department). Very strong stuff.
As with other parts of society, I was naturally drawn to others online that shared similar views as myself. One idea that really piqued my professional interest was the area of number sense in mathematics and its effect on student proficiency in math. As Bill Lombard explains, number sense is composed of:
- number magnitude
- mental computation
- mathematical properties
- effects of operations
Looking back through my experience with students in math classrooms and thinking about number sense, a light bulb came on: my highest students had a strong number sense, while the lowest students really struggled with the components of number sense. I ran a number sense lesson with my classes, and my hypothesis seemed to be playing out. The math 7 students had a hard time visualizing quantities and what happened when we applied operations to those quantities. At this point, it became very clear to me that I had to make a sustained effort to incorporate number sense into my daily lesson planning.
One important component of number sense is estimation, with which Andrew Stadel has done great work designing and incorporating estimation180.com into his classroom and sharing it will all of us to use with our students as well. In my openers for class, I always include a question that involves some sort of estimation task. I found that the students with relatively weak number sense had difficulty making reasonable estimates. I came up with a little "game" to help build better estimation strategies and therefore stronger number sense. Here it is:
As it turns out, this very simple and quick activity really made a difference with the estimation abilities of students. Now, I need to work out some similar activities to use for the other components of number sense.
- An estimation task is posed to the class.
- A student is chosen to provide their estimate.
- I tell them whether the estimate is too high or too low, in respect to the Price is Right's "Clock Game."
- Students use that information to adjust their estimate accordingly.
- We continue with this process until either the students get the correct answer, or ten turns have passed.
- Finally, to build a little competitive spirit and intellectual need, I keep a running score: teacher stumps students, or students get estimate.
Number sense, in my opinion, is one of the most crucial areas for students if they are to be successful in mathematics. As math becomes more abstract for them, the ability to visualize what is occurring with shapes, quantities and operations makes the abstractions easier to work with. If a curriculum does not address building number sense in a significant way, I do not believe that it's worth implementing in my classroom for my students.
Thanks Chris for sharing.