Tag Archives: math

The Beauty of the Cartesian Coordinate Grid

The Cartesian coordinate system is a fundamental necessity to mathematics.  Anyone beyond elementary school knows this.  However, when a student first encounters the system, it can be overwhelming.  Two number lines- one horizontal and one vertical- at the same time?  Negative numbers?  This can be a difficult system to master for many students.

Helpings students recognize the usefulness of a mathematical concept or system, before they are introduced to the technical terms and procedures, can be very helpful.  Surely students could learn about the Cartesian coordinate system by having the teacher stand in the front of class and lecture on about the origin, x-axis, y-axis, procedure for graphing, etc.  However, in the case, students do not fully recognize the utility of the system.  Additionally, all the terms, definitions, and procedures can scare students away.  Admittedly, this is how I taught it last year, resulting in low engagement and effectiveness.  Instead, having students discover the Cartesian system layer by layer would allow them to realize its beauty, before learning the ins-and-outs.

To do this, I had two students volunteer come to my interactive white board (IWB), which was simply a white screen.  I had Student A face the board, while Student B turned the other direction.  With student A watching, I marked the board in the upper-left hand corner.

I then created the same exact page, before I had marked the board, which in this case was simply another blank white page.  Student A would now give directions to Student B on where to mark the board, trying to get as close as possible to where I had marked it before.  However, Student A now had to turn around and face away from the board.  This forced Student A to only give verbal clues.  Student B would use these clues to make their best guess, resulting something similar to this:

Most cases resulted in the the students getting vaguely close, but never spot on.  As a class, we reflected and discussed how difficult this was.

I then had the students repeat the process, though this time I added an x-axis and y-axis (explained to them as a horizontal and vertical line).  Again, I marked the board with Student A watching, and Student B facing away:

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Video Story Problems

Last spring, at the tail end of my first year of teaching, I was pondering how to make my math classroom more engaging.  I wanted to make the math more meaningful for students (an almost universal desire among teachers, I think).  Don’t get me wrong, we had done math application problems, in the form of word problems.  However, I felt that there needed to be something more.

I attended a county Common Core mathematics workshop in April, focused on helping teachers develop strategies for teaching the eight math practices.  At lunch, the workshop head played this Dan Meyer bean counting video for us to think about.  A few days later, a colleague of mine, Ben Rimes, started posting his first video problems.  I finished the school year using a few of these videos in my classroom, and really saw a higher level of engagement and curriculum relevance.

This current school year, I have made math video problems a large part of the classroom.  I have produced many videos that have served as instructional pieces.  Furthermore, I have had students develop video problems of their own.  I will go into the process of both the teacher-created and student-created videos in separate blog posts in the near future.

For now, I just wanted to share the resources that have been created this year.  Ben created and managed a Video Story Problem channel on Vimeo, where several teachers have collaborated to create a collection of these videos.

I will post later this week, more specifically about the teacher and student video process.

Also, I will be speaking at MACUL about my experience with these videos, for those who are interested.


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