"What is math?" is an essential question a la Grant Wiggins for it is an open ended question that does not have a single answer, it definitely is ageless, it elicits different answers from different people, and it encourages deep thinking, and it may even arouse passions especially in our country where math and Physix tend to charge the air during conversations.
It is imperative that our students address this question to establish the kind of frame of mind that we ask of them and assist them to approach math more as we and math experts/practitioners approach the subject.
So, I start each semester (year) with a Critical Thinking Activity (CTA) that asks this very question and guides the students through a sequence of math problems that I adopted from RonRitchhart's PZC*2009: Views on Understanding (pg. 79). The key parts of the activity are listed below.
*** Start of Sample Items from the CTA ***
1) What is math? What does it mean to you?
2) List the 7 mathematical words/phrases that come to your mind when doing math.
13) Now that you have completed this activity, complete these last two tasks:
a) What do you think math is?
b) List 7 mathematical words/phrases that the above activity suggests to your mind.
*** End of Sample Items from the CTA ***
The new background that I adopted for this blog is a picture of my old blackboard (click here to view the full image) with my students' lists of mathematical phrases pre/activity (item 2 above) and post/activity (item 13b above).
The list on the right side of the board clearly demonstrates that students' perception of what math is all about has evolved and all one hopes is that they would carry this new frame of mind for the remainder of the semester (year).
Share what you do in the first few days of classes to guide your students toward a renewed look at what math is. Thank you
*PZC = Project Zero Classroom