Ramps, Pathways & Balls: A Constructivist Endeavor in Physical Knowledge (#10-DIFFERENTIATION 2.0 CONTINUED)

ACTIVITY: I was inspired by another classmates use of drawings and sketches created by students of their constructions.  So, I decided to make this our culminating activity.  Two sessions back, I asked the students to sketch their ideas and thoughts about how they could accomplish their individual goals but I did not photography or capture the ideas they shared on paper.  As a part of this last session, I asked the students to draw a complete design of their intended construction and label its parts.  I was excited to see what creations would come forth.

REMINDER: ALM created a task for BCC to complete which was to (with one ball drop) have the ball roll in three different directions with the last directional roll going to the right.  BCC created a task for CAC to complete which was to (using two balls and one ball drop) have the first ball roll to meet the second ball triggering it to roll in a different direction.  CAC created a task for ALM to complete which was to (with one ball drop) have the ball roll in two consecutive 'Z' formations or zig-zags.

REFLECTION: The students' drawings were much smaller than I anticipated.  They used only a fractional portion of the paper they were provided.  This sort of interested me.  I observed that CAC's drawing looked exactly like her last attempt at completing her individual task.  Somehow (as seen below in the drawing) CAC thought that (1) the slight curving of a pathway was a turn and (2) the second ball should be placed before the turn/curve.  This puzzled me.  She seemed to think that if she started the ball on its path repeatedly that eventually, it would do what she wanted instead of changing the design of her pathway.  BCC created a similar image as CAC and duplicated the same curving of pathways while ALM made substantial gains in her thinking using the drawing, she also missed some intricate aspects in her design.  ALM realized that the balls needed to maintain momentum during the long rolls back-and-forth but only made provisions for this momentum on one side of the entire construction.  This prompted me to ask, "Have you ever done any activities like this in any other classes, high school, middle school, elementary?"

SURPRISES: The biggest surprise that I experienced throughout this entire endeavor was the following statement (in response to my question above).  "NO ONE, NOT ONE TEACHER HAS EVER DONE THIS.  NO ONE HAS EVER ASKED US TO THINK THIS MUCH."  Wow!  Wow!  Wow!  We are responsible for what we complain about the most.  Teachers should know this.  The students fall short because we fell short!

NEXT STEPS:  We have come to the end of this particular project; however, I plan to continue in my efforts to increase logico-mathematical knowledge in these students and others.