On the importance of scaffolding within the zone of proximal development

I don't know about you, but my experiences with even the best Shell Centre tasks (their Formative Assessment Lessons, or "FALs") have been hit or miss. These are among the best anywhere, and while I generally love the ideas of their tasks, in practice, I almost always need to tweak their implementations to make them work in my classroom and with my students.

I wonder if this is not inevitable, given the highly customized nature of scaffolding.

I experienced this phenomenon yet again today when I used their Ferris Wheel task, which I brought out for my extremely able but easily discouraged Precalculus students:

    http://map.mathshell.org/materials/download.php?fileid=1252

The purpose of this task is to jump-start students' understanding of modeling and graphing trigonometric functions, using the movement of a ferris wheel cart together with some scaffolded information. The pre-assessment task scaffolded the process well, except for the crazy way they laid out the equations. But then when I ran the card sort task in my 1st period classroom, it was a complete trainwreck. The changes in set-up seemed to yank the problem out of the zone of proximal understanding and launched it into the stratosphere. When something is new, my students are easily thrown (and discouraged), so when they shifted from providing the period to providing the number of revolutions in some arbitrary number of minutes, my students' heads exploded. There was a domino effect of cascading fear and consequences — the equations are set up strangely and are given in degrees rather than radians (after all our hectoring!), the vocabulary changed from revolutions to rotations, etc etc etc.

So during my prep, I made new versions of the cards — ones that would allow my 5th and 7th period classes to recognize the new material and to connect it to things that were still strange, but at least strange in ways they could notice and recognize.

The differences were dramatic. 1st period groups were upset because they were unable to make what they considered meaningful progress on the task (in spite of excellent mathematical conversations) and left feeling unsteady and discouraged. Here is the work from an especially confident and capable 1st period group:

My two later classes, on the other hand, were able to attack the task, making meaningful connections, spot patterns, and really solidify their understanding. Here is the work from an often-cautious and un-confident (but still very capable) end-of-day group:

All in all, it was a good reminder to me to avoid changing horses in mid-stream when I am trying to help learners build conceptual understanding through good scaffolding!