Today I (Jim) saw a great lesson in an 8th grade
classroom in Melbourne, Australia.
The teacher was a young teacher, who admitted that he tended to lecture
to his students predominantly. He
had gone through a professional development session that introduced him to
open-ended, challenging tasks, with some suggestions on how to ask questions of
students, and how to push them to persist. For a neophyte, he really did a great job.
First of all, he gave the students FIVE problems that all
addressed the central ideas of mean, median, and mode, and how they each
represented a set of scores. Each
of the problems differed in the challenge they afforded, and students were
allowed to begin the lesson working on the problem where they felt
comfortable. Most groups began
somewhere in the middle, but some started with very challenging problems and
some began with relatively simple problems.
The key to this strategy was, no matter where the students
started, because THEY chose the level of challenge, they worked through the
challenge to success. When they
finished their first problem, they moved onto a more challenging problem,
building on this success.
At the end of the 50 minute period, all but one of the
groups had solved the second-most challenging problem, and some had tackled a
problem that the teacher made up on the spot that was at about an 11th
grade level. They were animated
and engaged, though periodically like all 8th graders, they lapsed
into non-mathematical socializing.
The teacher was a trooper, going around to each table, asking questions,
posing conjectures about what the impact of changing the data would look like,
and exhorting the students to persist and try more difficult problems.
Altogether, it was one of the best lessons I have seen that
show how providing challenge (tough problems) with control (choice regarding
what problem to begin with) can lead to situational interest, engagement and
superior mathematical performance.
Not all students were excited about the problems, but many were, and
several expressed that the problems were “very interesting!” Good on ya mate!
More from down under as my jet lag wears off!