"Education systems, teachers, school districts all over the world are going crazy about problem-based learning - nothing like a good problem to solve. But they are looking at the wrong bit of it. The thing we're neglecting is to find a generation of problem finders."

The above quote comes early in Ewan McIntosh's talk at TEDxLondon. This really connects with my goal to foster sustainable learning. Here is the entire talk (it is well worth the eight minutes).

At the recent Mathematical Council of the Alberta Teachers' Association [MCATA] Conference, I facilitated the following workshop: Making Mathematical Thinking Visible - Metacognitive Memoirs. Here is the workshop's description:

So far in this series I have discussed the need to empower learners by getting them to ask and explore their own "Now what?" questions (here), considered possible answers to a messy learner-generated word problem (here), and identified implicit conditions associated with the different answers (here). In this final post of the series, I share my preservice teachers' efforts to extend our understanding of one of the possible answers to this word problem:

Thus far we have considered ways middle school learners can extend their learning by generating their own problems based on young adult literature (here) and how preservice teachers  can extend their understanding by considering alternative solutions (here). Given the four different answers they usually come up with (1/15, 1/30, 1/21, and 1/36), the preservice teachers attempt to revise the original problem to match each answer.

In the prior post, I introduced a problem written by a seventh-grader as both an example of what middle school students could do when deciding what comes next and an opportunity for preservice teachers to develop and explore their own "Now what?" questions. This was the student-generated problem:

Josh earned $1,962 over the summer. Hilary earned $129 more than Josh during the summer. How much money did Hilary earn over the summer?

When I taught middle school math in the 80s and 90s, this was the type of word "problem" that filled the curriculum my district used. Furthermore, the "problem" was typically at the end of a worksheet entitled Adding with Two Addends that was filled with 12 other addition exercises. 

"The important thing is not to stop questioning."