Now watch an extended video excerpt (duration 3:04), at left, of the class you have just seen as they continue to work on the Hexominos problem.

The problem of finding and categorizing the hexominos encouraged students to connect mathematical concepts they had learned before and apply them to solving this problem. The nature of the problem encouraged students to then monitor their process, adjusting as necessary so that their understanding is more robust. Self-monitoring, or student reflection, is important for success in further study of mathematics and other disciplines.

After you have completed the activity and watched the video segment, reflect on the following questions (at least two of the three):

• Recall that problem-solving experiences should be linked to important mathematical content. What mathematical ideas were developed in this lesson?
• The teacher comments that she did not want to "push" the students who were sorting by resemblance to letters of the alphabet into thinking about the problem from a more mathematical point of view. Do you agree with her decision? Why or why not?
• What might you, as a teacher in this classroom, have done differently? Be specific.

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