Smaller Groups, Day 2

Today was the second day with groups of 6-7 students, rather than the Harkness standard of 12-14 students. Today went very smoothly. Groups got together independently; they started up where they left off; and although I would like for them to get to the discussions more quickly, they are volunteering/assigning problems and working on them.

One example of the (re-)learning that's occurring: Although the students solved problems like this...

\[\frac{2x}{3}+\frac{3x+5}{2}\leq5\]

...in Chapter 3 (Solving One-Variable Linear Equations), Chapter 4 (Solving One-Variable Linear Inequalities), and Chapter 11 (Rational Expressions and Equations), on Monday the students acted like they had never seen such a problem. You know, fractions are scary!

Today, two days later, and students in every group is showing solutions to this problem, and discussions about errors were occurring. Marvelous!

Using the Harkness method (I need to figure out a name for my evolving method) and selected, appropriate problems from the Exeter Math 1 book has shown me that the student forgot more than I realize--more than they realize. The student-led discussions are bringing back forgotten knowledge--or maybe that the students are actually owning and gaining understanding of work that they have done.

I have also realized that I will have to work hard this summer to rework the problems for my Algebra 1 students for next year. I stole used the Exeter math questions for my students, but I see that my students need to be led more directly in finding connections between problems. They aren't naturally looking for how problems relate. At Exeter and other private schools with small class sizes (Catlin Gabel!), one teacher with 12 students means that the teacher can watch and comment on every problem. With my 25-27 students per class, I cannot hear everything nor participate with each group every moment. I'm sure that connections are being missed, which means reduced conceptual learning. I've got some ideas for next year...

Tomorrow I am gone from school for my District's next CCSS Workgroup. I hope that the students handle themselves while I'm gone. I left a couple of questions for my substitute to answer about his perceptions of the discussions; I can't wait to find out what he thinks.