Today’s problem was from this year’s annual meeting of the Adult Numeracy Network (ANN) at the COABE conference in New Orleans. Christin Smith, Patricia Helmuth, and Heidi Schuler-Jones led the group through a series of activities over the course of the day. The theme of the ANN annual meeting was the idea of revealing algebra in basic mathematics. In our CAMI meeting, we explored an activity that starts with adding on a 100-grid and finding patterns and then moves towards generalization.
We started by considering the following statement: Students need to learn the basics before studying algebra.
The statement prompted questions: What are the basics? Do we mean counting? Basic adding and subtracting? For those who thought some basics were necessary, they weren’t considering operations with fractions, decimals, and percents as necessary before starting algebra. Maybe for some forms of algebra, but not for beginning.
We talked about how some work with basic math can be woven into an introduction to algebra, that students are working on skills and then finding patterns that can be generalized. We also discussed childhood development and the ability to generalize from arithmetic. Since we work with adults generally, maybe it’s a different question, but we did wonder at what age children start to develop the ability to generalize from arithmetic.
In teaching math to adults, there sometimes has been a desire to sequence all instruction so that algebra happens at the end, after other skills considered more basic are covered. In many classes this has meant a few weeks on operations with fractions, a few weeks on decimals, and a few weeks on percents, followed by a week or two at the end of the semester on algebra. If this sequence is followed and restarted each semester, our students will never learn algebra. On the other hand, many of students struggle with basic skills and will have trouble with more advanced algebra without them.
The ANN preconference was organized around the hope that there is a middle way and that we can give students practice with fundamental math skills while learning to generalize towards algebraic rules. The pentomino activity was one of the main activities of the day.
We started with a 100-grid and a piece of patty paper. I asked the group to trace a cross that covered 5 boxes like the one below.
I then asked the group to move the patty paper around and think about the sums of the numbers covered by the pentomino.
After we played for a few minutes, I led the group in Notice/Wonder.
I then asked participants to choose a question to explore and work independently for about 10 minutes. When people were ready to share, small groups talked about what they discovered and then continued working on new questions.
We explored generalizations with the pentomino cross and then started looking at other kinds of shapes and generalizations that could be made with them.
In Attendance: Alisa, Diane, Eric, Greg, Katrina, Kevin, and Lotus
Programs Represented: CUNY Adult Literacy PD team, CUNY Start, LAGCC ALC
Respectfully submitted by Eric.
