# Making Connections, 2006

This workshop focused on algebra in middle school, with regional teams from
Arizona, Georgia, and Montana. During Spring 2006, teachers in each
team collected student work on a packet of algebra problems, and the
teams met in the Summer to analyze the results.

## Participants

### Arizona team

- Terry Greer, Naylor Middle School
- Steve Kraus, Orange Grove Middle School
- Bill McCallum, University of Arizona
- Rebecca McGraw, University of Arizona
- Matt Ondrus, University of Arizona

### Georgia team

- Sybilla Beckmann, University of Georgia
- Brad Findell, University of Georgia
- Sherry Hix, University of Georgia
- Summer Tuggle, Clarke Middle School

### Montana team

- Terri Dahl, Charles Russel High School, Great Falls
- Johnny Lott, University of Montana
- Jenny McNulty, University of Montana

## Followup Activities

The Montana team held local Making Connections workshops in September
2006 and January 2007. More ....

## Workshop, June 7–9

### Day one

- Meetings in disciplinary groups (educators,
mathematicians, teachers) to discuss problems and the mathematical
and pedagogical points they present
- Reports on disciplinary meetings
- Teacher presentations of their students' work

### Day two

- Conclusion of teacher presentations
- Presentation and discussion of results of Tucson
student surveys
- Regional teams (Arizona, Georgia,
Montana) choose a particular problem or set of problems and
student work to look at, and a particular mathematical or
pedagogical point that they illustrate, and discuss from different
disciplinary perspectives

### Day three

- Whole group discussion: what we have learned, ideas for
curriculum modules (for inservice or preservice teachers, for
graduate teaching assistants, or for school students)
- Regional teams to plan and start work on a curriculum
module arising out of the problem analysis
- Reports on progress and plans for the future

#### Results of the workshop

Here are the problems that were produced by this year's teams:

- The Arizona Problems
- The Georgia Problems
- The Montana Problems
#### About the problems used in the workshop

The problems were intended to test strategic competence and
conceptual understanding in addition to procedural fluency. For
example:

(a) Say whether each equation has a positive
solution, a negative solution, a zero solution, or no solution.
- 7
`x` = 5
- 3
`x` + 5 = 7
- 5
`x` + 3 = 7
- 5 - 3
`x` = 7
- 3 - 5
`x` = 7
`x` + 11 = 2`x` + 3
- 11 - 2
`x` = 8 - 4`x`
- 8
`x` + 3 = 8`x` + 11
- 8
`x` + 3`x` = 2`x` + 11`x`

(b) Could you have predicted the answers for any of the equations without
solving it? Which ones, and how?