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
The Algebra Problems
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.
- 7x = 5
- 3x + 5 = 7
- 5x + 3 = 7
- 5 - 3x = 7
- 3 - 5x = 7
- x + 11 = 2x + 3
- 11 - 2x = 8 - 4x
- 8x + 3 = 8x + 11
- 8x + 3x = 2x + 11x
(b) Could you have predicted the answers for any of the equations without
solving it? Which ones, and how?
Here is a pdf file of the complete set.