I knew that algebraic thinking needed to be developed at the middle school level. But, I also understood that traditional methods of manipulation of numbers and symbols were not always appropriate for young adolescents. In response to that concern, my colleagues and I began to develop real-life, concrete lessons to teach algebraic concepts to our seventh and eighth grade students. By using our state's Essential Academic Learning Requirements to define what the students need to know and be able to do, we were able to focus our instruction and assessment practices and develop guidelines and models for classroom-based evaluations of student performance. Algebra tiles, graphing calculators, and problem solving were at the heart of almost every lesson.
Students begin by measuring rebound heights and organizing their information in a chart.
After collecting their data, they graph the information and formulate conjectures based on their charts and graphs. Students then enter the data into the table function on the TI 82 calculators and graph their data again, comparing results of various groups. We found that lessons like this develop mathematical models that help students in their construction of algebraic sense. We concentrated on designing questions to help students summarize specifically what they had learned. Student responses could then be used as assessment tools to help the teachers chart students' mathematical growth.