Teacher Observations of Students' Behaviors

1.  J. had trouble making cause-and-effect connections. Difficulty seeing relationships among ideas. Frequently had difficulty solving open-ended problems.

2.  L. faced several barriers. Purpose of activity seemed unclear. Did not understand that the goal was to do detective work, asking important questions and gathering clues to solve a mystery instead of randomly guessing a shape.

3.  Jo. And E. easily over-stimulated by loosely structured activities. Jo had difficulty controlling physical excitement. E was verbally impulsive.

1.  Started the lesson by asking all students for specific examples of a good geometry-based question AND a not-so-good question. Then discussed with students how each question led to either helpful information or a dead-end. Listed a few helpful questions on overhead and wrote "yes" or "no" under each question. Students talked about what shape each set of answers eliminated and why. Then the teacher changed the answer to each question and had the students talk about how the change in answer affected the next question. CLARITY WAS PROVIDED ABOUT THE TASK WHILE LEAVING A PROBLEM TO BE SOLVED.

2.  For L., the teacher helped her decide on her first question. Then she asked L to explain what clues an answer to the question would give her. This information showed the teacher that L needed more help on narrowing the task to questions that emphasized the particular characteristics of SHAPES. Throughout the activity, the teacher acted as a sounding board for L who would ask a student a question and then come explain to the teacher how the information helped her. If L got stuck, the teacher used open-ended questions to guide her to another question. In addition, based on previous information, the teacher realized the L couldn't visual shapes. So, she provided L with a sheet of paper that showed all the possible shapes on the cards in the activity. L then crossed off shapes as she asked questions to help herself narrow down the possibilities.

3.  For Jo and E the teacher took them aside and asked them to go over the directions with her before they began. She urged them to think ahead and remain calm. She gave Jo a sheet of illustrations to keep his hands busy and to reduce his physical excitement. She then talked privately with E about what types of talking were appropriate for the activity.

4.  Finally, the new shape cards included several examples and orientations of the shape rather than a single illustration. She felt this would prevent over-generalizations and would expand thinking.