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Journal of Online Mathematics and its Applications
Tool Building: Web-based Linear Algebra Modules
Student Responses, Part 2
The Work of Jack
Our purpose for the Transformer activity is to get students to explore, make conjectures, and adjust their conjectures. To give a sense of how students use Transformer2D, we provide the work of a randomly selected student named Jack.
The worksheet link on the preceding page downloads a one-page MS Word document with the full statement of the project. However, students were working with a multi-page version with space to fill in their answers. We provide that version here as a PDF file.
Here are the parts of Jack's work as scanned images -- each opens in a separate window, and you may want to have more than one open at a time.
It is evident from Jack's work that he has a growing need for language to describe the phenomena he is encountering. Terms such as "shear," "reflected," and "rotated" are being drawn from the text to help explain the changes he observes in the geometric figures. As a consequence of this type of encounter, students come to appreciate the discussion of the terms and their meanings because they have a need for precise definitions of what they are experiencing.
Jack's described his reactions to the transformer project in his weekly journal entry:
We are immersing students in a learning situation in which making sense of the environment is one major component as they grapple with their own limited perspectives and enhance their understandings of one or another concept piece by piece. In such an environment, they keep exploring, keep conjecturing, keep trying to organize thinking in new ways to accommodate the new bits of information being displayed, while at times experiencing considerable frustration because they lack the big picture. The tools and the corresponding projects are designed to eliminate the frustration and also to permit the teacher to assist, probe for understanding, point out significant hurdles, suggest alternative lines of thinking, and help equip students to manage their frustration and continue to pursue knowledge.
Next or page: 10. Eigenizer Tool and Sample Activity
Next page: 9. Discussion of Eigenizer Tool