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A Journey with Self-Assessment
            as a Compass
                        © 1995, 1998, 2001, 2016, A. Azzolino


      There is potential for change. Consider these three samples written over a period of years by the same instructor. Each was used as a review or debriefing of a lab on curve shifting or composition of functions.

Example 1: Sketch:

ai1.gif ex. 1

      Nouns provide the variety. In fact the focus is on the nouns rather than on the verbs. The instructor chose the verb "sketch," meaning "get to the message of the expression and depict it," rather than the verb "graph," meaning "show the exact relationship between input and output" and felt the students understood this meaning.

Example 2: Sketch:

ai2.gif ex. 2

      In Example 2, more attention was paid to the possible questions an instructor might ask of a student. An awareness of the possibilities and a desire to have students think about mathematics, rather than just perform algorithms, prompted the shift. Here the instructor demanded that students step back to look at the bigger picture. Students were asked to discuss, to explain, and to compare, not just to sketch. Here the student was asked pointedly in question 7 to compare a translated graph to the parent function's graph rather than the sequence of question 8, 9, and 10 used in Example 1 which "covers the same idea." Here in question 8, the instructor pinpoints the same idea as Example 1's question pairs 2 and 3 or 8 and 9.

      This very noticeable shift in focus caused the Assessment Inventory to be written. Example 2 improved the summary depicted by Example 1 and started a collection and organization of "math" verbs according to cognitive categories. A copy of the list next to the word processor still prompts experimentation and refinement of tests and assignments. It permits one to:

  1. fine tune the verb to fit the purpose,
  2. increase and experiment with the variety of questions, and
  3. include more higher-order thinking skills.

      Example 3 highlights more recent summaries and questions.

Example 3:

  1. Sketch the graphs of the identity function, the opposite function, the reciprocal, the squaring function, and the square root function.
  2. Describe the graph of y = x + 3
  3. Compare the graphs of y = x + 3 and y = (x + 3).
  4. Predict the graph of y = (x + 2)(sin(x)) based on the graph of y = x(sin(x)).
  5. Verify your prediction using your calculator and explain why it was correct or how it was incorrect.
  6. State the equation of the function [given a graph or a description of some sort or a table of values.]
  7. Explain how the domain effects the graph of the function.
  8. Suppose y = f(x) represents the graph of a function. What does the graph of y = f(x) + 3 look like?
  9. Create a quiz with answers to evaluate a student's understanding of ...
  10. Collaborate with classmates and design a test for this unit.
  11. Present a 10 minute lecture on the material of this section. Include written notes for this distribution at the time of your presentation.

      Let's be realistic. It is not practical to assign students to:

(as suggested above) and have them complete the task during a test. A longer period of time is required.

      In general, the higher the order of thinking skill of the verb, the more time the task takes.


      Continue on to the next page.

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