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


      What message does your sorted inventory have for you? What are the categories you use the most? Do you have variety? Is the message to your students the message you wish to send? Is it the most appropriate one? What are its strengths and its weaknesses? How does your inventory compare with your ideal inventory? With your vision of a poor inventory? With that of your colleagues?

      Your inventory may be thought of in three ways:

      Some readers might wish to know how they compare with other instructors. This additional information might be valuable before setting a new course. Samples of similar, earlier, Assessment Inventories of other instructors follow. A variety of styles exist. The six numbers represent the total number in each of the six categories: (1) evaluation, (2) synthesis, (3) analysis, (4) application, (5) comprehension, and (6) knowledge verbs.

Instructor 1: 2,3,1,4,2,0
EVALUATION: compare, contrast
SYNTHESIS: formulate, specify, write
ANALYSIS: contrast
APPLICATION: graph, sketch, simplify, solve
COMPREHENSION: draw, explain

Instructor 2: 3, 2, 1, 3, 5, 1
EVALUATION: compare, contrast, justify
SYNTHESIS: tell, write
APPLICATION: graph, identify, solve
COMPREHENSION: defend, demonstrate, estimate, explain, illustrate, define

Instructor 3: 0, 2, 0, 5, 0, 0
SYNTHESIS: combine, write
APPLICATION: compute, graph, sketch, simplify, solve

Instructor 4: 0, 0, 0, 4, 3, 1
APPLICATION: graph, operate, simplify, solve
COMPREHENSION: convert, draw, estimate
KNOWLEDGE: identify

      Of the group, Instructor 2 has the greatest variety of verbs, the highest number of higher level thinking verbs, and does not test the lowest level of cognitive skills. Instructor 4 may be the most typical test author, one who focuses on application and comprehension.

      The following list indicates frequency of use for a group of 18 instructors.

13 graph
12 solve
11 simplify
11 defend
9 draw
9 compare
9 estimate
9 simplify
8 define
8 write
8 explain
7 sketch
6 describe
6 compute
6 plot
5 choose
5 identify
5 combine
4 tell
4 identify
4 classify
4 complete
3 fill in
3 read
3 justify
3 interpret
3 contrast
3 rewrite
2 classify
2 translate
2 diagram
2 match
2 summarize
2 predict
2 create
2 rewrite
2 convert
2 fill in
1 illustrate
1 formulate
1 conclude
1 summarize
1 list
1 differentiate
1 demonstrate
1 specify
1 decide
1 point plot
1 use
1 change
1 apply
1 transform
1 relate
1 correct
1 organize
1 operate

      Their tests said to student, "In mathematics, we graph, solve, simplify, and defend. We also draw, compare, simplify, write, explain, sketch, describe, compute, and plot. Sometime we do other things." What statement do your graded assignments make about what mathematics is?

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