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

### USE THE INVENTORY TO DECIDE YOUR DESTINATION AND DIRECTION

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:

• a picture of where you were before the inventory was compiled,
• a reminder of what possibilities exist,
• and a benchmark against which future assessments might be made.

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 KNOWLEDGE:

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

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

 Instructor 4: 0, 0, 0, 4, 3, 1 EVALUATION: SYNTHESIS: ANALYSIS: 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 graph12 solve11 simplify11 defend 9 draw9 compare 9 estimate 9 simplify 8 define8 write8 explain7 sketch6 describe6 compute 6 plot5 choose5 identify5 combine4 tell4 identify 4 classify4 complete3 fill in3 read3 justify3 interpret 3 contrast3 rewrite2 classify2 translate2 diagram 2 match 2 summarize2 predict2 create2 rewrite2 convert 2 fill in 1 illustrate1 formulate1 conclude 1 summarize1 list 1 differentiate 1 demonstrate1 specify1 decide1 point plot1 use1 change 1 apply1 transform1 relate1 correct1 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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