arrow diagram, but does not present any kind of complete argument. For example, the student may say something like, ''Dana, because Dana beat Alex," or "Lee, because Lee beat two people," or "You can't tell, because they both lost to Robin."

Characteristics of the low response:

Questions 1 through 3 are answered correctly. However, there is little awareness of the relationship between the arrows in the diagram and the games that have been played. Hence responses to questions 4 through 6 are incorrect or lack any kind of justification.

The response to question 7 may be based on subjective feelings that have no basis in the information supplied in the arrow diagram. For example, the child may say something like "Dana, because I think she's better."

Mid-continent Regional Educational Laboratory (1992). Comprehensive School Mathematics Program. Aurora (CO): Author.