Each topic has several problems from the which we collected our data.
Categories of common errors found, correct responses, some brief
commentary, and unique answers are included for each problem.† More description of these are on the
Some of the errors are very general in nature (not following directions
for example). We report these not for mathematical reasons, but
pedagogical. For instance, in some cases, we reworded questions to help
students focus better on what we want.
What are not included? We do not necessarily describe how to counteract
the errors found when teaching.
Percentage Calculation: For the correct answers, we use % of the total.
For the errors , we report % of those who made errors, and call this the
Incorrect response Rate (or IR). Since some responses include multiple
errors, the total % is often over 100.
Strong Errors: Highlighted in bold italics; Appeared across both
campuses and in every classroom (7 different instructors). Other errors
appeared at only one of the two campuses but in multiple classrooms.
Unique Answers: Responses that are interesting. But not representative.