During a recent mathematical "dig" I uncovered the following shards:

Shard A

Student 1: "I wasn't able to do these homework problems last night because

you didn't show an example until today."

Student 2: "I wasn't able to do the homework because you go too fast."

Student 3: "Should we read the examples in the book before we try the

homework? I didn't have enough time to read it because I don't understand it."

Student 4: "I couldn't do the first problem, so I quit."

Student 5: "I won't be able to get a book until next week."

Student 6: "I took this course last semester and the instructor went very

slow and I understood this topic perfectly. But now you're going through

the same topic too fast and you've got me confused."

Student 7: "I'm still working on last week's assignment."

Student 8: "I worked on these 20 problems a full hour last night and

couldn't do any of them. You assign to many problems."

Shard A principle:

No matter how fast I go, or how slow I go, students are a week behind me.

Therefore I should go as fast as I can to finish all material a week before the test.

Shard B:

Student 1: "I didn't understand the assignment."

Meaning: "I didn't know you assigned anything."

Student 2: "I didn't understand the assignment."

Meaning: "I didn't know we were to turn it in."

Student 3: "I didn't understand the assignment."

Meaning: "I don't have a book."

Student 4: "I didn't understand the assignment."

Meaning: "I don't have a clue."

Student 5: "I didn't understand the assignment."

Meaning: "I couldn't do the first problem."

Student 6: "I didn't understand the assignment."

Meaning: "There was one problem I couldn't do."

Student 7: "I didn't understand the assignment."

Meaning: "Are you sure this course is required for graduation."