Case Title: 2. But percentage grades are more precise, right?

Element Title: Complexity vs. Standards (5 of 13)

In coming up with grading schemes a lot of people put individual standards (or targets) instead of assignments. This can be a little overwhelming because you can cover dozens of targets and they change every grading period. From a grade book/scheme, I like to think in terms of complexity/difficulty. Lets take a learning target created by a math teacher:

I can calculate the average of a set of numbers and find the missing data in a set of data. 

For this particular target she can develop different items that measure a students mastery of that target. For example the three problems below (think back to the bouyancy problems).

  1. Calculate the mean, median, AND mode of the following data set. 54, 62, 75, 76, 77, 77, 78, 82, 85, 95, 99 
  2. Lucy wants to get a 93 in her math class. Her first four test scores were 96, 92, 94, and 93. What will she need to score on her fifth test to reach her goal?
  3. There are five numbers in a data set. The lowest number in the set is 54, and the highest number in the set is 82. If 92 is added to the data set and the average is 85, what are the missing data values?
Wether you want to go with PISA levels, Blooms Taxonomy or Depth of Knowledge these are not equivalent items related to complexity/difficulty. She is going to have the same thing happen with other learning targets. So in thinking about her class we asked, "What does a student getting an A in your class tell oyu about that student?" From this conversation we came up with the idea of C -> Conceptual/Computation B -> Basic Application A -> Advanced Application. When constructing an assessment she can make sure that she not only covers targets, but that she addresses the different levels of complexity. Of course you won't cover all targets at all levels, but you do want to make sure you cover enough topics and all the complexity levels.

Element Assessment: items baby, items

Which is a better item:

A. The University is centrally located in the city.

B. The University is centrally located in the city with sufficient student parking.
Which of the following items is more difficult?

A. List the states and the capitals west of the Mississippi river.

B. Imagine you are in car, stopped at a traffic light, headed north in St. Louis, Missouri. Which way would you turn to head toward California?
Which of the following items is more cognitively complex?

A. List the states and the capitals west of the Mississippi river.

B. Imagine you are in car, stopped at a traffic light, headed north in St. Louis, Missouri. Which way would you turn to head toward California?
If the goal is to have a child add one digit numbers to get a one digit result the better item is:

A. What is 2 + 2?

B. There were two cats and two dogs in the window of a pet store. How many animals were in the window?
What level of cognitive complexity is the following:

Define the median of a set of scores.

A. Knowledge
B. Comprehension
C. Application
What level of cognitive complexity is the following:

Given a skewed distribution, choose an appropriate center; defend the choice.

A. Knowledge
B. Comprehension
C. Application
What level of cognitive complexity is the following:

Why does the census bureau report the median income in the United States rather than the mean?

A. Knowledge
B. Comprehension
C. Application