Creating a rubric takes time and requires thought and experimentation. Here you can see the steps used to create two kinds of rubric: one for problems in a physics exam for a small, upper-division physics course, and another for an essay assignment in a large, lower-division sociology course.

## Physics Exam Problems

In STEM disciplines (science, technology, engineering, and mathematics), assignments tend to be analytical and problem-based. Often holistic rubrics are the most efficient, consistent, and fair way to grade a problem set. When starting to grade a problem, it is important to think about the relevant conceptual ingredients in the solution. Then look at a sample of student work to get a feel for student mistakes. Decide what rubric you will use (e.g., holistic or analytic, and how many points). Apply the holistic rubric by marking comments and sorting the students’ assignments into stacks (e.g., five stacks if using a five-point scale). Finally, check the stacks for consistency and mark the scores. The following is a sample homework problem from a UC Berkeley Physics Department undergraduate course in quantum mechanics.

Homework Problem

A free electron of mass m 0 is initially at rest until a photon of energy E Compton scatters off of it. Find the equation describing the maximum recoil energy of the electron and evaluate it for E = 1 MeV.

Learning Objective

Understand Compton scattering and apply the concepts in a calculation. The discovery of Compton scattering was important in the early development of Quantum Mechanics because it illustrates the quantum nature of light and cannot be correctly described using classical electromagnetism.

Desired Traits: Conceptual Elements Needed for the Solution

• Compton scattering for photon: the relationship between the change in photon wavelength and angle of scattering (derived using energy and momentum conservation)
• Relationship between photon wavelength and energy
• How the electron recoil energy relates to the change in photon energy
• How to maximize this relationship
• Evaluate for the given photon energy

Scale

A note on analytic rubrics: If you decide you feel more comfortable grading with an analytic rubric, you can assign a point value to each concept. The drawback to this method is that it can sometimes unfairly penalize a student who has a good understanding of the problem but makes a lot of minor errors. Also, one must assign a point-value to every type of error made by your students, and the variety of mistakes can be staggering. Because the analytic method tends to have many more parts, the method can take quite a bit more time to apply. In the end, your analytic rubric should give results that agree with the common-sense assessment of how well the student understood the problem. This sense is well captured by the holistic method.

A holistic rubric, closely based on a rubric by Bruce Birkett and Andrew Elby:

 Points If… 5 The student clearly understands how to solve the problem. Minor mistakes and careless errors can appear insofar as they do not indicate a conceptual misunderstanding.[a] 4 The student understands the main concepts and problem-solving techniques, but has some minor yet non-trivial gaps in their reasoning. 3 The student has partially understood the problem. The student is not completely lost, but requires tutoring in some of the basic concepts. The student may have started out correctly, but gone on a tangent or not finished the problem. 2 The student has a poor understanding of the problem. The student may have gone in a not-entirely-wrong but unproductive direction, or attempted to solve the problem using pattern matching or by rote. 1 The student did not understand the problem. They may have written some appropriate formulas or diagrams, but nothing further. Or they may have done something entirely wrong. 0 The student wrote nothing or almost nothing.

[a] This policy especially makes sense on exam problems, for which students are under time pressure and are more likely to make harmless algebraic mistakes. It would also be reasonable to have stricter standards for homework problems.

## Sociology Research Paper

An introductory-level, large-lecture course is a difficult setting for managing a student research assignment. With the assistance of an instructional support team that included a GSI teaching consultant and a UC Berkeley librarian[b], sociology lecturer Mary Kelsey developed the following assignment:

This was a lengthy and complex assignment worth a substantial portion of the course grade. Since the class was very large, the instructor wanted to minimize the effort it would take her GSIs to grade the papers in a manner consistent with the assignment’s learning objectives. For these reasons Dr. Kelsey and the instructional team gave a lot of forethought to crafting a detailed grading rubric.

### Desired Traits

• Argument
• Use and interpretation of data
• Reflection on personal experiences
• Application of course readings and materials
• Organization, writing, and mechanics

### Scale

For this assignment, the instructional team decided to grade each trait individually because there seemed to be too many independent variables to grade holistically. They could have used a five-point scale, a three-point scale, or a descriptive analytic scale. The choice depended on the complexity of the assignment and the kind of information they wanted to convey to students about their work.

Below are three of the analytic rubrics they considered for the Argument trait and a holistic rubric for all the traits together. Lastly you will find the entire analytic rubric, for all five desired traits, that was finally used for the assignment. Which would you choose, and why?

#### Five-Point Scale

 Grade/ Point Characteristics 5 Argument pertains to relationship between social factors and educational opportunity and is clearly stated and defensible. 4 Argument pertains to relationship between social factors and educational opportunity and is defensible, but it is not clearly stated. 3 Argument pertains to relationship between social factors and educational opportunity but is not defensible using the evidence available. 2 Argument is presented, but it does not pertain to relationship between social factors and educational opportunity. 1 Social factors and educational opportunity are discussed, but no argument is presented.

#### Three-Point Scale

 Grade/ Point Characteristics 3 Argument pertains to relationship between social factors and educational opportunity and is clearly stated and defensible. 2 Argument pertains to relationship between social factors and educational opportunity but may not be clear or sufficiently narrow in scope. 1 Social factors and educational opportunity are discussed, but no argument is presented.

#### Simplified Three-Point Scale, numbers replaced with descriptive terms

 Ideal Outcome Proficient Fair Inadequate Argument pertains to relationship between social factors and educational opportunity and is clearly stated and defensible

#### Holistic Rubric

For some assignments, you may choose to use a holistic rubric, or one scale for the whole assignment. This type of rubric is particularly useful when the variables you want to assess just cannot be usefully separated. We chose not to use a holistic rubric for this assignment because we wanted to be able to grade each trait separately, but we’ve completed a holistic version here for comparative purposes.