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 Problems

In STEM disciplines (science, technology, engineering, and mathematics), assignments tend to be analytical and problem-based. Holistic rubrics can be an efficient, consistent, and fair way to grade a problem set. An analytical rubric often gives a more clear picture of what a student should direct their future learning efforts on. Since holistic rubrics try to label overall understanding, they can lead to more regrade requests when compared to analytical rubric with more explicit criteria. 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 mechanics.

### Homework Problem

John throws a baseball with speed v = 5 m/s at an angle θ = 60° relative to the ground. What is the maximum height the ball reaches?

### Learning Objective

Solve for position and speed along a projectile’s trajectory.

### Desired Traits: Conceptual Elements Needed for the Solution

• Decompose motion into vertical and horizontal axes.
• Identify that the maximum height occurs when the vertical velocity is 0.
• Apply kinematics equation with g as the acceleration to solve for the time and height.
• Evaluate the numerical expression.

### 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. 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.

#### Holistic Rubric

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.

#### Analytic Rubric

The following is an analytic rubric that takes the desired traits of the solution and assigns point values to each of the components. Note that the relative point values should reflect the importance in the overall problem. For example, the steps of the problem solving should be worth more than the final numerical value of the solution. This rubric also provides clarity for where students are lacking in their current understanding of the problem.

 Decomposition of motion into horizontal and vertical components 2 Student decomposes the velocity (a vector quantity) into its vertical component v_y. 1 Student realizes that the motion should be decomposed, but does not arrive at the correct expression for v_y. 0 No attempt at decomposing the 2D motion into its vertical component. Identification of maximum height condition 2 Student successfully translates the physical question (the highest point of the ball) to an equation that can be used to help solve the motion (v_y = 0). 1 Student identifies the maximum height condition with minor mistakes. 0 Incorrect or missing identification of maximum height condition. Application of kinematics equations 4 Applies the kinematic equations to yield a correct expression for the height in terms of the given variables. Solution uses the fact that the vertical motion has a constant downward acceleration due to gravity. The sequence of steps clearly demonstrates the thought process. Most likely, the solution includes solving for the time it takes to reach the top and then uses that time to see how far up the ball traveled. 3 Mostly correct application with minor error (e.g. algebraic mistakes or incorporating extraneous equations). 2 Equations include relevant parameters from the problem, but the student does not isolate relevant variables being solved for (such as time or distance). 1 Some kinematics formulas are written down but they are not connected with the information in the problem. 0 No attempt. Evaluation of final answer 2 Correct numerical answer with appropriate units. 1 Mostly correct answer but with a few minor errors. Still physically sensible answer (e.g. units and numerical values are reasonable). 0 No attempt or physically unreasonable answer (e.g. a negative maximum height or reporting the height in units of seconds).

Try to avoid penalizing multiple times for the same mistake by choosing your evaluation criteria to be related to distinct learning outcomes. In designing your rubric, you can decide how finely to evaluate each component. Having more possible point values on your rubric can give more detailed feedback on a student’s performance, though it typically takes more time for the grader to assess.

Of course, problems can, and often do, feature the use of multiple learning outcomes in tandem. When a mistake could be assigned to multiple criteria, it is advisable to check that the overall problem grade is reasonable with the student’s mastery of the problem. Not having to decide how particular mistakes should be deducted from the analytic rubric is one advantage of the holistic rubric. When designing problems, it can be very beneficial for students not to have problems with several subparts that rely on prior answers. These tend to disproportionately skew the grades of students who miss an ingredient early on. When possible, consider making independent problems for testing different learning outcomes.

## 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.