sample rubric for problem solving

Problem-Solving — Rubric

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Examples of Rubric Creation

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

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.

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:

[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.

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

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

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

Three-point scale, simplified three-point scale, numbers replaced with descriptive terms.

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.

Final Analytic Rubric

This is the rubric the instructor finally decided to use. It rates five major traits, each on a five-point scale. This allowed for fine but clear distinctions in evaluating the students’ final papers.

[b] These materials were developed during UC Berkeley’s 2005–2006 Mellon Library/Faculty Fellowship for Undergraduate Research program. Members of the instructional team who worked with Lecturer Kelsey in developing the grading rubric included Susan Haskell-Khan, a GSI Center teaching consultant and doctoral candidate in history, and Sarah McDaniel, a teaching librarian with the Doe/Moffitt Libraries.

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Site navigation, problem solving skills rubric.

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Problem Solving Methodology*

0. engage in the problem (motivation).

• I can do it!
• I want to do it!
• I spend sufficient amount of time thinking about and working on the problem.
• I do it because I realize the importance of developing problem-solving skills.

1. Define the problem - Rubric for evaluating your performance on Step 1

• Read the problem statement again
• Define what the problem states in a way that makes sense to you
• Sketch the information given in the problem
• List what is given / known
• List any constraints
• Define a criterion for judging the final product (design) / answering the question (problem)
• Determine the real objective of the problem (e.g. what do I need to calculate?)

2. Explore the problem - Rubric for evaluating your performance on Step 2

• Examine any issues involved
• Make all the necessary assumptions that will help you simplify the problem enough, so you can solve it using familiar theories.
• Guestimate the answer
• Albert Einstein quote

3. Plan the solution - Rubric for evaluating your performance on Step 3

• Select appropriate theory, principles, approach
• Map out any sub-problems
• List what needs to be found
• Write down all equations you need to carry out each step of the solution but do not substitute any numbers
• Draw free-body diagrams and control volumes as necessary

4. Implement the plan - Rubric for evaluating your performance on Step 4

• Substitute numbers into equations as necessary and carry out all calculations
• You may want to calculate several intermediate numerical results to make sure they make sense; it is difficult to pinpoint an error when all you have is the final numerical result and you know it can't be right!

5. Check the solution

• Check the accuracy of the calculations (redo)
• Check the units of the calculated parameters

6. Evaluate / Reflect on the Solution as well as on your Problem - Solving Process - Rubric for evaluating your performance on Step 6

• Is the answer reasonable? Does it make sense?
• Were the assumptions appropriate?
• How does it compare to guestimate?
• How could you improve your model to increase its accuracy?
• If appropriate, ask the question: is it socially / ethically acceptable?
• What were my strengths in solving this problem?
• What were my weaknesses in solving this problem?
• In what specific ways can I work on my weaknesses and improve my problem-solving skills?

*Woods D.R., Hrymak, A.N., Marshall, R.R., Wood, P.E., Crowe, C.M., Hoffman, T.W., Wright, J.D., Taylor, P.A., Woodhouse, K.A., Bouchard, C.G.K.,  Developing problem-solving skills: The McMaster problem-solving program.  ASEE J of Engng Educ., 86,  2,  75-91 (1997).

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