# Problem-Solving Test Items

Another form of a subjective test item is the problem-solving or computational exam question. Such items present the student with a problem situation or task and require a demonstration of work procedures and a correct solution, or just a correct solution. This kind of test item is classified as a subjective type of item due to the procedures used to score item responses. Instructors can assign full or partial credit to either correct or incorrect solutions depending on the quality and kind of work procedures presented. An example of a problem-solving test item follows.

It was calculated that 75 men could complete a strip on a new highway in 70 days. When work was scheduled to commence, it was found necessary to send 25 men away on another road project. How many days longer will it take to complete the strip? Show your work for full or partial credit.

## Advantages & limitations

Problem-solving items have several advantages. They:

- minimize guessing by requiring the students to provide an original response rather than to select from several alternatives.
- are easier to construct than are multiple-choice or matching items.
- can most appropriately measure learning objectives which focus on the ability to apply skills or knowledge in the solution of problems.
- can measure an extensive amount of content or a large number of learning objectives.

Problem-solving items also have several limitations. They:

- generally provide low test and low scorer reliability.
- require an extensive amount of instructor time to read and grade.
- generally do not provide an objective measure of student achievement or ability (subject to bias on the part of the grader when partial credit is given).

## Suggestions for writing problem-solving test items

- Clearly identify and explain the problem.
**Undesirable***: During a car crash, the car slows down at the rate of 490 m/sec*^{2}. What is the magnitude and direction of the force acting on a 100-kg driver?**Desirable**:*During a car crash, the car slows down at the rate of 490 m/sec*^{2}. Using the car as a frame of reference, what is the magnitude and direction of the gram force acting on a 100-kg driver? - Provide directions which clearly inform the student of the type of response called for.
**Undesirable***: An American tourist in Paris finds that he weighs 70 kilograms. When he left the United States he weighed 144 pounds. What was his net change in weight?***Desirable**:*An American tourist in Paris finds that he weighs 70 kilograms. When he left the United States he weighed 144 pounds. What was his net weight change in pounds?* - State in the directions whether or not the student must show his/her work procedures for full or partial credit.
**Undesirable**:*A double concave lens is made of glass with n = 1.50. If the radii of curvature of the two lens surfaces are both 30.0 cm, what is the focal length of the lens?***Desirable**:*A double concave lens is made of glass with n = 1.50. If the radii of curvature of the two lens surfaces are both 30.0 cm, what is the focal length of the lens? Show your work to receive full or partial credit.* - Clearly separate item parts and indicate their point values. Decide in advance how incorrect answers in earlier steps of a problem will affect the score on later steps.
*A man leaves his home and drives to a convention at an average rate of 50 miles per hour. Upon arrival, he finds a telegram advising him to return at once. He catches a plane that takes him back at an average rate of 300 miles per hour.***Undesirable**:*If the total traveling time was 1 3/4 hours, how long did it take him to fly back? How far from his home was the convention?***Desirable**:*If the total traveling time was 1 3/4 hours:**How long did it take him to fly back? (1 pt.)**How far from his home was the convention? (1 pt.)**Show your work for full or partial credit.*

- Use figures, conditions and situations which create a realistic problem.
**Undesirable***: An automobile weighing 2,840 N (about 640 pounds) is traveling at a speed of 300 miles per hour. What is the car's kinetic energy? Show your work. (2 pts.)***Desirable**:*An automobile weighing 14,200 N (about 3200 pounds) is traveling at a speed of 12m/sec. What is the car's kinetic energy? Show your work. (2 pts.)* - Ask questions that elicit responses on which experts could agree that one solution and one or more work procedures are better than others.
- Work through each problem before classroom administration to double-check accuracy.