Our assessment plan includes development of multiple choice, matching, short answer, and essay types of questions and is based on using the WebCT program. We will describe each type of question by the way we use it, illustrate it with examples, and classify it in the highest possible category in Bloom’s taxonomy framework.
Multiple-choice questions. Typically this type of question takes the form of a short question or implied question (the stem) followed by four or five optional answers, with at least one correct answer, and all of the others wrong (the distracters). Our goal was to use this type of question to assess higher levels of thinking. We often found that such questions also require activities at lower levels of Bloom’s taxonomy. Thus, tasks requiring lower-level thinking are used as bridges to higher-level tasks. For example, we use tasks that emphasize memorization as a part of the problem in a multiple-choice question, a part that leads to more comprehensive -- higher level -- activities.
With multiple-choice questions we use the following types of tasks:
- Calculation. The purpose of this kind of task is to ensure that students are learning necessary computational skills, in addition to conceptual understanding. Example 1 illustrates a question from this category. We assume the student’s approach would be to find that the coordinates of vector u are (1,3) and then to add those coordinates to the coordinates of the given point, P(2,2), to obtain that the coordinates of the displaced point as (3,5) [i.e., (1,3) + (2,2) = (3,5)]. Alternatively, the student may solve the problem graphically. Ideally, the student would work the problem both ways and compare the results. By providing an algebraic representation of P and a graphic representation of u, the problem requires the student to convert one to the other. Of course, with a given list of choices, the student may not do any calculation at all, but randomly select their answer from the list. We hope students are honestly using these quizzes as learning tools, not simply as work required for the course.
- Graphic representation. Students are required to use given information and a graphical representation in order to answer the question. In Example 2, students need to use the given graphical representation to identify vectors u and v, use the rule for geometric addition of two vectors, and then find the coordinates of the vector that represents the sum. In this particular case, students may also choose to solve the problem algebraically by adding the two given vectors to obtain the resultant vector, i.e. (3,1) + (-1,2) = (2,3), and then identify the case on the graph with all three vectors. A graphical representation problem with multiple responses (not just a single correct answer) is shown in Example 3.
- Algebraic manipulation. Students are expected to use algebraic formulas or factoring polynomials in order to find the answer. In Example 4, students need to factor a polynomial or use the binomial formula to simplify the left side of the equation and then proceed to solve the given trigonometric equation.
- Mathematical modeling. Students are expected to translate a word problem into the corresponding mathematical model. Example 5 illustrates a task in which students are expected to recognize and use the concepts of trigonometric functions to express parametrically the position of the free end of the minute hand on a clock. In doing so, they need to relate the given information about the rate of the minute hand and the angle that describes the position of the free end with respect to the positive x-axes.
All five examples of multiple choice questions
Matching questions. WebCT allows lists of matching items to be of different lengths. All that is required is a correspondence between the first list and a subset of the second list. We use this type of question in the following ways:
- Matching unknowns to items from a list of answers, or matching the answers to a list of unknowns. That is, students are given a list of possible answers and required to match them to a list of unknown variables or select NONE if there is no corresponding match. This kind of question may involve calculations, graphing or observation from a given graph, or algebraic manipulations and/or transformations.
- Matching the steps constituting a proof of a trigonometric identity to their justification, purpose, or order of appearance.
In these kinds of tasks, students need to identify all items relevant to their task and then match the corresponding items from the lists.
Four examples of matching questions
Short answer questions. This is the type of question we use least in our quizzes, and we use it with mainly short and simple tasks.
Example of a short answer question
Essay questions. The WebCT quiz tool has an option for creating an essay type of question. Our example illustrates a task that incorporates an interactive environment (applet) with student manipulation, observation, and writing. This item is not graded automatically. It has great value for students and instructors in fostering interactivity and developing observational and writing skills. The instructor may leave comments or feedback to the student on an "essay" type of answer, including challenging questions in the context of the student’s answer. This allows the student to access the question a second time to respond to those questions. This cycle could be repeated multiple times. It is also suitable for challenging tasks to be completed in cooperative learning groups.
Example of an essay question