Example 1. Figure 2 shows a multiple choice question concerning a point P displaced by a vector u. This is an example of the comprehension-level task in Bloom’s taxonomy, assuming that a student has not seen a similar problem before. It is a multi-step process consisting of a variety of tasks. It requires students to read and understand the meaning of information from a paragraph and from a diagram, to translate geometric information to algebraic form, and to calculate using algebraic information. Or, they may use only the geometric information to find the solution.

Figure 2: Multiple choice question – calculation

Example 2. Figure 3 shows a multiple-choice question concerning the graphic representation of vector addition. This is another example of a comprehension-level task. It is not enough to recognize that the vectors u, v, and u + v occur in the drawing. The student needs to analyze the drawing and be able to decide if the three vectors occur in a relation that can be interpreted in terms of vector addition.

Figure 3: Multiple choice question – graphic representation

Example 3. Figure 4 is another example in which the students need to use both graphic representation and conceptual understanding to identify all correct answers. For partial answers, students receive partial credit. The figure shows a multiple response question that can be answered using the graphs of the sine and cosine functions. To conserve space, not all of the 14 possible responses are shown here.

Figure 4: Multiple response question – graphic representation

In this task students need to interpret graphical information and read interval notation. They also need to identify a function and understand the meaning of a sign of a function given by its graph. This is an application-level task in Bloom’s taxonomy. Of course, depending on students’ previous experiences, the instructor may decide to use this task as a comprehension- or knowledge-level task.

Example 4. Figure 5 shows a multiple choice question involving the solution of a trigonometric equation.

Figure 5: Multiple choice question – algebraic manipulation

This is an application-type task. The question requires students to solve the equation and select the corresponding answer. Some students may decide to reverse these steps. That is, they may choose an answer, substitute, and check to see if it satisfies the given equation. In either case, students are expected to know the meaning of and symbolic notation for writing the multiple solutions.

Example 5. Figure 6 presents a problem asking for both parts of the parametric equations of a moving location.

Figure 6: Multiple response question – mathematical modeling

According to Bloom’s taxonomy paradigm, the question in Figure 6 is a higher-level type than the previous tasks. The task requires the ability to comprehend the text, analyze it and coordinate it with the geometric representation, and then to translate the given information into mathematical meanings and symbols -- or vice versa. In the process of problem solving, students need to use some general knowledge, such as reading the clock time or the rate of change, for example. If the student engages in a "step-by-step" problem-solving activity, we can identify at least four categories of cognitive processes from the paradigm that are included in this task: memorization, comprehension, application, and analysis. Additionally, we emphasize two features of the WebCT environment used with this type of question: allowing more than four options in the list and allowing students to select more than one answer. (In this case, the complete answer consists of choices 1 and 3.) WebCT refers to these types of questions as multiple-response. The directions for these types of questions are "Select all that apply".

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