Thursday, August 19, 2010

Trigonometry According to Bloom

I spent some time analyzing Chapter 1 of my Trigonometry Textbook and analyzed it according to Bloom's task levels. Here's what I discovered ...

Chapter 1 covers eight different topics on the basics of trigonometry. These basics include Radian and Degree Measure, the Unit Circle, definitions of the Trigonometric Functions, Graphs of the Trigonometric Functions, Inverse Trigonometric Functions, and Applications / Models.

Each section of the book begins with some teaching of the basic concepts within the section. After introduction of the concepts within the section, there are a number of examples given which explore the concepts. As a general rule, most of the examples are "cookie cutter" fashion examples. For example, in Section 1.1 on Radian and Degree Measure, the first example regards sketching and finding coterminal angles. After showing the example the "Checkpoint" refers to Exercise 17 in the Exercises section of Section 1.1. Example 2 references Exercise 21 ... Example 3 references Exercise 47 ... and so it goes.

The first set of exercises in the section are Fill Ins to check on vocabulary concepts. These clearly fall within the Knowledge level of Bloom's Taxonomy. The next set of exercises provides problems in the Comprehension level of Bloom's. The next set ... starting with exercise 17, would likely be the Application level of Bloom's, since the student is asked to apply concepts which were demonstrated in the classroom exercises.

This particular section of the book has a total of 128 - yes, 128! - exercises. The subtitle in the textbook for the final set of problems is Synthesis. So, clearly, the textbook author has Bloom's model in mind when creating these exercises. Here is a sample problem in this last section:

A fan motor turns at a given angular speed. How does the speed of the tips of the blades change if a fan of greater diameter is installed on the motor? Explain.

Clearly, this final set of problems is asking the students to use the information learned in this section of the book in a different way in order to determine the proposed solution. This is a perfect example of the Synthesis level in Bloom's Taxonomy.

In fact, every section in this Trigonometry textbook has a "Synthesis" set of exercises included. So, I am pleased to say that a quick overview of this text shows that the authors do an excellent job in focusing on Bloom's levels throughout the exercises.

Unfortunately, I do not (yet) have an electronic version of this textbook, but Trigonometry is one of those classes which lends itself very well to visualization. There are many, many online videos such as this
video on Solving Trignometric Equations which I will employ throughout my classroom instruction this year. I am looking forward to implementing these tools throughout the coming school year!

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