Open a math textbook of your choice. Analyze a chapter from it according to Bloom’s task levels. How is the level balance for your taste? Does assessment focus on all task levels appropriately?
The book I will be using this fall is Algebra and Trigonometry By Ron Larson and Robert Hostetler. Since a highly similar book is available on-line, Algebra and Trigonometry: A Graphing Approach By Ron Larson, Robert Hostetler, Bruce H. Edwards, I have used this for my review. This book is viewable at:
I have reviewed Ch. 3.1, Quadratic functions (p. 252–262) for this assignment.
This book does not fare real well in terms of mixing complexity levels of Bloom’s taxonomy.
I was reminded of parts of Devlin’s rant (at http://www.maa.org/devlin/devlin_06_10.html):
“In Math You Have to Remember, In Other Subjects You Can Think About It”
“Our mathematics curriculum contains far too many required topics, each of which can be taught only to a shallow degree – often referred to as the “mile wide, inch deep” problem;”
The text is challenging, in the sense that it takes on complicated topics, and it is polished and well crafted. However, I’m not satisfied with it, since I feel the topics are presented in a superficial way.
Section 3.1 is no different in style and structure than any section of any chapter I have looked at. In the exposition (p. 252–258) the reader is bombarded with facts. Topic after topic is presented by giving definitions followed by examples with study tips thrown in at the margins. There is little sense of discovery or exploration. The student reads the definition of a polynomial, a quadratic, the axis of symmetry, the vertex, and of standard form. Then there are examples where these definitions are applied or demonstrated. The student is also directed to recall rigid transformations (which were covered in Chapter 2) in order to apply them to parabolas.
The content of the expository section is entirely on teaching the basic facts and applying them. So the section is focused on the bottom part of Bloom’s pyramid, Knowledge, Understanding, and simple Application. The problem section is a little bit broader. The first 34 questions (plus the vocabulary drill preceding them) check basic understanding. There is some level of evaluation in problems #35-44. Problems #45-54 (the last group before the word problems begin) actually give the student an opportunity to be creative. The word problems (#55–62) are mostly direct application. Problems #62–72 require students to think outside of the box and target the upper levels of Bloom’s taxonomy. Even though there are problems that involve the upper levels of the taxonomy, it feels like they have been pushed to the back in order to get them out of the way.
I don’t agree with the level balance of this book at all. Math should not be about memorizing rules and techniques and how to apply them. I’d prefer it to be a creative intellectual journey.
Now, I’ll rant for a few lines. I believe the focus on learning rules in this book is due to the way schools are assessed. Committees look for easily measurable results, and it is easier to measure the digestion of factoids than more subtle and deeper mental activity. Unfortunately, this assignment has left me with some negative feelings about how education is often done.