Log 5

Teaching Secondary and Middle School Mathematics Chapter 4

General notes on chapter 4:

The chapter starts with a short history of how prescribed curricula (a course of study) have become commonplace.  Typically, a course of study goes from a high level district philosophy down to goals, objectives, and finally pupil performance objectives (PPOs).  The chapter then discusses how a PPO for a student may have the same subject (like permutations), but become more advanced with each year of study.

Next the chapter discusses how goal might be written ("The student will appreciate the use of algebra in solving real-life problems"), and how this might translate into more concrete objectives ("Given cost and a discount, student will calculate price.").  Objectives can be "affective" - dealing with attitudes or feelings, or cognitive - reflecting skills and understanding of concepts.  Cognitive objectives were discussed in terms of Bloom's Taxonomy:

1. Knowledge
2. Comprehension
3. Application
4. Analysis
5. Synthesis
6. Evaluation

The chapter then discusses the use of a textbook, and how it should be used as a resource and sometimes as a guide, but that teachers should not be a slave to it and need to pick what they will use.  This section of the chapter also discusses other print resources and web resources.  It ends with a quick discussion of organizing a resource file to keep track of information you find.

Question 3 - List several example objectives to fit goal "the student will apply the use of algebra and functions to solve problems."

This goal seems a little vague, since I'm not sure if it is only supposed to apply to using algebra and functions at the same time or what.  Still, I can think of the following examples that should fit the bill:

• Given the gravitational acceleration formula "x = 16t² + V₀t + h" and a set of initial values for velocity and height, students will be able to calculate the position of an object or calculate the time required to reach a given height.
• Given the gravitational acceleration formula "x = 16t² + V₀t + h" and a set of initial values for velocity and height, students will be able to calculate the the time required to reach a given height.
• Given the equation of a linear function, students should be able to solve for the inverse of the function.

Question 8 - Discuss some of the advantages and disadvantages of teaching mathematics without a textbook

There are a lot of advantages to teaching math with a textbook:

• It gives you an initial outline on what subjects to teach.
• It gives suggestions on how to teach a particular topic.
• It provides practice problems. 
• It gives the students a reference to go back to when they don't understand a problem.

I'm not sure there would be any real advantage to not having a textbook at all since if you do have a textbook it is always possible to not use it any more than you want to.  Still, I can see some possible minor advantages.

• There would be incentive to be more creative about finding other sources for course material.
• It would eliminate the temptation to be a slave to the curriculum laid out by the textbook.
• Students wouldn't have to carry the book around.
• It would tend to lead to a more constructivist learning environment.

Personally, I think the advantages of having a textbook far outweigh the advantages of not having one, since students need them as a reference and since it is always possible to de-emphasize them if you don't want them to dominate the classroom.