My Rationale for Not Emphasizing Numbers and the Blind Use of Formulas

Some commentary from the AP Physics College Board

Multiple Choice Questions

The purpose of the multiple-choice sections is to assess the breadth of students' knowledge and understanding of the basic concepts of physics. The multiple-choice questions emphasize conceptual understanding and qualitative applications. However, many physical definitions and principles are quantitative by nature and can therefore be expressed as equations. The knowledge of these basic definitions and principles, expressed as equations, is a part of the content of physics that should be learned by physics students and will continue to be assessed in the multiple-choice sections. However, any numeric calculations using these equations required in the multiple-choice sections will be kept simple.

Also, in some questions the answer choices differ by several orders of magnitude so that the questions can be answered by estimation. Students should be encouraged to develop their skills not only in estimating answers but also in recognizing answers that are physically unreasonable or unlikely.

Free Response Questions

The free-response sections emphasize solving in-depth problems where knowledge of which principles to apply and how to apply them is the most important aspect of the solution to these problems. Regardless of the type of calculator allowed, the examinations have been and will continue to be designed and graded to minimize the necessity of doing lengthy calculations. Except for some fundamental constants, most numerical values are selected so that calculations with them are simple and can be done quickly. When free-response problems involve calculations, most of the points awarded in the grading of the solution are given for setting up the solution correctly rather than for actually carrying out the computation.

Added by Mims

The College  Board is looking for knowledge of concepts, laws, theorems, etc. Not blind use of equations whose terms and restrictions for use are not understood. That is why they provide the equations. I provide detailed solutions for representative problems but I focus on the concepts being used. That is what I will always do and educators nationwide and at the Academy agree with me on this approach.

As I have discussed a number in times in class - in order to get student input concerning the approach - there is a fine line that I try to walk. On the one hand I certainly need to allot sufficient time to explain concepts, conduct demonstrations, work problems, etc. On the other hand, I would like to - at the request of all - provide some time in class for them to students to work the assignments, together or as individuals. Class time for the problems has also been necessary because of my use of the Physlets. These Physlets were discovered during my research prior to the course to find the most effective teaching methods. They have been used with great success nationwide. But, because of licensing restrictions, students must work assigned problems in class. I personally installed the software on each of the 19 computers in the lab for use by students.

I firmly believe, as do a lot of other educators, that the path to true learning is by taking the material that has been explained and then internalize it and use it in representative problems. Concepts are the import component and they are not learned through blind use of equations whose restrictions and applicability are not understood.

I am teaching the course as an AP course focusing on the fact that this is a college prep school. I discuss as many of the topics from the lesson in detail as possible given class time and schedule constraints. I am also available from the opening of the gates at 5:30 till closing for individual instruction and some have taken advantage of this. After discussing the necessary concepts, laws, principles, etc I then assign problems.  I do not give problems and walk around and explain in detail how they should be solved.

In general, I do not give solutions to identical problems and then assign them as homework (although sometimes I do give very similar ones if the student can figure out which ones - requires reviewing what I have covered). Some students may be used to both of the above approaches in some other classes (giving problems and then solving them for you).  I always explain representative problems in which the concepts, however, are covered.  In some cases, I have to make assumptions concerning what the student will either pick up from the text or ask questions on.