Using Multiple Choice Questions in Physics

The multiple choice question is a staple of American education.  The standardized tests a student sees during a school career are mostly those.  And for a school teacher, they are easy to grade.  Just run them through a machine, and the score comes out.

Up to a few years ago, I treated MC questions and written response ones as equivalent when designing a test or quiz.  However, I started to notice many students just "plugging in numbers" into formulae to get the "right answer" but showing little understanding of the physical situation.  I then decided to make the written response questions assessment on a test or quiz ones of more formal analytic technique and skill, and the multiple choice questions ones of intuition or estimation skill.

As an example, here is a "bad" MC question.

If a body is initially moving at 4.11 m/s and and accelerates at 2.74 m/s/s for 9.70 sec, how far does it go? 

167 m     168 m   169 m   170 m    171 m

The reason the above is bad is that there is no way for a typical student to make estimations and do mental calculations precisely enough to hone in on the right answer.  Students are forced into using a formula and a calculator.

Here is a better example. 

If a body is initially moving at 4.11 m/s and and accelerates at 2.74 m/s/s for 9.70 sec, how far does it go? 

55.6 m   169 m   349 m    567 m   898 m

By using the estimates of 4 m/s, 3 m/s/s, and 10 s, a student can with a little mental arithmetic figure out the average velocity is around 19 m/s, which gives a distance of around 190 m.  The nearest answer is 169 m.

However, it takes some time to get a typical student comfortable with doing the above without a calculator (most students see more than one significant digit and freak out).  So early in the year, we look at very simple examples like

If a body is initially moving at 4 m/s and and accelerates at 3 m/s/s for 10 sec, how far does it go? 

40 m   190 m   340 m    500 m   900 m

If I can get my guys to see that the minimum possible distance is 4 m/s * 10 s and the maximum possible is 34 m/s * 10 s or that since the starting speed is 4 m/s, the final speed is 34 m/s giving an average speed of 19 m/s (for 10 s), I can get them to see that they their mental calculator is sometimes better than their electronic one.

I have started to include a class early in the year on developing these estimations skills.  Students seem afraid to estimate since they believe they will not get "the right answer".  Students are paired off with each team using a web-enabled device as an anonymous response system (clicker).  I use BQ Learning because I can customize it for my needs, however I have also used Socrative with good results.  I flash a MC question on the front board and give a couple of minutes for teams to respond.  The first few are easy, so we can quickly discuss solution strategies.  As the questions become harder, we will spend more time on those discussions.  Usually one class is enough to get students to realize that they can estimate reasonable well in some situations.  However, I am realizing that I will have to do a class like this again later in the year just to reinforce this skill.