Bumper Mathing

In bumper bowling, there is no ‘gutter ball’ — every attempt hits something.

I’ve been thinking about this concept related to mathematics; do our developmental courses create ‘bumper mathing’, where all students hit something most of the time?

My college offers a course that I totally love … it’s a mathematical literacy course, covering a collection of really good mathematics.  It has only a beginning algebra prerequisite.  A common theme in the course is ‘applying percents’.

All of the students in this course have ‘mastered’ percents.  They have converted percents to other forms, they have solved percent ‘problems’ (like 80% of what is 60), and applied percents to life situations; in our beginning algebra course, they ‘mastered’ mixture problems dealing with percents.

Here is a chronology of percents in my ‘math lit’ course:

10% increase from a known value, find new value … almost all are okay

Old and new values, find the relative change … almost all are okay

10% increase from original unknown amount, express new value … almost none are okay, almost all need remediation

10% increase each year, express as a function … almost none are okay, almost all need remediation

95% confidence interval dealing with survey results … half think the 95% has to be used in the computation

10% probability of A happening, probability of ‘not A’ … almost all are okay

10% increase from original amount (known or unknown), express as a function … still difficult

10% increase from a known original amount, graph the function … almost all need remediation

Notice that there are 3 times that we revisit the ‘10% increase, represent new amount’ concept.  Each time, the majority of students do not see why we get ‘1.10n’ … they’d like to see ‘0.10n’.  The problem is that they want to compute with the percent stated (10%), because that has worked almost all of time in the past.  Part of the process of ‘remediation’ is to work through concrete examples (like 6% sales tax leading to ‘1.06n’), but this is a slippery process: The prior learning keeps drawing them down to computing with the 10%.

In our pre-algebra course, we cover perecents in a very template driven way … convert % to decimal, ‘2 places left’; ‘is over of’, and others.  These templates increase the proportion of correct answers (bumper mathing), but disguise the lack of percent understanding.  Our course is not alone in this problem; our collective pre-algebra courses are supposed to prepare students for algebra, which is all about generalizing … but percents are template-taught.  There is no transfer of learning, because of bumper mathing.

To create mathemtically literate people, there needs to be a chance for ‘gutter balls’ (as in real bowling).  We see 100 correct percent answers, and conclude that there is a good understanding of percents; that is not the case most of the time.  I’ve had a lot of students over the years say “I used to be good at math, and now I am struggling”.  Perhaps we have enabled this disability by practicing bumper mathing!

Join Dev Math Revival on Facebook:

No Comments

No comments yet.

RSS feed for comments on this post. TrackBack URI

Leave a comment

You must be logged in to post a comment.