Do the Math! What does that mean?

I was at a conference this past week, when a keynote speaker used the phrase “do the math!”.  A redesign methodology states that one of the benefits is ‘students spend more time doing math’.  If we ever needed evidence that the mathematics curriculum is mis-directed, these comments would seem to be conclusive evidence of a problem — they are quotes from fellow mathematics faculty.

Perhaps we have lost track of what mathematics is.  According to a dictionary (Merriam-Webster in this case, though they are all similar), mathematics is

the science of numbers and their operations, interrelations, combinations, generalizations, and abstractions and of space configurations and their structure, measurement, transformations, and generalizations

Open any developmental ‘mathematics’ textbook, and you will see something that resembles mathematics … a bit like a scary Halloween costume, where the outside looks different than the true character underneath.  We have gone far from the path of mathematics, much to the detriment of our students.

In particular, we have lost all elements of science within mathematics (especially in developmental math, but also in gateway college courses).  Science is a ‘system of knowledge’.  If it were not for the undeserved special treatment of mathematics, our science colleagues would have long ago challenged our mathematics courses as being a ritualistic mis-education of the masses.  Two hundred types of problems with remembered procedures to manipulate values and symbols to acquire a ‘correct’ answer does not represent knowledge; the resemblance is stronger with uninformed rituals performed with no redeeming value (practical or intellectual).

The emerging models (New Life, Dana Center Mathways, Carnegie Pathways) are all movements towards mathematics.  We can, and must, reform our mathematics courses so that students learn mathematics more than rituals.  As mathematicians, we have knowledge systems that help people understand the world around them … and a knowledge domain that is enjoyable just for the learning.

The person who said “Do the math!” was simply saying “you need to agree with me, because my view of the data says you should”.  The person who said “students spend more time doing math” really meant that students spend more time in some activity that resembles mathematics … but was most likely engagement in the rituals that have taken the place of mathematics.  The fact that the majority of American students believe that they are bad at ‘mathematics’ says more about our curriculum than it does about them.

I still spend a large portion of my teaching time in courses where the content is still traditional; change is not instantaneous.  However, whatever the course, we can take a more mathematical approach by focusing on concepts and connections even as we get students to accurately perform the rituals.  We each need to start on this path towards teaching mathematics so that we are ready for larger changes; our curriculum in 10 years will have little resemblance to that of 5 years ago.  The good news is that we will be truly teaching mathematics when that change comes.

I hope that you will begin your personal journey towards teaching mathematics; perhaps you can even contribute to the professional work that will lead to the change that is coming.

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