Logic Unfolds the Mythical Gene

Consider p and q where p:I oversleep. and q:I am late.
p⇒q
¬q⇒¬ p

As a math teacher, I get the privilege of teaching logic. Traditional truth tables and the formal notation is specific to Math Studies which is unfortunate because its conceptual understanding builds capacity for people to construct better arguments. Mathematical logic is fundamentally the art of discourse; when I construct an argument I analyze if for exceptions and falsehoods, if neither can be found, I accept the argument until I am disproven. Stephen Hawking did this with his theories on black holes: he proved them, disproved them, then proved a new set of theories. I find myself reflecting on my thoughts and actions, looking for contradictions. This is similar to my teaching methods. I will accept a conjecture (mathematical hypothesis) posed by students until it is disproven by students. I find this type of inquiry is essential to students not only building problem solving capacity, but also building a passion for asking the right questions. Students hear opinions and arguments all the time, mathematics is no exception. I formally teach logic to help students make better decisions and analyze the merit of the messages they hear.

A message I hear regularly is parents saying that neither of them have the self-diagnosed math gene which is why they are not successful at math or that their child needs to be successful in math because both of their parents have this gene. These anecdotes are logical fallacies, not only do neither of my parents have the math gene but I have yet to come across the scientific literature which identified the math gene. I understand that this math gene is usually used in a joking fashion but this comment can take root in a student leaving them feeling inadequate or with unrealistic expectations. I ask that our community to refrain from using this language. There is no logical argument to support the claim that the mythical math gene is the reason for an individual's failure or success in mathematics.

Chomsky's research on language is referenced in Keith Delvin's book The Math Gene when discussing the human capacity to do mathematics. Delvin's hypothesis states humans are pre-wired to learn language therefore pre-wired to learn mathematics. What makes mathematics such a challenging language is its employment. The 10,000 hour expert claim was suggested in the mid 2000's, after doing the math, this means that it would take about 23 years to achieve mathematical expertise within the parameters of a school schedule. I am not suggesting redesigning school schedules to get to 10,000 by the age of 18, instead I think awareness needs to be brought to this number. Language is taught eight of eight blocks whereas math is taught one of eight, this argument may not have a logical foundation but there is a probabilistic underpinning. It is easier to say that things are difficult rather than investing time. Two of the IB Learner Profile attributes are knowledgeable and communicator: I ask our community to embrace these virtues in the sphere of mathematics.

Consider p and q where p:I devote time to a skill. and q: I learn the skill.p

p⇒q
¬q⇒¬ p

If you would like more resources to continue to explore your mathematical journey, Google these: EngageNY, dydan, YouCubed, Numberfile, or mathshell.org.

Story by William Pamperin