Why students can-can’t think like mathematicians and scientists

Educational writers and researchers seem to enjoy hacking on each others’ ideas.  I love a good debate because I learn so much and often change what I think and do based on a new insight.  Some controversies, though, are a nit-picking waste of time.  I have often discovered after a lengthy discussion that clarifying definitions alone can bridge a divide and the hacking is just a distraction from our mission:  helping students.  Such is the case for people like me who got roped into a debate about the Common Core helping students to “think like mathematicians.”  Marzano, for example, says, “We will ask them to think like mathematicians rather than just do math.”  A Google search reveals many others with the same thought.

A favorite Twitter tweep, on the other hand, recommended a book to me by D. T. Willingham  (2009), Why don’t students like school?” because of Willingham’s  argument that students can’t think like mathematicians (Chapter 6).  Willingham’s tone seems to me to be something on the order of “How ridiculous to even think that…baaaahhh.” Willingham’s description of what it means to think like a scientist or mathematician include:

  • Scientists don’t know the outcome of an experiment before they do it
  • Their guesses make sense
  • They are better able to single out important details
  • They see the deep structure of the problems
  • They generate hypotheses
  • A capacity for sustained work
  • They create knowledge

I love Willingham’s  book (except for Chapter 6), and I think Marzano is a genius.  Surely Marzano and Willingham  have better things to do than to split hairs over whether or not students can work hard and pose hypotheses in the same exact way that scientists and mathematicians can. Willingham could always win by virtue of the idea that students don’t have the power of professional experience. However, the real point of having students “think like mathematicians” is to move students from thinking of math as sets of memorized procedures toward understanding math as connected, useful tools, translating complex ideas into symbols that can be analyzed. They can do that.

The ancient scriptures say that God made mankind in his own image.  Surely no man is omnipotent, omnipresent, or omniscient; and none of us can walk through walls without the benefit of a door.  The point is that humans have certain characteristics beyond that which the rest of creation possess.  As humans, we also have limitations.   It’s the same thing with students thinking like scientists.  With the Common Core emphasis on understanding the math we use, this generation of students can have procedural math skills, conceptual understanding,  and the ability to apply math beyond that which generations before possessed.  That doesn’t mean a 4th grader can get an internship as an actuary. It simply means that student is likely to be in a better position than so many before him. In my opinion, that’s something to celebrate, not denigrate.



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