Thinking about Teaching and Learning

Lives on the Boundary: The Struggles and Achievements of America's Underprepared

The Math Gene: How Mathematical Thinking Evolved and Why Numbers Are Like Gossip

Thinking about Teaching and Learning (1999)
Robert Leamnson

Leamnson admits early on that he believes he has no new ideas to present, but new approaches to old ideas and old ideas highlighted once again to remind us of which ones are worth revisiting.  This is just one of the indications that he does not take himself too seriously; the tone of the book also bears that out.  The result is that one does not feel preached to, but rather inspired to try new things, return to old ideas, and listen more attentively to colleagues' ideas.  I especially enjoyed his discussion against "metateaching" on the first day of class; I tried out avoiding it in the semester immediately after I read the book and it worked very well.  I also was able to use part of this as a student reading when we discussed what it means to learn.  I may not have agreed with everything he wrote, but he made me think about my teaching--something not every book on teaching can accomplish.

Lives on the Boundary: The Struggles and Achievements of America's Underprepared (1989)
Mike Rose

Again, a lot of what Rose had to say I had heard before, but the way he expressed it was significant and thought-provoking.  Also, although the statistics only go up until about 1980, he had some interesting information about the huge increases in the percentage of 18-22 year olds who attended college during the twentieth century.  He makes the intriguing point that we were the first country to try a democratic experiment in saying that higher education was for more people than just the elite.  As a result, we should not be surprised that many of those who now attend college are indeed underprepared in the skills needed to succeed, skills that used to belong only to an elite level of students and skills that students on certain tracks in high school may never have learned.  He does an important task in taking us inside the mindset of those students who have repeatedly failed at subjects.  He writes about how students who are convinced they should have learned a skill years ago are, quite naturally, almost never going to ask for assistance in learning that skill at the college level.  He writes about the power of labeling students at young ages in terms of their learning abilities.  A lot of what he had to say about the difficulties freshmen face in big research universities reminded me of how important it is to have places like the UW Colleges,  where I teach, places that specialize in transitioning students into college.  Those first two years are incredibly different from the junior and senior years.  Although his book focuses mainly on teaching writing and grammar, his ideas can be applied to different disciplines.

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The Math Gene: How Mathematical Thinking Evolved and Why Numbers Are Like Gossip (2000)
Keith Devlin

It is important to note at the outset that Devlin's title is metaphorical; he proves what many people already believe, that we are all born with the mental capacity to perform mathematics.  It is also important to note that by mathematics, Devlin means more than arithmetic and instead the abstract thinking that goes into the various fields of mathematics (topology, calculus, geometry, etc.).  Having duly noted those two things, this is not only a fascinating book but one that I am putting under education because of its importance to all educators, parents of children, etc.  So many of us contribute to students' math avoidance and anxiety without consciously knowing, and this is often the result of our own fears or feelings of inadequacy.  Devlin's book helps us to uncover the inherent ability we all have for both mathematics and language as he demonstrates that both rely on a level of abstract thinking--the ability to work with and talk about things that are not present in our immediate environment or are not even possible (i.e. unicorns).  Both rely on our ability to process and recognize patterns, something which we have at birth.  What distinguishes those who succeed in mathematics (or, I would add, in writing) is hard work, persistence, and the willingness to engage in the level of concentration that abstract thinking requires.  Devlin makes his case cogently and persuasively.  Once more of us acknowledge this case, we may go a long way towards breaking through the limits that we allow students to build for themselves, and to whose construction so many things in popular culture contribute.  My recent interest in scientific/mathematical literature and the intersections between math and writing anxiety led me to this book, and it has fed back into my understanding of both fields.