“Mathematics and Learning”

What subject should be learned first?  The question rightly troubles anyone who’s interest is in education.  Of course, young children often must learn in a very basic and rote fashion, applying their apt memorization skills to simple tasks that will serve them very well in later years when they go one to apply such knowledge to more complex topics.  However, when the time comes to designing curricula, an important question must be answered for older students, namely “What is most important first topic in these students’s education?”

 An argument can be made for the use of mathematics as a tool for teaching students how to reason more clearly.  This is not because mathematics is the basis of all knowledge.  Indeed not.  There are many important subjects including not only the humanities like poetry and history but sciences like biology and physiology too.   These topics are not strictly speaking mathematical in nature, even though mathematics can be used in it in many ways.

Our minds are best geared for learning things that we can sense, things that are visible and tangible.  Although mathematics is abstract, it can begin with this kind of sense derived experience.  Beginning with simple everyday examples, children can be taught the more abstract and difficult skills that must be learned for the sake of the development of mathematical skills.  In the process of learning these topics, the children will begin to learn important rules about reasoning.  He or she will learn how several propositions can serve as the basis for conclusions.  They will learn how certain properties are related to various geometric figures and arithmetical rules.  Although much of this will be memorized at first, with time, they will have the opportunity to see that human reasoning in mathematical subjects is orderly and logical.  On the basis of such “logical experience,” young learners can then begin to be taught the rules of logic that they have been using all along.  As the medievals used to say, they could go from logica utens, logic used in other subjects, to logica docens logic taught, as a unique, and separate subject.

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“Intellectual Virtues”

Whenever someone talks about being “virtuous,” we immediately think of someone whose very moral.  Perhaps we even think of people who are a bit boring for virtuous people can appear to have no fun at least in the popular imagination.  Whatever the case might be, almost any reader would be surprised to see the expression “intellectual virtues.”  What could this expression mean to designate!  At best, most people would say, “Such virtues must describe people for who knowledge is combined with devotion and rigorous discipline.”  That is; they would seem to describe the person who has a disciplined character in addition to being intelligent.

However, in ancient and medieval philosophy, certain intellectual capacities were considered virtues.  These character traits were not quite the same as moral character traits or virtues.  To understand this idea, it can be helpful to consider two example people, one whose skills are the fruit of a so-called intellectual virtue and the other whose skills are not.

It is easier to start with the person who does not have a given intellectual virtue.  We all know someone who is not very good at math, that is, someone for who math is difficult even though he or she might be quite skilled at many other tasks   It makes sense to say that this person doesn’t have an intellectual virtue.  Likewise, think of the person who is only able to memorize formulas.  Such a person is often very good at working through many problems with deft skill.  This person seems to be a “wiz” at geometry and algebra, quickly solving equations and proofs. 

However, this latter person might suddenly be presented with a difficult, new problem.  When we notice that he or she does not have the creative skill and insight to solve the problem, we realize that he or she does’nt have a so-called “intellectual virtue.”  This person merely has a habit—a particular skill that is helpful but does not indicate true and complete mathematical knowledge.  The person who is able to understand the mathematics and creatively apply this knowledge to solve new problems.  This person has a true intellectual virtue.  They have a particular ability for intellectual insight, able to probe the difficult domain of this topic.  This is much more noble as the mere habit of being able to balance equations and repeat facts about geometric figures!

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“On the Nature of Belief”

Belief and faith often are critiqued in a scientific culture.  It can seem that mere belief is a replacement for science made available to soothe the ignorant masses.  There is some truth to such accusations, and many people do use belief as a screen to cover their own ignorance about the truths of reality.  Everyone should be aware, however, that almost every single human being have these kinds of “blind spots.”  We all live with many things that we merely believe, all of which are so central to ones world view.

Even if we set aside all such types of beliefs, there still remains a broad terrain of human life in which faith and belief remain—even if we ignore all religious matters whatsoever.  Imagine the scientist who’s work on brain neurons depends upon many discoveries made by many other people.  Yes, if it were possible, it would be better for such a person to know all of the details that they accept merely at the word of other scientists.  In all cases, seeing directly is more fulfilling than merely hearing about something.

However, is the scientist better off when he or she knows only what they have experienced directly.  Although it is preferable that he or she knows such facts. However, it is impossible to investigate everything.  Sometimes, one must extend one’s own vision with the vision of someone else.  In a way, the person who thus “takes it on faith” gains a further vision.

Such faith always relies upon the credibility of the person who shares the experience, of course.  For one person to believe on faith what another person says, it is presupposed that the other person is not a liar and actually could have experienced the matter in question.  This means that even the “scientific believer” must take the risk of placing credibility in someone who has witnessed things that he or she has not seen.  While this does not vindicate every kind of faith that people have had, it does provide a telling sign that faith, as such, is not always the refuge of the ignorant.  Indeed, it is an important part of all of our lives, even the lives of scientists, who’s daring and investigative work is rarely criticized as being a refuge for ignorance!

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After the unbelievable fame of J.K. Rowling the author of the Harry Potter series hundreds of idealistic authors struggled to achieve similar success. Because of Rowling's legendary accomplishments, we have invited the author, herself to the book signing so that she can share her experience to anyone that wants to listen. Whether you're an amateur writer, expert author, or simply an eager fan, all kinds of people can benefit from her insight. After all, if a person wants to be successful, you have to be willing to listen to the advice of others. If anyone are interested in attending, please contact the office before the end of the month.

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