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Math Teacher's Lament

Steve McCrea

I like these points from this essay:


Discussions between "Simplicio" (the simple one) and "Salviati" (the saved one):  

SIMPLICIO: But isn’t one of the purposes of mathematics education to help 
students think in a more precise and logical way, and to develop their 
“quantitative reasoning skills?”  Don’t all of these definitions and 
formulas sharpen the minds of our students? 
SALVIATI: No they don’t.  If anything, the current system has the opposite effect 
of dulling the mind.  Mental acuity of any kind comes from solving 
problems yourself, not from being told how to solve them. 


SIMPLICIO: But surely there is some body of mathematical facts of which an 
educated person should be cognizant. 
SALVIATI: Yes, the most important of which is that mathematics is an art form 
done by human beings for pleasure!  Alright, yes, it would be nice if 
people knew a few basic things about numbers and shapes, for 
instance.  But this will never come from rote memorization, drills, 
lectures, and exercises.  You learn things by doing them and you 
remember what matters to you.  We have millions of adults wandering 
around with “negative b plus or minus the square root of b squared 
minus 4ac all over 2a” in their heads, and absolutely no idea whatsoever 
what it means.  And the reason is that they were never given the 
chance to discover or invent such things for themselves.  They never 
had an engaging problem to think about, to be frustrated by, and to 
create in them the desire for technique or method.  They were never 
told the history of mankind’s relationship with numbers. 
More importantly, no chance for them to even get curious 
about a question; it was answered before they could ask it.  


a good teacher can guide the discussion and the flow of problems so as 
to allow the students to discover and invent mathematics for 
themselves.  The real problem is that the bureaucracy does not allow 
an individual teacher to do that.  With a set curriculum to follow, a 
teacher cannot lead.  There should be no standards, and no curriculum. 
Just individuals doing what they think best for their students.     


How many people actually use any of this “practical math” they 
supposedly learn in school?  Do you think carpenters are out there 
using trigonometry? How many adults remember how to divide 
fractions, or solve a quadratic equation?  Obviously the current 
practical training program isn’t working, and for good reason: it is 
excruciatingly boring, and nobody ever uses it anyway.  So why do 
people think it’s so important?  I don’t see how it’s doing society any 
good to have its members walking around with vague memories of 
algebraic formulas and geometric diagrams, and clear memories of 
hating them.  It might do some good, though, to show them 
something beautiful and give them an opportunity to enjoy being 
creative, flexible, open-minded thinkers— the kind of thing a real 
mathematical education might provide.  


SIMPLICIO: But people need to be able to balance their checkbooks, don’t they? 


SALVIATI: I’m sure most people use a calculator for everyday arithmetic.  And 
why not?  It’s certainly easier and more reliable.  But my point is not 
just that the current system is so terribly bad, it’s that what it’s missing 
is so wonderfully good!  Mathematics should be taught as art for art’s 
sake.  These mundane “useful” aspects would follow naturally as a 
trivial by-product.  Beethoven could easily write an advertising jingle, 
but his motivation for learning music was to create something 


SIMPLICIO: But not everyone is cut out to be an artist.  What about the kids who 
aren’t “math people?”  How would they fit into your scheme? 


SALVIATI: If everyone were exposed to mathematics in its natural state, with all 
the challenging fun and surprises that that entails, I think we would 
see a dramatic change both in the attitude of students toward 
mathematics, and in our conception of what it means to be “good at 
math.”  We are losing so many potentially gifted mathematicians— 
creative, intelligent people who rightly reject what appears to be a 
meaningless and sterile subject.  They are simply too smart to waste 
their time on such piffle.  


Students learn about math from their teachers, and teachers learn about it from their teachers, so this lack of understanding and appreciation for mathematics in our culture replicates itself indefinitely.  Worse, the perpetuation of this “pseudo-mathematics,” this emphasis on the accurate yet mindless manipulation of symbols, creates its own culture and its own set of values.  Those who have become adept at it derive a great deal of self-esteem from their success.  The last thing they want to hear is that math is really about raw creativity and aesthetic sensitivity.  Many a graduate student has come to grief when they discover, after a decade of being told they were “good at math,” that in fact they have no real mathematical talent and are just very good at following directions.  Math is not about following directions, it’s about making new directions. 



Paul Lockhart
Lockhart's Lament

See the full article for 
Paul Lockhart, Lockhart's Lament

Here are questions by Dr. A.S. Fischler
Most teachers do not know the beauty of math. They took one required course in math in college which is called College Math.
Where do you find the teachers who can teach math t he way it is explained here. We can not findthem to teach math at all.

Dr. Fischler
Yuzenas helped me.   I was a dictator, I was a teacher, I was a professor, I professed and lectured until I watched him teach.

The Lockhart essay points out:
a good teacher can guide the discussion and the flow of problems so as
to allow the students to discover and invent mathematics for themselves.  The real problem is that the bureaucracy does not allow an individual teacher to do that.  With a set curriculum to follow, a
teacher cannot lead.  There should be no standards, and no curriculum.
Just individuals doing what they think best for their students.

I had this conversation with Dennis Yuzenas today:
"I just want to teach in a program where the students can learn HANDS ON, the kids stay interested because we talk about what they want to talk about, and we help them prepare for the tests that they have to take  (that part doesn't take long)."

Hands On
Keep it fun and interesting
Pass the test
(I'm inviting Francois Savain and Dennis Yuzenas into this conversation....)

I was lucky:
a)  My mother was a teacher and she didn't need a book or a curriculum to teach me something everyday
b)  I had time to watch Yuzenas tear apart a social studies / history text book... and I tried the same thing with my math textbook.
c)  I read a book that pointed out that half of math is not used by 80% of us.

Excellent book:  "When Are We Ever Gonna Have To Use This?"
I can be honest with the kid:   FRACTIONS, every day.    MATRIX?  Integrals?    Trigonometry?   Not you and not me.  Let's skip those chapters.

How do we find the teachers?   We make them.   We put out the job description and show people how they can remake themselves.

 When Are We Ever Gonna Have to Use This? 



This book helps teachers and students.

Teachers who are "good at math" often never think about how to use a technique -- it's obvious.  decimals and powers of ten are just so beautiful.  When it comes to dividing a fraction with a fraction, just flip and multiply.   Why?   Well, we do it that way.  When do we use this?   In a math class.

The focus of the book is to find REAL WORLD applications of trigonometry, geometry, algebra, calculus -- and it helps the teacher see that most students don't need to learn the steps of integration and differentiation and series and permutations, but the theory about why a ball has zero vertical acceleration at some point in the arc of its flight is a helpful concept.  ... and easily shown with differentiation (dy/dx).

"When are we ever gonna have to use this?" forces students and teachers to talk about the real-world uses of math, not just "Well, it's in the book, so we need to study this."

Brilliant book.   Who cares if there are no color photos?  Get a copy and enlarge the chart inside the book.   Work to keep students out of Calculus, save them from 9 months of brain torture and send these advanced students to Statistics -- which is about storytelling and describing groups and trends.

Steve McCrea

REPLY BY Dr. Fischler



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