Tag Archives: pdf

Books: “A Mathematician’s Lament” by Paul Lockhart

A Mathematican's Lament book cover
Anybody who teaches math should read this book!

This book perfectly summarizes my disgust with the state of “education” today. The author’s main thesis is that math is an art that should be taught in a way to cultivate appreciation and understanding. It is not merely a set of formulas and definitions that students should commit to memory. Here is a quote from page 29:

By concentrating on what, and leaving out why, mathematics is reduced to an empty shell. The art is not in the “truth” but in the explanation, the argument. It is the argument itself which gives the truth its context, and determines what is really being said and meant. Mathematics is the art of explanation. If you deny students the opportunity to engage in this activity— to pose their own problems, make their own conjectures and discoveries, to be wrong, to be creatively frustrated, to have an inspiration, and to cobble together their own explanations and proofs—you deny them mathematics itself. So no, I’m not complaining about the presence of facts and formulas in our mathematics classes, I’m complaining about the lack of mathematics in our mathematics classes.

And another choice quote about the evils of High School Geometry from page 67:

…never was a wolf in sheep’s clothing as insidious, nor a false friend as treacherous, as High School Geometry. It is precisely because it is school’s attempt to introduce students to the art of argument that makes it so very dangerous.

Posing as the arena in which students will finally get to engage in true mathematical reasoning, this virus attacks mathematics at its heart, destroying the very essence of creative rational argument, poisoning the students’ enjoyment of this fascinating and beautiful subject, and permanently disabling them from thinking about math in a natural and intuitive way.

The mechanism behind this is subtle and devious. The student-victim is first stunned and paralyzed by an onslaught of pointless definitions, propositions, and notations, and is then slowly and painstakingly weaned away from any natural curiosity or intuition about shapes and their patterns by a systematic indoctrination into the stilted language and artificial format of so-called “formal geometric proof.”

This book is available as a freely downloadable PDF.

Creating Printable PDF Flash Cards Using LaTeX

This post details how to make high quality, printable flash cards like I have available at my web site. I am assuming you are using Ubuntu Linux. I did this on Ubuntu 8.04 (Hardy Heron), but it might work on some previous and later versions as well.

First you want to install LaTeX, plus Andrew Budge’s flashcards package. Open a command terminal and type in the following command to install TeX and LaTeX. The flashcards package resides in the texlive-latex-extra Ubuntu package.


$ sudo apt-get install texlive texlive-latex-extra

I also recommend installing Kile which is a great program for editing TeX/LaTeX documents. You can do this with the following command. Depending on your system configuration, apt-get might require you to install several extra packages. The following is optional:


$ sudo apt-get install kile

At this point, if you try to compile a latex document that uses the flashcards package, you’ll get the following error:


! Package geometry Error: You must set \paperwidth properly.

To fix this, we need to create a small file called geometry.cfg, which tells the geometry packages which type of paper we will be using. Create the file using the following command:


$ sudo gedit /usr/share/texmf-texlive/tex/latex/geometry/geometry.cfg

Now copy and paste the following into gedit, save the file and exit from gedit.


%%
%% This is file `geometry.cfg',
%% generated with the docstrip utility.
%%
%% The original source files were:
%%
%% geometry.dtx (with options: `config')
%%
%% File: geometry.dtx Copyright (C) 1996-2002 Hideo Umeki
%% (hideo.umeki@toshiba.co.jp)
%%
%% This package may be distributed under the terms of the LaTeX
%% Project Public License, as described in lppl.txt in the base
%% LaTeX distribution, either version 1.2 or (at your option)
%% any later version.
%%

%% Uncomment and edit the line below to set default options.
\ExecuteOptions{letterpaper,dvips}

\endinput
%%
%% End of file `geometry.cfg'.

Now, you should be able to compile a LaTeX document that uses the flashcards package without errors, but there will be some warnings. To fix the warnings, we need to change one line in flashcards.cls.


$ sudo gedit /usr/share/texmf-texlive/tex/latex/flashcards/flashcards.cls

The following diff command shows the change you need to make:


$ diff -ru flashcards.cls.bak flashcards.cls
--- flashcards.cls.bak 2009-01-26 17:15:27.000000000 -0700
+++ flashcards.cls 2009-01-26 19:43:57.000000000 -0700
@@ -83,7 +83,7 @@
top=\topoffset,
left=\oddoffset,
right=\evenoffset,
- twosideshift=\oddevenshift,
+ twoside=true,
bottom=0.0in,
noheadfoot}
\ifthenelse{\boolean{flashcards@dvips}}{\geometry{dvips}}{}

Now you should be able to compile a LaTeX document without any errors or warnings, excepting for any errors in your own markup of course.