Alan Tucker
AMS 303, Graph Theory, is a sequel course to AMS 301 (see above). It goes into
the graph theory topics of connectedness, planarity and coloring in greater
detail than AMS 301 along with Polya's Enumeration Theorem, network flows,
progressively finite games, and elements of cryptanalysis.
Corrections to my text Applied Combinatorics, 6th and 5th ed., John Wiley and Sons
Link to Applied Combinatorics corrections.
Corrections to my text, Unified Introduction to Linear Algebra
Link to Unified Linear Algebra Corrections.
History of the Undergraduate Program in Mathematics in America,
written
for a Math Assoc. of America Centennial volume published in 2015. It
appeared in the October 2013 issue of the American Mathematical Monthly.
MAA History article
Park City Mathematics Standards Study Group
Each summer from 2004 to 2008, a group of research mathematicians
met at the Park City Mathematics Institute to discuss issues about school mathematics.
Three working papers were written by this author in collaboration with other
mathematicians. The first workshop in 2004 produced a working paper entitled
What is Important in School Mathematics
. This topic was suggested by state mathematics coordinators (who met the
week before our workshop) who felt that the long lists of state mathematics
standards had lost track of the core goals of the school mathematics
curriculum. The 2005 workshop refined the previous year's work to produce
Some Organizing Principles for K-4 Mathematics.
This document was the result of extended discussions with NCTM
representatives. These discussions also played a significant role in the
formulation of the 2006 NCTM Curriculum Focal Points report.
The 2006 PCMI workshop focused on fractions, with primary attention on the
preparation for fractions in elementary grades as opposed to the
middle grades teaching of fractions. The working paper from this workshop
is Preparation for Fractions.
Two more workshops were held to refine the topic of fractions.
The most important aspect of these workshops was that they set the stage
for mathematicians to play a major role in creating new school mathematics
standards, such as the 2010 Common
Core State Standards.
Problems with Standards-based Mathematics Tests
Prof. Tucker has investigated problems in the psychometric methodology underlying
the New York Regents Math A graduation test, and more generally in all
standards-based mathematics tests. Prof. Tucker was a member of the special 2003 Regents
Math A panel that investigated the failure of the June 2003 New York State mathematics graduation test.
This panel was given unprecedented access to confidential test
data which revealed the serious practical problems that arise in trying to
use Item Response Theory to design a demanding new standards-based mathematics
graduation test. Additionally, there was an extremely high correlation
between students' performance on the 8th grade math test and the high school
graduation test.
The
recommendations in this panel's report, including a redesign of the complete K-12 N Y math curriculum, were adopted by the NY Board of Regents. The
report documented the psychometric problems in the Math A test without explaining the source
of these problems. Subsequent analyses by Tucker
found systemic flaws in New York's use of the theory of standards-based tests.
Click here for a short version of Tucker's findings about
problems with the theory of performance standards, as it was applied to
the Math A test.
Click here for for a complete analysis of problems
with the Math A test. This article appeared in the May, 2011 issue of the American Mathematical Monthly.
alan.tucker@stonybrook.edu --
Applied Math & Statistics --
SUNY Stony Brook
Last update: November, 2025