MST Times

On September 26, 2011, the Program in Mathematics held the first session of the Fall 2011 series of Mathematics Colloquia.  The featured speaker was Dr. Zalman Usiskin, Professor Emeritus at the University of Chicago, Director of the University of Chicago School Mathematics Project, and Mathematics Education Trust Lifetime Achievement Award recipient (2001).

Usiskin’s presentation, entitled “Mathematical Modeling in the School Curriculum,” focused on one of the current “hot topics” in mathematics education, mathematical modeling.  In his presentation, Usiskin discussed the modeling process and the different types of mathematical models one finds in the real world.  He described the “typical” model one usually encounters in the mathematics school curriculum as “almost exact – theory based models,” which are those models that give fairly close representations of the real world, such as approximating a soda can as a cylinder or using a parabola to represent the motion of a thrown object. Both of these examples give close models to the actual situation, but both ignore some aspects. Additionally, Usiskin defined “exact models,” which are those models that are born from the mathematics themselves, such as networks of airplane routes, and “impressionistic models,” which are models that seem to fit a situation but are not derived from theory, such as those used to predict new world records.  This broadened view of the range of models beyond those typical “almost exact – theory based” ones may help teachers themselves broaden their own views on modeling and its role in the curriculum.

Usiskin also discussed the teaching of mathematical modeling in schools by describing possible progressions for modeling in the curriculum. An algebraic progression begins with the uses of numbers. Then, students are introduced to the uses of the operations, combining those operations to make expressions, and finally using those expressions to create functions.  The teaching of mathematical modeling, according to Usiskin, occurs by means of teaching students to recognize characteristics of real-life situations and their relationships with the varied mathematical concepts, such as the operations.  This is in opposition to teaching students to recognize certain “key” words and phrases in word problems and to translate these into mathematical symbols.  If students understand how mathematics can be used, they are more likely to be able to use it as a tool themselves.  So, instead of teaching mathematics and then teaching applications and uses, a teacher with a modeling view begins with a real-life situation and its characteristics that can be translated into mathematics.

Usiskin’s treatment of mathematical modeling through the entirety of the K-12 curriculum provided an excellent starting point from which teachers can begin to incorporate mathematical modeling into their practices.

The three other colloquia in the Fall 2011 semester’s series are as follows:

October 10:  Katherine Merseth, “The Developmental Math Challenge in Community Colleges;”

November 7:  Al Goetz, “Behind the Scenes at NCTM School Journals;” and

December 5:  Matt Larson, “Do We Have an Achievement Gap?”

Lectures occur in the evening from 7:00 to 9:00 and are preceded with a light supper and conversation at 6:30.

By Heather Gould, Mathematics Education Student