Association for Symbolic Logic
Logic in the Undergraduate Mathematics Curriculum
Subsession of the AMS-MAA-MER Special Session on Mathematics and Education Reform at the Joint Mathematics Meetings in New Orleans, January 7, 2011 (organized by Marcia Groszek and Tamara Lakins)
Breadth, Depth, Disputes, Drama, and Campus Pranks: The Possibilities and Pleasures of Co-teaching Logic
I teach introductory logic with philosopher Jay Gar field. The collaboration allows us to reach farther and deeper into logic. The dissonance of our perspectives excites and entertains students. Working together magni fies a natural tendency toward wild and experimental ideas. The result is a course that teaches basic skills and sophisticated abstractions, breeds logic minors and majors, and keeps the campus on edge. [Presentation]
A Course Emphasizing Mathematical Logic and Reasoning that is Appropriate for General Education and Elementary Education Majors
Mathematics is a language in which mathematics is written and thought. Like other languages, it has symbols, vocabulary, grammar (principles which govern its correct usage), synonyms, negations, conventions, abbreviations, and sentence structure. Some of its paragraphs are called proofs and they employ logic.
This talk describes a 100-level course called "The Language of Mathematics," originally designed for math majors, that turned out, somewhat surprisingly, to be remarkably good for non-math majors including elementary education majors. Although the elementary education majors in the course typically do not love algebra, they became very good at some high-level algebra and reasoning skills.
The goal is for the students to become fluent in the symbolic language of mathematics so they can efficiently read, write, learn, and think mathematical thoughts. Proofs occur occasionally throughout and are the focus at the end. Research shows that even students who are not mathematically inclined develop abstract mathematical concepts normally taught only to advanced college math students, and they enjoy doing it. [Website] [Presentation]
Seemingly Abstruse Logical Principles Have Practical Importance
Logic, especially the logical principles governing quanti fied statements, is both essential to and ubiquitous in mathematical proof. This talk will analyze examples of common incorrect proofs given by university students, focusing on (1) the use of bound variables as if they continue to exist beyond the statements in which they are quanti ed, (2) the implicit use of existential instantiation, (3) the "dependence rule" for existential instantiation, and (4) universal instantiation and its use with existential instantiation. Suggestions for responding to student errors will be off ered. [Presentation]
Applied Logic Courses in the Mathematics Curriculum
By 'applied logic' I mean the parts of logic that are inspired by, or developed in connection with, some subject which is outside of mathematics. The most important application area is computer science, but there are other important ones including linguistics and areas in the social sciences. The topic is mathematics and logic, but it is not really mathematical logic in the usual sense.
I have been developing courses that could be called applied logic for some time. My talk will share my experiences with some of them, and also mention possible courses that others might like to try.
The overall point is that courses in applied logic could serve as highly stimulating mathematics courses, both for majors and non-majors. [Presentation]
Technology in Logic Education: Courseware, Automated Assessment and Data Mining
For the past twenty- ve years, our project has been producing high-quality courseware for teaching the undergraduate logic curriculum. These courseware packages consist of textbooks, desktop applications and an Internet-based assessment service which acts as an always-available teaching assistant for students. Our applications provide learning environments allowing students to explore truth-tables, proofs, rst-order and modal structures, and notions of heterogeneous reasoning. Our courseware is used in more than twenty- ve countries at approximately four hundred institutions including high schools, community colleges, state and highly selective private universities.
In this talk I will describe the courseware packages that we have developed and demonstrate several of our applications, including a couple that not yet published, and indicate ways in which our courseware may be used in the undergraduate logic curriculum.
As a result of our Internet-based assessment service we have a large corpus of student work (containing in excess of 1.8 million items) produced while learning introductory logic. I will briefly describe preliminary work data mining this corpus for insights into student learning trajectories.