**List of Contents**

**December 2009**

**Teaching-Research**

**Using the Number Line to Teach Signed Numbers for Remedial Community College Mathematics**

*Alice Welt Cunningham*

**Signed Arithmetic of Integers: The Case for Consistency in Counting Proofs**

*Richard Pan*

**Reflection From Practice**

**The Didactic Contract, a Handshake and Compromise A Teaching-Action-Research Project**

*Vrunda Prabhu, Bronislaw Czarnocha, Howard Pflanzer*

**Problem Solving and Remedial Mathematics**

*Bronislaw Czarnocha, William Baker, Vrunda Prabhu, Olen Dias*

**Logic in Undergraduate Curriculum**

*Roman Kossak*

**Editorial**

The current issue (Volume 3, Number 4) of the **Mathematics Teaching Research Journal** on line has been delayed by ongoing efforts at (1) increasing submission formats for articles to include Latex in addition with Word, and (2) at increasing the visibility and accessibility of the journal.

The current issue is about the nuts and bolts of classroom work in mathematics classroom at the college and high school, written by teachers and instructors of mathematics on the basis of their teaching experience. We present two articles about the operation on integers each written from a significantly different perspective. While Alice Cunningham presents the arrow model of integer operations, Richard Pan views the same situation with two color chips. Comparison of the two models invites reflection on this standard subject.

We follow with a collection of classroom notes of Roman Kossak concerning teaching logic and informing about its classroom challenges and successes. It leads us through a route of connecting existing student knowledge with the formal language of mathematics and it culminates with the collection of interesting logical problems to be solved by students.

Problem – solving is an integral part of the discovery process essential to enjoyment and learning of mathematics. Problem-solving has been widely diagnosed as a weak area among students in large department wide assessments (McInerney & Prabhu), and in individual classrooms (Baker et. al.). In the recent university-wide initiative at CUNY to reform undergraduate mathematics education, reform could be further enhanced by learning from efforts at individual college campuses. The proposal by Czarnocha, et.al. in this issue describes a proposal to address problem-solving on a broader scale starting with the classrooms participating in a joint teaching experiment. The editors extend a warm invitation to the CUNY community to disseminate their ideas for reform of undergraduate mathematics.

The article by Vrunda Prabhu, Howard Pflanzer and Bronislaw Czarnocha signalizes a new direction of teacher’s concern in the classroom – student motivation and interest in learning mathematics. It describes short drama episode introduced into the mathematics classroom, which helped students to overcome their inhibitions of past experiences with mathematics.