**List of Content**

**October 2006**

**How does an idea for the Teaching-Research investigation arise?**

*B. Czarnocha, HCC*

**Addressing Arithmetic/Algebra divide at CUNY**

*B. Czarnocha, HCC*

**Independence of learning**

*Vrunda Prabhu*

**High School for Law and Public Service**

*Action Research Group*

*Shannon Curran-Reflections*

**Using ESL Strategies in the Math Classroom**

*Elish Sari – ESL teacher*

**Editorial Introduction**

Teaching-Research is the process of conducting classroom research investigations simultaneously with teaching.

Teaching-Research, NYC model, assumes that the Classroom investigations are made in order to improve both instruction and learning of mathematics in this classroom, and beyond. Contemporary situation in mathematics classrooms of New York City and other urban centers is in dramatic need of rapid improvement and teaching-research methodology developed in the Community Colleges of the Bronx is geared to this task. A Teacher-Researcher in the context of Teaching-Research/NYC model (Czarnocha,2001), is a professional:

- whose classrooms are scientific laboratories, the overriding priority of which is to understand students’ mathematical development in order to utilize it for the betterment of the particular teaching and learning process;
- who as a teacher can have the full intellectual access to the newest theoretical and practical advances in the educational field, knows how to apply, utilize and assess them in the classroom with the purpose of improving the level of students understanding and mastery of the subject;
- who as a researcher has a direct view of, and the contact with, the raw material of the process of learning and development in the classroom, acts as a researcher in the context of the daily work of and uses that process to derive new hypotheses and general theories.

What does the Teaching-Research methodology do for us in the mathematics classrooms?

First and foremost, it increases teacher’s intellectual involvement with the teaching process and its content, allowing for the systematic attacks on classroom learning issues, such as student misconceptions, difficulties with logical thinking or, for example, use of natural and algebraic language in the mathematics classroom. The incorporation of systematic research methods into classroom teaching helps to formulate every day’s teaching issues as subjects of rigorous investigations and demonstrate their possible general nature. Mastering the process of classrooms investigations helps to utilize the research results in the classroom and assess their usefulness.

Secondly, classes of Teacher-Researchers are characterized by a new feeling of “comradeship in thinking”, which arises when a teacher in the classroom is involved in understanding student mathematical thinking while the student is involved in understanding the relevant piece of mathematics. At this simultaneous moment of thought there is a full equality between the student and the teacher in their intellectual efforts as both of them ponder different aspects of the same mathematical issue at hand. As a result the teacher becomes very familiar with the peculiarities of student mathematical thinking, while the student is guided along its most optimal trajectory of mathematics learning.

Thirdly, use of Teaching-Research techniques helps bringing to the fore the deep while implicit professional experience of an in-service mathematics teacher while transforming it into explicit, verifiable knowledge

The Mathematics Teaching-Research Journal on Line is directed to the mathematics teacher-researchers from all walks of life in mathematics education, especially to teachers who are interested in developing a TR profile. The pages of the journal contain simple description of the components of the process, TR notes, thoughts and articles from the field. The methods of Teaching-Research differ significantly from the standard method of educational research, and the discussion about the best TR techniques is only now starting in the field; a significant amount of time and space in the journal will be devoted to that issue.

The intent of the journal is to create a vibrant, supportive community of Mathematics Teaching-Research in the Bronx and in the Metropolitan area, which, with time can develop teaching-research tools to deal with the complex problems of our multicultural, multilingual classrooms. It is only us, mathematics teachers of the New York City, and beyond, that can successfully transform the mathematics learning in mathematics classrooms and bring it to the acceptable intellectual and practical level. The editors extend a warm invitation of welcome to all who, on the pages of this new Mathematics Teaching-Research Journal on Line, want to join them in the exploration of this useful, challenging and promising approach to our mathematics teaching.