OVERVIEW

Boston College received funding from the National Science Foundation to assist in the implementation of the NCTM Standards on Discrete Mathematics. The project entitled Implementation of the National Council of Teachers of Mathematics Standard in Discrete Mathematics, was designed to form a nationwide cadre of middle and secondary school teachers and collegiate mathematics teacher educators who would acquire some basic knowledge of discrete mathematics topics, activate the discrete mathematics standard in their respective classrooms and share instructional experiences with their students and teacher colleagues.

In Phase I, during July 1992, a three week leadership training program was conducted at the Chestnut Hill Campus of Boston College that prepared six leadership teams. The teams studied the discrete mathematics topics: social decision making, graph theory, counting and finite probability, matrices and recursion. They developed instructional practices based on the recommendations of the NCTM Professional Standards for Teaching Mathematics and prepared an inservice model delivered at six regional sites each in the Summers of 1993 and 1994. In Phase II this same model was delivered at six regional sites each in the Summers of 1995 and 1996. In the Summer of 1997 there was one three-week program at Boston College for middle and secondary mathematics teachers.

SUMMER COMPONENT

The intensive instructional program operated daily between 8:30 am and 4:15 pm. There were regular informal evening study gatherings as well as a few special evening sessions. The program targeted five specific content areas of discrete mathematics namely Social Decision Making, Graph Theory, Counting and Finite Probability, Matrices and Recursion. Graphing calculators, spreadsheets and other computer software packages were an integral part of the discrete mathematics instruction. Participants explored effective leadership development practices and issues such as assessment and equity. All teachers modeled discrete mathematics presentations before their colleagues. Homework was assigned daily while the teachers worked individually and in groups to complete assignments.

ACADEMIC YEAR FOLLOW-UPS

All participants returned to the campus site for two all day Saturday meetings. Teachers shared their experiences in teaching discrete mathematics topics and interacted with area leaders in mathematics education.

OVERVIEW

This workshop was designed to assist the classroom teacher in achieving a global view of the emerging curriculum at the middle/secondary levels. It also afforded the teacher attendees the opportunity to collaborate with a colleague and do some curriculum development. This latter experience is important for teacher growth and yet the hectic pace of the school year discourages it.

The workshop course, Focus On Mathematics: A Middle/Secondary Emphasis, surveyed five major areas of middle/secondary level (grades 7-12) mathematics: algebra, geometry, pre-calculus analysis, discrete mathematics, and number theory. In each area, content development, instructional practice, problem-solving and applications' ideas, motivational enrichment, and assessment alternatives were treated.

SUMMER COMPONENT

The workshop course was divided into two parts.

Part 1: Overview of content in five topical areas team taught by two course instructors-participants organized in groups of four. Each session was a mix of lecture, discussion, and group problem-solving. There were two sessions of 90 minutes each in the morning followed by lunch followed by two sessions of 75 minutes each in the afternoon. The class atmosphere was informal; interaction was encouraged. The five content days were split by a weekend to allow the students to become involved in an assignment that called for reflection, creativity and engaged them in problem solving and problem posing.

Part 2: Three days of intensive work in curriculum development for Palms-DOE participants. Participants carried out some curriculum development and classroom implementation of the materials constructed. Specifically, teams of participants were assisted in developing a brief unit (three lessons or more) of their choice which will be field-tested in the subsequent school year. The unit should expand upon a topic that supports and demonstrates

a) Integrating discrete mathematics in algebra or

b) Integrating discrete mathematics in geometry

A suggested list of topics was provided but participants also had the option of choosing other appropriate topics that meet the requisite above. After being given some basic organizational and formatting instruction, the participants worked in teams of two or more to accomplish the goal. The course instructors met with the teams for a morning and afternoon feedback session and were available at all times to answer questions and provide direction during the three days. Reference materials and technology was readily accessible to the participants to help facilitate their work. On the last afternoon the participant teams made a brief report to the entire group detailing their units.

ACADEMIC YEAR FOLLOW-UP

There will be two all day Saturday followup meetings whose main focus will be on the instructional activity carried out by the participants with their students. The participants will share the outcomes of fieldtesting with one another, offer suggestions for revision and expansion of units, and in some instances may arrange to exchange instructional units with one another for additional testing for one half the day. The other half day will be used to present some new content and new instructional ideas.