The high school tutor and course materials are now called "Cognitive
Tutor Algebra" and are being marketed by the PACT Center's spin-off
company, Carnegie Learning. The PACT Center is currently developing tutors for Middle School math.
The Nintendo Problem
The development of Algebra throughout the curriculum is based on the students' own informal knowledge of mathematics and on problem situations. Modelling situations such as the Nintendo Problem, shown above, students begin to construct intuitive understandings of and connections between multiple representations of functions. From the beginning of the course students are asked to make the connections between the various representations and to construct each representation based on their understanding of the problem situation.
A mere listing of topics covered does not adequately provide the necessary framework for the curriculum. Consequently, we use a matrix which attempts to show the development of the curriculum in a more meaningful way; however, a three dimensional framework showing the multiple representations as the core which expands from the first quadrant with simple direct variation to mx+b to all four quadrants to systems to data analysis to quadratics would probably be more appropriate.
The U.S. Shirts Problem is a sample three day lesson module from the first quarter of the classroom curriculum. Teachers are encouraged to read over the problem situation at the beginning of the period and then give the students time to work in cooperative groups to solve the problem. Groups are given overlays to describe the problem and asked to present their results to the rest of the class.
Learning in Cooperative Groups
The PUMP project is committed not only to providing the opportunity for all students to enroll in Algebra, but also to providing the students with the human and technological support to enable them to be successful in Algebra. This support includes the computer tutors, the support of the Chapter One reading specialist, after school tutoring, Family Algebra Nights, the inclusion of Special Education students and teachers, support for the teachers including summer workshops and on-going help, and new assessment strategies.
Family Algebra Night
Student assessment is a major area of emphasis. The first semester final exam and the year end final exam from the1993-94 school year are presented to the new students at the beginning of the school year along with level 4 student responses in order to clearly communicate our expectations to the students. Students are assessed on their performance on group tasks in the classroom, individual on demand performance tasks, portfolios, and their work on the computer tutors, as well as on more the traditional homework and tests. At the end of each grading period students are given an individual on-demand performance task similar to the situations that they have worked on in the classroom. Each of these requires the student to do a mathematical analysis of a situation and to produce a writen report based on their analysis. At the end of the first and third grading periods, these tasks are graded by the individual teachers; but at the end of each semester these tasks are graded using the New Standards Type Grading Conference Model.
Conference Model Grading Session