Pathways to Algebra and Geometry is a two-year comprehensive middle school curriculum, based on the Middle School Mathematics through Applications Program (MMAP). Pathways is published by Voyager Expanded Learning. MMAP was developed at the Institute for Research on Learning and was designated as a Promising Program by the US Department of Education. The MMAP/Pathways Implementation Center is now housed at WestEd and is led by MMAP's developers.

Philosophy of MMAP Curriculum: MMAP has developed a comprehensive middle school mathematics curriculum centered around applications projects that involve students in real-world problem solving and require them to learn and use mathematics. We hypothesized that these contexts would be engaging to students who were alienated from mathematics as a school subject and would provide grounding for all students' mathematical reasoning and argumentation. Research and development over the last six years has confirmed our initial hypothesis: real-world application projects provide students with both the reasons and the resources for learning important mathematics.

We based our curriculum on the assumption that no matter what we are doing, we are learning. The question, then, is not "How do we get young people to learn?"; rather, "What are young people learning in our classes?" In traditional school mathematics, youngsters take on the role of students who learn to carry out pre-existing algorithms to solve problems carefully matched to the algorithm. On the other hand, when people use math outside of school, roles are different, changing the character of the math that is learned. We believe that middle schoolers can attain greater conceptual understanding of mathematics, as well as developing meaningful math skills, when they participate in activities like those of people who use math in their work. In the Guppies unit, for example, students assume the role of population biologists. Each student plays a role in a group, and a "community" of population biologists is formed. Through group work, shared goals, and discourse, mathematical problems emerge. Because understanding the math can be helpful in solving a real problem, the math becomes functional. Discussion about the problems takes place, and new mathematical understanding emerges.

The MMAP curriculum has three components from which teachers and curriculum decision makers can choose to construct a complete and balanced middle school curriculum. Application units support four to eight weeks of activity, use specially designed software and plunge students into an extended role play in which they learn and use math. Two other kinds of shorter units fill out the curriculum: extensions bridge the understanding students attain in the projects to standard notations and skills; investigations introduce students to pure math topics and methods.

The mathematics content of the MMAP comprehensive curriculum provides depth of focus through two important middle school math concepts-proportional reasoning and algebra/function-as well as breadth of coverage. Middle school is the time for important transitions within proportional reasoning and understanding and use of algebra and function. These math topics are revisited again and again over a series of application units in a variety of real-world contexts, each one adding to students' deepening conceptual understanding, with extensions that connect this understanding to conventional representations. This depth is balanced with breadth: all of the Standards are addressed within the materials, and students have opportunity to develop important skills and concepts in each one, with investigations ensuring coverage of topics outside the scope of the applications units.

MMAP technology was designed to push the boundaries of current classroom practices while still remaining "do-able" in today's classroom. Each application project is accompanied by a specially created computer design tool, needed for about half the project. The software is a tool for students to use together to solve a design problem and creates opportunities for students to work on and learn math through experimentation, model-building, representation, and argumentation. Most teachers borrow six to eight computers to make a classroom set for a month or arrange to use the school's computer lab. In addition to MMAP software, the use of spreadsheets and calculators are encouraged when appropriate.

Our assessments include a variety of activities that help teachers and students engage in, capture, reflect on, and demonstrate mathematical growth. As the NCTM Assessment Standards suggest, we designed ways for teachers to create assessment systems making us of student writing, peer reviews, teacher conferencing, and classroom tests. These assessments help teachers and students track mathematical growth and demonstrate that growth to other stakeholders such as parents and administrators. And, of course, the assessments are designed so teachers can calculate a grade.