The MMAP curriculum is a flexible set of materials designed to allow teachers, schools or districts to custom design a middle-school mathematics program to suit their needs. Yet, within that flexibility is structure which guides us in the development of our units and in putting together year-long instructional plans. The purpose of this section is to discuss three learning trajectories that we intend for MMAP-using students within our overall goal of increasing and changing students’ participation in the practices of mathematics.

First and foremost, MMAP-using students should learn to participate in the activity of mathematics, as it is observed to be practiced by mathematicians, by math-using professional such as engineers and party planners, and as it is defined within school mathematics. While students are participating actively in the practice of doing mathematics, the character of that participation should change along a number of dimensions.

With any arrangement of MMAP and other materials, middle-school students should be progressing from sixth through eighth grade along a number of mathematical dimensions: concepts, standard notations and work organization. MMAP materials are designed to facilitate and guide student's growth in all three areas and our sample year plans reflect this.

First, students should experience conceptual growth. Their notions of mathematical concepts such as variable, function, fraction and proportion should become increasingly more sophisticated and fluid as they progress through math classes. For example, consider the concept of variable: sixth graders will experience a “variable” as a column in a table of values, and they should gain the understanding that this variable can take on a number (maybe an infinite number) of values. But by the eighth grade, students will use variables in the form of letters, words or columns and should be able to work with several variables at a time, to differentiate between constants and variables, to write and understand algebraic expressions. Curriculum materials should facilitate this conceptual growth, building on common experiences that students using MMAP units will have. A paradigm example of variable for MMAP-using students will be ArchiTech’s R-value slider. This slider is under their control and as they change it other variables with ArchiTech change their value.

Also, students need to move toward comfort and ease with standard symbolic notations for mathematical concepts. We know it is important for people to be able to talk with each other about mathematics. Although not completely standardized, there are more or less standard ways to note proportions, equations, exponents, etc. Students need to know what these are and be able to use them as tools to ease their conceptual load, as ways to communicate with others math users and mathematicians, and as ways to use mathematics in the world. Extensions, in particular, build on students’ growing conceptual understanding to bridge to standard notation. For example, Direct and Inverse Variation allows students to explore these categories of functions and their mathematical properties after creating and using examples of them in the Antarctica Project. In the Codes: Privacy unit, the standard symbols and terminology for functions are introduced within the software Coding Toolbox, and students become adept at using terms such as domain and range to identify sets of values for variables. X and Y as variables are demystified as students use them to create secret codes.

Finally, students need to learn to organize their mathematics work in such a way that it adequately communicates their thinking to others. This includes writing coherent mathematics and arranging tables and graphs in such a way that readers can make the associations the student has in mind. In MMAP materials, we do a lot more structuring of students’ writing and presentation on the page in materials intended for 6th and 7th grade than those aimed at 7th and 8th grade. We also vary this supplied structure between our applications units and our extensions and investigations. For example, Dream Home math activities ask students to organize their own work on the page as part of keeping a record of their project work. The extension that builds on their experiences in Dream Home, Problems with Proportions, provides students with templates of the proportion equation to fill in so that students can learn how to set up and manipulate a proportion to solve problems relating to scale drawings.