Our Process
            Over the course of the summer, we worked to unify a single, powerful curriculum - derived from a fusion of national Montessori guidelines, the scope-and-sequence of the leading mathematical textbook publishers, and Massachusetts State Standards.
            The result was the codification of 228 discrete skills that form the aspirations of these mathematic programs, from fourth through seventh grades (why stop at sixth with kids as bright as these?).  Mapped out into a step-by-step taxonomy of concepts, this skill set has become what is referred to as the scope-and-sequence (the range and order) of this aspect of Upper Elementary education.  The process is being led by Richard Eyster (an expert in developing math curriculum), Kim Hand (the guru of all things Upper El), and Elise Mostello (our irreplaceable Teaching Assistant).
            From this curricular model, we then derived a comprehensive, 12-page assessment.  We have created the first of a set of 300+ individualized cards that form the backbone of the Mad Math process.  Additionally, we created graphic answer forms and answer keys.  Students each have a personal folder in which to keep their accumulating work.  And we have developed tracking structures to follow the individual pace and accomplishments of each student.

Their Process
            The full student body of Upper El has already completed the 12-page assessment as a pre-test to determine individual and collective strengths - and areas in which each student needs to focus.  We have tabulated the results of each student on each concept.  Students will take the assessment three more times during the course of the year, so that we can precisely monitor their progress.
            We have also added three additional periods per week - specifically devoted to Mad Math.  During the course of these high-energy periods, students tackle the set of concept cards.  Each card is dedicated to one of the discrete skills - with a top section teaching the process, and the lower section providing six problems of increasing difficulty.  The students must get every problem correct.
            It is, therefore, not only that we have created a comprehensive, ambitious curriculum, nor that we are now tracking each student, and allowing them to move strongly ahead at their own pace.  It is a fundamental part of Mad Math that the student-teacher interaction is focused on what each student needs.  During the course of working on a card, the student may seek out a teacher for extra help with understanding a new concept.  In addition, when the cards are checked - there is a high-speed feedback system that provides students with the results of their work within two minutes.  Some students will inevitably be able to recognize and correct (and hand in again) their own errors.  But the requirement that every student achieve 100 percent understanding of each card again motivates the student to seek out one of the three available teachers immediately in cases where their understanding is still incomplete.  The result is that students are exposed to the broad cross-section of grades 4-7 math concepts, unleashed to tackle them at their own pace, and assured of complete mastery before moving on to the next topic. 

Advantages
            In the end, the advantages of this program are compelling.
            Unlike the independent/public school model of requiring every student to be on page 83, this system liberates students to move strongly ahead at their own pace.  The motivation toward mastery isn't coming from the teacher - but from the students (and you should see the energy and focus of their work during these periods!). 
            The feedback speed is almost instantaneous - and a student who gets two wrong doesn't just go blithely (and with a brain still Swiss-cheesed with misunderstanding) on to the next concept.  The requirement of 100 percent mastery assures that students are building foundations of genuine comprehension.  Finally, the availability of three teachers during most periods provides unprecedented access to feedback, support, and instruction.

Conclusion
          Mad Math was created to distill and to unify the best in Montessori and independent school education.  Based on the comprehensive program design - and their own mighty dedication to achievement - we fully expect each of our Upper Elementary students to emerge from the year with unprecedented progress.
          In the end, of course, we want to do everything in our power to ensure that our students are masterfully prepared graduates - and sought-after applicants when they apply for seventh grade at their next schools.  We want them not only prepared - but coming in with a clear, compelling advantage.  Finally, we know from countless studies that the one most critical criterion for students' assessment of their own intelligence is their confidence in mathematics - and we want them to graduate with an enduring understanding of just how smart they are.