By creating our own library of materials, we can most easily create programs tailored to 1) the dynamics of one-on-one tutoring and 2) the specifics of Minnesota Graduation Requirement Examinations such as the MBST and the MCA-II.

For more on our motivation, please see Appendix A of Catalyst's Approach to Teaching Mathematics

We developed a beta-level material creation system that allowed a user to enter the materials in a custom xml markup language -- a language that looks a lot like HTML. The idea behind this engine is to make it much easier to create and maintain a large database of materials. Using off the shelve tools from Microsoft or Adobe can make become difficult when working with large number of files. Overall, the system is designed to let the author focus on content while all layout and style matters are taken care of by the material creation system.

Meanwhile, we also worked with teachers on developing the overall educational approach (see below for more information on our approach).

After receiving much feedback over the last two years, we working towards upgrading this project. Please contact us for more information.

Currently, library content development is guided by 1) the National Council of Teachers of Mathematics K-8 Curriculum Focal Points and 2) the mathematic Graduation Requirement Examinations (GREs) set by the Minnesota Department of Education .

Originally, our materials were developed to help students pass the Minnesota Basic Skills Test (MBST) math exam; we will be editing our database for necessary changes needed to help students pass the 8th and 11th grade Minnesota Comprehension Assessment II exams which replaced the MBST in 2006.

Major content that will be available in our 2007 database will include:

• Understanding number notation, place value, number magnitude, and number lines.
• Basic arithmetic (+, -, x, /) using whole numbers, fractions, decimals and percentages.
• Understanding and working with prime numbers and factoring.
• Understanding exponential notation and computing with scientific notation.
• Rounding, estimation, "mental math", and calculator computation.
• Understanding and calculating with positive and negative numbers.
• Understanding, measuring, and calculating length, area, and volume.
• Understanding, naming, and converting between common units of measurement for length, area, and volume.
• Names and properties of two and three dimensional shapes.
• Understanding and measuring angles.
• Understanding, reading and creating plots, charts, tables, and graphs.
• Introductory statistics such as mean, median, surveys, and basic probability.

All material is covered computationally and in context. With these programs in place, we will begin building on this work to extend the library with content (e.g. algebra) needed for the 11th grade MCA-II and ACT/SAT tests.

We are hoping to have this initial library completed during the Winter of 2007, but this date is contingent on our fund raising efforts.

A substantial debate on how best to teach mathematics emerged when the National Council of Teachers of Mathematics (NCTM) released its first Principles and Standards document in 1989 and launched the mathematics education reform movement.

Generally, reformers cast this debate as the teaching of fundamental mathematical concepts in real-world applications versus the more traditional "skill-and-drill" approach that centers on isolated computational/algorithmic fluency and route memorization of mathematical facts. The reform debate, however, is also a continuation of a larger (and older) debate surrounding constructivism or "discovery learning" versus explicitly teacher-led direct instruction.

At Catalyst, we place strong emphasis on the NCTM process standards. We strongly believe that conceptual foundations are more important than disconnected route memorization and isolated repetitive algorithmic practice. Students need to be able to talk about mathematics; to be able reason with and compare mathematical ideas; and to be able use multiple representations to express mathematical concepts and solve problems. Foundational conceptual knowledge is lasting and it is generative; that is, it makes learning increasingly easier and easier.

However, it was not the intent of the Principles and Standards nor is it our intent to avoid the building of computational and algorithmic fluency. But, following the NCTM guidelines, we stress practice and fluency after strong conceptual foundations are in place.

The NCTM reform movement and educational theory in general is a very complicated issue, to say the least. For more on these issues and for a detailed exposition of the philosophy behind our materials please see our position paper Catalyst's Approach to Teaching Mathematics .

The purpose of this document -- and Catalyst in general -- is to be very explicit about our education philosophy. This way, as we grow and work with more schools, students, teachers, and other experts -- we can systematically fix the problems and reinforce the strong points.

The fruit of this process is a technology that will lead tutors to be as effective as possible. This way, all of students and our tutors using our materials will benefit from our work and our growing experience on how to best tutor students in a one-on-one environment.