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1. The RM Environment is a collection of tools designed to either supplement or replace regular classroom and home practices. It can be used in class and/or at home as directed by a teacher. The tools can be employed to master selected topics or to study the entire curriculum.
2. An automated tutor using artificial intelligence technology (AI Tutor) controls the learning process.  The AI Tutor selects the path and pace of learning, tailored to the individual characteristics of each student. This is accomplished through the continuous analysis of students' performance on assignments given by the Tutor.
3. Key learning tool: an extensive database of exercises and problems. Exercises target the acquisition of solid skills in applying basic rules in the manipulation of numbers and of other mathematical objects. Problems combine the practice of these skills with the development of the logical, non-standard, and creative thinking required for understanding mathematical concepts.
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 4. The AI Tutor enforces the main objective of the achievement of a minimum (required) level of knowledge by all children. Students will continue to practice every essential rule/topic until they meet the minimum requirements for math proficiency. The "Failure is not an option" principle will be exercised in a firm fashion with regard to minimum requirements. The RM project's methodology holds the belief that the basics can and should be mastered by all students.
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5. No student will be artificially held back in his or her drive to master more complex notions and further develop mathematical and logical thinking skills. The Tutor gradually raises the level of academic complexity, ensuring that every student is challenged according to his or her interests and talents.
6. The AI Tutor implements a "spiral" path of learning, which has proven its effectiveness in the history of K-12 education worldwide. All concepts and skills learned at the earlier phases of the course are continuously practiced and reiterated throughout the entire school year.
7. The RM curriculum emphasizes learning how to think and reason, as opposed to just learning "plug-and-play" methods for solving simple standard problems; the goal is to build the foundation for children's intellectual development. This is accomplished by requiring that students explain how they arrive at solutions to exercises and problems as well as through offering special problems that practice reasoning techniques. The testing of students' progress through multiple-choice exams is minimized.
 8. A comprehensive reference system to math theory including (1) rules for performing math operations as well as (2) methods for and examples of solving problems is available through Internet links. The system allows for a topic-by-topic review mode as well as a hypertext-based reference index accessible from all exercises and problems.
9. All educational materials offered by the Environment are in strict compliance with State standards.
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 10. Learning is not necessarily fun in itself. Learning is hard work, and children in grades 6-7 are prepared to face this reality. However, learning can and should be made fun as long as having easy fun does not become student's prime motive. To make the process of learning more exciting and enjoyable, much of the problem solving is done in game settings. Problem-solving (academic) games especially designed for this purpose add a new dimension to the studying process. Children compete with their peers either individually or in teams, creating an interactive learning environment. Student-to-student interaction is a powerful pedagogical technique utilized in our teaching practices.
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11. Effective Tutoring. Automated computer-based learning has its limits. When it comes to answering students' questions or aiding the comprehension of a math concept, live tutoring is the only solution. RM's Web-based system will make teacher-performed tutoring more focused by helping with the early diagnosis of problems. Also, an organization of tutors recruited from college students, parents, and retired professionals will be created to monitor students’ performance, answer questions, and assist with overcoming difficulties in understanding concepts. Tutors communicate with students over the Internet through e-mails and live sessions. Each student has an assigned mentor tutor, who observes the student's progress and gives help when needed.
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12. Ratings and Awards. Students' performance is measured by a specially designed rating system – an assessment tool seamlessly integrated into the learning process. Ratings serve as a powerful means for monitoring students' progress and effort and present a comprehensive multidimensional picture of students’ academic proficiency, logical and reasoning skills, ability to learn, and teamwork skills. The key point behind the rating system is that anything a student does in RM adds to his or her rating. Since ratings never decrease, students can only improve the indicators of their learning by doing more work in RM. Minimum targets in various topics, as measured by ratings, are required of everybody. The AI Tutor will rely on ratings in creating an individual path of learning for each student. Besides bringing such new dimensions into teaching practices, ratings combine the best features of grades and test scores, overcoming many of their deficiencies. First, ratings are built over time and encourage an individual pace of learning, thus reflecting not only the achieved level of knowledge but also the cumulative effort put in by the student. Second, ratings (as opposed to school grades) have no ceiling and will provide for more visible differentiation between different track records. Third, ratings are measured with a common yardstick and are independent of each teacher's grading system and biases.
