It is not hard to make a student excel at math. At school, constantly drill him on math. After school and on the weekends, he should attend extra math training classes outside of school. Finally, in addition to his homework and extra math classes, he should do additional math practice at home. This method is common in many Asian countries, where “cram schools” are the norm, and it obviously works. But it is neither efficient nor elegant. One of AVE’s earliest goals was to develop a system that was more rigorous that the aforementioned system, but took no more time than standard math education in America. The result was AVE’s Accelerated Math Curriculum. Currently in version 3, AVE’s Accelerated Math Curriculum is the backbone of all of AVE’s math training programs. This curriculum, which makes heavy use of what AVE calls “cognitive incentives”, ensures that each student excels. With redundant failsafes that prevent any students from falling through the cracks, the Curriculum allows students to gain a rigorous understanding of mathematical concepts more than twice as rapidly and effectively than do standard curricula. Fees: Accelerated Math Curriculum for grades 3-12, including initial diagnostics, development, integration, teacher training, presentations to students, parents, and faculty, and updates for 3 years: $75,000. Grades 9-12 only: $45,000. Travel expenses are additional. Also consider our teacher training seminars, which start at $2000. To learn more or set up a free initial phone consultation, please call 301-320-3634. Additional Information for Education ProfessionalsThe Curriculum reflects AVE's view that mathematics is most importantly a means to develop cognitive skills. This belief contrasts with the view of mathematics solely as an underpinning of the natural sciences. Thus, trigonometry is not introduced so that the student may solve problems involving the height of a mountain. Instead, a problem about the height of a mountain may be used to develop specific problem-solving and reasoning skills. The Curriculum is also developed around the cognitive processes of the student, rather than the structure of the discipline. Topics are presented in an order and manner that best facilitates long-term understanding. This is most significantly evident in two ways. First, the order of presentation of topics occasionally differs from those used by earlier methods. Secondly, fundamentals of several related topics are introduced before esoteric aspects of any topics are examined. For example, students learn the fundamentals of limits, derivatives, and integrals before they learn methods to find the derivative of an inverse function. This method creates a conceptual framework in which such abstruse topics can be understood, appreciated, and incorporated into a permanent understanding of the method. As part of its focus on developing reasoning and problem solving skills, the Curriculum develops and understanding of mathematics from the bottom up. This means that students learn core principles and methods, and learn to connect them to solve increasingly challenging problems. This contrasts with methods in which students learn a set of problem types and associated formulas, and must choose the right formula or sequence of steps for each problem. AVE feels that such methods encourage rote, temporary memorization, rather than a long-term permanent understanding. AVE also avoids the more extreme version of this method, in which the student learns to identify the problem type and execute a set of calculator steps. Despite its numerous innovations, the Curriculum is markedly traditional in many ways. Mathematical proof forms a significant part of the study of algebra, geometry, and calculus. Secondly, calculators are not used at all until precalculus, and even then are used extremely sparingly. This reflects the Curriculums goal of developing problem solving skills and a strong mathematical foundation. Third, the bottom up approach is drill intensive at times. The somewhat popular belief that a student of mathematics has only to learn the "big picture", and that facility with basic methods is not necessary, is not one shared by AVE. The relationships and patterns associated with more fundamental parts of math are similar in important ways to those associated with higher levels of math. Adding numerical fractions are similar in obvious ways to adding more complicated. Additionally, students insufficiently comfortable with basic fundamentals may not be able to thoroughly understand more advanced topics. Instead of developing a complete understanding of the topic, students may end up memorizing enough formulas and rules of thumb to get by. Finally, students who have not integrated basic principles and formulas into their understandings may be overwhelmed when they see problems that require the simultaneous use of several of these. A student who does not know basic area formulas may find a problem that requires the using interconnections between area formulas and the Pythagorean theorem to be completely overwhelming. Such a student would be forced to consciously hold all these formulas in his conscious mind while attempting to solve the problem. The difficulty he would face would be akin to the difficulty of memorizing three separate phone numbers while mentally subtracting two large numbers. One concern shared by many excellent educators is that if math is made too easy, talented students will not be challenged. Thus, their problem-solving and reasoning skills will not develop as much as they could. AVE shares this concern. Because the Curriculum introduces advanced topics much sooner than other curricula, students have to struggle. However, rather than struggling with topics made artificially difficult, they struggle with topics intrinsically difficult. A related concern is that a student's cognitive development may not be ready for advanced topics. This concern is also shared by AVE, and is addressed in two ways. First, methods are used to accelerate the development of cognitive skills necessary to study advanced topics. Secondly, the manner of presentation is at times adjusted to allow younger students to learn more advanced methods. The former method is generally preferred; when the second method is used, the topic is revisited when the students' cognitive skills are appropriately developed. You may also want to consider: Curriculum X |
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