As competition becomes increasingly global, many American schools are closely examining their educational methods. Since mathematics education is such an important part of developing the cognitive abilities of a students, it has received particular attention from many educators. AVE offers guidance for schools who wish to enhance or redesign their current curricula to give their students an advantage over their international peers. The curriculum development process seeks to meet the particular needs and goals of each individual institution. Although the process varies significantly in terms of both scope and method, much of the process is informed by the Arvin Vohra Accelerated Math Curriculum and related research.
Since its introduction in 2004, the Arvin Vohra Accelerated Math Curriculum has dramatically influenced AVE's mathematics teaching and tutoring strategies. The Curriculum increases the speed and rigor of mathematics education using a perspective that places the cognitive development of the student above all other concerns.
The 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 an 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.
AVE's Mathematics Curriculum Development process ranges from subtle adjustments to existing curricula to complete redesigns. Pricing depends on the level of service requested.
Frequently Asked Questions
Can the Arvin Vohra Accelerated Math Curriculum be used to prepare students for the AP Calculus exams?
Preparation for the BC calculus exam is built into the standard form of the Curriculum. Preparation for the AB calculus exam can also be incorporated.
What levels of mathematics does the Curriculum cover?
In its current form, the Curriculum covers topics from Algebra I to Advanced Placement Calculus BC. The Curriculum can be extended to include the fundamentals of Multivariable calculus. AVE is currently developing a version of the Curriculum that will extend into abstract mathematics.
How much faster does the Curriculum allow students to progress?
The Curriculum can allow most students to progress at twice the standard rate in algebra, precalculus, and calculus. Depending on the nature of the current Geometry class, the Curriculum will allow students to progress at between one and a half and two times the current rate.
In what ways does AVE use the Curriculum?
The Curriculum forms the foundation of the Fundamentals of Calculus and Fundamentals of Algebra classes. It strongly influences the mathematics portion of the Advanced SAT Seminars. Finally, it is used in all aspects of mathematics tutoring.