There are probably a few gifted math students in your school. They always do well in math, even though they often seem to work less than others, and hardly study for exams. It is almost as if they see math totally differently, and that gives them some kind of special advantage.
As it turns out, these students do see math differently, and that actually does give them a special advantage. But the good news is that the skill that gives them these advantages is one that you can learn.
AVE teaches you to look at math like an excellent student. In fact, the system that we use ensures that your brain will do just that. In other words, AVE will not just tell you how to perceive a problem. Our methods will make absolutely 100% sure that you are perceiving it that way.
Our progressive math training program is intense, and it can be challenging at times. But you will never see any busywork or pointless assignments. Every challenge will be designed to directly benefit you, and to improve your math skills.
Our programs can either help you succeed in your school courses, or can work independently of your school. In fact, many of our advanced students cover the entire course in the summer before. For example, they cover calculus at AVE during the summer before they take calculus at school. Not surprisingly, they end up doing extremely well.
Fees: $200/hour. Initial Consultation: Free.
For more information or to schedule a free initial consultation, please call 301-320-3634.
You may also want to consider: The Equation for Excellence; SAT Math Cognition
Frequently Asked Questions
Does the Curriculum affect all of AVE's math tutoring?
To some extent, the Curriculum affects all of AVE's math tutoring. However, when tutoring is used to help a student with a specific school class, the effect is less pronounced than when math is studied independently of a school class.
If students move too quickly, is there a danger that they will not retain fundamental information?
This was an issue during the earliest stages of development of the Curriculum. Later versions took this into account, and incorporated continual review of fundamentals. The current version places a heavy stress on fundamentals and reviews them repeatedly, ensuring that the student will retain and integrate them appropriately.
Is the curriculum appropriate for home-schooled students?
Although it is often combined with school education, the Curriculum is designed to stand on its own. Thus, it is appropriate for home-schooled students.
Is there a danger that the student will learn the same thing in two different ways if he or she is taking a similar math class in school?
The Curriculum may approach a topic differently than the student's school. If the school's method is effective, the Curriculum may be adjusted to incorporate the school's method. However, if the Curriculum's method is significantly more beneficial to the student, the student will probably learn the same material from more than one perspective. In most cases, an additional perspective is beneficial when approaching a math problem.
Is the Curriculum the same for every student?
Methods of presentation are generally tailored to the student, and order of presentation may be varied. Content varies less, though it may vary in unusual situations.
Additional Information for Education Professionals
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 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.