AVE's Integrated SAT Math Curriculum
Imagine a school in which all students excelled at math, in which 750+ SAT math scores were the norm, and in which virtually every student scored above 700 on the SAT math section.
Letís take this up a level. Imagine that the school had no unusual admissions requirement. Imagine that the school could make average and even below-average students gain outstanding SAT math scores and excel at math in school. A school with that ability would have a dramatic advantage over its competition.
|Ensures that 100% of students master fundamentals.
||Many students end up with significant gaps in their fundamentals.
|All students develop problem solving skills necessary to solve the hardest SAT probems.
||The most advanced students develop these skills; the rest do not.
|Integrated across years, to ensure systematic skill building. For example, 7th grade teachers correctly develop skills to allow students to later succeed on the SAT and on more advanced courses.
||Not well integrated across years. For example, 7th grade teachers may teach shortcuts that could have negative impacts later on.
|Every single student will be ready to gain an outstanding SAT math score.
||Many students will lack the necessary problem solving abilities.
It is hardly surprising that few schools have integrated SAT math training into their math curriculum, and for good reason. After all, would any self-respecting math teacher willingly teach the inefficient gimmicks that comprise standard SAT training methods? Would any serious algebra teacher teach students techniques like “plug-in” and “backsolve”, which only encourage students to use inefficient gimmicks instead of direct algebraic techniques? Would any rigorous precalculus teacher focus on process of elimination, rather than direct solutions?
AVE’s Integrated SAT Math Curriculum (ISMC)
In reality, these over-hyped techniques are not actually the most effective. Instead, they are generally the easiest to teach, and allow mass market companies to use inexperienced staff and even college students, rather than professional educators.
The most effective methods actually involve direct algebraic solutions, strong mathematical reasoning, and creative problem solving. In short, the most effective problem solving methods for SAT math problems embody everything that an excellent math education strives for. Examples of SAT problems with AVE’s solutions are included in the free sample of SAT Math Cognition.
AVE’s Integrated SAT Math Curriculum systematically develops students cognitive abilities and knowledge base, allowing them to succeed on the SAT.
Integrated Curriculum Enhancements
The following is an actual SAT problem (source: College Board’s 10 real SAT’s)
x-y=5 Find x+y
The solution is to factor the first equation to get:
Then substitute 5 for (x-y) to get
And then divide by 5 to get
(x-y) = 2
Although factoring and substitution are standard parts of every math curriculum, most students do not get the above problem right. Although students are familiar with the techniques, the style of thinking used to solve the problem is unfamiliar.
The Integrated SAT Math Curriculum (ISMC) addresses this lack by incorporating specific SAT challenge problems into the existing curriculum. Soon after students learn a basic math concept, they practice it on advanced SAT problems, solidifying their understanding and developing their problem-solving ability.
Additionally, the Curriculum contains several modules that are added to your school’s curriculum. These modules cover such methods as termwise comparison to calculate the difference of two series and combinatorics.
There are often many ways to solve a specific math problem. For example, students can learn addition and subtraction of negative numbers by remembering the rule that two negatives equals a positive, or they can use the “leave, change, change” method. Students can learn to multiply binomials using distribution, or they can use the FOIL acronym. They can learn to solve percent problems using ratios, or by directly translating English statements into mathematical statements.
While all of these methods work, they are not all equal. The more effective and flexible methods can be effectively applied to increasingly difficult problems. They can be seamlessly integrated with other methods to approach complex problems. Ineffective methods, on the other hand, turn into cumbersome and limited formulaic approaches.
The ISMC adjusts the existing curriculum to ensure that every method taught is the most flexible and rapid method available. With each critical math step done with maximum efficiency, students are able to more rapidly and effectively solve challenging SAT math problems.
Responsive Diagnostics and Failsafes
Certain math topics are not essential for effective development of mathematical cognitive abilities. For example, a student who forgets Descartes’ rule of signs will still be able to solve most types of math problems. Practically speaking, the only math problems he will not be able to solve are the ones that specifically deal with Descartes’ rule of signs.
However, other techniques and modes of thought are absolutely essential for effective development of mathematical ability. A student who forgets the laws of exponents or is unable to use the principle of substitution will have severe deficiencies in his problem-solving abilities. There will be many problem types he will be unable to approach and solve.
The ISMC uses Responsive Diagnostics to ensure that students thoroughly master these concepts. Responsive Diagnostics differ from standard tests in that the Diagnostics immediately address any key areas of weakness. A standard test may detect weaknesses, but rarely addresses them sufficiently. AVE’s Responsive Diagnostics address any issue immediately. For example, a student who misses any factoring problem immediately goes through a process to ensure that he masters factoring. The system ensures that every single student, without a single exception, masters the key fundamentals.
As every math teacher knows, strong math students are not the ones who memorize the greatest number of formulas. They are the ones who most effectively understand and apply fundamental concepts. AVE’s responsive diagnostics ensure that every single student masters each fundamental concept.
Building Foundations Across Grades
The Integrated SAT Math Curriculum works across grades, emphasizing critical elements and adding elements that might be missing. By making teachers in lower grades aware of which elements will be most critical to success in advanced math classes and the SAT, the Integrated SAT Math Curriculum
For example, integer division with remainders is one of the cornerstones of SAT math (and of number theory and abstract algebra, for that matter). However, many elementary school teachers view division with remainders as merely a prelude to division with decimal answers. When teachers are fully aware of the importance of this process, they are better prepared to train students accordingly.
The ISMC builds upon this principle by reinforcing these key concepts across grades. Responsive Diagnostics incorporate these elements, so that students practice and thoroughly master these fundamental skills.
The same principle applies in high-school math. By emphasizing the importance of key concepts like factoring, substitution, combinatorics, slope, and fractional exponents, teachers in lower grades help ensure the success of their students in advanced math courses, the SAT, and in college.
Shifting to a Problem-solving Mode of Mathematics
Some people view mathematics as a process of learning and applying formulas. As any math teacher knows, real mathematics is something different. It is a creative process that involves cleverly combining concepts to approach and solve a problem.
To succeed on the math section of the SAT, students must approach math from a problem solving perspective. In other words, knowing formulas is simply not good enough. Students have to be able to cleverly figure out how to approach and solve novel problems.
The ISMC develops this skill by repeatedly exposing students to novel challenge problems. These problems follow a systematic pattern of difficulty that helps students develop mastery over various approaches.
Because the ISMC rigorously develops the cognitive skills associated with math in general, not just with SAT math, the benefits to students are not limited to SAT performance. Instead, students mathematical ability increases with respect to algebra, geometry, calculus, and college math courses.
Fees: Integrated SAT Math Curriculum: $75,000
- Diagnostics & Curriclum Review
- Initial Presentations to Students, Faculty, and Parents
- Curriculum Materials, Including Failsafes, Challenge Problems, and Training Modules
- 2 Day Faculty Training Program
- Upgrades for 3 years
For more information or to schedule a free initial phone consultation, please call 301-320-3634.
- Exclusivity Agreement: An institution using the Integrated SAT Math Curriculum has a significant advantage over competitor institutions; in many regions, this advantage represents significant economic value. Exclusivity agreements for up to 10 years can be purchased, with fees based on the number of competitor institutions and length of term.
- Standalone SAT seminars: In the Washington, DC area, AVE offers standalone SAT seminars. The standard SAT seminar runs 6 weeks, 4 hours per week. Fees are based on number of students and length of the seminar. For example, a 6 week, 4 hours per week seminar for twenty students would cost $20,000.
You may also want to consider: AVE’s Teacher Training Seminars; Curriculum X
For more information or to schedule a free initial phone consultation, please call 301-320-3634.