When preparing my students for the SAT exam I always start by developing an individualized plan. The key is to identify the weaknesses in material knowledge as soon as possible and ensure that all those gaps get filled before the test date. I also teach SAT specific problem solving techniques and time management skills.
Hiring a private tutor for the SAT preparation is probably one of the best investments for parents. High SAT math score brings the student a step closer to getting accepted to top colleges as well as receiving a scholarship.
The GRE test requires knowing less material than the SAT test, and you are allowed to use the calculator throughout the whole quantitative section, so it seems that it should be easier to pass the GRE versus the SAT test, however many students, especially those who are in the humanitarian field, tend to avoid math classes in their college years, and therefore pretty much forget everything by the time the need to apply to grad schools.
It takes patience and persistence on the side of both the student and the tutor to review the material studied in the past, as well as to get the hang of the new types of the problems that quantitative section on the GRE favors.
High school topics often include: quadratic equations, polynomials, graphs of the functions and inequalities, geometry with formal proofs, introduction to trigonometry, probability and statistics, limits and derivatives. Many of these concepts can seem abstract to the student and this perception makes it difficult to comprehend new topics.
I believe the key is to bring as much concreteness as possible to any given topic. With my students I always use real life examples and applications. I also believe that the only way one could check if the student truly understands the concept is by presenting the material in a different and non-conventional form.
Middle school is the time when the students become comfortable with fractions, decimals, percentages, negative numbers, inequalities, basics of geometry. They get a taste of linear equations and start using mathematics to solve real world problems of higher significance than before. This also happens to be an extremely important habit forming period.
Helping to develop structure in the mathematical solutions is one of the greatest gifts a tutor can provide to a student of this age. I always encourage all of my students to label their work correctly and be organized in their solutions. As problems will get more and more complicated, this would become an extremely value skill.
I have worked with all kinds of students at the college level. Students varied from those who chose mathematics as their life-time passion to those who would never use a single formula after they have passed their mandatory pre-calculus class. Obviously the approach is different with every single student. Some just need a guide and a knowledgeable companion on their mathematical adventure, others need a tutor who motivates them to get more than just a passing grade in their math class.
All those experiences are differently rewarding and I cherish them all. As I always say, individuality matters! Thus I adjust my approach for every single student.
I love mathematics competitions! I have spent my whole childhood participating in them and they have always been extremely entertaining for me! I enjoy working with kids who feel the same way about math competitions. I like to use the Art of Problem Solving books with my students as the main guide, and then I supplement with additional materials upon need.
Surrounded by a vast number of educational methods one often wonders which would be the best in the teaching process. And while I enjoy having many tools at hand to assist me, I have found that no approach works for all the students. I often remind myself of Maria Montessori’s thoughtful advice to “follow the child”. Often it’s better to take time to observe the child and identify their genuine interests in order to be able to adjust the teaching approach accordingly. I believe that the teacher’s goal shouldn’t be to take away students’ freedom and turn them into submissive followers, but to let them be free in expressing their genuine interests and finding ways to incorporate math into activities of their own pursuit. One would be amazed to find that use of math can be found in pretty much everything.