301-717-8224 / ray.dykeman@gmail.com
Math
Middle School Math
Many students who excelled in elementary school suddenly lose confidence when mathematics becomes more abstract. Ray helps students make that transition successfully by building genuine understanding and confidence, giving them the foundation they need for success in algebra and beyond.
Algebra
Algebra is the foundation for nearly every advanced mathematics and science course that follows. In a fast-paced classroom, there is often little time to explain not just how the mathematics works, but why it works. Ray carefully breaks down each topic so that students understand the reasoning behind the formulas and procedures they use. That deeper understanding builds confidence and provides a solid foundation for success in geometry, pre-calculus, calculus, chemistry, physics, and beyond.
Geometry
Geometry introduces students to a new way of thinking about mathematics. Success requires them to connect algebra, logic, spatial reasoning, and formal proofs in ways they have not encountered before. For many students, this transition can be challenging.
Some students also find it difficult to visualize geometric relationships or mentally manipulate figures in space. Ray is particularly skilled at helping these students develop the visual and spatial reasoning skills needed to understand geometry, write proofs, and apply mathematics with confidence.
Pre-Calculus
In pre-calculus, students face many challenging subjects including applied trigonometry; two- and three-dimensional vectors; sequences and series; exponential and logarithmic equations and more. These concepts can be intellectually challenging even for strong math students, and rightly so. It is in pre-calculus that the work of the math greats appears. Students are asked to grapple with and apply math developed by Gauss, De Moivre, Euler, Fermat, Pascal and others. Ray helps his pre-calculus students to understand and appreciate the richness and power of mathematics in terms of both the intellectual challenge and its applications in science, technology, economics and much more. Pre-calculus is the foundation for calculus and advanced engineering mathematics. Mastery is especially critical for any student who plans to further pursue math, science (including environmental science and medicine), engineering, or economics. Ray helps his students to understand and integrate this important branch of mathematics.
Calculus
Calculus is often the course that determines whether students continue toward engineering, physics, mathematics, economics, or medicine. Ray helps students see the relationship of calculus to the real world and develop a deep conceptual understanding that allows them to solve challenging problems with confidence.
Science
Biology
Biology requires students to master an enormous amount of information while also understanding how living systems function. Today's courses often include a significant amount of biochemistry and molecular biology, making the subject more conceptually challenging than many students expect.
Ray helps students organize this information into a coherent picture so they understand how the concepts fit together rather than trying to memorize isolated facts. That deeper understanding makes the material easier to learn, easier to remember, and much more meaningful.
Chemistry
Chemistry is unlike any science most students have studied before. It is based on the behavior of atoms and their subatomic particles, which obey physical laws that cannot be seen in everyday life. Because of this, many students struggle to develop an intuitive understanding of the subject.
Ray is particularly skilled at helping students understand not only how chemistry works, but why it works. For example, the Periodic Table is not simply something to memorize. Its organization, the properties of the elements, and the periodic trends all arise from the underlying structure of atoms. Once students understand these fundamental ideas, they can often predict chemical behavior instead of memorizing it.
Chemistry also requires strong problem-solving skills. Ray helps students develop the reasoning and analytical skills needed to solve problems with confidence.
Physics
Physics is often the most mathematically demanding of the sciences because students have to learn to translate real-world situations into mathematical models. Success requires much more than simply knowing equations. Students have to analyze a problem, identify the important physical principles, and draw a diagram that clearly represents the important features of the physical situation.
Ray teaches students a systematic approach to solving physics problems. He helps them identify the relevant quantities, understand how vectors and other physical quantities are related, apply dimensional analysis to check their work, and use mathematics to understand and predict the behavior of the physical world.
Organic Chemistry
Organic chemistry is often considered one of the most challenging courses in the sciences. Success depends on a solid understanding of the fundamental concepts introduced in general chemistry. Ray helps students build that foundation first, giving them the confidence to tackle more advanced topics.
With those fundamentals in place, Ray helps students master nomenclature, structure, reaction mechanisms, resonance, stereochemistry, and multi-step synthesis through careful explanation and systematic problem solving.
Standardized Tests
MCAT
The MCAT is one of the most demanding standardized examinations, requiring mastery of biology, biochemistry, chemistry, physics, psychology, critical reasoning, and scientific problem solving. Ray enjoys helping students develop both the scientific understanding and analytical skills needed to succeed on this exam. He helped to develop Princeton Review's first set of MCAT materials, and taught MCAT prep classes for the company. His students averaged close to 3 point gains in these classes. When he took the test himself, he scored a perfect 15/15 on the Physical Science section (99.9th percentile) and 12 on the Biological Science section (95th percentile).
AP Biology, Chemistry, Physics
Most students taking these tests work with Ray throughout the year, and so have a solid foundation going into the test. As the test approaches, Ray helps both new and long term students to focus on the test itself. Ray provides a comprehensive review of the material, and works with practice tests and problem solving as necessary to ensure that students are well prepared for this important test.
ACT & SAT
Ray helps students master the mathematics tested on both the ACT and the Digital SAT. For students taking the ACT, he also develops the mathematical reasoning, graph interpretation, and scientific analysis skills needed for success on the optional Science section.
Have questions, or ready to get started? Call me at (301) 717-8224 or email me at ray.dykeman@gmail.com. I'd be happy to discuss your goals and how I can help.