All of
Carlos’s current tutoring subjects are listed at the left. You
can read more about
Carlos’s qualifications in specific subjects below.
Algebra 1
The first steps in Algebra are very important for the young student. She/He has to develop precision and clear concepts before the subject becomes tangled and confusing. Replacing numbers with letters, which is what algebra is about, confuses some students a bit. Clear concepts and careful explanation of the procedures are the key to a successful ride in further mathematics.
Algebra 2
Algebra is the language of science and modern technology. The student will learn to think precise and strait thoughts. Not guessing here.
Work problems are scary to younger kids, but they should not be. Formulae and calculators should become familiar to the student and the student must feel comfortable with their usage.
Some new concepts must be explained carefully and accurately before attempting to solve problems.
My students say that I explain concepts in an easy to understand manner.
Calculus
Calculus is my favorite math. Abstract concepts and relationships are used with numbers and graphics, which make them easy to understand. Derivatives and integrals become part of your life.
Any modern technology or science will require a strong basic calculus knowledge. Be ready to handle curves and graphics with equations and formulae.
I taught calculus at La Roche College for over ten years and the students say I explain tough concepts in an easy way to understand.
Civil Engineering
Carlos is a professional civil engineer (PE) certified in Pennsylvania and in New Jersey. He graduated with a M.S. from the University of Illinois, Urbana in 1969 and he practiced environmental engineering design with various firms in Pittsburgh and also in Colombia, designing roads, landfills, water and sewage treatment plants. Now Carlos has retired from the profession, and he taught civil engineering at the U. of Pittsburgh in Johnstown for six years.
Elementary Math
I teach all kinds of math, but teaching the elementary requires patience and love of the subject matter.
The initial steps into math are very important and the basic concepts take some doing to get them clearly. My father taught me the basics and I love math since. Let me try introducing your child to this marvelous knowledge that is mathematics.
ESL/ESOL
As a foreign born individual,
I experienced and recognize the difficulties of learning a new language. I know the pitfalls and
I am very patient with my students. But be positive !, English is NOT a difficult language: grammar is easy, and the vocabulary relates to many other languages. Besides you will be using it very frequently, right? Actually you are using it right now... ha ha ha
GED
Carlos have taught High School Spanish and mathematics. He has helped many students with homework, and math problems. Carlos is very patient and understand the difficulties that students have in certain subjects.
Geometry
Geometry is a good subject for "visual" persons. Every concept and formula is drawn in lines and curves. Most people come to like geometry because of that. But you will find some formulae hard to use and tricky.
The maths of geometry is not difficult and a calculator, graph is better but not required. will be very helpful. Quad paper is also helpful.
Physics
Physics is an interesting study of the laws of nature in the physical world. The laws are very precise and are followed by formulas and applications to real life. A strong background in mathematics is very important. As an engineer, Carlos can explain the applications of those rules to real life and to practical uses.
Prealgebra
All you can prepare for algebra is useful.
You will have to think in abstract concepts, but they will help you in science and technology. Algebra will require precision, and ability to use your calculator correctly.
Using letters instead of numbers will become easier as you prepare for advanced algebra.
Precalculus
Pre-calculs is advanced algebra with some trigonometry and initial theory of limits... many new concepts that need to be explained.If you have a "math" mind you will love it. Trigonometry is the theory of triangles and angles and a calculator will help a lot. I know you will enjoy it.
Carlos
Proofreading
Proof-reading is a patience job. If you know other languages, like I do, you realize that each language has its own nuances and that each language's grammar differs in details. It takes patience and detailed knowledge to proof-read a paper, particularly if it is a technical writing.
SAT Math
For the SAT exam in mathematics you have to know the material, but you better know the techniques for timing, fast thinking, and tricks of solving problems.
I am in the process of getting a certificate as instructor for the SAT students. I do not deal with the essay part, only with the maths of the SAT. I have reviewed tens of exams and read books on the subject. I know I can help you prepare for it.
Spanish
Spanish is my language, I learnt it from my mother and my father, they did not speak anything else. I do have a degree in Spanish literature and I taught Spanish at La Roche College and to grade school students.
I love my language, Spanish is NOT an easy language, but as a Romance language it is very musical and it is becoming popular in the United States.
Statistics
Statistics is not a difficult subject, but it requires new ideas and concepts like: standard deviation, hypothesis testing, probability curve, etc. Those need to be explained carefully.
The math requirements are not hard and a decent calculator will be very helpful.
I taught Stats at La Roche College for over ten years and my students liked the way I explained the new concepts and the use of formulas.
In any modern science or technology, Stats become very useful. Take stats seriously and you will be ahead.
Trigonometry
Trigonometry is the science of angles and triangles. It is a little abstract because it deals with relationships between angles and lines in the trigonometric circle.
Surveyors and engineers use trigonometry all the time. A lot of formulae and tables, with frequent use of calculators. For electricity studies trigonometry becomes a second nature.
I taught trigonometry at La Roche College for over ten years. My students say I explain concepts in an easy to understand way.