Ralph’s current tutoring subjects are listed at the left. You
can read more about
Ralph’s qualifications in specific subjects below.
The ACT, a college admissions test, was developed as an alternative to the SAT. In contrast to the SAT, the ACT focuses more on knowledge rather than reasoning. There are five sections to the test: English, Reading, Math, Science, and Writing. The writing test is optional.
Algebra has changed in recent years. It is no longer a course about solving equations; it has become a course in functions. This can be approached as a discovery project, a computer based visual learning program, a tactile course taught with manipulatives a traditional textbook based approach or a combination of any of these.
Algebra 2 expands on the topics covered in algebra 1 by focusing on symbolic reasoning. We study functions, equations, and their relationships. We examine the relationship between algebra and geometry. We examine the underlying mathematical processes in a more formal way than was previously done in algebra 1. All of this is done to prepare the student to move on to the study of precalculus and statistics.
I have taken undergraduate courses in discrete math and graduate courses in number theory. Some of my other graduate courses included some topics in discrete math. My graduate GPA is 3.9.
I took 4 semesters of undergraduate linear algebra which included my 2 semester senior series. I have taken two more graduate courses in linear algebra. My graduate GPA is 3.9.
For 10 of the last 15 years, I have taught a course in elementary logic at UHD.
In prealgebra, we start to look at the structure of arithmetic. We analyze the decimal system, break numbers into their prime factors, formalize operations with fractions, decimals, and percents, and start to learn proportional reasoning. In addition, we begin to work with variables to prepare us for algebra.
Precalculus is the study of functions as a preparation for calculus. The course focuses on polynomial functions, rational functions, and trigonometric functions. Once the basic functions have been introduced, the various transformations of the functions are studied.
Unlike the math ACT, which is a test of specific learning objectives a student should have mastered in high school, the math SAT is a test of reasoning ability. Because of this, it is necessary to understand the logical foundation of mathematics in order to do well on the math SAT. Mathematical logic starts with the "common notions" of Euclid's geometry. From there, each branch of mathematics has its own axioms or postulates and develops its theorems according to the requirements of the material being studied. This is an approach to learning and organizing information which the math SAT seeks to measure and which students can learn to emulate.
Statistics is different from any other math class. There is a lot of writing and describing in statistics. Often, instead of one right answer, there are a range of possible or plausible answers. At its heart, statistics is a way of reasoning along with a set of tools and methods that help us understand the world. For most students, it is a new way of thinking.
I have prepared Texas students for standardized testing since the program began. I have prepared students for TABS, TEAMS, TAAS, and now TAKS. I have experience with students from 8th grade through exit level. I attribute my success to an intimate knowledge of the SE's (student expectations specified by the state of Texas). The TAKS pass rate for my students in the last few years is near 100% In addition to the traditional workbook approach I am able to use a variety of manipulatives and technologies to enable students to succeed.
Trigonometry started as the study of triangles. However, it has grown to be much more than that. The unit circle approach allows us to calculate distances and areas that would be very difficult or even impossible to calculate without trigonometry. Trigonometry forms one of the foundation stones of calculus and has many applications is engineering.