Algebra is the subject that generalizes the principles of arithmetic and other areas of math. The rules that apply when all the numbers are known still apply when some of the numbers are missing.
One benefit of the study of algebra is that a student learns to take specific information and use it in new ways. This skill applies to areas outside of math, and it is part of the reason why the study of algebra is useful to students who do not plan to go into math-related fields.
While the distinction between algebra 1 and algebra 2 is an artificial one, algebra 2 picks up where algebra 1 leaves off.
As a student gains skill in algebra, they experience the benefit of creating processes for commonly-repeated tasks. This experience is useful even for students who will not be working in math-related fields.
My approach to algebra 2 is designed to make the study as useful as possible to students in the long term, while encouraging the best current results in their classroom and testing experience.
I received a certificate of graduation from Fairwood Bible Institute, a three-year Bible school in Dublin NH. Five years after graduation I participated in a one-year program offered to graduates. This program was divided between classroom and fieldwork. The fieldwork included youth ministry and teaching Sunday School, among other things.
In addition to my Bible training, I have extensive experience in on-on-one tutoring, Bible-study leadership, expository Bible study articles and public speaking.
My knowledge of the Bible is deepened by the fact that I have read it through approximately ten times.
Calculus studies the quantities that are related to change. If algebra and trigonometry are tools, then calculus can be thought of as a maker of tools. Many formulas that are used by students from an early age were created using calculus.
While only a small percentage of students will use differentiation and integration in their career, those who don't will also benefit from the study of calculus. This is because calculus gives the student practice with solving challenging problems, which is applicable in any career. Students learn to analyze problems, identify solutions, modify solutions that worked for other problems, and create new solutions independently.
Elementary math provides a foundation for all other mathematical concepts and principles. Because of this, it is important to be sure that students have an intuitive understanding of the processes and rules that they learn.
My approach to elementary math provides this intuitive understanding along with the practice that allows them to become fluent in the processes of arithmetic.
By definition, geometry is the study of shapes or three dimensional objects. As a part of this study, students learn definitions, theorems, postulates, and proofs.
While not every student will use these things in their future career, there is a more general skill that should be of use to any student.
The study of geometry provides practice with the skill of strict logical thinking, and the ability to organize small pieces of seemingly-disconnected information in a way that allows them to solve complex problems.
As a defined area of study, prealgebra provides a bridge between arithmetic and algebra. It is the point where students have to begin to grasp concepts that are more abstract.
Whole numbers, fractions, and decimals are easy to represent with objects, along number lines, or in the real world. Negative numbers, roots, and radicals are slightly more difficult, but they can be represented visually or with metaphors. My approach includes these representations as students begin to make the transition into the abstract.
Abstract thinking is a skill that has countless applications for students after they graduate. Every time they need to think about something without seeing it, they will be engaging in abstract thinking.
Precalculus is a sort of bridge course that is offered in some schools and colleges. It provides a way to transition from advanced algebra and trigonometry into calculus.
Typically precalculus will review topics such as logs, exponentials, limits, sequences and series, and functions. As such it can seem dry to some students. The concepts are very abstract, and they haven't had the opportunity to see them in application in calculus itself.
My approach to precalculus includes some illustrations that will help to see more of the "why" of some of these concepts.
Trigonometry is by definition the study of triangles. That said, the applications that arise from the study of trigonometry go far beyond three-sided geometric figures. The motion of springs and pendulums, as well as the changing voltage of alternating current can all be quantified using trigonometry.
While there are many careers that do not use trigonometry directly, there are skills that are learned in trigonometry that can be applied in a wide range of ways. One example is that trigonometry provides experience in looking at one problem from a wide range of perspectives. This is a skill that is useful in any profession.