Algebra 1
Algebra in primary and secondary schools is often divided into two classes meant to nurture development from the concrete mathematics of arithmetic accounting towards an abstract understanding of the behavior of mathematical concepts including numbers, operations, relations, and functions. The student starting in algebra should be introduced to algebraic techniques as they relate to concrete problems that might be solvable through more cumbersome methods. Students will do well in algebra if they...
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Algebra 2
Algebra in primary and secondary schools is often divided into two classes meant to nurture development from the concrete mathematics of arithmetic accounting towards an abstract understanding of the behavior of mathematical concepts including numbers, operations, relations, and functions. The student in their second class of algebra should begin to use the algebraic techniques they have learned to form a coherent structure that explains the behavior of algebraic objects. Students will do well...
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Calculus
Calculus is the study of infinitesimal change. Unfortunately, the way most students approach calculus is to memorize rules and formulae which does not lead to a deeper understanding of the subject nor does it lend itself to a long term skill set that can be called upon to answer problems as they arise. I encourage students to develop a practical approach to calculus which emphasizes problem solving, practical reasoning, and a new way of thinking about the world to help them to truly master the...
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Chemistry
Chemistry is the science of atomic arrangements. I am not a chemist, but familiarity with basic chemical concepts of college-level introductory chemistry is a must for any physical scientist. I have taught basic chemistry at the high school and community college level.
Vocabulary
How does one best learn vocabulary? The best way to learn vocabulary is to learn language and word etymology in depth. The champion spellers already know this trick and have extensive (if not fluent) understanding of Latin, French, German, and Middle and Old English antecedents of many words. This helps with being able to identify the meanings of words that are new to the reader or the listener.
However, the other aspect to vocabulary is simply having a familiarity and ease with obscure...
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Grammar
Grammar is the study of the structure of languages. There are many approaches to this subject, and a serious investigation would generally require a person with a degree in linguistics or a related field. However, in terms of the English language, many of the rules and stylistic guidelines for grammar follow a kind of logical consistency that can be likened to mathematics. Occasionally, some who are overwhelmed by grammar are experiencing something similar to math phobia. That's the approach I...
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Microsoft Excel
Microsoft Excel is software that functions much like all other spreadsheet software. Most students who are having difficulty with the program are either unfamiliar with the program itself and computers in particular, or have not sufficiently learned the concepts underlying spreadsheets and data analysis, or both. I can work with students needing help in any of these areas.
General Computer
Astronomers work most of their lives with computers. We are not computer scientists, but we use the machines to complete onerous and repetitive calculations for our theories and models as well as to complete complicated data analysis. I take the approach when helping people learn about computers that the easiest way to learn to use a computer is to get to understand its functionality bit by bit.
Geometry
Geometry is the application of mathematical concepts to spatial relationships. A rather extensive amount of mathematics can be deduced from geometry and there is a fundamental connection between it and algebra that is the subject of many higher level mathematical studies. Geometry's reliance on spatial reasoning gives it a unique position in the mathematical canon, so students who are struggling with the subject are often in need of building tools for understanding space. This is the general philosophy...
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Microsoft Word
Microsoft Word is a "What You See Is What You Get" word processing program that is fairly straightforward to use, but has many features that users may not know about. If you are curious about how to use the full functionality of Word to its greatest ability, I can help you explore and exploit capabilities of this program.
Physics
Students struggling with physics most often are having difficulty with the mathematics being employed. Physics relies heavily on mathematical descriptions because it uses the measurable quantities of space, time, matter, motion, and interactions to come up with the answers. The organizing principle for learning physics is the same as the answer "How do I get to Carnegie Hall?" -- "Practice. Practice. Practice." Those who receive tutoring from me in the subject can expect to practice solving problems...
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Microsoft PowerPoint
PowerPoint has become a ubiquitous presentation tool. Most people who need help with using the program are generally trepidatious of computers generally, but others have been told by colleagues, supervisors, or teachers that their presentations need to be improved. I'm willing to work with students in all these areas.
Prealgebra
Before students take a detailed study of algebra, most schools request that they take a course that emphasizes the important aspects of arithmetic and mathematical problem solving often dubbed "pre-algebra". This course is meant to bridge the gap between the concrete questions answered in primary school mathematical challenges to the more abstract notions and complexities that will present themselves in secondary school mathematics. My approach to this subject is to make sure that all the abstract...
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Precalculus
Often coupled with trigonometry, a course in precalculus is the inheritance of what was once the capstone course in secondary school education. "Precalculus" concepts include many ideas that didn't show up in other courses such as algebra and geometry but are absolutely vital for doing calculus. Ideas such as trigonometric functions, exponential functions, restricted domains, rudimentary set theory all set the stage for being able to appreciate the full import of calculus. Students should pay...
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Reading
Students learn to read by practicing. Effective one-on-one private tutoring with an reading coach who is willing to patiently help a student improve is one of the most effective ways to improve this skill. Students having trouble with reading in a classroom setting are often subject to anxiety over their skill level and this can hamper learning opportunities. Additionally, ineffective tutoring where students are given inappropriate prompts or are dealt with impatiently can also be a problem. As...
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Trigonometry
Nominally the study of the relationships found in reference to right triangles, the study of trigonometry rapidly expands to include concepts that spread from the mathematics of circles, oscillations, and even exponential relations. Understanding the character of trigonometry is vital for moving to more advanced mathematical concepts, and trigonometry is uniquely suited for solving advanced measuring problems and real-world applications in engineering, design, and surveying. Becoming comfortable...
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Writing
In spite of the proliferation of graphics, visualizations, and video that have come with technology, writing still remains one of the most efficient and effective ways of communicating ideas. To that end, writing is a skill that requires both literacy and craft.
Young students who first are introduced to writing usually find the organization of thoughts to be the most difficult aspect of the task. The youngest students who, after learning basic literacy, are asked to write will tend...
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Astronomy
I am an astronomer. I have taught all levels of the subject to all levels of students.
Statistics
In the social sciences, statistics is the dreaded "last course" in mathematics and the most onerous hurdle that many students face when hoping to pursue a career in such a subject. Unfortunately, the widespread aversion to mathematics and statistics has created a situation where quantitative methods are either treated as magic or are farmed out to the "quants" who charge exorbitant fees to tackle fairly straightforward problems. The best way for a student to come to terms with statistics is to...
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English
English is a terribly complicated language that has torturous syntax, arbitrary spelling, and a treatment of verbs that confounds even native speakers. Learning to communicate effectively in the English language requires careful study of the rules and the exceptions to the rules. Fluency is the most important rule of engagement and, to that end, my students of English are encouraged to approach the subject methodically and to pay careful attention to detail.
ESL/ESOL
English for speakers of other languages is best taught in an immersive environment where the student is encouraged to read, write, and speak in English with as many opportunities as possible. The approach to tutoring should be interactive and tailored to the needs of the individual student. Above all, continual practice with the language is what will ensure increased proficiency and comfort.
SAT Math
The SAT Math portion is designed to test students on all mathematical skills up to the traditional end point for college preparatory mathematics in the United States: a second course in algebra which deals with subjects up to and including polynomials and rational expressions while trigonometry and calculus are excluded. Some students will struggle with computational accuracy while other students will struggle with conceptualization or understanding the problems. I employ a simple method to helping...
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GRE
The Graduate Record Exams (GRE) are meant to provide a rough rank of the competence of potential graduate students. In my experience, students setting out to take the general exam who ask for tutoring often say that they lack the mathematics literacy that is meant to be obtained through a Bachelor's level college or university education. Most students looking to the take the GRE have had enough mathematics education but need the most help with the mathematics section. This portion of the GRE is...
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Proofreading
Being a good proofreader requires a keen eye for grammatical construction, common syntax and typology errors, as well as an understanding of style expectations and guidelines. I am willing to proofread manuscripts and papers in any and all subjects as well as help students hone their own proofreading skills. I tend to focus on clarity and comprehensibility as the most important aspects when editing.
GED
The General Education Development test seeks to summarize a secondary school education. This includes the subjects of Language Arts including reading and writing skills, Mathematics to the level of basic algebra and geometry, Social Studies including history, geography, anthropology, sociology, economics, and political science, and Science including basic concepts of earth, life, and physical sciences. Depending on the preparation of the student, tutoring can take the form of either a general...
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SAT Reading
My general philosophy about test preparation is that students should practice taking tests and then evaluate their performance to determine where their weaknesses lie. The SAT Reading Test is generally about reading comprehension and, as such, it is important that students practice reading short passages and answer summative, analytical , and evaluative questions about them.
SAT Writing
My general philosophy about test preparation is that students should practice taking tests and then evaluate their performance to determine where their weaknesses lie. The SAT Writing Test is divided into two parts: one a 25 minute essay and one a 35 minute multiple choice assessment of proofreading and editorial skills. Some students may find that they are better at one part than another; traditionally, test preparation has been more focused on techniques for improving scores in multiple choice...
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Physical Science
Physical Science is a catch-all term for the study sciences dealing with the non-living natural world. Thus, the subjects generally studied are geology, meteorology, astronomy, physics, and chemistry. My primary expertise is in astronomy, but having taught Physical Science at the Community College level for two years, I am familiar with the standards and outcomes expected for most introductory courses in the other subjects as well. Students needing help with Physical Science are often struggling...
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Geology
As an instructor of physical science at Harold Washington College, I taught students the fundamentals of geology as part of certain introductory courses in the subject. I will be able to help students who are struggling with introductory geology courses because of a lack of conceptual understanding of physical and chemical processes that govern the characteristics and changes of the Earth as a whole. As an astrophysicist, my perspective will be a bit more contextual than someone who is a straight...
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Probability
The study of probability is a very deep mathematical concept, but its basics can be explored by children in primary school. The topic begins as concretely as exploring the question of what happens when you flip a coin, but soon becomes very involved as conditions, assumptive priors, and elaborate formulae that let you decide what the chances are that certain events will or will not happen. People studying probability are most helped by having a strong conceptual basis for calculating what they...
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PSAT
Tutoring for the PSAT is usually done by those students who wish to become proficient enough to earn the distinction of National Merit Semi-Finalist, Finalist, or Scholar. As the competition for this has greatly increased over the years, it is important that a high-quality student hone their ability to perform to their utmost capacity on the exam. Tutoring for this examination should only be done for those students who are scholastically accomplished but need help in overcoming test-taking anxiety...
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SSAT
Many parents who are concerned about their child's likely performance on the SSAT are worried because they do not think the student has had enough exposure to a test-taking environment. This is a legitimate concern and can be rectified through administering practice exams. It is important that after these exams are administered, the student is given a chance to reflect on what was difficult and what was not difficult about taking the exam so that any areas that may need improvement can be identified...
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Spelling
As a subject, spelling is becoming as outmoded as handwriting, but there is a reason we still ask elementary students to learn to spell. Familiarity with how to spell words is important for future forays into writing. Even with spellcheck and autocorrect, students who learn to spell will be more efficient writers, have improved vocabularies, and, at the highest echelons, win scholarships to college.
Tutoring a student in spelling is generally a matter of first learning the particular...
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ACT Reading
My general philosophy about test preparation is that students should practice taking tests and then evaluate their performance to determine where their weaknesses lie. The ACT Reading Test is generally about reading comprehension and, as such, it is important that students practice reading short passages and answer summative, analytical , and evaluative questions about them.
ACT English
My general philosophy about test preparation is that students should practice taking tests and then evaluate their performance to determine where their weaknesses lie. The ACT English Test has three broad areas for which students should be prepared: usage, mechanics, and rhetoric.
ACT Math
My general philosophy about test preparation is that students should practice taking tests and then evaluate their performance to determine where their weaknesses lie. The ACT Mathematics Test should be doable by any student who has taken geometry and algebra in their high school education with some basic trigonometry. Emphasis for this test is on basic mathematical skills rather than advanced or abstract concepts.
ACT Science
My general philosophy about test preparation is that students should practice taking tests and then evaluate their performance to determine where their weaknesses lie. The ACT Science Test has three broad areas for which students should be prepared: Data Representation, Research Summary, and Conflicting Viewpoints, with emphasis on the first two sections. Students will benefit most from reading and interpreting highly regarded scientific journalism, introductory texts, and essays about scientific...
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Elementary Math
Mathematics is the exploration of how quantities relate to each other. Students usually find trouble in mathematics when they lose sight of its ultimate simplicity. The way to approach learning mathematics most effectively is to encourage a careful consideration of the problems that mathematics can solve. Once this is understood, students find the concepts and ideas to be nearly self-evident. That is the way not only to do well on examinations and homework, but to master the subject.
Elementary Science
Science at its core is about investigation. There is a certain vocabulary and understanding about the world that proceeds from scientific investigation, but ultimately students who are trying to learn science at an elementary level are best served by adopting an inquiry-based methodology and exploring the world through a systematic approach to collecting empirical knowledge.
Elementary (K-6th)
I have teaching certification from the Princeton University Teaching Preparatory Program where I worked extensively with issues in primary and secondary education. The major focus of Elementary (K-6th) education in this country (USA) is literacy, and it applies across all subjects. Typical issues in literacy are lack of facility or discomfort in reading and/or writing, fear of failure, and boredom. Students who are struggling with such issues related to literacy usually have underlying reasons...
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Study Skills
Students who are interested in improving their study skills are usually one of two varieties: 1) students who find they are distracted, unable to focus, or procrastinating or 2) students who have a hard time knowing what is important to study, what to focus on, and what to leave for later. I address these two different kinds of problems differently.
For students with the first problem, I will help them set-up a regimen and an accountability scheme to keep them focused on completing...
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Discrete Math
Inasmuch as I am an astronomer and a physical scientist, I rely on the tools and techniques taught in discrete mathematics on nearly a daily basis. Students needing help with discrete mathematics often have specific concerns and very particular topics with which they need help, and I usually try to identify these areas early on to focus on them. Many of these other related areas of mathematics can be found in my profile including, algebra, calculus, computer science, differential equations, geometry,...
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Differential Equations
As a scientist, I use differential equations as models in many different contexts, and, from experience, I believe that the best way to approach learning the topic is to look for applications rather than memorize the cookbook. While there is also pure math interest to consider in courses on differential equations, most of the students who will want tutoring in this subject are going to be most interested in the applications, so that is most often where my pedagogical emphasis will lie. These days,...
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College Counseling
Having been involved in higher education at all levels and in a wide variety of environments—from large public universities to small liberal arts colleges to the elite private universities to local community colleges— I generally have found that students thrive in the environments where they are most comfortable. An effective guide for college choice takes into account the needs and abilities of the students, the goals of the education, the expectations of cost, and the likely outcomes. Getting...
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ADD/ADHD
I have worked in the past with students who suffer from medically diagnosed and undiagnosed conditions that are associated with a lack of concentration or attention deficit as well as children with hyperactivity disorders. There are a number of methods that I use to help such students. One method is to make sure that study areas are free from distractions, that the space is organized, and that the tasks are clearly laid out and the goals are reachable. Students with attention deficits are usually...
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Aspergers
I have worked in the past with students with Aspergers. Such students are generally extremely motivated in certain ways while occasionally struggle in areas that they find less interesting or more challenging. Tutoring the student with Aspergers generally requires finding a way to engage with material that is slightly outside of the comfort zone of the student and making gradual progress toward engaging the uncomfortable environments or material. References available upon request.
Computer Programming
My skills in programming are practical and are focused around scientific computing, numerical calculations, and data analysis. I use Python, FORTRAN, and IDL as my main coding languages, and so can help primarily with students who are working with those. Students who are interested in help with application programming, Java, or Visual Basic would best be served by looking elsewhere, but basic computer science, programming issues involving statistical interpretations or data analysis, and data...
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Computer Science
While I am not a computer scientist, the basic principles of this subject impact my professional work as an astrophysicist more profoundly than almost any other subject. Having an understanding of mathematics, science, and languages is important for developing, implementing, and explaining projects, but ultimately most data storage, analysis, and even presentation requires the use of computers, and the theory, practice, and optimization of computer systems is therefore the underlying architecture...
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Linear Algebra
Linear algebra is the study of the relationships between vector spaces (usually identified as matrices) and encompasses a set of widely used and high regarded mathematical techniques in the physical sciences. As such, I use much of the content of typical linear algebra classes in my day-to-day work as an astrophysicist. While the topic is also a precursor to many deeper mathematical subjects, it also stands on its own as a convenient and efficient tool for handling numerical data and statistics...
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Linux
I can help students who are just starting out with learning how to use Linux at the command prompt understand their systems and get a basic handle on what the capabilities are. However, people hoping to learn advanced shell scripting, tricks for effective system administration, or the peculiar details related to linux system are best to look elsewhere. If however, you need someone to guide you through the very beginning, I'm the tutor for you.
Macintosh
I use a Macintosh as my main work machine and, for the most part, am a big fan of the OS X operating system platform. The Macintosh system relies on a number of proprietary software applications that are different from those found on Windows or Unix machines, but the advantage to Macintosh is that much of the functionality of unix is accessible through the well-designed terminal application. Additionally, the file structure and Xcode tools available for advanced users make Macintosh an appealing...
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Python
My primary use of the Python language is as a means to run modeling, numerical calculations, and data analysis. The Python community includes a large contingent of scientists who are working on creating and maintaining packages that are useful for almost any serious computing need. The most advantageous packages and the ones I encourage students to take advantage of are found in the scipy library: ipython, numpy, matplotlib, and pandas are all excellent tools to use. I can help students who are...
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Finite Math
Inasmuch as I am an astronomer and a physical scientist, the formulae, techniques, and concepts associated with finite mathematics are a subset of the mathematics in which I am an expert. Students needing help with finite mathematics often have specific concerns and very particular topics with which they need help, normally related to compound interest and probability. I usually try to identify these areas early on to focus on them. Many of these other related areas of mathematics can be found...
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