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I am an astrophysicist finishing a PhD with Columbia University while completing research at the Harvard College Observatory. My expertise is in the physical sciences and mathematics with a particular emphasis on physics and astronomy. I have a background in community college education having taught introductory physics, physical science, and astronomy for two years in Chicago and also completed the Teacher Preparation Program at Princeton University with an emphasis in mathematics, physical science, chemistry, and physics. I have worked in the past with middle school students needing special instruction due to needs associated with learning disabilities or personality disorders.
My teaching and tutoring style is very much individualized depending upon the particular need that a student shows. Most of the time, I find that that students are missing key conceptual approaches to the subjects in which they need help, and so tutoring often will center upon acquiring this understanding along with the basic skills necessary to complete problems and projects in the relevant academic area. Problem solving and, in particular, practice with assigned homework and attainment of an independent ability to complete work will be emphasized.
If you're looking for a tutor who will help you understand the material, I'm your guy. If you're looking for someone who will help you copy, cheat, or slide on by with minimal effort, you probably will want to find someone else.
My motto: Everybody learns; everybody teaches.
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.
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.
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.
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 topics.
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 better able to reach learning goals when the lessons are succinct and there are scheduled short breaks that are made part of the lesson with a switch to different activities made approximately every 45 minutes. Study skills and self monitoring skills are also useful emphases for general help in this area. References available upon request.
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 can recognize the utility of the methods and incorporate them into a toolbox that they can rely upon to help them solve problems they encounter.
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 in algebra if they can recognize the utility of the methods and incorporate them into a toolbox that they can rely upon to help them solve problems they encounter.
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.
I am an astronomer. I have taught all levels of the subject to all levels of students.
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 subject.
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.
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 the decision right the first time is the key to making sure the student succeeds and even thrives during their college experience.
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 science generally are my areas of expertise. I am an astrophysicist finishing a PhD with Columbia University while completing research at the Harvard College Observatory.
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 of everything I do as a scientist.
The basics of computer science come from certain fundamental abstractions in mathematics. Introductory computer science classes usually focus on these and exploiting the necessary characteristics that such computational systems have (binary mathematics, algorithms, system architecture, data handling, languages, programming, computation, numerics, and design). I am by no means familiar with the entirety of computer science as a subject, but I am an expert in applying computer science to quantitative problem solving. If this is the major issue you are having, or if you are simply completely new to the subject, I can certainly be of help. If you are intending on majoring in computer science, are interested in deep questions of optimization, system management, or advanced theory, I would suggest finding a person who is a professional computer scientist. I can offer a practical and basic introduction, but I'll leave the advanced and nuanced treatments to the experts.
I have lately worked as a Teaching Fellow for Harvard's Data Science course (cross-listed in the statistics and computer science departments), but there is no opportunity at WyzAnt to be certified in Data Science. My expertise is not necessarily relevant to computer science as a whole which an expansive subject and general CS certainly involves many subjects that I would rather not spend my time tutoring (e.g. advanced systems architecture or security).
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, solutions to differential equations are typically found using computer programs, and many courses in applied differential equations require students to learn how to use solvers and visualization software. Students who are not used to computing may need additional help in these areas which I can provide. I am an astrophysicist finishing a PhD with Columbia University.
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, linear algebra, probability, and statistics.
Discrete mathematics is an overbroad subject. The study of "discrete mathematics" can be done at all levels starting from the first steps of basic arithmetic and continuing right up to cutting-edge academic research. Students who are taking classes titled "discrete mathematics" are often doing so on the basis of a requirement, and often the subjects are wide-ranging and disparate from statistics to linear algebra to logic. Properly, discrete mathematics is simply the mathematics of systems that are not continuous, and formal definitions of what that means can be had at the asking. However, typically the utility of dealing with discrete as opposed to continuous distributions is that many practical applications of mathematics are fundamentally discrete. A classic example of this is computing and numerics which are fundamentally discrete and finite tools for solving quantitative problems.
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 ranging from learning disabilities to giftedness. Dealing with the underlying issues is usually the key to unlocking the individual student's potential, and so developing an individualized program for each student is the key to success.
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.
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.
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.
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.
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 in my profile including, algebra, calculus, computer science, discrete mathematics, differential equations, geometry, linear algebra, probability, and statistics.
Finite mathematics is an overbroad subject serving as a typical business course that is meant to cover almost all the mathematics necessary in the business world. The study of "finite mathematics" can be done at all levels starting from the first steps of basic arithmetic and continuing right up to cutting-edge academic research. Students who are taking classes titled "finite mathematics" are often doing so on the basis of a requirement, and often the subjects are wide-ranging and disparate from statistics to linear algebra to logic. Properly, finite mathematics is equivalent to discrete mathematics, and formal definitions of what that means can be had at the asking. The typical class is trying to deal with the applications to real-world problems where the results of using mathematics are emphasized over the reasons why they work, but understanding the underlying principles can help a lot in doing well in such a course.
People studying finite mathematics are most helped by having a strong conceptual basis for calculating what they want to calculate. Trying to rely on formula memorization generally will not work because there are so many different ways of asking finite mathematics-type questions. Tutoring will focus on building this conceptual awareness of what the various concepts and calculations entail, what questions can be answered, and, perhaps most importantly, what questions can't be answered.
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 curriculum or specific test preparation.
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.
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 geologist, but for introductory courses this distinction will not be seen by the students.
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 that I apply to the teaching on this subject.
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 can and will take in tutoring this subject.
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 tuned towards a specific score to be able to do quite well on this test, though often prospective students in the social sciences or humanities will have avoided many of these mathematical subjects in their academic careers. I can work to help review and polish mathematics skills for an improved score on the GRE. Additionally, I can help with verbal and writing portions as well as the physics subject test.
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 in the context of scientific computing.
I find that student understanding of this subject is best accomplished by gaining a conceptual basis. Direct physical comparisons for important concepts such as dimensionality, bases, orthogonality, and transformations can be made to great effect. This is the way I try to get students to engage with the subject, and those interested in learning linear algebra from me can expect a treatment of the subject that will emphasize practical application as a means to motivate learning the subject.
I am an astrophysicist finishing a PhD with Columbia University.
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.
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 choice for those interested in scientific computing or more serious use of their processors. I can help those who are just getting started all the way to those who are interested in higher-level administration and system management.
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.
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.
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.
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 with the mathematical tools necessary to solve problems posed in the homework or on tests. If need be, much of the tutoring can focusing on sharpening math skills.
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 about the physical world using the tools and techniques provided to us by the fundamental theories of physics.
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 concepts are tied back to concrete examples. Students will not just learn how to "solve for x" but, instead, will learn why one might want to do so in the first place.
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 close attention to new concepts in this course and tutoring will emphasize the connections between these new ideas and the mathematical skills and tools already learned.
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 want to calculate. Trying to rely on formula memorization generally will not work because there are so many different ways of asking probability questions. Tutoring will focus on building this conceptual awareness of what probability calculations entail, what questions can be answered, and, perhaps most importantly, what questions can't be answered.
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.
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 or want to increase their precision in answering questions correctly.
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 starting out in learning these aspects of the python language and who want to get started on serious programming to answer scientific and mathematical questions. I am an astrophysicist finishing a PhD with Columbia University.
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 a reading tutor, I provide the encouragement and sense of security necessary to be able to make mistakes, learn from them, and improve reading skills.
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 students understand the mathematics needed to excel on this portion of the SATs, one that promotes consistency, efficiency, and metacognition (knowing what you know and what you don't know) to obtain the highest possible score. Students who are seriously concerned that their mathematics abilities are not high enough will benefit the most from this approach. Those trying to "top out" and already have a very high score are better served by anxiety alleviation measures: practice test taking and learning specific test-specific skills to avoid common pitfalls.
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.
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 scenarios rather than the more open-ended format of essay writing. The best way to improve a student's score on open-ended essay questions is for them to learn a standard essay form and then practice pacing themselves through the relatively unstructured period of time. Pacing is everything in these situations.
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 rules that characterize the quirks of English spelling. It's then a matter of learning the particular exceptions to those rules that are based in etymology and the study of borrowed words from foreign languages. Latin and Greek are, in particular, useful starting points. Excellent spellers do not generally work of memorization alone (although this, of course, helps). Excellent spellers, such as those you see on ESPN, can work out the spelling of a word they have never before come across. I can teach you how to learn tricks so that you can learn how to do this as well.
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. Often anxiety and confusion can be bigger hurdles to performing well on young student entrance exams than actual unfamiliarity with the content, though their intellectual strengths and weaknesses, of course, should be evaluated. In the context of SSAT preparation, I will work with trying to diagnose all the relevant issues and develop a plan to improve the comfort level and performance of the student so that the best school placement will be possible.
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 get a handle on the types of questions that statistics is best able to answer and what assumptions go into its use. After this is understood, the rest of the subject is little more than looking up a number in a table or obtaining cross-tabs on a computer. Most students asking for tutoring in the subject are so afraid of the numbers that they miss the real challenge of the course: understanding the concepts. This is what my tutoring will focus on.
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 their goals. Generally, students who have a hard time concentrating on their studies are experiencing certain reluctance to engage with the material. Addressing the underlying issues sometimes helps as does making sure that environmental factors are considered. Keeping a study area clean, quiet, well-lit, and organized is particularly important, I have found.
For students with the second problem, the issue is often one of literacy within the subject. This can often be addressed through intensive work on the major features of a subject to make sure that the background knowledge and broad overview is understood. Students having problems studying the details are usually unable to see the bigger picture, and a review of the subject (or prequel) tends to be the best way to organize for the most effective outcomes.
I am an astrophysicist finishing a PhD with Columbia University while completing research at the Harvard College Observatory. I have worked with students over the years that have had any number of problems with study skills, and I can refer you to students who have worked with me in the past if you are interested in learning about the results I have achieved with such students.
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 using the tools of trigonometry is the best way to master the subject, and that is the emphasis I place when tutoring this subject.
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 words and being able to use them yourself. One of the best ways to learn new words beyond voracious reading and keeping handy dictionaries to identify those bits of writing you do not recognize is through word lists and flashcards. Making your own is particularly useful.
Students needing tutoring help in vocabulary should expect a lot of work with the former treatment of the etymological and word construction sort rather than the latter treatment of quizzing and rote memorization. I can help you construct lists and flashcards, but drilling yourself is eminently possible and much less expensive than paying me to do it for you!
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 to need help with grammar, syntax, and sentence construction. From there, composition becomes the main focus with organization of thoughts, presentation of paragraphs, and rhetorical techniques being the most important foci. Finally, students who are in secondary education and into college will need to work primarily on thematic and piece architecture. Organizing sources, developing arguments, and editing are generally the last pieces necessary for a student who is on their way to becoming an accomplished writer.
At any point along this journey, tutoring might be worthwhile. Older students often approach me about papers and the research process while younger students and their parents are more interested in the aspects of writing that appear on entrance examinations and standardized tests. This is rather unfortunate because the craft of writing is something that can be pursued independent of these artificial educational boxes. One of the best things a student can do who wants to improve their writing is take a creative writing course. As with most things, practice really does make perfect and a creative writing course will force you to write! You will also tend to identify which of your skills are your best when the pressure of performance is removed. For example, Joyce Carol Oates informed me in a creative writing class I took with her that my writing skills are predominately in editing. This is now a useful thing that I know about myself and my writing craft. It means that what I have to focus on in my written work is composition and organization so I can properly use my gifts for editing in making a work as good as it can be.
What's your strength in writing? How can you use that strength to make your writing as good as it can be? These are the kinds of questions I hope to help you answer as a tutor in writing.
Passionate and patient — Joshua combines in one the passion for astronomy with the passion for teaching. He is extremely wise in strategizing the material and providing access into the most difficult concepts. His definite strength is to model what has just been learned! ...
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