Vern H.

Patient and understanding math tutor - 46 years of teaching experience

Patient and understanding math tutor - 46 years of teaching experience

Algebra 1

In some ways algebra can be viewed as a generalization of arithmetic in which letters can be used to represent numbers. In many cases algebra requires less effort than arithmetic. In arithmetic, one is required to carry out the arithmetic operation to get the result-For example: 2*18 = 36. In algebra the product of two numbers represented by a and b is a*b or simply ab. The operation is implied. There are, of course, many other applications of algebra: minipulating formulas, solving equations, etc. Almost every college major requires some expertise in algebra. It has been my experience that students who have difficulty with algebra are lacking in their understanding of arithmetic concepts. In my tutoring efforts, I stress the importance of understanding basic algebraic concepts and applying these concepts in a variety of application. I initially lead the student through the logic of problem solving with the goal of turning over the ownership of the thought processes to the student.

Algebra 2

Algebra II, sometimes referred to as advanced algebra, includes a review of algebra I. It takes a more in-depth view of certain topics studied in algebra I. In addition algebra II introduces the student to new concepts such as a study of functions including higher order polynomials, exponential, logarithm, and trigonometry. This is by no means an exhaustive list of topics covered in algebra II. A thorough understanding of algebra is required for further study of mathematics or applications of mathematics. As is the case with all my tutoring efforts, I begin by helping students understand the basic concepts of the subject. I help them with problem solving logic by working through a variety of exercises (we learn by doing). Initially I take initiative and give direction as we work through problems. As the student gains confidence,I help them take ownership of problem solving techniques.

Calculus

Students who are beginning their study of calculus generally must first learn the concept of limits, which must then be applied in the study of derivatives and integrals. In the introduction to calculus, the derivative is presented as the slope of a line tangent to the graph of a continuous function. The integral is initially presented as the area between graphs of continuous functions. These applications serve only to give to the student a geometric image of these concepts, and are by no means rigorous nor exhaustive. There are, of course, many and varied applications of differential and integral calculus. I have a masters degree in mathematics, and I have taught differential and integral calculus for over 40 years as the the terminal college prep mathematics course offered to seniors in high school; in addition, I have tutored students who are studying calculus in college. It has been my experience that calculus students generally have at least an intuitive grasp of the concept of limits. Any difficulties experienced with calculus generally stem from an inadequate grasp of topics usually presented in advanced algebra, and precalculus; therefore, when helping them work through their calculus problems, I take every opportunity to thoroughly review algebra as well as topics in precalculus.

Prealgebra

Prealgebra, as the name suggests, is a course designed to prepare students for algebra. The course reviews some concepts in arithmetic including arithmetic operations, working with percentages, decimals, fractions etc. The course also introduces some concepts in basic algebra. This list of topics is not exhaustive of course. I have tutored students who struggle with mathematical concepts from basic ideas in arithmetic to calculus and statistics. I fully understand the difficulties that students face in the process of learning mathematical concepts; and therefore, I am very patient and understanding of my students struggles.

Precalculus

Precalculus, as the name suggests, is designed to prepare students to study calculus. This course requires a thorough understanding of topics treated in algebra II. While there is some review of topics studied in advanced algebra, this course gives a more rigorous treatment of the concepts. Generally speaking, the major ideas of this course include a study of functions with special attention to polynomial, rational, and trigonometric functions. An informal treatment of limits is included since this is important in the study of calculus. The emphasis in tutoring students in this course includes making sure that students have a good grasp of concepts studied in algebra. Also it is important that they understand the concept of mathematical functions with special emphasis on trigonometric functions, since this is where students have the greatest difficulty. As is the case in all my tutoring efforts, I give clear direction to problem solving with the goal of building the student's confidence so that they are able to analyze and solve porblems on their own.

ACT Math

A satisfactory score in the ACT is required by most colleges and universities in Michigan in order to be enrolled in a degree program. The ACT is generally administered to students during the second semester of their junior year in high school. The questions in the mathematics portion of the ACT covers materials typically studied in algebra I, geometry, and algebraII. My experience includes 30 years of administering or helping to administer the ACT as well as preparing students to take the mathematics portion of the ACT.

Algebra 1

In some ways algebra can be viewed as a generalization of arithmetic in which letters can be used to represent numbers. In many cases algebra requires less effort than arithmetic. In arithmetic, one is required to carry out the arithmetic operation to get the result-For example: 2*18 = 36. In algebra the product of two numbers represented by a and b is a*b or simply ab. The operation is implied. There are, of course, many other applications of algebra: minipulating formulas, solving equations, etc. Almost every college major requires some expertise in algebra. It has been my experience that students who have difficulty with algebra are lacking in their understanding of arithmetic concepts. In my tutoring efforts, I stress the importance of understanding basic algebraic concepts and applying these concepts in a variety of application. I initially lead the student through the logic of problem solving with the goal of turning over the ownership of the thought processes to the student.

Algebra 2

Algebra II, sometimes referred to as advanced algebra, includes a review of algebra I. It takes a more in-depth view of certain topics studied in algebra I. In addition algebra II introduces the student to new concepts such as a study of functions including higher order polynomials, exponential, logarithm, and trigonometry. This is by no means an exhaustive list of topics covered in algebra II. A thorough understanding of algebra is required for further study of mathematics or applications of mathematics. As is the case with all my tutoring efforts, I begin by helping students understand the basic concepts of the subject. I help them with problem solving logic by working through a variety of exercises (we learn by doing). Initially I take initiative and give direction as we work through problems. As the student gains confidence,I help them take ownership of problem solving techniques.

Calculus

Students who are beginning their study of calculus generally must first learn the concept of limits, which must then be applied in the study of derivatives and integrals. In the introduction to calculus, the derivative is presented as the slope of a line tangent to the graph of a continuous function. The integral is initially presented as the area between graphs of continuous functions. These applications serve only to give to the student a geometric image of these concepts, and are by no means rigorous nor exhaustive. There are, of course, many and varied applications of differential and integral calculus. I have a masters degree in mathematics, and I have taught differential and integral calculus for over 40 years as the the terminal college prep mathematics course offered to seniors in high school; in addition, I have tutored students who are studying calculus in college. It has been my experience that calculus students generally have at least an intuitive grasp of the concept of limits. Any difficulties experienced with calculus generally stem from an inadequate grasp of topics usually presented in advanced algebra, and precalculus; therefore, when helping them work through their calculus problems, I take every opportunity to thoroughly review algebra as well as topics in precalculus.

Prealgebra

Prealgebra, as the name suggests, is a course designed to prepare students for algebra. The course reviews some concepts in arithmetic including arithmetic operations, working with percentages, decimals, fractions etc. The course also introduces some concepts in basic algebra. This list of topics is not exhaustive of course. I have tutored students who struggle with mathematical concepts from basic ideas in arithmetic to calculus and statistics. I fully understand the difficulties that students face in the process of learning mathematical concepts; and therefore, I am very patient and understanding of my students struggles.

Precalculus

Precalculus, as the name suggests, is designed to prepare students to study calculus. This course requires a thorough understanding of topics treated in algebra II. While there is some review of topics studied in advanced algebra, this course gives a more rigorous treatment of the concepts. Generally speaking, the major ideas of this course include a study of functions with special attention to polynomial, rational, and trigonometric functions. An informal treatment of limits is included since this is important in the study of calculus. The emphasis in tutoring students in this course includes making sure that students have a good grasp of concepts studied in algebra. Also it is important that they understand the concept of mathematical functions with special emphasis on trigonometric functions, since this is where students have the greatest difficulty. As is the case in all my tutoring efforts, I give clear direction to problem solving with the goal of building the student's confidence so that they are able to analyze and solve porblems on their own.

Probability

A brief discription of probability theory could be stated simply: It is a branch of mathematics that studies situations in which there is an element of uncertainty. Flipping a coin or rolling a die come to mind. We say the outcome is uncertain because there are too many unknowns involved. For example, if we knew the exact initial orientation of the die as well as all of the forces acting upon it as it is rolled, and perhaps also the coefficient of friction of the surface upon which it lands, we could predict the outcome exactly. We do know however, that a die very closely approximates a perfect cube; therefore, each of the six faces are equally likely to turn up. We may conclude then, that the probability of turning up a five, for example, is 1/6. Even elementary probability problems can quickly become more complicated: What is the probability of turning up exactly three fives in ten tosses? The answer is 5/9. This is not as evident as the answer to the first question above. In general, probability problems require more careful thought and analysis than say, applications of algebra to solving equations. I have an MA in mathematics, and I have taught, or tutored mathematics for over 46 years. I fully understand that most students find it difficult to fully understand and grasp mathematical concepts. Patience is my greatest asset.

Trigonometry

Trigonometry is usually introduced in terms of the ratio of sides of a right triangle. The sine (sin) and cosine (cos) are the basic trig functions. The other four trig functions are defined either as reciprocals or ratios of the sine and cosine functions. The domain of trig functions defined as stated above are restricted to angle measures between 0 and 90-degrees. Later in trigonometry courses, the domains of the sine and cosine functions are expanded to included all real numbers with some exceptions with respect to the tangent, cotangent, secant, and cosecant functions. Angle measures for trig functions are usually given in terms of degrees or radians. I have an MA in mathematics and I have taught mathematics, including trigonometry, for over 46 years. I realize that many mathematics students struggle with some concepts of trigonometry. I understand the difficulties that they encounter and I am patient with my students as we work through their difficulties.

Algebra 1

In some ways algebra can be viewed as a generalization of arithmetic in which letters can be used to represent numbers. In many cases algebra requires less effort than arithmetic. In arithmetic, one is required to carry out the arithmetic operation to get the result-For example: 2*18 = 36. In algebra the product of two numbers represented by a and b is a*b or simply ab. The operation is implied. There are, of course, many other applications of algebra: minipulating formulas, solving equations, etc. Almost every college major requires some expertise in algebra. It has been my experience that students who have difficulty with algebra are lacking in their understanding of arithmetic concepts. In my tutoring efforts, I stress the importance of understanding basic algebraic concepts and applying these concepts in a variety of application. I initially lead the student through the logic of problem solving with the goal of turning over the ownership of the thought processes to the student.

Algebra 2

Algebra II, sometimes referred to as advanced algebra, includes a review of algebra I. It takes a more in-depth view of certain topics studied in algebra I. In addition algebra II introduces the student to new concepts such as a study of functions including higher order polynomials, exponential, logarithm, and trigonometry. This is by no means an exhaustive list of topics covered in algebra II. A thorough understanding of algebra is required for further study of mathematics or applications of mathematics. As is the case with all my tutoring efforts, I begin by helping students understand the basic concepts of the subject. I help them with problem solving logic by working through a variety of exercises (we learn by doing). Initially I take initiative and give direction as we work through problems. As the student gains confidence,I help them take ownership of problem solving techniques.

Calculus

Students who are beginning their study of calculus generally must first learn the concept of limits, which must then be applied in the study of derivatives and integrals. In the introduction to calculus, the derivative is presented as the slope of a line tangent to the graph of a continuous function. The integral is initially presented as the area between graphs of continuous functions. These applications serve only to give to the student a geometric image of these concepts, and are by no means rigorous nor exhaustive. There are, of course, many and varied applications of differential and integral calculus. I have a masters degree in mathematics, and I have taught differential and integral calculus for over 40 years as the the terminal college prep mathematics course offered to seniors in high school; in addition, I have tutored students who are studying calculus in college. It has been my experience that calculus students generally have at least an intuitive grasp of the concept of limits. Any difficulties experienced with calculus generally stem from an inadequate grasp of topics usually presented in advanced algebra, and precalculus; therefore, when helping them work through their calculus problems, I take every opportunity to thoroughly review algebra as well as topics in precalculus.

Prealgebra

Prealgebra, as the name suggests, is a course designed to prepare students for algebra. The course reviews some concepts in arithmetic including arithmetic operations, working with percentages, decimals, fractions etc. The course also introduces some concepts in basic algebra. This list of topics is not exhaustive of course. I have tutored students who struggle with mathematical concepts from basic ideas in arithmetic to calculus and statistics. I fully understand the difficulties that students face in the process of learning mathematical concepts; and therefore, I am very patient and understanding of my students struggles.

Precalculus

Precalculus, as the name suggests, is designed to prepare students to study calculus. This course requires a thorough understanding of topics treated in algebra II. While there is some review of topics studied in advanced algebra, this course gives a more rigorous treatment of the concepts. Generally speaking, the major ideas of this course include a study of functions with special attention to polynomial, rational, and trigonometric functions. An informal treatment of limits is included since this is important in the study of calculus. The emphasis in tutoring students in this course includes making sure that students have a good grasp of concepts studied in algebra. Also it is important that they understand the concept of mathematical functions with special emphasis on trigonometric functions, since this is where students have the greatest difficulty. As is the case in all my tutoring efforts, I give clear direction to problem solving with the goal of building the student's confidence so that they are able to analyze and solve porblems on their own.

Algebra 1

In some ways algebra can be viewed as a generalization of arithmetic in which letters can be used to represent numbers. In many cases algebra requires less effort than arithmetic. In arithmetic, one is required to carry out the arithmetic operation to get the result-For example: 2*18 = 36. In algebra the product of two numbers represented by a and b is a*b or simply ab. The operation is implied. There are, of course, many other applications of algebra: minipulating formulas, solving equations, etc. Almost every college major requires some expertise in algebra. It has been my experience that students who have difficulty with algebra are lacking in their understanding of arithmetic concepts. In my tutoring efforts, I stress the importance of understanding basic algebraic concepts and applying these concepts in a variety of application. I initially lead the student through the logic of problem solving with the goal of turning over the ownership of the thought processes to the student.

Algebra 2

Algebra II, sometimes referred to as advanced algebra, includes a review of algebra I. It takes a more in-depth view of certain topics studied in algebra I. In addition algebra II introduces the student to new concepts such as a study of functions including higher order polynomials, exponential, logarithm, and trigonometry. This is by no means an exhaustive list of topics covered in algebra II. A thorough understanding of algebra is required for further study of mathematics or applications of mathematics. As is the case with all my tutoring efforts, I begin by helping students understand the basic concepts of the subject. I help them with problem solving logic by working through a variety of exercises (we learn by doing). Initially I take initiative and give direction as we work through problems. As the student gains confidence,I help them take ownership of problem solving techniques.

Calculus

Students who are beginning their study of calculus generally must first learn the concept of limits, which must then be applied in the study of derivatives and integrals. In the introduction to calculus, the derivative is presented as the slope of a line tangent to the graph of a continuous function. The integral is initially presented as the area between graphs of continuous functions. These applications serve only to give to the student a geometric image of these concepts, and are by no means rigorous nor exhaustive. There are, of course, many and varied applications of differential and integral calculus. I have a masters degree in mathematics, and I have taught differential and integral calculus for over 40 years as the the terminal college prep mathematics course offered to seniors in high school; in addition, I have tutored students who are studying calculus in college. It has been my experience that calculus students generally have at least an intuitive grasp of the concept of limits. Any difficulties experienced with calculus generally stem from an inadequate grasp of topics usually presented in advanced algebra, and precalculus; therefore, when helping them work through their calculus problems, I take every opportunity to thoroughly review algebra as well as topics in precalculus.

ACT Math

A satisfactory score in the ACT is required by most colleges and universities in Michigan in order to be enrolled in a degree program. The ACT is generally administered to students during the second semester of their junior year in high school. The questions in the mathematics portion of the ACT covers materials typically studied in algebra I, geometry, and algebraII. My experience includes 30 years of administering or helping to administer the ACT as well as preparing students to take the mathematics portion of the ACT.