Math Tutor (Elem - College)

Sarah W.

Algebra 1

Math Courses Completed in College: Calculus III & II: Studied functions of several variables, vectors, partial derivatives and multiple integrals, techniques of integration, improper integrals, differential equations, infinite series, conic sections, curves in parametric form and polar coordinates. Calculus I: Studied algebraic and transcendental functions, continuity and limits, derivatives and anti-derivatives of algebraic, trigonometric, exponential and logarithmic functions. Relative and absolute maxima and minima, points of reflection, evaluated integral by use of the fundamental theorem of calculus. College Algebra: Studied real numbers, graphs, theory of functions, sinusoidal equations, and their applications to science. Linear Algebra: Studied vector spaces, linear transformations, orthogonality, eigenvalues and eigenvectors, normal forms for complex matrices, positive definite matrices and congruence. Algebra II & I: Studied trigonometric identities (cosines, double angle, and others), reciprocal ratios, rotations, radians, Pythagorean and quotient identities, rotations, matrices, coordinate geometry (circles, ellipses, hyperbolas), quadratic equations/functions, powers and roots, complex numbers, polynomials and factoring, systems of equations/inequalities, graphs/functions (graphing functions, slopes).

Algebra 2

Math Courses Completed in College: Calculus III & II: Studied functions of several variables, vectors, partial derivatives and multiple integrals, techniques of integration, improper integrals, differential equations, infinite series, conic sections, curves in parametric form and polar coordinates. Calculus I: Studied algebraic and transcendental functions, continuity and limits, derivatives and anti-derivatives of algebraic, trigonometric, exponential and logarithmic functions. Relative and absolute maxima and minima, points of reflection, evaluated integral by use of the fundamental theorem of calculus. College Algebra: Studied real numbers, graphs, theory of functions, sinusoidal equations, and their applications to science. Linear Algebra: Studied vector spaces, linear transformations, orthogonality, eigenvalues and eigenvectors, normal forms for complex matrices, positive definite matrices and congruence. Algebra II & I: Studied trigonometric identities (cosines, double angle, and others), reciprocal ratios, rotations, radians, Pythagorean and quotient identities, rotations, matrices, coordinate geometry (circles, ellipses, hyperbolas), quadratic equations/functions, powers and roots, complex numbers, polynomials and factoring, systems of equations/inequalities, graphs/functions (graphing functions, slopes).

Calculus

Math Courses Completed in College: Calculus III & II: Studied functions of several variables, vectors, partial derivatives and multiple integrals, techniques of integration, improper integrals, differential equations, infinite series, conic sections, curves in parametric form and polar coordinates. Calculus I: Studied algebraic and transcendental functions, continuity and limits, derivatives and anti-derivatives of algebraic, trigonometric, exponential and logarithmic functions. Relative and absolute maxima and minima, points of reflection, evaluated integral by use of the fundamental theorem of calculus. My experience in Physics I includes the following topics: Motion in plane, Kinematics (Motion Equations for Constant Acceleration Forces and Equilibrium), 2-D Kinematics (Vector Addition & Subtraction, Projectile Motion), Force and Newton's Laws of Motion (Inertia, Concept of a System, Symmetry in Forces), Uniform Circular Motion & Gravitation, Linear Momentum and Collisions, Conservation Laws, Work and Potential Energy, Rigid Bodies and Rotational Dynamics, Statics & Torques, Thermodynamics, Speed of Sound, Frequency & Wavelength, Electric Charge & Electric Field, Magnetism, Geometric & Wave Optics.

Dyslexia

Experience and knowledge in working with children and adults who have special needs. My master's degree in general psychology entailed understanding the cognitive processes and systematic techniques utilized, such as applied behavior analysis. For instance, the Learning and Behavior graduate course entailed the systematic exploration of the processes through which learning is obtained, sustained, and modified. The focus was on the behavioral, social, cognitive, affective, ethical, and motivational aspects that influence human learning. I was responsible for teaching middle school math and developing lesson plans that catered to the varying skill levels of students, including those with ADHD, dyslexia, autism spectrum disorder, and other learning disabilities. I assessed students’ comprehension of lessons/skills and provided support services to improve students’ learning and retention of math concepts. The instructional method will be tailored to the learner.

Econometrics

I have taken college courses in Statistics and Probabilities for Econometrics. Topics include Probability Distributions for Joint, Marginal and Conditional Probabilities, Variance and Co-variance for Discrete and Continuous Random Variables. Methods also include Simple Linear Regression, Least Squares Estimators to estimate non-linear relationships and interpret the results. Interval Estimation and Hypothesis Testing, Regression with Time-Series Data to describe the average or systematic behavior of many individuals or systems. Other Economic Models include Qualitative and Limited Dependent Variable Models (Linear Probability Model, Probit Model, Models for Count Data), and Statistical Inferences.

Geometry

My experience in Geometry includes the following topics:Foundations of Geometry (Lines, segment, angle measure, axiomatic structures), Triangles, Quadrilaterals, Circles, Hypothesis & Congruence (SAS, ASA, SSS), Exterior Angle Inequality, Euclidean Geometry (Similar triangles and Trigonometry, Regular Polygons, Circle Theorems, Non-Euclidean Geometries (Hyberbolic & Elliptic Geometry).

Logic

I have completed extensive math classes in college while majoring in Electrical Engineering. Advanced math classes related to Logic include Calculus I, II, III, Differential Equations, and Digital Logic and Systems. The Digital Logic class include constructing Truth Tables for statements such as Negation, Conjunction and Disjunction, Conditional and Bi-conditional, Tautologies and Contradictions, Fundamental Properties of Logical Equivalence.

Physics

My experience in Physics I includes the following topics: Motion in plane, Kinematics (Motion Equations for Constant Acceleration Forces and Equilibrium), 2-D Kinematics (Vector Addition & Subtraction, Projectile Motion), Force and Newton's Laws of Motion (Inertia, Concept of a System, Symmetry in Forces), Uniform Circular Motion & Gravitation, Linear Momentum and Collisions, Conservation Laws, Work and Potential Energy, Rigid Bodies and Rotational Dynamics, Statics & Torques, Thermodynamics, Speed of Sound, Frequency & Wavelength, Electric Charge & Electric Field, Magnetism, Geometric & Wave Optics.

Prealgebra

My experience in Pre-Algebra includes Principles of Algebra (Expressions, Integers, Equations and Inequalities), Rational Numbers (Operations & Equations), Graphs, Functions, and Sequences, Exponents and Roots, Ratios, Proportions, and Similarity, Percents, Foundations of Geometry (Two-Dimensional & Patterns), Perimeter, Area, and Volume (2-Dimensional & 3-Dimensional), Data, Probability and Statistics, Multi-Step Equations and Inequalities, Graphing Lines (Linear Equations & Relationships), Sequences and Functions, Polynomials & Operations. Algebra II & I: Studied trigonometric identities (cosines, double angle, and others), reciprocal ratios, rotations, radians, Pythagorean and quotient identities, rotations, matrices, coordinate geometry (circles, ellipses, hyperbolas), quadratic equations/functions, powers and roots, complex numbers, polynomials and factoring, systems of equations/inequalities, graphs/functions (graphing functions, slopes). Linear Algebra: Studied vector spaces, linear transformations, orthogonality, eigenvalues and eigenvectors, normal forms for complex matrices, positive definite matrices and congruence. College Algebra: Studied real numbers, graphs, theory of functions, sinusoidal equations, and their applications to science.

Reading

My experience that helps students in Reading includes: Foundational Reading Skills (Print Concepts, Phonological Awareness, Phonics and Word Recognition, Fluency), Identifying Key Ideas and Details (retell stories, including details, and demonstrate understanding of their central message or lesson), Craft and Structure (identify who is telling the story at various points in the text), Integration of Knowledge and Ideas, Range of Reading and Level of Text Complexity.

SAT Math

Algebra and Functions (Simplifying Algebraic Functions, Word Problems, Functions, Solutions of Linear Equations and Inequalities, Quadratic Equations, Properties of Exponents, Rational and Radical Equations, Absolute Value, Equations of Lines). Number and Operations (Properties of Integers, Rational Numbers, Sets, Sequences and Series, Percent, Ratio, Proportions). Geometry and Measurement (Application of Pythagorean Theorem to determine unknown measurements of triangle sides and angles, Areas, Perimeters, Circumference and Volumes of Geometric Shapes, Coordinate Geometry, Slopes, Similarity, and Transformations). Data Analysis, Statistics, Probability (Tables and graphs, Mean, Median, Mode, Probability of Outcomes or Events).

Special Needs

Experience and knowledge in working with children and adults who have special needs. My master's degree in general psychology entailed understanding the cognitive processes and systematic techniques utilized, such as applied behavior analysis. For instance, the Learning and Behavior graduate course entailed the systematic exploration of the processes through which learning is obtained, sustained, and modified. Focus was directed towards the behavioral, social, cognitive, affective, ethical and motivational aspects that influence human learning. The instructional method will be tailored to the learner.