Harrison Kmiec
Private Mathematics Tutor for all grades and skill levels. The goal is to promote consistent improvement and fun in the mathematical journey!
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Harrison Kmiec
Bachelors degree
/ 55 min
Harrison - Know your tutor
My name is Harrison Kmiec, and I am a private mathematics tutor situated in Chapel Hill, North Carolina. Regarding my educational background, I have a Bachelor's degree from UNC-Chapel Hill and majored in Mathematics, as well as Statistics and Analytics. I have been doing private mathematics tutoring for 3 years, and have tutored from elementary school all the way up to the undergraduate college level. Subjects within math that I tutor for include Algebra, Geometry, Calculus, and Probability. My style of tutoring/teaching focuses on using simple examples to build up the muscle memory for concepts and formulas, then using more complex examples to strengthen the students' flexibility on those very topics. My goal is to create a collaborative environment for math that communicates how fun math can be as a subject dedicated to problem-solving.
Harrison graduated from University of North Carolina at Chapel Hill
Specialities of your tutor
Gamification of Math
Advanced Placement (AP) Program (USA)
Homework help
Common Core State Standards - CCSS (USA)
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Practice Drills
CoTutorAI modules
Summary
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Zero Risk Guaranteed
15-days refund
Free tutor swap
No cancel fee
1-yr validity
24/7 support
Student types for classes
College students
Anxiety or Stress Disorders
Home schooled
High School students
ADHD
Middle School students
Learning Disabilities
Elementary School students
ASD
Class overview
My tutoring/teaching style focuses on addressing weak spots in students' fundamental understanding of the math they are learning in their courses, and keeping the students engaged once they have demonstrated a solid understanding of the current math concepts they are working on. I use simple examples to identify where a student does not fully grasp certain mathematical ideas, as well as to help them hone the missing skills to a comfortable level. Then, once the student shows consistency with the topics they are working on, I use complex examples to keep them engaged with the problem-solving aspect of math. My belief is that there is no need to "gamify" math because math is inherently very similar to a game. Math is akin to a puzzle or any activity where there is a defined end goal and you are given a base set of information to work with. After working with a lot of students over the years, I find that students naturally discover the fun in math as long as someone is there to ease the frustrating parts.
Harrison also teaches
Algebra
Algebra 2
Arithmetic
Calculus
Calculus 2
Calculus 3
Mathematics concepts taught by Harrison
The tutor and student conducted a review session focusing on calculus topics relevant to a final exam, including volumes of solids of revolution using the shell method and centroid calculations. They practiced solving problems by setting up integrals and working through calculations, and the student gained clarity on formula application.
Volumes of Revolution: Shell Method
Finding Centroids (Center of Mass)
Volumes of Revolution: Disc/Washer Method
The tutor and student worked on problems involving parametric equations, including identifying shapes of curves, eliminating parameters to find rectangular equations, and performing parametric differentiation. They also discussed upcoming review for a final exam covering parametric and polar coordinates.
Parametric Equations for Circles and Ellipses
Eliminating the Parameter
Derivatives of Parametric Equations
The student and tutor reviewed and practiced problems related to binomial and Maclaurin series, including finding radii of convergence and expanding functions into series. They worked through examples involving inverse tangent, exponential functions with modifications, and general binomial expansions, preparing for an upcoming exam.
Parametric and Polar Coordinates Introduction
Maclaurin Series Manipulation
Radius and Interval of Convergence
Binomial Series Expansion
The student and tutor worked through problems related to binomial series expansions. They practiced applying the binomial coefficient formula, particularly for negative and fractional exponents, and worked on correctly substituting and raising terms to the appropriate power within the series. They planned to continue reviewing these concepts due to the complexity.
Binomial Theorem for Arbitrary Powers
Calculating Binomial Series Terms
Binomial Series General Formula
Applying Binomial Series to Functions
Generalized Binomial Coefficients
The student and tutor reviewed the concepts of Taylor and Maclaurin series, focusing on constructing Taylor polynomials for various functions and estimating function values. They practiced calculating derivatives and applying the Taylor series formula for different center points and polynomial degrees. Future sessions were planned to cover binomial series and review for upcoming exams.
Taylor Series Expansion
Maclaurin Series
Approximation using Taylor Polynomials
Power Series Representation
The Tutor and Student worked on differentiating and integrating power series and determining their intervals of convergence. They practiced applying these techniques to various functions and discussed methods for finding the constant of integration and checking interval endpoints.
Power Series Differentiation
Handling Constants in Power Series Operations
Power Series Integration
Interval of Convergence
Teaching tools used by tutor
Graphing Tools
Digital whiteboard
Lesson Planning Tools
Visualization & Exploration
Practice worksheets
Interactive lessons
Open Q&A
Parent feedback
Weekend lessons
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