Tutoring

In addition to concrete skills like algebra and calculus, I also teach students metacognitive skills that improve their problem-solving and critical thinking across the board. When I ask a student of mine to explain their reasoning, it isn’t for the sake of “grading” them or preventing plagiarism; instead, I use it as a gateway to raising their awareness of how they’re thinking. This helps them catch mistakes more automatically, recognise similarities between the current problem and ones they’ve solved in the past, and discover underlying structures that enable old intuitions to be brought to bear in new contexts.

I’m an ardent believer that understanding a given concept in two (or more) ways is exponentially more robust than understanding it in one way. As such, many of my explanations to students involve an intuitive visual explanation, a rigorous algebraic justification, and/or a direct analogic connection to a more familiar concept. Not only does this build confidence in the accuracy of each lens we use to view a given problem, it also gives my students a great deal of flexibility in how they solve the problem: how they begin, how they proceed, and how they pivot when they get stuck.

Traditional classrooms aren’t for everyone. Some students have teachers who explain everything in abstract conceptual terms, when a visual approach could be much more helpful. Some are bored in class and aiming to skip a grade. And some are completely off the beaten path, learning math through independent study and seeking mentorship and guidance. Whatever your reason for seeking a deeper understanding of math or physics, I can help you get there.

I don’t have any hard-and-fast rules for who I will or won’t take on as a student, but my favourite students to work with possess some or all of the following qualities:

• Possess an innate curiosity about math or physics
• Challenge me with deep and insightful questions
• March to the beat of their own drum
• Like to move quickly and have a math teacher who can keep up with them
• Enjoy solving difficult puzzles and actively seek them out

If you’d like to book a virtual session, or if you’d like talk things over on a video call first, you can schedule a time with me using the Calendly widget below this collapsible menu. It lists all the times I’d be available for a chat or a session, so you can pick whichever time works best for you and it’ll automatically get added to my calendar (as well as yours, if you so desire). You can also visit my Calendly page if that’s easier than using the scheduling widget, and if you don’t see any times that work for you on Calendly, you can reach out to me about alternate times using the contact details at the bottom of this page. I can’t guarantee that I’ll be able to find a time that works for both of us, but I will certainly try!

My scheduling page assumes that each tutoring session will be over Zoom rather than in-person, so while I do budget in a bit of buffer time between consecutive sessions, there’s no automatic allowance for travel time. If you happen to live in the Denver area and would like to schedule in-person sessions, reach out to me using one of the contact methods at the bottom of this page, and we can sort out the logistics for that as needed.

Current rate: \$120 per hour.

Tutoring costs are prorated after the first hour. For example, a tutoring session that lasts an hour and a half would cost (1.5 hours) × (\$120 per hour) = \$180, whereas a tutoring session that lasts an hour or less would cost \$120 even.

In the event that I raise my rate in the future, all current clients will keep their previous rate rather than being charged the new one. (I regard a current client as anyone who’s had a tutoring session with me in the past year. Once a year or more has passed, I regard them as a new client for the purposes of pricing, so the cost of subsequent sessions will be whatever is listed here.)

Flexibility in how I run my business is one of my favourite aspects of working for myself. If you’ve tried a free hour with me (detailed in the section below) and we seem to be good fits for each other, but cost would be an obstacle to working with me regularly, let me know and we can discuss pricing plans that work for both of us.

Free first hour: Choosing a tutor is a major investment for any student or parent, and I want the people I work with to feel confident in the value I offer before making that investment. With this in mind, I offer one hour of free tutoring to anyone who requests it, as a no-risk sampler to see whether my style is a good fit for what they’re looking for in a tutor. Just mention this offer sometime before or during our first session, and I’ll give you the first hour free of charge.

Referrals: I enjoy the work of tutoring far more than I enjoy the work of advertising, and I therefore heartily appreciate when people recommend my tutoring to their friends and family. Whenever you refer someone to me and they end up booking and attending a tutoring session, your next hour of tutoring with me will be absolutely free. (Just make sure that one or both of you mentions that you referred them to me, so I know whom to credit!)

Payment: I usually handle payments over Venmo, but I also accept Paypal, Zelle, and cash depending on what is most convenient for you. I always wait until after a session has concluded to send a payment request through Venmo/Paypal/Zelle, so that the amount you pay reflects the amount of time we actually spent in the session. (Usually this will be the same as the amount of time we initially scheduled, but we’ll sometimes go shorter or longer than our scheduled time depending on your/your student’s needs.) While I don’t currently maintain any hard-and-fast payment deadlines, if a client has outstanding payments on two consecutive tutoring sessions, I will put a pause on scheduling further sessions with that client until those payments have been received.

Prorating: For any session lasting longer than an hour, I prorate the cost in 5-minute increments, where the cost of each additional 5 minutes is one-twelfth of my hourly rate. Since I block out an hour in my schedule for each session by default, I do not prorate the cost of sessions that take less than a full hour, so those will generally still cost the same as a full one-hour session. However, if you let me know ahead of time that you will only need (for example) half an hour for a particular session, I can adjust my schedule blocking accordingly, and in that case I am happy to prorate for a shorter session.

Price lock: I occasionally update the pricing for my tutoring services, both to reflect my increased experience as a tutor and to allow myself more flexibility for taking on unpaid projects. At the same time, I want my clients to feel comfortable relying on me for their ongoing tutoring needs, without worrying that I might raise the price on them without warning. Hence, should I change my prices in the future, all current clients (defined as those who have had a session with me in the past year) will keep their existing pricing rather than being bumped up to the new rate.

Rescheduling: If something comes up and you/your student can’t make it to a session we’ve scheduled, that’s A-OK! Just get in touch with me as soon as you know that our original time won’t work, and we can figure out an alternative time at some other point in the week.

Cancellations: Sometimes, it won’t be possible to find a time to reschedule a tutoring session to, and we will simply need to cancel it. If a session is cancelled more than 24 hours prior to its scheduled start time, there’s no fee for the cancellation. For cancellations within 24 hours of the scheduled start time, I charge a cancellation fee equal to 50% of the session cost, due to the relative difficulty of finding another student to fill that time slot on such short notice.

No-shows: If 5 minutes have passed since our scheduled start time and a student hasn’t yet shown up to our meeting place or video call, I’ll send a text asking whether they’re still coming or if they need to reschedule. If 5 additional minutes pass without me hearing back from them, I’ll take that to mean that they aren’t coming and will charge a no-show fee according to the following progressive scale:

• First time no-showing: 50% of session cost
• Second time: 75% of session cost
• Third and subsequent times: 100% of session cost

Below is a list of subjects I’ve helped people with in the past, which fall into three categories:

• Curriculum from Art of Problem Solving (AoPS), which includes students self-studying an AoPS textbook as well as students currently enrolled in an AoPS class and seeking extra help and/or one-on-one instruction. With students in the first group, I start by finding out their desired timeline for getting through the textbook, then spend our sessions using problems from the book as inroads to building intuition, developing mathematical fluency, and deepening conceptual understanding. My approach with the second group is much the same, except that we typically use the pacing and problem sets determined by their course instructor.
• Preparation for math competitions in both middle school and high school. I typically have these students work through past years’ tests, determining which topics and strategies are sticking points for them and focusing our session time on strengthening those areas. Once we’ve been meeting for a while, I have them complete a past test under test conditions (time limit and no outside resources) in their own time, and then go over their results during our next session.
• Help with other courses at the high school or university level. Most of these students are currently taking a class and need help with homework and/or exam prep; I’ve also had a few self-study students who have scheduled sessions with me for the sake of structure, accountability, and help with sticking points. Many of my students are taking AP classes, which I’ve marked in the list below with an asterisk (*).

I’m always looking to broaden my repertoire, so if you’re looking for tutoring in math or physics and don’t see your particular subject listed below, worry not! Just reach out to me using the contact form below, let me know which subject you’re seeking tutoring in, and I’ll let you know if it’s a topic I have the requisite knowledge to tutor.

AoPS

• Beast Academy 2-5
• Prealgebra
• Intro to Algebra
• Intro to Geometry
• Intro to Counting & Probability
• Intro to Python
• Precalculus
• Calculus

Competitions

• Math Kangaroo
• MATHCOUNTS
• AMC 8
• AMC 10
• AMC 12
• F = ma
• USAPhO

Other

• Algebra
• Geometry
• Trigonometry
• Precalculus*
• Statistics*
• Probability
• Calculus AB* / Calc I
• Calculus BC* / Calc II
• Multivariable Calculus / Calc III
• Vector Calculus
• Linear Algebra
• Differential Equations
• Chemistry*
• Physics (mechanics)*
• Physics (E&M)*
• Physics (quantum mechanics)
• Quantum Computing
• Engineering Mechanics
• Microsoft Excel
• Python
• C++

I have taught classes for Art of Problem Solving (AoPS) since 2021, starting with their Virtual Campus (VC) in June 2021 and adding AoPS Online classes to my rotation beginning in May 2022.

Below is a list of classes I’ve taught (or am slated to teach) for each division of AoPS, up-to-date as of August 2024. If you’d like additional information about any of the courses below, you can either click on its name to visit its info page on the AoPS website, or you can reach out to me using the contact details at the bottom of this page.

Virtual Campus

• Honors Math 4A/4B
• Honors Math 4C/4D
• Honors Math 5A/5B
• Honors Math 5C/5D
• Honors Math 6A
• Honors Math 6B
• Middle School Math Contests: Number Theory and Geometry

AoPS Online

• Intro to Geometry
• Intro to Number Theory
• Intro to Counting & Probability
• Intro to Physics
• Intro to Python
• Intermediate Number Theory (starting June 2025)
• Intermediate Counting & Probability
• Intermediate Python
• Precalculus
• Calculus
• MATHCOUNTS / AMC 8 Basics
• MATHCOUNTS / AMC 8 Advanced
• Special AMC 8 Problem Seminar
• F = ma Problem Series
• PhysicsWOOT

In addition to my work as a tutor and AoPS instructor, I’ve also spent several years as an AoPS teaching assistant and message board halper (not a typo!), which has given me oodles of experience in helping students overcome obstacles without undermining their learning process of wrestling with hard problems.

More information about my educational background, accreditations, and other interests can be found on my About page.