Case study
Turning Curiosity Into AMC Power
Meet the student
Student
Riley (11th grade)
Parents
Amanda and Brian
Challenge
Gifted, curious, and intrinsically motivated — but new to the structure, pacing, and depth required for high-level math contests
Services Used
MC coaching, diagnostic work, timing training, foundational skill-building, targeted summer intensive
Outcome
Strong upward trajectory in AMC performance, increased metacognition, and readiness for a serious run at AIME qualificationg
“Most students come to learn AMC techniques. Riley came to learn thinking — and was willing to use AMC to get there.”
— Wes Carroll
The Challenge
Riley has always loved thinking. Puzzle contests, linguistics problems, logic games — she’s been doing them “just for fun” since elementary school. She and her dad regularly attempt challenging problems together, often taking separate runs and comparing ideas before converging on a solution.
But the AMC was different.
Not because it was more advanced — but because it required a new type of structure:
-
- solving under real timing,
- maintaining accuracy at higher volume,
- building a repeatable decision process,
- and learning strategic content she’d never been exposed to.
Her parents were clear from the beginning:
They wanted her to go far, but never at the cost of killing her love for math.
They also knew something important:
Riley was capable of much more — but needed an environment that could match her independence, her quick uptake, and her natural curiosity without over-structuring her or putting pressure in the wrong places.
The Turning Point
When Wes first met Riley, he noticed something unusual:
Most AMC students come with a competitive goal and pick up thinking skills along the way.
Riley came with thinking skills — and was willing to learn AMC in service of those skills.
That flipped the usual script.
Riley didn’t need motivation. Or pressure. Or external accountability.
She needed:
-
- diagnostics,
- strategy,
- gaps identified cleanly,
- and a coach who could push her without making math feel like a grind.
Early work revealed that her thinking was deep, playful, and flexible — but that she hadn’t yet been trained in the full AMC toolkit, especially topics she’d never seen before or mastered only partially.
That meant the path forward was clear:
Build foundational AMC skills, reinforce them until bulletproof, then push into advanced territory.
The WCTC Approach
1. Diagnose where she was strong — and where the scaffolding needed to be built
Riley’s untimed problem-solving was sophisticated, but AMC performance requires:
- content knowledge (especially geometry, combinatorics, number theory),
- timing discipline,
- strategic abandon-and-return habits,
- and the ability to quickly assess when you truly understand a concept.
Wes focused first on building self-awareness: Does she know how much she knows? Where the edges are? What she hasn’t seen yet?
She was unusually honest about these boundaries — exactly what a coach needs.
2. Protect the joy — while building structure
Riley’s parents were committed to keeping math joyful and playful, not turning the AMC into a pressure-driven grind.
WCTC brought structure without heaviness:
- weekly coaching
- a light but consistent cadence
- clear goals
- no fear, no pressure
Riley responded beautifully. She did the work consistently because she wanted to — a rare trait in AMC students, and one we leaned into.
3. Invest in a summer AMC “build phase”
By early summer, she had:
- comfort with the major AMC concepts
- increasing metacognition
- experience with diagnostic sessions
- and growing confidence in her ability to improve
That’s when Wes proposed an intentional shift: Move from “learning the basics” to “building the foundation for qualifying.”
This included:
- twice-weekly sessions with Phil (90 minutes each),
- 4–6 hours/week of homework,
- timed problem sets,
- targeted content gaps,
- and consistent feedback loops.
Riley wasn’t only willing — she was excited.
4. Bring in Phil to sharpen accountability and expand the coaching frame
Wes made a strategic move: Riley needed coaching from someone who wasn’t also charmed by her curiosity and ease of rapport — someone who could push her with crisp intensity.
Phil’s approach complemented the work perfectly:
- clear expectations
- sharper pacing
- attention to detail
- accountability without pressure
This also ensured Riley’s progress wasn’t limited by the ease of her relationship with Wes.
5. Build the habit of “getting all the early problems right”
A major summer goal was to get Riley bulletproof on the first ~60% of AMC questions.
Not glamorous.
Not as “fun” as enrichment.
But absolutely essential for:
- reducing variance,
- building confidence,
- and making AIME qualification a realistic target.
Riley took to this challenge more seriously than most students her age — helped by her natural desire to “totally ace things” once she commits.
The transformation
Before |
After |
| Loved puzzles and problem-solving | Increasingly sophisticated metacognition about what she knows and what she doesn’t |
| No timing system or pacing strategy | Able to handle timed sets without losing joy or confidence |
| Wanted challenge without parental pressure | Comfortable with rigorous, structured problem sets |
| Unfamiliar with major AMC-specific topics | Strong command of AMC fundamentals across major topics |
| Highly independent but under-experienced with AMC structure |
Ready for a serious run at the AMC 10/12 and AIME track |
Riley is now positioned not only to qualify — but to enjoy the process of becoming an AIME-level thinker.
What Made the Difference
Riley’s transformation didn’t come from grinding problem sets. It came from:
- anchoring the work in her natural curiosity,
- treating AMC as a vehicle for deeper thinking,
- diagnosing actual gaps instead of over-training,
- adding structure without suffocating joy,
- and letting her independence be an asset rather than a liability.
WCTC matched the coaching to the student — not the other way around.
And yes, her enrichment project helped shape all this: she already knew how to think deeply, iterate, and stay patient. AMC work simply gave those skills a new arena.
Would We Recommend It?
“We don’t want her to hate math — we want her to love math, play with math, still think it’s great.“
— Amanda, Riley’s parent.
Riley’s parents entered the process with the right goal: help her love math, stay curious, and grow as a thinker. The AMC became a powerful tool for that — not a source of pressure.
With the foundation built this year and the intensive summer ahead, Riley is on track not just for the AMC… but for the kind of long-term STEM trajectory where problem-solving, independence, and disciplined joy matter most.
Names and identifying details have been changed to protect the privacy of the student and family.