Behind-the-Scene Wisdom: Navigating the High School Math Journey with Your High-Achieving Student

This summer, Julia Gooding of One Sky Education interviewed me in order to introduce me to her clients.

We had a much more powerful conversation than I expected! Find it here.

In particular, there’s a lot of valuable but hard-to-find advice here for parents who want to help but don’t want to helicopter, as well as parents of AMC competitors.

(It’s 26 minutes in all, so check the top comment to skip to the part that’s most interesting to you.)

Transcript

Also, here’s a paraphrased transcript of the 21st-minute question that inspired this post today:

Julia Gooding:

What guidance can you offer to parents who may feel uncertain about their child’s academic progress and how to support them effectively? Are there ways for parents to assess their child’s situation and determine how best to address any specific challenges they may be facing?

Wes Carroll:

So, I want to start by emphasizing that a moderated conversation, especially in the initial session, can be exceptionally impactful. It’s challenging to make broad generalizations about every family because each conversation is unique. One of the main reasons for this, and perhaps some general advice I can offer, is that parents often face two, maybe even three, distinct challenges.

Firstly, they’re not just trying to support the student who lives in their household; they are also the parents of a nearly adult child. This dual role can sometimes lead to conflicts between the parent-child relationship and the student-helper dynamic. I’ve encountered situations where parents are fully qualified to assist with math, for instance, but due to their parental role, they can’t have the necessary conversations to foster academic growth effectively.

Secondly, parents often understand this intellectually, but deep down, they might lose sight of how much their child has evolved, even in just six months. Evolution happens in fits and starts, making it challenging to track in a linear fashion.

Another factor is that, generally, the parents of my students tend to be successful themselves. Much like their children, they’ve achieved success by leveraging their own unique strengths and working around their weaknesses. The issue arises when the parent’s strength and weakness profile differs significantly from the student’s. This can lead to frustration and the belief that “if you’d just listen to me, you’d succeed.” However, success depends on profile compatibility, which doesn’t always align.

Dealing with a child who has a vastly different profile can feel strange, especially since it’s your own son or daughter. Yet, it can and does happen. Additionally, we must remember that our success as parents with our specific profiles doesn’t make us masters of all possible profiles.

There’s no easy fix, but recognizing the complexity of the situation is a significant first step. In my experience, families that have succeeded in this dynamic share a common blend of patience, competence, and humility. Patience is crucial because when the student is ready, seizing that moment can lead to great success. Until then, we must lay the groundwork.

Competence is essential too, as we all have different strengths to offer the student, and we should be ready to assist as soon as they are ready to accept help. However, humility plays a critical role because, when done correctly, students will often pleasantly surprise us with their capabilities, even in areas we didn’t think they were prepared for.

This creates a harmonious dynamic where we all look toward the future while appreciating the present and the rapid progress being made. It’s a truly beautiful thing.

Other Key Takeaways from the Interview

These are mostly facts for our audience to get to know Wes Carroll Tutoring and Coaching:

Wes Carroll runs a small team specializing in tutoring high-achieving students in math and sciences, primarily high school level, with a STEM focus. We also help students develop essential skills beyond subject matter expertise.

We work with high-achieving, serious, and gifted students, often those who struggle to connect with traditional teaching methods. Our focus is on middle school through undergraduate education and we specialize in math and science subjects.

We assist students not only with subject matter but also with various skills like time management, motivation, and emotional engagement with the material.

I initially started tutoring because I personally experienced challenges in traditional education and wanted to help students overcome similar obstacles.

We also prepare students for competitions like the AMC (American Mathematics Competitions) but emphasize the importance of developing problem-solving and analytical skills beyond memorization.

Ready to unlock your full potential in math and science?

Whether you’re a high school student aiming for the stars or an undergrad seeking mastery, we’re here to guide you. We understand that you’re capable of high-level work, but you’re not getting the guidance or developing the specific skills you need to perform at that level. Reach out to us.

Unknown unknowns

You probably remember the quote:

There are known knowns. These are things we know that we know. There are known unknowns. That is to say, there are things that we know we don’t know. But there are also unknown unknowns. There are things we don’t know we don’t know.

When it comes to STEM tutoring, test preparation, and contest preparation for especially strong students, this is a shockingly important concept.  After all, strong students know a lot; they know what they know; and they are aware of things that they ought to know but don’t yet.

But typically there are things that they are missing that they don’t even know that they are missing.  And this is where most of the real trouble lies.  I help these students recognize these “unknown unknowns” in their academic lives.

The most common unknown unknown is a deficit in one of three qualities (which some colleagues helped me identify in a previous post):

  • Fluent: the successful student knows the material and how it all interconnects.
    Otherwise, success is necessarily limited (of course). This category includes not only “I need to study more” but also “I had memorized that fact, but didn’t know how it was relevant to this question.”
  • Present: the successful student is fully focused when engaging with the material.
    Otherwise, knowledge doesn’t matter; you’ll still flub it, e.g. by misreading the question, answering a different but related question, making an arithmetic error, doing too much in one’s head rather than on paper… in essence, a forehead-slapper. This is often missing in students who are so fluent that they aren’t used to having to focus 100% of their attention.
  • Bold: the successful student is willing and able to make progress with incomplete information.
    It’s often called creativity, critical reasoning, or problem-solving. But at its core, it’s about reasoning successfully even when some pieces of the puzzle appear to be missing. This is often missing in students who are so fluent that they aren’t used to having anything less than complete information in the first place.

That’s it in a nutshell: to be extremely successful academically, you should aim to be fluent, present, and bold. But most strong students consider any academic issue to be a failure only of fluency, which means they often use the wrong tools for solving their problems.

This can cause extreme frustration, and can threaten both morale and identity.

My diagnostic systems identify gaps in these categories, and my interventions help students build the new habits that bridge these gaps.  This eliminates these frustrating “unknown unknowns” for most students.

I’m glad to finally have a way to easily discuss these issues with students and parents, so that we can all help the student as a cohesive team.