# Math for kids outside of the Calculus Sequence

### The Enrichment side of the "Accelerate vs Enrich" dichotomy in math education for kids who love math.

## The Calculus Sequence

Math is amazing in that there is a very clear learning path from 6 years old until a Math Ph.D. qualification exam, with everything in between.

So when you start to help a kid who loves math, do more math, it is very easy to start accelerating your kid down the math path from arithmetic to Calculus and beyond.

If you’re not familiar with it, it’s basically arithmetic all the way to pre-algebra, then algebra, geometry, algebra II, trigonometry, pre-calculus, and then calculus. You can more in-depth information about the USA’s Common Core State Standards for Mathematics (PDF, Nov 2022) in the linked document.

This works great until the kid starts to get too far ahead of the school and then your kid runs into a bunch of related problems:

they don’t get called on in class because they always know the answer

they are too far ahead of the class so don’t get help in school

they aren’t learning it “the school’s” way so their solutions get marked wrong

they get graded extra hard because “they already know it so they need to get 100% every time”

you as an adult get asked to “stop helping them get ahead of the class”

they, especially in middle school and high school, run out of classes to take (see “

*Don’t Fall Into The Calculus Trap*”)

Rather than “rushing ahead / accelerating”, there’s another path to give your kid more math: “enrichment”.

## Enrichment: more math, but not on the path

Since public schools (mainly speaking about US schools here) are generally setup to get the kids from arithmetic to Calculus, they visit only a small portion of math that is “doable” with a pre-algebra, algebra background, or pre-calculus background.

This is where you might have heard people talk about “enrichment” vs “acceleration”.

Acceleration is going through the sequence to Calculus faster (grade skipping, grade compacting, etc…)

Enrichment is math that either explores subjects in more depth or explores subjects not seen in the Calculus Sequence. This depth or exploration can be seeing additional content and/or project-based learning that explores these other areas.

Okay, but what areas of math can we look into for this “other math”?

## Math for kids outside of the Calculus Sequence

For now, I’m only going to list the topics as I’ll later include many examples of problems, websites, books, classes for each one as this is just an introductory post to enrichment.

Potential topics for your math kid:

Number Theory

Logic in Philosophy

Mathematical Logic

Combinatorics

Statistics

Probability

Graph Theory

Game Theory

Boolean Algebra

Information Theory

Naive Set Theory

Relational Algebra

Algorithms

Modular Arithmetic

Mathematical Finance

Discrete Mathematics (note that many of the above are parts of “Discrete Mathematics” classes)

There are probably a few that I missed (and if you think of you, please let me know in the comments so that other people can look into it :) ).

An example of a resource on a specific topic from the list above: “Information In Small Bits: Information Theory for Kids”, a book by Christina Fragouli, Anna Scaglione, and Dawn Faelnar.

The key here is to look for problems that a kid can do without having to understand too much mathematical machinery.

## How can I help them if I just did the Calculus sequence?

If you know some of the math topics above, then you’re set.

However, there are many of us who haven’t seen the topics above or feel inadequate about trying to guide a student through them.

There’s a few ways to help the student:

You learn it ahead of them. This is fun and it can show the child that you too are learning math.

You find a tutor. This can help the student with having an older child or adult show interest in math and someone outside of the family who loves math.

You find a math circle where they focus on these types of topics. For now whether the math circle focuses on competitions or non-competition math, it doesn’t matter as you’re just getting started in the “enrichment” area of math.

Find “edu-tainment” videos in the related areas that can work on sparking interest in your child.

## The next small step

The next small step for you to explore with your child is looking through the list above and seeing if there are any topics on Wikipedia

You just might find a new topic for your math kid to explore!

Try it soon and let me know how it goes!

Until next time,

Sebastian

We used the Art of Problem Solving (AOPS) online classes to provide our child courses outside the normal path (Number Theory, Counting and Probability), and it was a very good program. Doing this in middle school around Algebra II time left the high level math courses through Calculus in most of high school to have peers, and those classes were easier compared to peers due to the rigorous foundation of the AOPS classes.