Alex Smith

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@ninja_maths

Chief content architect @_MathAcademy_ | Math PhD | AKA MathNinja. Developing the world's largest online math curriculum.

mathacademy.com Joined October 2010

897 Following 20K Followers 2.7K Posts

Latest posts 5

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Alex Smith @ninja_maths Jul 6

For anyone wondering how a third-grader can complete six years' worth of math in a single year AND score a 5 on the AP Calculus exam.

This knowledge graph spans 3,000 math topics, from 4th grade to the university level, providing the perfect basis for mastery learning.

Students can go as fast or far as they want! There are no restrictions whatsoever. The only requirement is that they must demonstrate mastery of each topic before moving on to the next.

Kids are capable of incredible things when given that kind of freedom and support.

Nadja Verified account @unrealNadja Jul 6

They did it, my beamish boys! ⚔️🐉

My 3rd and 6th graders have slain the AP Calc BC dragon and just got their 5s!

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Alex Smith @ninja_maths Nov 2

Here are some great ideas for managing anxiety. Don't let it hold you back.

Kremi Smith | Counsellor (MBACP) Verified account @kremismith Oct 30

Your brain loves playing the “What If” game?

What if I fail? What if they get angry? What if everything goes wrong?

The tricky part about anxiety is that it only ever tells you the scary end of the story. It drops a terrifying scenario in your lap and leaves you stranded there.

The next time your mind starts spiraling with “what ifs,” try taking control of the game using these three steps:

1️⃣ Identify & Name It
Say it out loud: “What is the worst-case scenario I’m actually imagining right now?” Then, label it: “I am catastrophising.” Simply naming the thought creates a little bit of space between you and the loud voice in your head.

2️⃣ Test Your Capability
Ask yourself: “If this worst-case scenario actually happened, could I handle it?” Remind your nervous system of a simple truth: you have survived 100% of your worst days so far. You are far more adaptable than your anxiety gives you credit for.

3️⃣ Balance the Picture
Anxiety gives you a one-sided script. Force your brain to look at the rest of the picture by asking: “What is the best-case outcome?” or “What is the most likely, realistic outcome?”

Remember: Your thoughts are just suggestions, not predictions. You don’t have to believe every story your anxiety tells you.

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Alex Smith @ninja_maths Oct 26

A lot of apparent “lack of talent” in math is really unresolved prerequisite debt.

This debt compounds. When too many early gaps accumulate, new material arrives faster than students can integrate it.

From the student’s perspective, it feels like they “just not good at math.”

Alex Smith @ninja_maths Oct 24

One thing that stands out when mapping our new ACT Math Fundamentals course (905 topics) is how much higher the ACT's upper boundary is than the SAT's.

Alongside core algebra, geometry, and data analysis, the ACT reaches into:

- Matrices and 2x2 determinants

- 2D and 3D vectors (including dot products)

- Complex numbers and the complex plane

- Ellipses, hyperbolas, and focus-distance invariants

- Logarithms, recursive sequences, and infinite geometric series

- Full trigonometry (identities, double-angle formulas, law of sines/cosines, inverse trig graphs)

A student who is completely ready for the SAT can still be missing over 300 ACT topics.

That is why separate test prep matters.

Alex Smith Verified account @ninja_maths Oct 23

Today we are launching ACT Math Fundamentals on Math Academy (905 topics).

While building it, we uncovered 88 new "missing middle" topics - skills that appear regularly on the ACT but are rarely taught in a standard curriculum.

What's the missing middle? I'm glad you asked...

Most people assume that if a student earns A’s in Algebra, Geometry, and Precalculus, they have been taught all the math on the ACT exam.

Often, they haven’t.

Between standard textbook exercises and the problems that appear on standardized exams sits a large "missing middle": problems where familiar concepts are combined in non-standard ways, disguised in unfamiliar representations, or constrained so that standard textbook scripts fail.

With only about a minute per question on average across the ACT math section, encountering these structures for the first time on test day can kill your pacing. If you spend three or four minutes inventing a method on a few unfamiliar problems in the middle of the section, the clock runs out before you even reach the questions at the end.

Step one of serious test prep is making sure you never have to invent those methods on the spot.

ACT Math Fundamentals spans the entire breadth of the exam - from core algebra, geometry, and statistics up through matrices, 2D and 3D vectors, complex numbers, conic sections, logarithms, and full trigonometry - and integrates all of these "missing middle" skills directly into our knowledge graph.

Students begin with an adaptive diagnostic and work through the lessons untimed (with periodic quizzes to verify retention), first repairing upstream prerequisite gaps and then building fluency across every problem structure the exam tests.

And once students complete Fundamentals, they will promote into ACT Math Prep (launching soon) - a dedicated training ground of high-fidelity practice exams designed purely to master the strict timing of the actual test.

Over the next week, I’ll share a mini-series unpacking what this "missing middle" looks like and why standard curricula miss it.

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Alex Smith @ninja_maths Oct 23

While building our new ACT Math Fundamentals course (launched today), one of my favorite parts was cataloging the "missing middle".

These are problems where routinely using standard habits can catch students off guard.

Look at what happens on this deceptively simple problem...

Suppose you are given

(3x - y)/(x + y) = 5/8

and asked to find the value of x/y.

Watch what happens when a conscientious algebra student sees this for the first time:

In school, students are trained on a rigid script: one equation solves for one variable; two variables require a system of two equations.

So, they cross-multiply, get 19x = 13y, and stall - looking for a second equation so they can solve for x and y individually.

They know all the algebra required. What they are missing is a specific piece of structural reasoning: recognizing a homogeneous equation as determining a ratio x/y = 13/9 directly, rather than a unique pair (x, y).

School textbooks almost never isolate this as its own skill.

In our ACT course, it is a dedicated topic (Finding Variable Ratios From Homogeneous Equations), scaffolded across three knowledge points from monomial denominators up to full linear proportions.

Once a student has practiced that structure explicitly, a problem that used to eat three minutes of their section clock takes 15 seconds.

Alex Smith Verified account @ninja_maths Oct 23

Today we are launching ACT Math Fundamentals on Math Academy (905 topics).

While building it, we uncovered 88 new "missing middle" topics - skills that appear regularly on the ACT but are rarely taught in a standard curriculum.

What's the missing middle? I'm glad you asked...

Most people assume that if a student earns A’s in Algebra, Geometry, and Precalculus, they have been taught all the math on the ACT exam.

Often, they haven’t.

Between standard textbook exercises and the problems that appear on standardized exams sits a large "missing middle": problems where familiar concepts are combined in non-standard ways, disguised in unfamiliar representations, or constrained so that standard textbook scripts fail.

With only about a minute per question on average across the ACT math section, encountering these structures for the first time on test day can kill your pacing. If you spend three or four minutes inventing a method on a few unfamiliar problems in the middle of the section, the clock runs out before you even reach the questions at the end.

Step one of serious test prep is making sure you never have to invent those methods on the spot.

ACT Math Fundamentals spans the entire breadth of the exam - from core algebra, geometry, and statistics up through matrices, 2D and 3D vectors, complex numbers, conic sections, logarithms, and full trigonometry - and integrates all of these "missing middle" skills directly into our knowledge graph.

Students begin with an adaptive diagnostic and work through the lessons untimed (with periodic quizzes to verify retention), first repairing upstream prerequisite gaps and then building fluency across every problem structure the exam tests.

And once students complete Fundamentals, they will promote into ACT Math Prep (launching soon) - a dedicated training ground of high-fidelity practice exams designed purely to master the strict timing of the actual test.

Over the next week, I’ll share a mini-series unpacking what this "missing middle" looks like and why standard curricula miss it.

View quoted post on X