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About this app

Understanding Math makes school mathematics comprehensible—not by memorizing procedures, but by deriving and naming each calculation step.

For students from grade 5 through high school graduation. Specifically for those who didn't pay attention consistently in their early years of high school and are now struggling with the material in the higher grades.

THE GAP FINDER
Mathematics is a chain. Those who don't have a firm grasp of the laws of exponents will later struggle with differentiation and won't know why. They think they don't understand derivatives—but they don't understand negative exponents.

The Gap Finder presents problems from across the curriculum. If one goes wrong, it goes down a level instead of moving on. The result isn't "6 out of 15 correct," but rather: "Your problem isn't the derivative. Your problem is the laws of exponents—here's how to work your way up from there."

And he remains honest: What wasn't asked about, he explicitly states

"nothing is known about that" — instead of simply acknowledging it as "you know it."

EVERY STEP HAS A NAME
No result without a process. 3x + 5 = 14 doesn't become "x = 3," but rather: both
sides − 5, then both sides ÷ 3. This can be read aloud and repeated in the
test. Calculations are done precisely in fractions: One-third times
three is 1, not 0.9999999998.

YOUR OWN CALCULATION PROCESS
You can type in your process line by line. The app then tells you not
just "wrong," but from WHICH LINE it's no longer correct — and why.

WHAT'S INSIDE
Numbers: Fraction arithmetic with visible common denominator — the step where
things get stuck and which a calculator misses. Percent and logarithms (decibels, pH).

Terms: brackets, binomials, factoring, roots, simplifying fractions, rearranging formulas—with the caveats that a formula collection omits (t ≠ 0).

Equations: linear and quadratic, inequalities (where the sign is reversed), and systems of equations using all three methods.
Functions: zeros, vertex, slope, graph.
Analysis: derivatives with the name of each rule, drawing a tangent, antiderivatives and integrals—including the difference between integrals and area.

Geometry: Pythagoras, trigonometry, areas, vector calculus.

Probability: Laplace, tree diagrams, combinatorics, binomial distribution, hypothesis testing.


This includes the mathematics needed in physics—not as a separate chapter, but as continuous example material: rearranging v = s/t, the half-life, acceleration as a derivative.

THE INFO BUTTON
Next to each technical term is a small "i." One tap is all it takes: first the answer in everyday language, then the "why," then a concrete number to grasp, then the links one level deeper. A stumble becomes a path down instead of a dead end.

WHAT THIS APP DOESN'T DO
It doesn't guess. Division by zero, the square root of a negative number, a quadratic equation without a real solution: it says that it doesn't exist, instead of inventing a number that looks plausible.

And it tells you what it can't yet do. Sine, exponential function, and logarithm are missing for differentiation, as is integration by parts. Where a rule doesn't apply, the app tells you and explains why—instead of applying a formula that doesn't even apply there.

The calculation logic is machine-tested: over four thousand automatic checks are performed before a version is built. These include the ones that ensure everything—every transformation must remain the same value, every derivative must match the difference quotient, and every antiderivative must be differentiated back to the original function.

DATA PROTECTION
Understanding Math does not collect any personal data. No user account, no advertising, no in-app purchases, no tracking, and no internet connection is required. Your learning progress remains on your device and is not sent anywhere; you can delete it yourself at any time.

NOTE: A learning aid for mathematics lessons. It does not replace lessons or teachers.