The science

Why Rika works.

Rika builds understanding, not just answers. Here’s the science, written for parents, not engineers.

Just want the basics? See how it works →

Seven things Rika studies that a test score can’t tell you

A grade says “72%.” It doesn’t say why. Rika tracks seven different dimensions of your child’s mathematical thinking, every time they pick up the stylus.

1

Are they getting it right?

Not just overall: by topic, by difficulty, and over time. Scoring 80% on easy problems is very different from 80% on hard ones. Rika knows the difference.

Updated after every single problem.
2

Is the work smooth or strained?

How fast do they move through steps? How much do they erase? A child who solves a problem correctly but slowly and with lots of restarts is in a very different place than one who writes fluidly.

Measured from writing speed, pauses, and eraser use.
3

Will they remember this next week?

Understanding something today doesn’t mean remembering it Thursday. Rika tracks how quickly each skill fades for your child and schedules a review at exactly the right moment – before they forget.

Timed using proven spaced-repetition research.
4

What kind of mistakes do they make?

A careless arithmetic slip is different from a deep conceptual misunderstanding. A child who catches their own errors needs different guidance than one who doesn’t notice. Rika classifies every mistake.

Categorized into conceptual, procedural, and careless errors.
5

How confident are they?

A correct answer written with hesitation and doubt is a warning sign. A wrong answer written with confidence is a different kind of problem. Rika reads the confidence behind the work, not just the result.

Inferred from writing patterns and timing between steps.
6

How hard can they go?

What’s the toughest problem your child can solve reliably? This ceiling adjusts automatically as they improve – always pushing them just past comfortable, never into overwhelmed.

Tracked per topic and updated each session.
7

Are they actually improving?

Week-over-week trends, breakthrough moments, and early warning signs. You’ll see when they’re gaining momentum – and when something needs your attention before it becomes a problem.

Weekly parent reports with clear trend lines.

412 math skills from 5th grade through precalculus

Every skill your child encounters in school is mapped, organized, and connected. When they struggle with algebra, Rika can trace it back to the fraction skill from three years ago that’s causing the problem.

Most apps cover topics. Rika covers skills – and knows which ones depend on which.

72

Numbers

Fractions, ratios, integers, proportions

158

Algebra

Expressions, equations, systems, functions

96

Geometry

Angles, triangles, area, coordinate geometry

44

Statistics

Data, graphs, probability, distributions

26

Trigonometry

Right triangles, unit circle, identities

16

Precalculus

Polynomials, exponentials, sequences

Rika doesn’t just track what your child knows. It tracks how they think.

Getting the right answer matters. But how a child gets there matters more. Rika analyzes 12 different kinds of mathematical thinking and builds a profile of your child’s strengths and blind spots across all of them.

Recall

Can they pull facts and formulas from memory when needed?

Execute

Can they follow a procedure accurately, step by step?

Think backward

Can they reverse an operation or work from the answer back to the question?

Translate

Can they turn a word problem into an equation, or a graph into a sentence?

Compare

Can they spot what’s the same and what’s different between two problems?

Estimate

Can they ballpark an answer before they calculate, and know when something looks wrong?

Sort and classify

Can they recognize what type of problem they’re looking at and choose the right approach?

Break it down

Can they split a hard problem into smaller, manageable pieces?

Build something new

Can they construct a solution or create a new representation – not just follow one?

See the pattern

Can they extend a pattern or find a rule that applies to many problems?

Prove it

Can they explain why something is true, not just that it’s true?

Find the best way

Can they choose the most efficient approach when there are multiple paths?

RecallExecuteReverseTranslateCompareEstimateClassifyDecomposeConstructPatternProveOptimize

One student’s thinking profile

StrongestRecall, Execute, Estimate
DevelopingTranslate, Compare, Classify
Focus nextProve, Pattern, Construct

A balanced profile means a child can approach problems from multiple angles. Lopsided profiles reveal exactly where to focus – and Rika adjusts automatically.

The way your child solves a problem matters as much as the answer

When your child writes with a stylus, Rika doesn’t just read what they wrote. It studies how they wrote it – the pauses, the speed, the erasures, the restarts. These tiny signals reveal what’s really going on in their head.

Long pauses

When your child stalls between steps, it often means they’ve hit the limit of what they can hold in their head at once. Rika notices and simplifies the next prompt.

Frequent erasing

Are they fixing careless slips or second-guessing everything? Combined with timing, Rika can tell the difference – and responds accordingly.

Side work and scratch notes

Using scratch space shows your child is managing a complex problem by breaking it into pieces. That’s a sign of good strategy, not struggle.

Writing speed

Fast, fluid writing usually means confidence and fluency. Slow, careful writing might mean deep thinking – or it might mean confusion. Rika reads the context.

Starting over

Rewriting the same step multiple times is a signal that your child isn’t sure of their approach. Rika shifts to more supportive guidance before frustration builds.

Every child gets a unique math portrait

Rika combines what your child knows (412 skills), how they think (12 thinking types), and how well they’ve mastered each combination. The result is a detailed portrait that’s unique to your child – and it updates with every problem they solve.

One child might be strong on procedural execution but weak on translation – fluent at solving equations the moment they’re written down, but lost on word problems. Another might have the opposite shape: great at intuiting what the problem is asking but shaky on the procedure. They’d score the same on a test. Rika can tell them apart.

A sample portrait · darker means stronger mastery

Needs work
Developing
Strong

No two children’s portraits look the same. The light areas are where Rika focuses next.

This isn’t guesswork. It’s decades of learning science.

Every decision inside Rika is grounded in peer-reviewed research on how students actually learn math. Here are the principles that drive it.

Mix it up, remember more

When students practice different problem types in the same session instead of repeating one type over and over, they remember nearly twice as much a month later. Rika mixes concepts automatically. Your child won’t even notice it’s happening.

Review at the right moment

Forget too soon and the review is wasted. Wait too long and the knowledge is gone. There’s an optimal window for reviewing each skill – and Rika tracks it for every skill your child has learned.

Hard enough to grow, not so hard they quit

Learning happens when the work is just past comfortable – challenging enough to stretch, but not so hard that a child shuts down. Rika keeps every session in this zone by adjusting difficulty in real time.

Writing by hand matters

Writing math by hand activates different parts of the brain than typing or tapping. The physical act of forming equations engages spatial reasoning and memory in ways that clicking an answer button never will.

Practice the weak spots, not the easy stuff

Random practice doesn’t build expertise. Practice has to target what’s actually weak, and at the right difficulty. Rika uses your child’s math portrait to prescribe exactly the right problems.

Seeing your own progress changes everything

Students who can see what they know and don’t know make better decisions about where to focus. Rika makes learning visible – and that visibility builds motivation and ownership.

Rika’s design draws on peer-reviewed research from Rohrer, Kornell, Bjork, Cepeda, Vygotsky, Sweller, Mueller & Oppenheimer, Longcamp, Ericsson, Schraw & Dennison, and Zimmerman. Full bibliography on request.

Read this far? You’re our person.

Rika is free on iPad. Download it, snap the first worksheet, and watch what happens.

Download on the App Store

Free. Requires iPad and Apple Pencil. We never sell your child’s data.