Artificial intelligence for science education.

Prepare a lesson explaining the derivative as the slope of the tangent line, for a final-year high school class

Mathematics

The derivative is a slope

Project co-funded by the European Union

PrismaX is our AI agent: it builds interactive courses for teachers and tailored lessons for learners, with animated figures and self-checking exercises.

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Mathematics, physics, statistics, data analysis, machine learning.

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Whole courses, chapter by chapter.

Every chapter has an explanation, an animation and exercises.

How a machine learns

The line that follows the data

For a machine, learning means finding the numbers that make it wrong as little as possible. Here there is only one: the slope $w$ of the line $y = wx$ , which must pass as close as possible to six points.

For each point we take the residual, how far the point lies above or below the line. The error is the mean of the squared residuals:

L(w) = \frac{1}{n}\sum_{i=1}^{n} \left(y_i - w\,x_i\right)^2

where $(x_i,\,y_i)$ are the points and $n$ is how many there are.

Drag the line or the point on the curve: the error changes with w.

Try it

Exercise

With the line $y = x$ and the two points $(1,\,1)$ and $(2,\,3)$ , what is the error $L$ ?

0.5Check

Correct!

The residuals

$1 - 1 = 0 \qquad 3 - 2 = 1$

The mean of the squares

$L = \tfrac{0^2 + 1^2}{2} = 0.5$

Problems and solutions, step by step.

New variants whenever you want, each one checked automatically.

Exercise

Solve $2(x - 3) = x + 4$ .

AnswerCheck

See how each student answers.

Teacher only

Students’ results

sample data

ChapterThe derivative4 students · 26 answers checked

By student

Student	Checks	Right	Wrong	Solutions opened	Last active
Emma R.	6	5	1	0	14 Nov, 10:42
Jack B.	9	5	4	2	14 Nov, 10:41
Sophie L.	4	4	0	0	14 Nov, 10:37
Liam T.	7	4	3	1	14 Nov, 10:33

Recent activity

10:37

Sophie L.Right(6)

Check · Ex. 1Right(6)

10:33

Liam T.—

Opened the solution · Ex. 2—

10:31

Liam T.Wrong(12)

Check · Ex. 2Wrong(12)

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How we built PrismaX.

A first call to the model plans the request in JSON; the next ones write the lesson, the figure and the exercises. The code runs in an isolated sandbox and, if it fails, goes back to the model with the error.

Request

“Three chapters…”

Plan

the director, in JSON

Lesson

text and formulas

Figure

three.js code

Exercises

with their checks

Sandbox

isolated iframe

Chapter

cost recorded

Request

Plan

Lesson

Figure

Exercises

Sandbox

Chapter

Development

Claude CodeNext.jsTypeScript

Infrastructure

CloudflareSupabaseStripe

Models

OpenRouterGeminiOpenAI

Figures and math

three.jsJSXGraphKaTeXmath.js

Our services.

For schools, universities, companies and startups.

StudentRightWrong

Emma R.51

Jack B.54

Sophie L.40

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PrismaX for everyone enrolled and every teacher in the course, with restricted access and results by student and by exercise. For companies too, with seats for in-house trainers.

We start with a pilot on one class.

Turnkey interactive module

We build it for you: animations, exercises with automatic checking, an entry and a final test, with your brand.

What do you want to change or add?

Workshop

Creating interactive lessons with AI: hands-on training for teachers and trainers, with one year of access included.

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AI agents

We also build agents, data analysis and products on request, with processes and technologies similar to those we used to build PrismaX.

About us.

Edukai was founded in Rome in November 2023 to develop intelligent, accessible technologies that help startups, universities, companies and young talent design solutions with high technological, educational and social impact.

Andrea De Cosmo

Founder and CEO, Edukai

Instructor at Temple University Rome

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