MathTrail
Olympiad coach · Grade 3A fence is 12 metres long. Posts stand every 3 metres, including at both ends. How many posts are there?
|--3--|--3--|--3--|--3--|
Why olympiad maths for your child
School teaches how to solve a problem by an example worked in class. Olympiad problems teach how to find a way when there is no example to follow. Up to grade 6, a parent can prepare a child for them, and MathTrail is made for that.
Grades 1–6FreeOpen source
A school sum
You need to know how to divide.
12 ÷ 3 = 4
An olympiad problem
A fence is 12 metres long. Posts stand every 3 metres, including at both ends. How many posts are there?
|--3--|--3--|--3--|--3--|
Answer: 5Trap: 4 is the gaps, not the posts
You need to understand what is going on.
What research has found
Olympiad problems have been set to children for more than a century, yet careful studies of what they do are few. These are four of them.
Preparation shows at school too
In Germany, third- and fourth-graders took a course of olympiad-style problems. At the Mathematical Olympiad they did clearly better than children who entered without the course, and the fourth-graders also did better on a school maths test. Their teachers had picked them for the course.
Olympiad schools score higher in maths
Brazil's maths olympiad for public schools is open to every pupil, and 19 million took part in 2009. Schools that entered it had better maths results among their ninth-graders on the national test, and better still the more years they had entered.
Strong olympians go far in science
The higher a teenager scored at the International Mathematical Olympiad, the more often they went on to a doctorate, published research, were cited and won the highest prizes in mathematics.
Reasoning is learned from the age of six
How well six-year-olds reasoned logically foretold their maths 16 months later. Children who were taught to reason this way made more progress in maths than children who were not.
School and olympiads teach different things
This is no reproach to school, which has a different job. But the knack of finding a solution when no method is given does not appear by itself. It is trained.
| A usual lesson | An olympiad problem | |
|---|---|---|
| How the problem is built | A method is shown, then repeated on similar examples | No method is given, and it has to be found |
| What counts | Working fast and without slips | Understanding what is going on, and explaining why |
| What a mistake means | A mark lost | A sign of where the reasoning turned the wrong way |
| What it teaches | To use a tool you know | To invent one when there is none |
Why school has no time for it
A syllabus for the whole class
A teacher has to bring every pupil up to the standard. Hours for problems beyond the syllabus are hard to find.
A test sees the answer, not the thought
A test checks the result. There is seldom time to go through how a child reasoned, and where exactly it went wrong.
A maths circle is not everywhere
Not every school runs an olympiad circle, and the nearest one may be far away or take only older children.
A parent can prepare a child
What you do not need
- A degree in maths
- To know the solutions in advance
- To find and check problems
The problems, their answers and the explanation of mistakes are MathTrail's part.
What you need
Your child's curiosity
An olympiad problem is a puzzle, not a test. A child should be curious, not afraid of being wrong.
To explain what it is for
Not “to get top marks”, but to learn to invent a way when nobody has shown how.
Your time and interest
A little time beside your child, better often than a lot at once. Your interest in a problem is catching.
How to explain to a child what it is for
- “It's like a riddle: the answer is hidden, and you can find it.”
- “Here you are allowed to be wrong: a mistake shows where to think again.”
- “The best part is not the answer, but how you got to it.”
How MathTrail teaches to think
Not by the number of problems, but by what happens around each one.
One problem, one idea
Every problem belongs to a topic, such as “Enumeration”, “Parity and alternation” or “Knights and liars”. The topics form a map, from the simple to the hard.
A problem within reach
Every topic has a rating of its own. By it MathTrail chooses what comes next, the topic and the difficulty; the grade only sets the start.
A mistake is a diagnosis
Behind every wrong option stands a named trap. The explanation starts from how the child reasoned, not from the right answer.
A hint instead of the answer
A child can ask for a hint, or ask in their own words, “why not 6?”. The model answers about this very problem.
Why this is no ordinary app
In a study of the apps that three-to-five-year-olds play, about two in three had designs that keep a child playing longer (Radesky et al., 2022). MathTrail is built differently, and that can be checked.
A program checks every problem
The model writes a problem and a program that solves it. The server runs the program in a sealed sandbox and checks that exactly one option is right, that the answer agrees, that the text suits the grade and that it does not repeat the text of earlier problems. A problem that fails never reaches the child.
Free, and plainly why
MathTrail has no AI of its own. The problem is written by the model of your chat, within your plan, and Claude's free plan will do. The server has almost nothing to pay for, so there are no subscriptions, no ads and no locked topics.
The data stays with you
The child's profile is a file in your Google Drive. Only the answer and the solution of the problem being solved are sealed, so that the child cannot peek. The server keeps nothing between requests and sells nothing.
Nothing to keep a child at the screen
No coins, no chests, no timers, no ads. Once the problem is solved, the chat can be closed and the problem talked over at dinner.
The code is open, and every claim this page makes about MathTrail can be checked in it.The code on GitHub
Start with one problem, together
Connecting takes a few steps. The first problem is best solved side by side with your child.