Month: May 2025

Engaged Students, Better Results: La Salle’s Math Learning Platform With WirisQuizzes

Post author By Aida Alsina
Post date May 30, 2025

From Textbooks to a Personalized Digital Math Learning Platform

When La Salle San Ildefonso set out to replace printed math textbooks with digital tools, they needed more than just online worksheets—they needed a complete math learning platform. With WirisQuizzes integrated into Moodle, their teachers built a collaborative system that supports independent learning, personalized feedback, and scalable assessment.

What started as one teacher’s initiative has become a model adopted across multiple La Salle campuses, reshaping how students engage with math.

The Challenge

When La Salle San Ildefonso first decided to phase out physical math textbooks, they faced a critical question: How do we offer high-quality math learning in a wholly digital format without sacrificing feedback, rigor, or accessibility?

As teacher Javier Melchior explained, early digital tools offered little beyond binary right-or-wrong grading

“The only feedback we could give was whether the answer was right or wrong. That wasn’t enough”, Javier explained. ”What students needed was guidance – not just the solution, but the how behind the solution”.

This insight became a turning point for La Salle’s approach to digital education. It wasn’t just about digitizing content but about ensuring that students could learn actively and reflectively within a new system.

At the same time, the shift to digital demanded a scalable infrastructure for:

Creating large volumes of exercises quickly.
Providing real-time, personalized feedback.
Supporting teachers across varying levels of technical proficiency.
Giving students the tools to practice independently and meaningfully.

Other platforms like Google Classroom, while helpful for document sharing, lacked the sophistication for in-depth math evaluation and formative feedback.

The Solution

That’s when WirisQuizzes came into focus—not just as a plugin but as the core engine behind La Salle’s custom-built math learning platform.

Led by Javier and math teacher Guillermo Pérez González, the department began building a shared bank of exercises directly within Moodle using WirisQuizzes. These weren’t just questions—they were intelligent, dynamic exercises that could offer step-by-step feedback, track partial understanding, and regenerate with different data for unlimited practice.

“We discovered the true power of WirisQuizzes when we realized we could break down a problem into parts,” said Javier. “It’s not just about getting the final answer. If a student does the first 20% right, the platform can recognize and score that.”

WirisQuizzes became more than an assignment tool for students—it was their personal study assistant. “Now they ask us, ‘Is there a quiz for this topic?” Guillermo shared. “It’s become a natural part of how they study and prepare.”

The Implementation Process

La Salle’s implementation of WirisQuizzes was a grassroots initiative that grew into an institutional innovation. Here’s how it evolved.

Assessment

The shift began nearly a decade ago when La Salle removed printed textbooks for some math levels. With a digital-first model on the horizon, Javier started exploring alternatives. “I found WirisQuizzes online by chance,” he said. “And after testing its capabilities, I pitched it to my colleagues. From there, it just took off.”

Customization

Using Moodle’s system-level question bank, the teachers created hundreds of questions organized by topic: polynomials, functions, geometry, probability, and more. Every question included custom feedback. “Almost all our questions show the solution process,” said Javier. “This makes it easier for students to learn independently—even their parents can follow along.”

Importantly, this work was collaborative. Teachers built and reused each other’s content. “We never assigned categories formally,” said Guillermo. “If someone had free time, they’d jump in and add to the bank. It’s a shared resource for everyone.”

Deployment

WirisQuizzes was deployed through Moodle across the school. Teachers could:

Select questions from a shared bank.
Build quizzes quickly.
Offer time-limited assessments or practice exercises.
Use quizzes for classwork, homework, or even during substitute hours.

The school also exported question banks to other La Salle campuses in Tenerife, Madrid, and Gran Canaria. Adoption varied depending on each site’s IT support and teacher training, but the system was designed for easy export/import.

Training

While many core users were math or STEM teachers with programming experience, others found the “programming” aspect intimidating. Guillermo acknowledged this gap. “Some teachers hear ‘programming’ and think of C++,” he joked. “But it’s not like that. They’d see how simple it is if they just took one step.”

To address this, La Salle and Wiris discussed tailored training sessions that start simple, focusing on quiz-building basics before moving into more advanced logic and scripting.

The Results

La Salle’s math learning platform, powered by WirisQuizzes, delivered transformative results across several dimensions.

Improved Student Autonomy & Motivation

Students began voluntarily requesting quizzes to practice new topics. “It’s like they have a personal tutor,” said Javier. In one memorable example, he logged in on a weekend to find nine students had already completed a practice quiz and scored a perfect 10. “They were competing healthily. It became fun.”

Collaborative Efficiency Among Teachers

The math department created a bank of over 600–700 questions, reusable across grade levels and subjects. This significantly reduced prep time while increasing question quality and consistency.

Parental Engagement and Transparency

Because quizzes included feedback, parents could follow along, even if they weren’t strong in math. “Some told us they were thrilled to see their child working independently,” Guillermo shared.

Formative Assessment at Scale

Teachers used quizzes to diagnose student progress week by week. “In Bachillerato, I might run three quizzes weekly,” said Guillermo. “And they all count toward the grade. It keeps everyone working consistently.”

“WirisQuizzes isn’t just a quiz engine,” Javier added. “It’s a full feedback system. It’s the backbone of our math learning platform.”

The Future of WirisQuizzes at La Salle

La Salle continues to expand the use of WirisQuizzes beyond math:

They’ve developed questions for economics, technology, and even geography.
Some teachers are exploring how AI-based feedback could provide personalized remediation paths.
A growing number of educators across La Salle’s network are joining upcoming training sessions to learn how to build questions and customize feedback.

They’ve also expressed interest in exploring remote proctoring, integrating with other LMS platforms like Google Classroom, and co-developing content with other schools.

Rounding Off

La Salle’s transformation is a shining example of how a school can build its own collaborative, intelligent, and scalable math learning platform. By integrating WirisQuizzes into every level of instruction—from the classroom to home study—teachers empowered students with autonomy, parents with transparency, and the school with data-driven teaching strategies.

What started as one teacher’s experiment has become a system-wide initiative that is changing how La Salle teaches and how students learn.

👉 Want to build your own feedback-driven math platform?

Get in touch today

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Towers of Hanoi: A Math and Programming Challenge

Post author By Aida Alsina
Post date May 21, 2025

Towers of Hanoi: A Math and Programming Challenge

The Towers of Hanoi is one of the most iconic puzzles in the field of mathematics and computer science. With its simple structure and transparent rules, this problem has captivated mathematicians and amateurs alike, making it an intriguing challenge since its creation.

According to the legend, the Towers of Hanoi were conceived by a group of monks in an ancient temple in India. In the center of this temple, three golden pillars stood, upon which rested 64 disks of various sizes, arranged in the first pillar in an orderly fashion: the largest disk at the base, with progressively smaller disks stacked on top, until reaching the smallest disk, placed at the top.

The monks’ objective was to move all the disks from the first pillar to the third, using the central pillar as an auxiliary. To accomplish this task, they had to follow a strict set of rules:

Only one disk can be moved at a time.
A disc can never be placed on top of a smaller disc.

Legend says that when all the disks were correctly transferred to the last pillar, the world would come to an end. However, how close is the end of the world, really? How long would it take to complete this challenge?

This challenge was officially introduced by the French mathematician Édouard Lucas in 1883 as part of his research in number theory and quickly became a popular problem.

Next, we will analyze the solution of this problem from a mathematical perspective, breaking down its key principles and explore how it transforms into an interesting programming challenge.

Recursion as a Solution to the Puzzle

The challenge of the Towers of Hanoi is not only in moving the disks from one pillar to another following the strict rules but also in calculating how many moves are needed to solve the problem of moving n disks from the origin pillar to the destination pillar.

The most efficient way to approach this problem is through recursion, a fundamental technique in programming. Recursion allows the problem to be divided into smaller subproblems, where the solution of each subproblem leads to the solution of the original problem.

In the case of the Towers of Hanoi, recursion applies naturally, and we can divide the problem of moving n disks into three steps:

Move the first n – 1 disks from the origin pillar to the auxiliary pillar, using the destination pillar as the auxiliary.
Move the largest disc (the disc n) from the origin pillar to the destination pillar.
Move the n – 1 disks from the auxiliary pillar to the destination pillar, using the origin pillar as an auxiliary.

We can repeat this pattern recursively, reducing the number of discs with every step until we reach a base case where only one disk remains, which we just directly move.

In mathematical terms, the minimum number of moves to solve the problem with n disks equals the number of moves needed to solve it for n – 1 disks, plus one to move the largest disk, plus the number of moves needed to solve it for n – 1 disks again. This formula yields the result:

TH( n ) = TH( n – 1 ) + 1 + TH( n – 1 ) = 2TH( n – 1 ) + 1

Where TH( n ) represents the number of moves needed to solve the problem with n disks.

From the above formula, we will substitute each TH( i ) by its corresponding expression until we reach TH( 1 ) . Then, we will replace TH( 1 ) by 1, since, with only one disc, it is possible to move it directly to the destination pillar, which justifies that the minimum number of moves in this case is 1.

Let’s see the expression developed:

We first substitute TH( n – 1 ), and we obtain:

TH( n ) = 2TH( n – 1 ) + 1

TH( n ) = 2( 2TH( n – 2 ) + 1 ) + 1 = 2²TH( n – 2 ) + 3

Now we substitute TH( n – 2 ):

TH( n ) = 2²TH( n – 2 ) + 3

TH( n ) = 2²( 2TH( n – 3 ) + 1 ) + 3 = 2³TH( n – 3 ) + 7

If we continue substituting in this way, we will arrive at a general formula:

TH( n ) = 2^k TH( n – k ) + (2^k – 1)

Where k is the number of steps backward in the recursion.

For k = n – 1 we arrive at TH( 1 ), the base case:

TH( n ) = 2²TH( n – 2 ) + 3

We know that TH( 1 ) = 1, then we obtain:

TH( n ) = 2^{n – 1} · 1 + ( 2^{n – 1} – 1 ) = 2ⁿ – 1

We have shown that the number of moves needed to solve the Towers of Hanoi with n disks is:

TH( n ) = 2ⁿ – 1

Solving the Puzzle Using Mathematical Induction

Another way to approach the solution to the Towers of Hanoi puzzle is to use mathematical induction, a technique used to prove that a statement is true for all natural numbers, based on two fundamental steps: the base case and the inductive step.

In this case, the goal is to show that to move disks from the first pillar to the third pillar, 2ⁿ – 1 moves are required. Let’s break this process down with a demonstration by induction.

Base case:

Suppose we have only one disk. In this scenario, it is clear that only one move is needed to move the disk from the source abutment to the target abutment. That is, for n = 1, the number of moves required is 2¹ – 1 = 1, which is true.

Inductive step:

Now, suppose that the statement is true for n = k, i.e., that to move k disks requires 2^k – 1 moves. What we must prove is that the statement is also true for n = k + 1.

To move k + 1 disks, we first need to move the upper disks from the origin pillar to the auxiliary pillar, using the destination pillar as an auxiliary. According to our inductive hypothesis, this will take 2^k – 1 moves.

Next, we move the larger disk (the disk k + 1) from the origin pillar to the destination pillar, which requires just 1 move.

Finally, we move the k disks from the auxiliary pillar to the destination pillar, using the origin pillar as an auxiliary, which will also take 2^k – 1 moves, according to our inductive hypothesis.

Therefore, the total number of moves required to move k + 1 disks is:

(2^k – 1) + 1 + (2^k – 1) = 2^k+1 – 1

Thus, we have shown that if the statement is true for n = k, it is also true for n = k + 1.

As we have observed, it is true for 1. By mathematical induction, we can conclude that for n disks, the minimum number of necessary moves is 2ⁿ – 1.

Going back to the legend, if the monks were extremely fast and could move a disk in just one second, we could calculate how long it would take to complete the challenge with 64 disks. According to the formula, the total number of moves would be 2⁶⁴ – 1, approximately 18.4 quintillion moves. With each of these taking just 1 second, this gives us 18.4 quintillion seconds. Converting these into years, we get that the total time would be approximately 581.4 billion years. So, if the legend turned out to be true, the end of the world would still be a long way away!

CalcMe formula We note that the function describing the number of moves needed to solve the Towers of Hanoi is exponential, meaning that it grows rapidly as we increase the number of disks. In the following graph, we can visually see how this function spikes, clearly illustrating the exponential growth.

graphic formula

This visual support allows us to confirm, once again, that completing the challenge with 64 discs would take an extraordinary amount of time.

If you liked this mathematical challenge and you were surprised by its solution, don’t hesitate to share this article! And if you dare, test your skills by solving the Towers of Hanoi puzzle: will you manage to move the disks in the exact number of steps? Let us know your experience!

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AI in Mathematics: The Revolution in Scientific Writing

Post author By Aida Alsina
Post date May 6, 2025

Artificial Intelligence (AI) is a field of computer science that seeks to develop systems able to perform tasks that traditionally require human intelligence, such as logical reasoning, problem solving, and learning. Based on advanced algorithms and machine learning models, AI can analyze large volumes of data, identify complex patterns and adapt autonomously to new contexts.

In mathematics, these capabilities are transforming the way knowledge is generated, verified, and communicated. From automating demonstrations to generating detailed explanations, AI is facilitating the work of researchers, teachers, and students. In addition, its ability to process natural language is improving the writing of mathematical papers, making texts more accessible, accurate and structured.

In this article, we will explore how AI in math is revolutionizing mathematical writing and how Wiris’ tools are part of this advancement.

The Role of AI in math and the Creation and Editing of Mathematical Content

Writing scientific papers in mathematics has always been a challenge due to the complexity of their notations and symbols. Traditionally, mathematicians have relied on handwriting or the use of complex typesetting languages. However, with the advent of AI, the process of creating and editing scientific documents has evolved exponentially.

Artificial intelligence has brought multiple benefits to the writing of mathematical papers, facilitating both the writing and the editing and publication of academic papers. Below are some of the main ways in which AI is impacting this area.

Handwriting recognition

One of the most significant advances has been the development of systems capable of interpreting and digitizing handwritten notes. Traditionally, mathematicians wrote their equations and proofs on paper, which was time-consuming if they needed to transcribe them into a digital format. With AI-based handwriting recognition tools, such as those built into MathType, it is now possible to directly handwrite equations into our touch devices and automatically convert them into editable digital text.

This not only saves time but also reduces transcription errors and allows you to work more efficiently. In addition, this type of technology is especially useful for students and teachers, as it facilitates the conversion of notes into organized documents without the need for manual typing.

Formula automation

In the creation of mathematical articles, writing formulas accurately is essential. Traditionally, this required specialized tools that, while powerful, could be complex and demanded a deep understanding of their syntax and structure, such as LaTex.

Advancements in technology have enabled the development of tools like MathType, which simplify equation writing without the need for coding. Instead of memorizing commands and code structures, users can simply enter their formulas through an intuitive graphical interface. This democratizes access to mathematical writing, allowing more people, regardless of their technical expertise, to create high-quality mathematical documents.

Another key aspect is the automatic correction of errors in equations. AI in math can identify inconsistencies in formula writing and suggest real-time corrections, preventing mistakes that could compromise the validity of an academic paper.

Optimization of editing

Another benefit that AI has brought is the optimization of the editing of mathematical documents. In the past, mathematicians and scientists had to manually check their documents for errors in equations, notation and text structure. Today, there are AI algorithms embedded in editing programs that can analyze the consistency of mathematical expressions, suggest improvements in writing and detect inconsistencies.

AI-based writing assistants, such as those integrated into advanced text processors, can help improve the clarity and readability of mathematical articles. In addition, they provide stylistic recommendations to give the paper a logical and easy-to-follow structure, which is crucial in academic paper writing.

The integration of AI into mathematical writing is not just an evolution but a revolution that is transforming the way we create, edit, and share scientific knowledge. Tools like Wiris, with their powerful capabilities, are making mathematical writing more accessible, efficient, and error-free. As these technologies continue to advance, they will further bridge the gap between human intuition and machine accuracy, making the work of researchers, teachers, and students alike easier. If you found this exploration interesting, share it with your peers and join the conversation about the future of AI in math.

If you’d like to find out more about our products, please feel free to get in touch with our Sales team at sales@wiris.com for more information.