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Protected: What is the Collatz Conjecture?

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Instant Feedback in Open-Ended Math Questions: Key Takeaways from BETT 2025

Recently, we had the exciting opportunity to showcase our approach at BETT 2025: Enhancing Open-Ended Math Questions with Instant Feedback to teachers, publishers and educators alike at the conference in London. Feedback plays a crucial role in guiding learning, and at the event, we focused on how instant feedback in open-ended math questions can dramatically enhance students’ mathematical understanding, all the while assisting teachers and making their day to day more efficient.

Unlike traditional multiple-choice problems, open-ended mathematics questions require deeper thinking as they are questions that a student can freely answer without a predefined format, making personalized feedback more vital. In this article, we will explore the significance of instant feedback in open-ended math questions and discuss how different types of feedback—corrective feedback, confirmatory feedback, and suggestive feedback—can help students improve.

 


 

Why Instant Feedback Matters in Open-Ended Math Questions

The Power of Feedback in the Learning Process

Feedback is integral to the learning process, helping students refine their thinking and improve their understanding. This is especially true for open-ended mathematics questions, where there is often no one right answer. In such cases, instant feedback in open-ended math questions can make a significant difference in guiding students toward the correct solution.

During BETT 2025, we discussed how instant feedback in math questions not only helps students correct mistakes quickly and builds their confidence but how it also assists teachers in the class environment making the teaching and learning process much more efficient.

 

Types of Feedback for Open-Ended Math Questions

Different types of feedback are required depending on the student’s needs and the nature of the question. The three main types of feedback we focused on at BETT 2025 are suggestive feedback, confirmatory feedback, and corrective feedback.

Suggestive Feedback in Math Questions

Suggestive feedback in math questions guides students to discover the solution themselves. Instead of providing the correct answer outright, suggestive feedback encourages independent problem-solving. For example, if a student suggests “2 and 8” as the two numbers whose sum is 10 and product is maximum, suggestive feedback might be: “What happens if you try numbers closer together?”

 

Confirmatory Feedback in Math Questions

Confirmatory feedback in math questions is designed to reinforce correct answers. When students solve problems correctly, feedback like “That’s correct, well done!” helps to affirm their understanding and boosts their confidence.

In the case of open-ended math questions, confirmatory feedback is invaluable for ensuring students stay motivated, especially when they are tackling complex problems.

This type of feedback fosters critical thinking and encourages exploration, making it an essential tool for developing problem-solving skills in open-ended math questions.

 

Corrective Feedback in Math Questions

Corrective feedback in math questions identifies mistakes and provides the correct answer. For example, if a student incorrectly solves x^2=4 as x=4, the corrective feedback would be “The correct solution is x= +-2”.

While effective for addressing misunderstandings, corrective feedback should be used in moderation, as over-reliance on it can hinder the development of problem-solving skills.

 


 

The Teaching Cycle: A Framework for Feedback Application

At BETT 2025, Mrs. Brook, a fictional high school math teacher, shared her teaching cycle, which integrates corrective, suggestive, and confirmatory feedback seamlessly. Her cycle is designed to maximize learning outcomes by aligning feedback strategies with the different stages of teaching.

The Four Stages of Mrs. Brook’s Teaching Cycle

  • Delivering the Content

Mrs. Brook begins her teaching by introducing and explaining the content to her students. This step ensures all students have a baseline understanding of the topic.

  • End-of-Class Knowledge Validation

Following the lesson, Mrs. Brook conducts an end-of-class knowledge check. This is where corrective feedback plays a crucial role. For example, if a student misunderstands a concept or calculation, Mrs. Brook provides immediate corrective feedback to clarify misconceptions.

 

  • Recommending Practice at Home

Mrs. Brook encourages her students to practice independently. At this stage, she often employs suggestive feedback to guide students without directly giving them answers, helping them to think critically and explore solutions. Additionally, confirmatory feedback is used to reinforce correct solutions and build student confidence. When students solve problems accurately, Mrs. Brook provides positive reinforcement such as “Great job!” to motivate them and affirm their understanding.

 

  • Assessing Students’ Knowledge Levels

After students have had the opportunity to practice, Mrs. Brook assesses their progress to identify areas of improvement. During this phase, she focuses on encouraging students to reflect on their learning journey and strive for continued growth. She fosters a positive environment by recognizing their efforts and offering motivation to help them stay engaged and confident in their abilities.

This cyclical model of teaching and feedback showcases how structured feedback enhances learning and ensures students’ needs are addressed at every stage​Tech.

 


 

Wrapping up: Embracing the Future of Math Education with Wiris

At WIRIS, we’re committed to supporting educators with the tools they need to provide effective feedback. Our Learning Lemur and WirisQuizzes products ensure that instant feedback in open-ended math questions is accessible and customizable, helping students succeed in their math learning journey.

As technology continues to evolve, the integration of instant feedback into open-ended math questions will only become more critical. We look forward to the continued evolution of math education, driven by personalized learning and real-time feedback.

Unlock Instant Feedback Today

 

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Celebrating International Day of Education: Empowering Minds

Education is the foundation of progress, fostering knowledge, understanding, and innovation across the globe. The International Day of Education, celebrated annually on January 24th, underscores the importance of education as a fundamental human right and a key driver for sustainable development, serving as a reminder that quality education is crucial for achieving global goals, including reducing inequality and cultivating growth.

As we celebrate the International Day of Education, it is an opportune time to reflect on the transformative power of learning tools that enhance educational experiences. Among these tools, MathType and WirisQuizzes stand out in the realm of mathematics’ education, making a significant impact on the way we teach and learn.

Empowering Mathematics Education

Mathematics is a universal language that transcends borders and plays a crucial role in developing critical thinking and problem-solving skills. However, teaching and learning mathematics can often be challenging, requiring innovative approaches and tools to engage students effectively.

MathType is a powerful equation editor that allows educators and students to create mathematical expressions and equations digitally with ease. The intuitive interface of MathType empowers users to focus on mathematical concepts rather than struggling with the complexities of formatting.

WirisQuizzes, on the other hand, provides an assessment tool for STEM subjects, withinteractive and personalized quizzes. This tool goes beyond conventional assessments, offering a diverse range of question types and adaptive feedback to enhance the learning experience.

On this International Day of Education, let’s celebrate the strides made in advancing educational technologies that empower both educators and students. These tools contribute to fostering a more inclusive, interactive, and effective approach to mathematics education. Together, we can pave the way for a future where education is not just accessible but also a source of inspiration and empowerment for generations to come.

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Wiris’ New Partnership with Moodle

MathType, the New Moodle’s Certified Integration Partner

Wiris is pleased to announce our new strategic partnership with Moodle. Wiris has earned the title of Moodle’s Certified Integration Partner by offering MathType, a powerful and reliable add-on that elevates the quality of the online learning experience. This integration meets exacting technical standards and security requirements, addressing real-world educational needs.

With MathType, Moodle users can easily create and edit mathematical equations and formulas directly within the platform. It allows the inclusion of math expressions and formulas into assignments, questions, or communications between users. Whether users prefer the intuitive toolbar or the touch screen capabilities with handwriting recognition, MathType offers versatile methods for expressing mathematical concepts within the Moodle environment.

This partnership will benefit both companies, streamlining the process of selecting and integrating the necessary tools to extend Moodle’s functionality. It provides the assurance of tools that have demonstrated compliance with rigorous technical standards and security requisites, ultimately enhancing the learning experience for our users with user-tested, endorsed integrations. 

“Our solutions have been integrated with Moodle for over 15 years. As we continue to collaborate closely with Moodle, we’re inspired by the positive impact our joint efforts will have on students and educators worldwide,” says Ramon Eixarch, CEO and Co-Founder of Wiris.

At Wiris, we are excited about this new chapter, enthusiastic to further enhance our services, and deeply appreciative of the confidence placed in us.

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Overcoming Math anxiety

 

How many times have we heard people say ‘I am not a numbers person’ or ‘Math gives me the jitters’? Many times, it would seem. Math anxiety is, at the very basic level, a fear of using numbers in any form, be it calculating or understanding concepts through numbers and data, large or small. 

The Mathematical Association of America has said that according to some estimates, 93% of American adults experience some form of Math anxiety. Math anxiety has been studied by psychologists and scientists for years, the first such identification of ‘number anxiety’ going way back to 1957. 

An initial understanding of Math anxiety tried to separate it from general anxiety and performance. If we are confident in Math, we perform better at it. The Program for International Student Assessment conducted a massive global study of 15-year-old students across 64 countries in 2012. The study found that Math anxiety was negatively related to Math performance. Students with high levels of Math anxiety performed poorly in the subject compared to those who displayed lower levels of anxiety. The Math anxiety lights up a fear centre in the brain, and it shuts down the problem-solving ability of the student, even though he/she is very capable. 

Math anxiety’s negative impact 

Math anxiety is very real, and could prevent a student from reaching his/her optimum career potential. The lack of confidence in Math, and the early years of negative beliefs about one’s innate ability with numbers is known to lead to a persistent anxiety that is prevalent throughout one’s student years and even later. As a result, many students hesitate to choose STEM, instead opting for subjects that do not involve Math. Even though they may have a great ability to grasp complicated concepts, and the intellect to solve problems, students evade STEM subjects so as not to deal with numbers on a daily basis. 

Gender inequality

Several studies show that math anxiety seems to be higher in females than in males, although gender-related differences regarding math performance are small or non-existent. This illustrates that math anxiety has a gender bias due to the impact of gender stereotypes. These stereotypes generate subconscious self-barriers among girls, who regard themselves as less capable of performing well in math and STEM.

Math at work

As the future of work demands more use of Big Data, analytics and quantifying human experiences, the need for talent in numbers is only set to increase. The US Bureau of Labor Statistics has estimated that between 2016 and 2026, there will be a 28% increase in occupations that use math heavily. This means that students who are comfortable with Math can lean into these professions and have better job prospects. But what about those dealing with Math anxiety? It will be a choice of facing the anxiety and overcoming it, or finding other occupations that do not need Math. 

Overcoming Math anxiety

The love (or the hate) for Math has seeds sown in childhood. Parents and teachers have a crucial role to play in making math fun for children. They can do this by ensuring that their own anxiety, if any, is not transferred to the child. 

It is also important to break stereotypes and imaginaries concerning math: We need to overturn the perception that maths is a difficult, boring and men-concerning subject.
Parents can be conscious of introducing Math concepts of problem-solving in everyday life situations. Math should be positioned as a fun subject through games, puzzles and fun activities that take the fear out of using numbers and calculation. Also, schools and institutions must perform a task to draw attention to women role models in STEM. 

Technology can help make Math fun in the larger context of game-playing, problem-solving and fun-based learning activities. Apps and websites with an interactive experience can appeal to students’ achievement goals, therefore reducing the fear of numbers. 

Dealing with Math anxiety demands a holistic societal approach with increased awareness at all points of interaction in a student’s upbringing – home, school, education system and peer group. The good news is that Math anxiety is increasingly being recognised as a psychological problem. The solutions are forthcoming, too, if we are willing to pay attention. 

Sources:

  • npr.org: Math anxiety is real. Here’s how to help your child avoid it.
  • girlsschool.org: The math-anxiety performance link. A global phenomenon.
  • Frontiers in psychology: Gender differences regarding the impact of math anxiety on arithmetic performance in second and fourth graders
  • Harvard business Review: Americans need to get over their fear of math.

 

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Creating accessible STEM content

Wiris pushes against the lack of accessible STEM content. 

Our platform uses the MathML standard to be accessible for everybody.

One of the biggest obstacles for the educational community is the lack of accessible STEM content as well as the absence of adequate tools to create said materials. STEM is the acronym of Science, Technology, Engineering and Mathematics, an area of education specialized in interdisciplinarity and application of science and mathematics.

STEM content accessible for people with vision impairments are not common. Although nowadays there are many tools to generate accessible materials, the problem lies in the few options available  for the creation of accessible and adequate resources for STEM classes. This creates many obstacles for disabled Stem professionals to make their content available for everyone.

Luckily there are successful initiatives that mitigate this problem. Wiris has built MathType in a way that is totally navigable with the keyboard and fully compatible with the majority of the screen-readers in the market, which allow people with visual impairments to be guided by an off-voice. Thus, Wiris makes sure its products are accessible to everybody.

These accessibility options work for both the process of creating STEM content, and of using and working with it. Besides, WirisQuizzes is also built so that the students can answer exam questions in a fully accessible and autonomous way.

 

Available for your computer and on-line.

MathType works both for the desktop framework(text editors), and for on-line services(Google services and most LMS platforms), thus making it the most advanced mathematical authoring tool in the market. MathType can achieve this goal by automatically adding alternative text to the created equations, adding it in the HTML code when you are working in a web platform, or to the images when you work with the desktop app.

In addition, all Wiris products are based on the MathML standard, a coding language that incorporates both the structure and the content of the mathematical expression. Many screen-readers are equipped with MathML format reading capability, which makes Wiris accessible in the majority of devices. Moreover, the MathML language has many features that make it very useful for people with disabilities. 

For its ease of navigation with the keyboard and its use of the MathML language, MathType has created a new accessibility standard in mathematical tools both for students and professionals.

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Wiris stands with Ukraine

From Wiris, we would like to express our deep concern about the situation in Ukraine, and join so many voices from around the world in calling for peace. We stand with all the people who are suffering at this moment and condemn the use of any military action. 

 

Wiris joins the firm condemnation against the war in Ukraine made by the ACUP (Catalan Association of Public Universities).

 

For this, we have made the decision to provide all Ukraine accounts with free MathType licenses until the 20th of September 2022.

 

Please contact support@wiris.com if you have been affected by this conflict and wish to receive a free license.

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5 reasons to switch to online software

In the last few years, digital tools are gaining popularity. As in many other aspects of life, digitalization is finding its place in the laboratory environment. It is not a surprise. The list of advantages that the switch to online software has in day-to-day work is long.

On the other hand, the jump from paper to digital can be a bit overwhelming at times. To help you in your decision, here is a list of 5 reasons why you should consider making the move, if you haven’t done it yet. 

1. FLEXIBILITY: 

Coronavirus showed us how important it is to be able to access your data and your work when you are far away from your laboratory or workplace. Now that we are leaving the pandemic behind, there’s still plenty of situations where we need to work remotely: when you work from home as a way to improve work-life balance (specially important to solve gender gap 1, 2); when you are abroad for a conference or visiting another lab; or even when you move forward in your career and start a new position. In all these cases, the flexibility of online software can be a great advantage: You can access it anytime, anywhere and from any device. The possibilities are virtually endless. 

2. REPRODUCIBILITY: 

One of the biggest concerns in science is reproducibility. According to a Nature’s survey3 of 1,576 researchers, 52% of them think that there is a significant “crisis” of reproducibility. Under the same line, an online poll of members of the American Society for Cell Biologist4, more than 70% of those surveyed afirm to have tried and failed to reproduce an external experiment, and even more surprisingly, 50% of them have failed to reproduce their own experiments. 

The reasons behind this are many: from poor analysis or experimental design, to human error or lack of complete methods’ information. The list goes on, but in many of these cases, using online software could help increase reproducibility. They are designed to be consistent, follow industry standards and facilitate automated experiments and data collection.   

3. SHAREABLE:

Online tools are also designed to share your files and results easily with colleagues and collaborators. Aside from facilitating record-keeping and making your life easier, sharing is more important than ever. In the past years more publishers and funders are encouraging, even demanding, depositing raw datas and protocols in a repository. In this scenario, using online tools can become a huge advantage. 

Also, improving the way you share your raw data, results and protocols positively impacts the reproducibility of your experiments. A study published in Plos One5 indicates that sharing detailed research data is associated with increased citation rate. Sharing not only improves your work but also the quality and robustness of science in general. 

5 reasons to switch to online software: flexibility, reproducibility, shareable, save time, increase productivity.

4. SAVE TIME: 

Online tools help you to simplify your workflow and save time. Although in many cases you can do the same work with pen and paper, the online versions make it quicker. They are designed to free you from normally boring and time-consuming tasks and to improve one, or several, key steps of an experiment (creation, execution, data collection, data processing and calculations). 

Moreover, using a toll helps to compare results across multiple runs and, even more exciting, when you deal with large amounts of data and samples, it can help you see the results in a global way and find connections. 

5. INCREASE PRODUCTIVITY: 

And last but not least, using online tools improves productivity and efficiency. Besides saving time, using online software avoids the mistakes and typical human errors that can ruin an experiment: misscopy data, transcription errors, data loss, haphazard record storage… They also help to optimize workflow and automate processes. In summary, using online tools is a great way to  boost your productivity in the lab.

As you can see, everyone can benefit from changing to online software. From small labs to big biotech companies. There are plenty of options out there. If you are thinking of making the transition, we recommend to start small first and try different solutions to find the one that suits you and improves your workflow. 

At Bufferfish, we do our best to create chemistry software and result analysis tools to make your life easier so you can really focus on your research. 

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Celebrating the uniqueness in every student

Bridging the gap between classrooms and real world 

The formulaic, rote learning approaches to classroom education are increasingly outdated in a fast-changing, technology-driven world. As technology advances at a fast clip with every passing year, the most rewarding careers are those in which the professionals can use innovative and creative approaches to what they studied from textbooks. 

Take math and science, for example. We live in a complex world where our every habit and behaviour have the potential to be quantified. We want to know how many hours we sleep, how many steps we walk every day, how our heart beats while grocery shopping, and how our body is responding to a type of music. This is the era of Big Data, analytics, pattern recognition and artificial intelligence. Classroom education can be most effective if teachers make meaningful connections between the academic lessons and the real world

Personalized pathways for learning

If education can be flexible enough to make room for every student’s strengths and learning inclinations, it is more than half the battle won. If students are equipped with the power to design their education and choose what to learn and how to learn (through informed decision making), they are likely to be more invested in making the most out of their classroom hours and beyond. 

Every student is unique. The education system must be flexible to celebrate this uniqueness and help students achieve their career goals. This is already being done in some places. For instance, Leiden University in The Netherlands offers flexible learning pathways in which students can take charge of their education to align with their personal ambitions. They will be guided by the teachers in creating a unique education pathway that complements their talents and interests.

One student may be naturally inclined towards numbers while another may be good at understanding concepts. One student may be quick at spotting errors while another may be good at words and writing. Teaching can be most effective if each student’s strengths are optimized to create a wholesome learning experience. 

Universities started offering flexible learning pathways.

A plan for the future 

Personalized learning pathways have benefits that go beyond the classroom learning experience. Take the example of Rhiannon Dunn, a ninth-grade teacher at Science Hill High School in Johnson City, Tennessee, USA, who has applied the concept of personalized learning that students can choose for themselves. Dunn started a literary circle in which students have the freedom to choose any book for their independent reading time. They also get to decide how the teacher assesses them on this learning activity. It gives a strong message to students that they have a voice in their learning journey. 

The student takes an active interest in charting a course of action for the future by linking education to the career that they most likely see themselves in. They take into account their interests, natural strengths and curiosity while aligning them with the profession of their choosing. Students are able to draft a plan for their professional life, and be proactive in the decision making as they pursue their education. 

Since students take ownership of their education, they are likely to be more interested and invested in the learning process. They become active learners from passive observers in the classroom. When a personalized learning pathway for a student includes creative teaching methods, students will ideally continue learning beyond the classroom, too. 

What happens if a student changes her/his mind after a while on the pathway? This could happen as students cannot be expected to know for sure what they want. The education pathway should be flexible enough to allow a student to explore additions or changes without feeling like she/he is at a loss or has to completely start over. Education counselling is, therefore, extremely important to ensure that the student is making a commitment, and is allowed some elbow room to tweak the learning pathway.   

Instilling the spirit of curiosity 

A creative approach to learning has to start in the classroom, where students gain the confidence that learning need not to be fixed or given. It is, rather, a lifelong process that can be playful and encourages the student’s spirit of inquiry. Curiosity and the desire to know is at the heart of meaningful education. This curiosity is then given wings by personalizing learning so that the student can move forward at her own pace and time, using the format that gives the best results. 

A unique path for every student 

We live in a world that is increasingly celebrating our uniqueness, and offering personalized solutions to our needs. Be it advertising, technology, health, beauty or fitness, personalization has seeped into every part of our lives. Why should education be any different

Charting out a unique pathway for every student is an exciting prospect in which the student, the main stakeholder of education, has the maximum say and also the maximum benefit from the process. 

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