7

Technology Tools and Frameworks

Technological tools, and the concepts and practices associated with their use, have a direct impact on K-12 mathematics education. The emergence of widespread access to and applications of artificial intelligence (AI), the growing importance of data and data science, and the identification of computational thinking as an important goal for K-12 education are challenging long-held norms and assumptions about K-12 mathematics education. Understanding the role that technological tools play in supporting computational thinking, data science, and AI in the mathematics classroom is a critical question faced by educational stakeholders at all levels. Furthermore, this review will explore frameworks to support ways of thinking about what these impacts may be, as well as frameworks for supporting educational stakeholders in making informed decisions related to the role of technology in the ever-changing landscape of K-12 mathematics. Such frameworks can help support teachers in bringing AI, data science, and computational thinking into their classrooms in effective, engaging, and equitable ways.

Moderated by David Weintrop, presenters from Germany, South Korea, Singapore, Brazil, and Finland discussed in a panel the role that these technologies are playing in the classrooms in their countries, frameworks for thinking about and organizing the mathematics education technological landscape, and strategies to future-proof the technologies for computational thinking, data science, and AI.

GERMANY: EDUCATION IN THE AGE OF AI

Steffen Schneider (KI macht Schule & Helmholtz Munich) underscored the need for interdisciplinary exchange. His own background is in AI and machine learning, but he comes to the workshop as founder of a national nonprofit to bring education with and about AI in a sustainable way to schools. It begins with recognition that AI is transforming all aspects of society and everyday life, and the education system must prepare students for the future. However, education’s classical way of going from a task to a solution to acquire competence is endangered through unreflected use of AI as important skills may be skipped. He also pointed to the opportunities of AI, such as enabling more individualized learning through adaptive tutoring systems. AI could also be a driver to establish future skills in schools around creativity, collaboration, creative thinking, and communication.

A challenge in Germany and other countries is that education systems change slowly, but AI changes fast. It is good to be resistant to trends but it is also becoming a problem. Another challenge is that teachers are creating excellent materials and best practices to deal with AI, but lack effective ways to share them. AI is not a subject; it reshapes every subject, he stressed.

Schneider highlighted different solution frameworks on the international, national, and state levels. The Organisation for Economic Co-operation and Development is developing an AI literacy framework. It is in draft form, and he encouraged participants to review and provide feedback on it.¹ Germany has had a policy recommendation on AI since 2024, developed by the Standing Conference of the Ministers of Education and Cultural Affairs. Individual federal states have also developed their own recommendations, often directed toward teachers. Solutions and best practices are being developed by a range of stakeholders, including state agencies; nonprofits, companies, and publishers; university researchers; and teachers themselves. “I would argue that the people doing things are already there,” he argued. “The problem is we are dealing with a scattered system with a lot of different stakeholders, and the question is really how to bring these stakeholders together to have impact on the national level.” The missing piece is a joint collaborative platform where all could contribute, he suggested. He offered a concept for education similar to the software development process in which all can review, provide feedback, discuss, and use the materials.

Schneider shared a few examples of possible solutions. At a systems level, an open education hub could cross state and national borders and be open source. The platform could contain hundreds of thousands or millions of learning objects, annotated with metadata. It could serve as the backbone for an adaptive tutoring system, in which agentic AI queries databases and helps teachers design better instruction plans and students get more individualized feedback. It could connect to existing infrastructure. Doing this on a national scale can help ensure that opportunities are not so scattered. Instead, data go into a public infrastructure, and policy makers can decide how the data can be used.

Germany has launched an adaptive tutoring system, called the Adaptive Intelligent System. It is coordinated by the Media Institute of the Federal States and implemented together with a consortium of technology companies, universities, research institutes, and nonprofit organizations.² Importantly, it contains an open and participatory marketplace, so no one is forced to do material development in a certain way. People contribute, and then policy makers and teachers can decide what to adapt for the classroom.

SOUTH KOREA: TECHNOLOGY TOOLS AND FRAMEWORKS FOR K-12 MATHEMATICS

Sejun Oh (Hongik University) presented the range of technology taught to Korean students, from block-based coding with AlgeoMath to AI mathematics with Python.

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¹ For more information, see https://ailiteracyframework.org

² For more information, see https://ais.schule

Block-based coding has shifted from being rare (two tasks found in two of the ten 2015 revised grade 7 textbooks) to routine (all nine 2022 revised grade 7 textbooks included at least one coding task, with 19 tasks in total). Coding is concentrated in topics where mathematical relationships can be expressed procedurally: nearly half of the tasks focus on regular polygons and exterior angles, for example. A key classroom challenge is the students’ gap between observation and the explanation behind their observations. Thus, many tasks push students to modify, extend, or write new code. This is mostly done with AlgeoMath, a free national platform.

As noted by Kyungwon Lee (see Chapter 3), Korea offers AI mathematics as a high school elective. Oh was part of the national research team to draft the course, which launched in the second semester of 2021. At the time, there were few other such government-endorsed courses internationally. The choice was made to align AI ideas with the existing mathematics curriculum progression, as he showed with several examples, including one with AlgeoMath.

SINGAPORE: CODING WITHOUT CODING: GENERATIVE AI SUPPORT FOR INTRODUCTORY STATISTICS

Tianming Zhu (Nanyang Technological University) discussed her recent work to incorporate generative AI tools into an introductory statistics course. She noted the challenge of the “syntax wall.” Hand-drawing is no longer sufficient or practical for complex datasets. The Singapore Ministry of Education requires students to move beyond paper and pen in data handling and analysis. She agrees that programming is essential to statistics and data science, but it represents a major roadblock for beginners. As students transition from no code (blocks) to high code (R/Python), syntax errors often halt discovery and lead to student frustration. Limited class time makes it nearly impossible to teach programming and also teach deep statistical concepts.

In thinking of how to help these students, Zhu turned to AI to achieve “coding without coding.” She built a solution on GPT-4.1 and the Dify platform and optimized it for educational support rather than generic assistance. It provides code only and is forbidden from making decisions or interpreting data, to ensure the students do their own analysis. It uses students’ natural language (e.g., “I want to draw a histogram”) to code into R or Python syntax. Students can run it on any laptop without installing new software, and it can be embedded into the existing course portal. She recognized there are existing AI code assistants, but chose to build her own because of cost and the ability to customize.

Zhu offered two examples she has used with students. Without having to program the code, students needed limited instruction before they could

do the assignments. They also had to solve a six-question assignment on data visualization using the “coding without coding” framework, and they did well.

Students were surveyed about their views in terms of accessibility, efficiency, pedagogy, and trust. While the survey was limited (8 of 11 students in the class), Zhu said responses were very positive. Students said they saved time and felt more confident about their statistical abilities.

In summary, Zhu said that programming is now a tool in mathematics learning, similar to the introduction of calculators in the past. Generative AI assists students with syntax generation and debugging. Designed properly, an AI tool can allow learners to focus on statistical concepts and interpretation, asking good questions and interpreting results.

BRAZIL: TECH TOOLS AND FRAMEWORKS

Lucas Rocha (Nova Escola) is the head of AI at Nova Escola, the largest digital platform for public school teachers in Brazil. He shared a lesson that, he said, was learned the hard way: In education, the distance between a good idea and change in the classroom is large. Teachers must plan lessons for different grades for students with different levels of proficiency. Math teachers in secondary schools lack specialized training. It is not their fault, he stressed. They are part of a system not designed for the complexity it faces.

Brazil is pursuing parallel national strategies for mathematics education. Traditional approaches strengthen math foundations, which is necessary, but are silent on technology in the curriculum. At the same time, some pilots with computational thinking and AI are taking place. For example, Piauí state is piloting a cutting-edge AI curriculum for grade 9 and high school involving 130,000 students and 900 educators. It took political courage to conduct the pilot and it points to where education needs to go, he posited.

Rocha shared an image of a painting of a storm high above an ocean reef. The storm does not move the reef below the water, just as education policy does not move the classroom. The question is how policy can reach the classroom. Nova Escola has spent 40 years in the mission of “every teacher evolving and every student learning, day after day.” It logs more than 1.3 million visits to its website for resources every month. More than 133,000 visitors have used AI support for personalized teaching, and 436,000 have used its AI-assisted lesson plans.

A 2025 survey of Brazilian teachers (not just those who use Nova Escola) found that 53 percent now use AI, up from 23 percent in 2023. Most users do so frequently. Benefits include to expand their teaching repertoire and personalize teaching, but the main benefit, according to 51 percent of users, is to save time. Nova Escola offers an AI assistant to teachers through

WhatsApp. Rocha showed an example in which a teacher poses a question, an orchestrator interprets the intent and routes the request to the right specialized AI agent, and content is generated that is grounded in national standards and local context. A pedagogical feedback agent can draw on student assessment from that teacher’s own classroom to produce a diagnostic and suggest targeted interventions. Thus, it is truly local and can, harkening back to the painting he showed, reach below the surface. Generating content at scale is easy, Rocha commented, but generating quality content is more challenging. Nova Escola has implemented an evaluation framework that consists of content generation, human labeling, automated evaluation, and continuous improvement. This is not a checklist but it is how to earn the right to be at scale. A rigorous impact evaluation on these AI-powered WhatsApp lessons is being conducted in partnership with the World Bank. Teachers have reported saving significant time, and almost all report that the generated lesson plans are applicable in their classrooms. Final results and recommendations are expected in August. Policies, frameworks, and commitments are necessary, but the real thing to look at is what changes in the classroom below the surface.

FINLAND: GENERATION AI

Matti Tedre (University of Eastern Finland) said, prior to 2023, computational thinking and programming were integrated in math and crafts in Finland. It was no one’s specific responsibility, and so no one was really doing it. There was also no clear approach to AI education. An initiative called Generation AI (GenAI) was launched with an aim to future-proof AI education by teaching principles and not just tools. Invisible mechanisms are made visible through a range of tools and teaching materials. One example is a social media simulator called Somekone. Students use an Instagram lookalike, then hook to another device that provides a live stream of the data collected about them in real time as they use it. They see how a profile is created about them. Profiles of the entire class are clustered to learn how recommendation algorithms and filter bubbles work.

Tedre touched briefly on several other GenAI-developed tools. Through a spoofing machine, students compete to see who can trick an AI system to think they are, for example, a doctor. They learn how to exploit an AI model’s weaknesses. Through a profiling game, younger students see data traces from different sources come together to make profiles. With a Little Language Machine, students train a transformer on their own computer to see how a model can improve.

Tedre explained that Generation AI adopted a no-code approach to minimize the conceptual burden from programming and to go straight to AI concepts. Programming should not be a prerequisite for AI literacy, he

stated. The no-code approach offers a low floor for entry, including for resource-limited settings, is more equitable, prioritizes disciplinary concepts, and is scalable. Teachers need less training. It shifts the focus from syntax to probabilistic reasoning, model evaluation, and data distributions. “We believe AI education is as much a societal issue as a technical one, so AI education should be for everyone, not just those who can program,” he said.

Generation AI is based on a contextualization, exploration, design, and ethical reflection pedagogical model. It is based on the United Nations Convention on the Rights of the Child, is General Data Protection Regulation safe, runs locally in a browser, and is open source. It was co-designed with teachers and students. Finally, it offers a cumulative learning path, comprised of year 1 (data-driven design), year 2 (social media mechanisms), year 3 (impacts on the individual and others), and year 4 (generative models).

DISCUSSION

Padhu Seshaiyer asked whether students are able to understand the mathematics behind the tools developed. In Finland, Tedre said, the tools and materials are designed to be taught in different disciplines. Mathematics teachers can explain the math behind them, but a media literacy teacher, for example, can use them without explaining the math. Oh said that math concepts are taught in Korea’s AI mathematics elective.

Ana Ferreras Fiel asked how schools in developing countries can access new tools when high-speed Internet and technology can be a barrier. Tedre noted his own academic background began in Tanzania. Generation AI’s tools are built for low-end devices and tools.

Eboney McKinney asked the presenters how they support current classroom teachers to deal with the changes ahead, in addition to pre-service teachers. Rocha said teachers say the first barrier is not technical, but prejudice from colleagues who warn they are giving away their jobs by using AI. It is important to understand and help overcome this barrier. In addition, one-third of math teachers do not have a math background. AI can help them understand concepts and feel confident about teaching the content to a classroom with 30 to 35 students. It is important to bring in teachers’ voices so they are part of the solution.

Claudia Vargas Díaz asked Zhu about the coding aspects of her statistics course. Zhu said she started with data visualization in which programming is usually required because graphs cannot be drawn from pocket calculators. Students do not worry about R or Python, although she noted that if students want to learn code, they can. Her survey was small but asked about their previous programming experience, how they had tried to visualize data before, whether they trusted the result, and the amount of

time required. She noted that students also learn how to choose the appropriate graph for the task.

Hollylynne Lee asked Rocha and Schneider about artifacts that could be built into their systems to help teachers teach data science and computational thinking. Schneider stressed the importance of grounding to the curriculum. Tagging learning objects with metadata is important. AI can be a copilot in creating lesson plans, but not create the entire plan. Artifacts should be web-based materials that ideally run in a browser. Future-proofing can occur with interfaces to language models. It is important to preserve the option to fall back to traditional forms of teaching, he said. Rocha said in Brazil, computational thinking standards are national but each state implements them in its own way. Nova Escola does metadata mapping by hand, working with each state. The artifact is a WhatsApp message, which is very low bandwidth and works everywhere. Every class is unique, and almost all teachers adapt the lesson plans generated. So the artifact is more about generating ideas and co-authoring than having a ready-to-use product. Lee suggested giving teachers more access to real-world data to teach data science.

Deborah Stine asked how more funding might help these initiatives grow, as well as what other policy barriers they face. Rocha said Nova Escola is philanthropy funded, and often for something specific and time bound. He expressed the wish for patient, long-term funding to work with states over multiple years. With more funding, more teachers could be reached to change their classrooms. Policywise, he noted teachers often do not have time to really understand the students in their classes, especially when five or six assessments a year must guide the curriculum. Tedre said that more funding would speed up tool development. There is a backlog of ideas. Policywise, he said the situation in Europe is good. Schools are alert to technology hosted by big data giants. The decision to make tools that are local—“you own your own data, and everything runs on local machines”—is very well suited for the current climate. The AI Act in Europe has changed a lot. For example, image recognition tools are now banned in schools. Schneider also commented on the need for effective spending of available resources in Germany. Sometimes the wheel is reinvented. One consequence of regulation, for example related to data protection, is that every stakeholder develops a solution from scratch, which must absorb the additional costs. He urged a culture where regulation issues are mitigated in order to build a playing field. Another component is an open-source philosophy to access tools and modularity for flexibility. These are factors worth investing in, he suggested. Rocha added that a standard way of using data across states in Brazil would help. Zhu said she would like funding to build cluster rooms for teachers.

Farshid Safi asked how the presenters see the evolution of the job description of a professional educator or teacher. Zhu said the challenge is human. AI is a tool with an end point. The key is whether teachers know how to identify the points for their classrooms, as they are still the ones who know their classrooms best. Training can help do this. In Germany, a competency for teachers is to manage AI, Schneider said. With adaptive learning, there may be 30 individualized tutors in the classroom. The teacher orchestrates in what could be an exciting opportunity if done right. It reinforces the role of human interaction in teaching and becomes more feasible when some of the more tedious tasks can be offloaded to AI. Rocha quoted Brazilian educator Paulo Freire, who said teaching is not about transferring knowledge, it is about creating the opportunities for the production and creation of that knowledge. The role of the teacher has not changed, but new technologies can bring more possibilities to create. Tedre said AI is not seen as a subject to learn but rather a design medium in which to express ideas. In that sense, the teacher’s role remains the same. Oh reflected that, when he was a teacher, he was more of a content deliverer. Now teachers are designers, curators, and percolators of thinking. Their jobs have become more complex.

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