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Assessment Techniques and Student Learning

Assessment techniques and the interpretations of student learning have a direct impact on how data science, computational thinking, and artificial intelligence (AI) are taken up across K-12 mathematics education. Figuring out which skills and understandings should be assessed, and which may become obsolete, is a tricky challenge. Experts often investigate how to balance the assessment of core mathematical objectives with data science, computational thinking, and AI learning goals at different grade bands. Understanding the role that assessment plays in shaping opportunities for students to engage with data, modeling, proportional reasoning, probability, coding, and algorithmic thinking in both K-8 and high school mathematics is therefore a critical concern for educational stakeholders at all levels.

The second panel explored how assessment practices can make visible students’ conceptual understanding and learning of computational thinking, data science, and AI ideas and their connections to core mathematics. The international experts discussed how AI tools might be leveraged to assess students’ learning in mathematics, and what this implies for validity, equity, and classroom practice. Furthermore, the panel tackled how to use assessment information to guide instructional decisions. Richard Velasco (University of Florida) moderated the session with presentations from educators from New Zealand, Italy, Austria, Chile, and Ireland.

NEW ZEALAND: STATISTICS, DATA SCIENCE, COMPUTATIONAL THINKING, AND AI IN YEARS 1 THROUGH 13

According to Pip Arnold (University of Auckland/Waipapa Taumata Rau), New Zealand is 4 years into a curriculum refresh with more work in store. It began under the previous government and has continued under

new Ministry of Education officials, with the next elections scheduled for November 2026. The first stage encompasses two subjects: mathematics and statistics, and English.

Mathematics and statistics is compulsory in years 1 through 11, and available in years 12 and 13, often taught as separate subjects. The probability strand begins in year 5 to align with new assessment tools. A statistics and data science course is being developed for year 13. Computational thinking and AI are in the technology curriculum, currently in draft. The Ministry of Education and New Zealand Qualifications Authority have offered guidance about how to address generative AI in assessment: Valid assessment evidence must be the student’s own work, and use of generative AI should be more limited in assessment than in teaching and learning contexts. Relatedly, a proposal is under way to change the National Certificate of Educational Achievement for school leavers from standards to a whole-subject approach.

Arnold shared an overview of statistics and probability in the curriculum across years 1 through 13. She highlighted several elements in the draft technology curriculum of relevance: “design, make, and innovate,” digital technologies, and computer science. By years 9 and 10, there are separate digital technologies and computer science strands. Students move from step-by-step exercises to complex programming through their schooling.

Arnold identified challenges that she sees related to teaching computational thinking and AI. In years 1 through 8, students usually have the same teacher teaching mathematics and statistics, and technology. In years 9 and 10, students will have different teachers for these subjects. Materials and professional learning must be developed with this in mind. She questioned how much technology curriculum developers are talking with those in mathematics and statistics. Secondary school subjects tend to be siloed, but conversations across subject areas need to happen. Moreover, computer science is one of five strands (students must take two of five strands), so students could miss it, although she expressed the hope that schools make sure that students have access to all five strands over the 2 years.

Challenges related to statistics and data science include teacher preparedness. The changing focus on the statistics taught at the schooling level means many teachers did not learn the statistics that is now taught in their own schooling. Moreover, many out-of-subject teachers fill in to teach junior secondary classes. Primary and intermediate teachers have less extensive knowledge of statistics, and the little professional development that is offered is usually very number focused.

Arnold noted that the Census at School offers valuable resources for teaching and learning.¹ New questionnaires are developed every 2 years,

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¹ For more information, see https://new.censusatschool.org.nz/explore/

and there are now 11 New Zealand and 13 U.S. databases that students can use for statistical problem solving. She also pointed to research conducted by the Teaching and Learning Research Initiative,² teaching materials compiled by Anna Fergusson,³ and an annual Statistics Teachers Day through which teachers share new ideas.

The expectation in New Zealand is that statistics is in the curriculum from year 1, and students use technology beginning in year 4. Resources and books are available in statistics and probability. There have been potential ideas for introducing data science in the early years, but it is more likely to enter into curriculum from years 7 and 8 onward. Work is ongoing about how to introduce predictive modeling into the secondary curriculum as part of the refresh.

ITALY: REDESIGNING CURRICULUM AND ASSESSMENT FOR COMPUTATIONAL THINKING AND AI IN K-12 MATHEMATICS

Stefania Bocconi (National Research Council of Italy) began with an overview of efforts across Europe before homing in on the Italian context. Many countries are revising their curricula, as synthesized in a 2022 study by the European Commission.⁴ Across the 22 member states, computational thinking is being addressed through three main models: implemented as a separate subject, embedded into existing subjects such as math or technology, or dealt with as a cross-curricular theme with a variety of approaches at different levels. In common across the countries, computational thinking core skills are embedded into broader digital competency and are connected with basic computer science concepts.

In 2025, Italy’s Ministry of Education released new national curriculum guidelines for primary and lower secondary, grades 1 through 8. The guidelines distinguish between digital competence and computational thinking and/or computer science competencies. AI integration is predominantly articulated as an extension of digital competence. Under these guidelines, schools have the autonomy to introduce modules or activities related to AI and digital literacy. She also noted two recent Ministry initiatives. In 2024, a 2-year pilot was launched to provide AI-based virtual assistants in 15 classes across 4 regions to personalize learning in science, technology, engineering, and mathematics (STEM) and languages. The results of the

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² For more information, see https://tlri.org.nz/research/doing-research-that-matters/

³ For more information, see https://teaching.statistics-is-awesome.org/

⁴ European Commission. 2022. Reviewing Computational Thinking in Compulsory Education. http://www.eun.org/documents/411753/817341/Reviewing+Computational+Thinking+in+Compulsory+Education/a88b8d18-9065-4755-adb1-54b1c3b2d31f

pilot will determine future rollout. In addition, in 2025, INVALSI (Italy’s national body for assessments) launched a national assessment of digital competence, using the EU DigComp 2.2 framework for grade 10 as a reference.⁵

Bocconi reviewed some computational thinking and AI concepts in the 2025 curriculum, embedded in math, STEM, and digital competence in grades 1 through 5, and in technology, math, and STEM in grades 6 through 8. In addition, in 2025, Italy adopted national guidelines for introduction of AI into schools. The guidelines provide a structured system for ethical, technical, and regulatory compliance, and they safeguard the centrality of humans and the educational relationship. Under the European AI Act Framework, she pointed out, AI systems used to assess learning outcomes are classified as a high-risk application that requires significant human oversight. Responsibility lies with individual schools to comply, which allows for opportunities for local innovation but also amplifies risk.

Bocconi briefly highlighted three on-the-ground AI educational initiatives. The first, LUCY, is a 3-year curriculum that introduces AI to students in lower secondary education.⁶ They move from an introductory linguistic, historical, and cultural exploration in grade 6; deepened skills through programming, logic, and the mathematical foundations of machine learning in grade 7; and a capstone project in grade 8. Assessment is artifact based, and the capstone project functions as both a learning activity and summative assessment. The second, AI for Teachers, was designed by several European countries, including Italy, to provide professional learning and resources to teachers in grades 1 through 8.⁷ The third, InspAIr, comprises three laboratories for grades 8 through 12: an introduction to key concepts, speculative world building, and a final hackathon. For assessment, student learning becomes visible through micronarratives, GPT-mediated critical revisions, speculative artifacts, and final debate.

Assessment is a critical frontier, because traditional models struggle to capture computational practices, creative artifact development, and critical engagement with AI systems. She noted that the emerging scholarship frames AI as a natural extension of core informatics concepts, requiring a spiral program from foundational computational thinking to critical and ethical AI engagement.

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⁵ For more information, see https://op.europa.eu/en/publication-detail/-/publication/50c53c01-abeb-11ec-83e1-01aa75ed71a1/language-en

⁶ For more information, see https://www.ic3modena.edu.it/progetti/lucy-scuola-di-intelligenza-artificiale-per-ragazz/

⁷ For more information, see https://www.ai4t.eu

AUSTRIA AND GERMANY: TEACHING AI AND DATA SCIENCE IN THE MATHEMATICS CLASSROOM

Sarah Schönbrodt (University of Salzburg) noted her talk would touch on AI and data science in Austria and several German states. Data science, AI, and machine learning concepts are not part of the mathematics curricula in Austria and most German states. Instead, in Austria, they are part of digital media education and in both countries (Austria and Germany) they are part of computer science. While mathematical modeling is part of the mathematics curriculum, programming and AI are not. This limits the opportunity within a mathematics class to tackle real-world applications.

Schönbrodt focused her presentation on three questions: How and when can data science and AI concepts be introduced, which connections to traditional math can be established, and what might be appropriate forms of assessment? She explored these questions using the Computational and Mathematical Modeling Program (CAMMP) as an example. CAMMP has locations in several universities in Germany and Austria to provide workshops and other resources to high school students and teachers. The program uses open-ended mathematical modeling activities, prestructured mathematical modeling, and unplugged approaches for regular classroom teaching.

In open-ended mathematical modeling, students work on real-world problems in multiday projects. They come up with their own ideas for data analysis using Jupyter notebooks with Python as a tool. Their product, a computational essay, also serves as an assessment artifact to show how they engage with the problem. The goal is to make the programming and modeling process, data analysis, and results understandable and reproducible.

In prestructured mathematical modeling, students use the Jupyter notebooks with programming in the background to get introduced to machine learning methodology. Exercises include image classification, word predictions, and life expectancy predictions. Students do not need to know programming but can focus on the math concepts. Assessment can consist of the process data in the notebooks.

Unplugged materials lower the technology barrier further. Students do pen-and-paper work adapted to 45-minute classroom conditions. These activities are less authentic but can be linked to secondary mathematical concepts. Assessments consist of the students’ written solutions, short quizzes, and class discussions.

CHILE: AI, TEACHERS, AND STUDENTS

Claudia Vargas Díaz (University of Santiago) noted a tension between teachers and AI. Many are concerned about their students’ use

of AI. As a professor teaching calculus and abstract algebra, she herself sees students turning to ChatGPT for answers. This requires assessment to move from monitoring learning to evaluations that capture authentic understanding. The connections between AI and education are complex, she noted.

Vargas Díaz said there is limited empirical evidence about Latin American teachers’ preparedness to use AI in a formative and responsible way. In Chile, the issue is not the use of technology but rather teachers’ pedagogic preparedness to use it critically. She pointed to research that suggests that AI use may affect cognition without pedagogical mediation, similar to how reliance on GPS technology lessens people’s ability to navigate independently. Ethical concerns also arise because it is not clear whether children’s rights are fully protected in AI-mediated environments. These concerns include safety, nondiscrimination, well-being, and the risk that digitalization deepens inequalities. This tension affects mathematics education, she added.

Chile’s AI policy is based on the idea that AI has broad societal impacts and requires a national strategy to anticipate its effects. Three main axes guide the policy: (1) enabling factors (talent, infrastructure, and data), (2) development and adoption (implementation across sectors), and (3) ethics and regulation (addressing labor, equity, and human–machine interaction). AI has exposed regional gaps in infrastructure, education, and gender participation in STEM.

Educational initiatives in Chile include 2023 guidelines for teachers on use of ChatGPT; a program from the Innovation Center on foundations, citizenship, and ethics for grades 9 and 10; curricular recommendations; a learning pathway in computational thinking; and a guiding framework for teachers’ digital competencies.

Vargas Díaz said the missing dimension, in her view, is human emotion. Learning and assessment must remain mediated by teachers. Generative AI has no feelings and cannot recognize students’ emotions, yet these emotions are essential information for teachers’ instructional decisions. In Chile, she said, conversations about integrating AI into education cannot be separated from broader structural challenges affecting the school system. Nearly 23,000 trained teachers under age 40 are outside the education system, and these professionals are needed to mediate use of AI. Moreover, new university admission requirements have resulted in a 17.5 percent decline in the number of young people interested in pursuing teaching degrees.

A key question for the region is how to respond to generative AI in mathematics education considering not only the technology but also ethics, critical thinking, and students’ emotional development. AI may offer transformational tools, but education remains a human endeavor, she stressed.

IRELAND: ASSESSMENT REFORM AS A PATHWAY TO COMPUTATIONAL THINKING, DATA SCIENCE, AND AI IN MATHEMATICS

Keith Young (Mary Immaculate College) said Ireland is in the middle of curriculum and assessment changes across all levels, and assessment is the lever. Assessment does not just measure learning, he said, but defines what counts as learning. Generative AI makes this more critical. He does not advocate a stop to AI but to determine what evidence is needed to make claims about student performance and mathematical understanding. Young urged triangulating the evidence to assess reasoning (why the student chose a certain approach), performance (how the student does the work), and judgment (how the student can verify and critique outputs). The practical implication is that this leads to a deliberative mix of assessment formats, he observed.

Ireland’s ongoing reform process is creating new assessment spaces. At the primary level, there is a move toward more integrated learning through STEM, which creates a natural context for data science and computational thinking to sit alongside mathematical ideas, especially through modeling, representing information, and explaining choices. The lower secondary level includes classroom-based assessments that legitimatize forms of evidence that are closer to practice, and not just timed written responses. At the upper secondary level, an additional assessment component in math will probably start in 2027 and will feature a system-level mechanism to assess richer constructs like modeling, data reasoning, and verification and evaluation.

Classroom evidence is balanced with high-stakes certification as well as external signals from large-scale assessments like the Programme for International Student Assessment. These layers shape what gets valued and therefore what data science, computational thinking, and AI integration look like in practice. These reforms create the conditions to embed them and not be add-ons.

National guidance on AI in schools came out in October 2025, intended as an initial step that will evolve as evidence and practice evolve. Given the pace of change, it is guidance rather than detailed guidelines and does not prescribe an approved set of student uses. It is a shared reference point, not a complete playbook of prescribed practices. The challenge is to design assessments so students can use AI as a support tool while still making valid claims about their mathematical thinking. A useful takeaway is the principle of human oversight, transparency, and the necessity of verification of AI, which translates into how tasks for students are designed.

Ireland is part of the United Nations Educational, Scientific and Cultural Organization (UNESCO) project “Futureproof Education: Supporting

Schools in the AI Evolution.”⁸ The project includes stakeholder engagement and as-is and gap analysis to inform next steps. Assessment and curriculum decisions are likely to be shaped by this immediate guidance but also by a growing evidence base. When AI is available, assessment of mathematical correctness, clarity of communication, appropriate representations, and quality of the conclusion can still be assessed. What changes in the generative AI world is that the product cannot stand alone as evidence of learning. A second layer of assessment that shows evidence of thinking and analysis behind the final product is needed.

Young offered two potential patterns of assessment. In the first, students critique an AI output rather than generate a solution. They audit an AI-generated solution or model output to identify what is correct and what is unsupportable. In the second, students conduct an investigation with an evidence trail to show the choices they made, verification checks, and limits and uncertainty.

Young closed with several questions that led to the open discussion. What evidence should count as learning in the generative AI–rich assessment, particularly in project-style components? Relatedly, what safeguards protect equity while still allowing students to learn with AI tools? Possible safeguards could include in-school access time for approved tools and supports. Overall, this moment of transition and the rapid spread of generative AI are forcing a reconsideration of what counts as evidence in math. Data science and computational thinking can be practical vehicles to do this.

DISCUSSION

Velasco asked the presenters about the efforts being undertaken by their countries’ ministries to prepare pre-service and in-service teachers, as well as teachers’ responses to moving toward AI. Vargas Díaz said in Chile, universities are training teachers to prepare them, noting that each has its own program, but it is too soon to know the response. Young said the Teaching Council is Ireland’s professional accrediting body. Its most recent cycle states that teacher preparation programs must offer digital literacy, defined broadly, and will start to include AI. At the same time, the government is being cautious and waiting for results of studies from UNESCO, as well as the final versions of guidance from the European Commission and the Organisation for Economic Co-operation and Development. Austria has focused on using AI as a tool more than teaching about AI, Schönbrodt said. Interest among teachers is high, she continued. She receives many requests to set up teacher training at the pedagogical universities,

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⁸ For more information, see https://www.unesco.org/en/articles/futureproof-education-supporting-schools-ai-evolution

although the tension is that AI is not included in the math curriculum. Bocconi commented that a crucial point in Italy is how to prepare future teachers in addition to upskilling current teachers. Each school of education within the universities acts differently. There is not a reference Italian framework beyond the overall European framework. Training is often theoretical without the opportunity to practice or even reflect in a prospective way. Another high-risk topic is how teachers should use generative AI in the classroom. Many say they use generative AI mostly to prepare materials and assessments but not frequently with students. Arnold said New Zealand currently provides primary teachers 4 days of training over 2 years, with a choice from a series of modules covering the curriculum revisions. Time is also spent on resource development, including modifying textbooks purchased from overseas. She said changes in behavior and uptake are not known, and she is not sure how these concepts will be introduced in the other subjects yet to be revised. Secondary teachers have more compressed schedules and teachers in training may get exposed to these concepts by luck in their placements.

An online participant asked how K-12 developments in AI and data literacy began in the different countries and about the use of Guidelines for Assessment and Instruction in Statistics Education (GAISE) produced by the American Statistical Association as a resource for statistics and data science education.⁹ Arnold, who was a GAISE co-author, commented on the three different levels, cross-curricular links, and progressions in GAISE and urged looking across subject areas for interesting datasets. She again called attention to the data generated and provided through the Census at School. When asked by Markku Hannula about the impact of AI in the assessment of lower-performing students, Young suggested adaptation based on the level of individual students. A well-designed tool should be able to scaffold and assist lower-performing students by breaking down complex tasks into more simple ones, he suggested. As noted in the previous session, generative AI was not designed as an educational tool, but it can be used to develop solutions.

Hollylynne Lee asked presenters about secondary students’ learning experiences, the data with which they engage, and what tools they use to engage with the data. Vargas Díaz stressed the importance of engaging students in math. She looks for projects that model problem solving, and letting them create solutions as a means of assessment. Young said the Irish context is fragmented in terms of tools. Within the overall goals for what to achieve, teachers have autonomy. At the primary level, examples may be block-based programming with microbits. In some schools, sensors are

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⁹ For more information, see https://www.amstat.org/education/guidelines-for-assessment-and-instruction-in-statistics-education-(gaise)-reports

placed around a school to collect and learn how to visualize data from local environments. At the lower secondary level, students develop the problems they want to solve. In addition, Ireland has a government-funded teacher support service that is offering many workshops on technology and teaching. Teachers can choose which tools they want to adopt.

Matti Tedre asked about the role of programming in AI literacy. He observed that no-code approaches lower the cognitive burden, but there may be benefits of programming-heavy approaches. He also wondered about a possible conflation between assessing programming skills and AI literacy. Schönbrodt said the open-ended projects she has been involved with in Austria focus on data exploration. It is hard to assess specific AI literacy but rather data literacy and mathematical modeling. She clarified that students do not program with Jupyter notebooks in the project she described. In her view, especially with a short timeframe, programming takes too much time and students should start with a no-code approach. Young underscored Tedre’s point about not conflating programming with AI literacy.

Farshid Safi emphasized the value in the United States in learning from other countries. He asked the presenters for their recommendations for teacher preparation programs. Arnold said not to forget the expectations for students in introducing changes. When the curriculum changed for New Zealand students in years 9 and 10, for example, it was important to remember that those in year 10 had not experienced the year 9 new curriculum. It is important not to wait, but it is also important not to disadvantage students who have not been exposed to new concepts. She also noted that statistics assessments in New Zealand changed from graphing to broader statistical thinking, which was great. The flip side was that teachers did not feel confident with the new concepts, and rote responses resulted. Although the result may have been the same, these issues should have been thought of in setting up the new assessment, she said.

David Barnes commented that U.S. teachers and school administrators feel overcommitted and exhausted, and many leave the profession. He asked how AI may help save them time and make them more successful. Arnold urged putting time into teachers by giving them time out of the classroom. Education systems run on a lot of good will, she commented. If a change is important, money must be invested in making that change, such as through release time or enabling them to teach a bit less. What should be taken out of the curriculum is “where the rubber meets the road,” Conrad Wolfram said. Whether or not to explicitly code is a critical question, he continued. His organization’s materials jump between interactive activities and activities that do require code through three levels: (1) scaffolding, (2) narrative level, and (3) presentation of a problem that must be figured out. An added complexity is how to integrate AI.

Steffen Schneider related an experience at a multistakeholder workshop in which many participants turned to their smartphones for answers to various questions. There is a divide in how people, including teachers, use AI, and he asked what the presenters see. He also asked whether teachers have provided feedback to inform policy development. In Italy, Bocconi said development of guidelines for informatics education looked at new formative assessments that align more closely with teacher attitudes. She agreed with the disconnect between efforts to foster creativity and paper-based summative tests. It is a critical point not yet easy to address, she observed. Young called for cultivating self-regulation strategies in students. Restricting access to AI at school will not eliminate, but may mitigate, risks.