Generative artificial intelligence (genAI, or here simply AI) has arrived in the educational discourse – often with grand promises, sometimes with apocalyptic fears. A broad, albeit heterogeneous, empirical base now exists. Meta-analyses report significantly positive effects of AI chatbots like ChatGPT on learning performance, motivation, and higher thinking, but under very different conditions, with sometimes questionable study designs, and predominantly through studies with older pupils or university students (Alemdag, 2025; Deng et al., 2025; Wang & Fan, 2025; Wu & Yu, 2024; Zheng et al., 2023). The question, therefore, is not whether, but rather how these positive effects can be achieved. Because, of course, ChatGPT and similar technologies are not a guaranteed success in the field of learning support, but rather a tool that can be used didactically.

Therefore, authors warn against misunderstanding the sometimes observed "learning effect with AI" as a property of the AI technology itself, instead of asking about the underlying learning environment and didactic pre-structuring (Dinsmore & Fryer, 2026; Kirschner, 2025). In short: AI can effectively support learning – but only if it is designed and integrated in a didactically sound manner. However, it can be just as pointless if it replaces and prevents learning instead of supporting it.

The question I want to explore here is: How can AI be used to support learning processes through personalized feedback? In the following, I outline fundamental, empirically and theoretically supported considerations regarding design principles for AI learning companions and AI tutors in mathematics learning, with a particular focus on primary education. These considerations form the basis for the development and testing of app-integrated, AI-supported learning guidance within the project. PRIMA-KI.

Adaptive scaffolding: Help for self-help instead of quick fixes

AI-supported learning environments generate learning gains particularly when they adapt to learning progress, errors, and strategies, rather than simply providing correct answers. In the TALPer study, for example, lower-achieving fifth-grade students benefited especially from adaptive support in mathematics lessons, while higher-achieving students developed more complex interaction patterns with the AI learning companion (Kuo et al., 2025). Similarly, a comparable learning system showed significant performance gains in word problems, with the perceived benefit—that is, the quality of the support—having a strong influence on motivation and learning outcomes (Liu et al., 2025). Son's (2024) systematic review confirms the positive effects of well-designed intelligent tutoring systems on mathematical learning performance, especially when these systems adapt to individual learning needs.
In the field of self-regulated learning, several studies indicate that adaptive, AI-supported scaffolding (instead of static support sequences) can improve the quality of self-regulated learning processes and offers advantages over a concept of "equal support for all students" (Liu et al., 2025; Wu et al., 2025). New multi-agent approaches and LLM-as-Judge procedures show that the quality and reliability of scaffolds can be improved through self-assessment procedures, and that hallucinations during feedback can be significantly reduced (Cohn et al., 2025; Gonnermann-Müller et al., 2025; Qian et al., 2026).
At the same time, limitations of some tools not specifically designed to support learning became apparent: AI systems that provide unregulated access to complete solutions on demand during practice may increase performance in the short term, but impair long-term learning when the AI is withdrawn (Bastani et al., 2025). This is also referred to as "de-skilling," as it hinders rather than promotes actual learning and only superficially creates the illusion of learning. Learning analyses from AI-based tutoring systems also show that some learners try to "click through" tasks without truly engaging with them (Jancafik et al., 2023). This should be prevented as much as possible through appropriate pre-structuring and design of the AI feedback in order to prevent superficial learning and enable deeper, more comprehension-enhancing learning.

Conclusions: An AI learning companion should primarily:

• Diagnose errors and misconceptions based on subject-specific didactic background information on the topic and adapt accordingly. Notes give (Bewersdorff et al., 2023),
• Encourage a change in strategy and provide informative guidance for independent problem-solving, instead of delivering finished results.,
• Provide support in measured doses, stagger it over time (fading), and, if necessary, "withdraw" it if students become too dependent (i.e., request too many hints).
• Implement mechanisms against superficial problem-solving by strengthening children's ability to solve problems independently through questioning and referencing previous work.
• Individualize: Adapt task formats to the competence level to avoid over- or under-challenging students (Son, 2024).

Good AI tutors encourage independent thinking.

Research on Large Language Models (LLMs) in learning suggests that the sequence of thinking and explaining is crucial. AI feedback is particularly effective when learners first attempt to solve problems themselves (Kumar et al., 2023). Even rare, erroneous LLM explanations in such settings still led to learning gains, without participants systematically adopting incorrect strategies (Kumar et al., 2023). Systems that intervene too early ("reactive feedback") risk suppressing metacognitive processes (Chudziak & Kostka, 2025). Furthermore, hybrid intelligence models—that is, the combination of human thinking and AI support—often lead to better results and lower cognitive load than pure AI solutions (Cosentino et al., 2025).

This corresponds to the learning psychology critique that genAI often tempts users to take a "shortcut" in their thinking: While directly consuming the solution saves effort, it hardly builds robust knowledge structures (Gisiger, 2025; Dinsmore & Fryer, 2026). Studies on AI in practice also show that if AI offers complete solutions during practice, long-term learning outcomes are worse than without AI—unless the AI is regulated to provide only step-by-step hints (Bastani et al., 2025). In their theoretical framework for LLM-based educational agents, Cohn et al. (2025) explicitly emphasize the necessity of "guided discovery over direct answers"—that is, guided discovery instead of direct answers.

Analysis of real-life tutoring dialogues also shows that pure instruction without active learner participation generates little constructive learning. Primary school students respond positively to targeted, interactive questions, but remain passive when the tutor remains monologic and solution-focused (Wang et al., 2025). Ruan et al. (2020) demonstrate a similar finding in their study of narrative-based chatbot tutors: learning gains were achieved primarily when the system provided interactive feedback and hints rather than direct solutions.

Conclusions: An AI learning companion in mathematics lessons should consistently work according to the principle: "First you – then me."„
That means:

• First, a own attempt at a solution demanded.
• The AI only comes into play when needed, either on request or automatically in case of errors, and asks for ideas, sub-strategies, and observations.
• Explanations will be "docked" to existing foundations of understanding„.
• Complete model solutions should remain the exception and be used as a reflection tool, not as the primary learning format.
• Learners are encouraged to critically examine AI responses – a skill that children can practice as early as primary school, for example by detecting errors in AI statements (Helal et al., 2024).

Without a sound pedagogical foundation, the AI tutor becomes a "linguistically gifted random number generator".„

While generative AI can produce linguistically and formally impressive results, it often generates superficial, poorly problem-oriented tasks from a subject-didactic perspective if it is not specifically controlled and the output is not pre-framed according to subject-didactic principles (Schneider, 2025). Literature reviews on AI in mathematics education emphasize the potential for visualization, individualization, and problem-solving, but also point to the weak or overly unspecific theoretical foundation of many systems, presumably because the systems are not specifically optimized for subject-didactic issues (Almheiri et al., 2025; Awang et al., 2024; Holmes & Tuomi, 2022; Pesemowo & Adewuyi, 2024). The systematic analysis by Cárdenas et al. (2025) identifies a lack of theoretical framework as one of the key obstacles to effective AI tutoring systems. Successful systems like ChatTutor or specific frameworks are therefore explicitly based on educational theories such as Social Cognitive Theory or Evidence-Centered Design (Cohn et al., 2025; Dwivedi & Rejina, 2025). It is not enough to view AI as a mere technical "add-on".
Theory-driven tutoring systems are therefore significant: Building on Generative Learning Theory, the study by Makransky et al. (2024) shows that a model specifically trained in didactics promotes conceptual knowledge, confidence, and enjoyment significantly more than a generic LLM or traditional instruction—and that these effects remain stable in the follow-up. The same applies to models specifically adapted for learning tutoring, such as Google's LearnLM. Studies on GeoGebra and AI-supported environments clearly show that conceptual understanding and self-efficacy only increase when subject matter and subject-specific didactics are explicitly incorporated into the system design, rather than simply adding "technology on top" (Cononigo, 2024; Kortenkamp, 2024).
Cohn et al. (2025) made an important contribution with their framework for adaptive scaffolds in LLM-based educational agents, which combines evidence-centered design with social cognitive theory. This theoretically grounded approach enables high-quality formative assessment and interaction.

Conclusion: An AI tutor requires extensive content-specific knowledge as context in the prompt or special follow-up training with subject-specific didactic knowledge, for example:

• a mathematical model Competence development for the content area,
• Error and strategy taxonomies, which depict typical student pathways and errors (Nauryzbayev et al., 2023),
• explicit rules and guidelines, Which forms of support are useful in which learning phase? are,
• A clear understanding and recognition of misconceptions is crucial so that the AI can tailor its approach to promote routine skills (e.g., computational fluency) or conceptual understanding. This can also mean, for example, embedding a learning history so that the generative AI can respond appropriately and avoid endless loops.

Metacognition, self-regulated learning and "teachable agents": The tutor as a mirror of one's own thinking

Chatbots and AI systems can be used not only as guides and task explainers. They can also stimulate processes of planning, monitoring, and reflection in problem-solving—if they are designed to do so. The meta-analysis by Wu et al. (2025) shows that chatbots can support self-regulated learning technically, socially, and reflectively when their scaffolds are linked to models of self-regulated learning. Guo et al. (2025) confirm in their systematic review that AI systems can fulfill basic psychological needs for autonomy, competence, and relatedness—key factors for motivation and engagement.
Studies on so-called teachable agents demonstrate that learners can perceive AI-supported systems as learning companions, moderators, and collaborative problem solvers when they address their own explanations to these agents (Song et al., 2024). At the same time, it is evident that many current generative AI systems do not yet reliably fulfill key tutorial roles—such as the targeted stimulation of planning, strategy selection, and reflection—without specific prompts or retraining, and tend toward a prescriptive style (Chudziak & Kostka, 2025; Contel & Cusi, 2025). This underscores the need for proactive metacognitive scaffolds that go beyond reactive feedback.

Conclusions: AI learning companions can be explicitly designed as metacognitive learning partners::

• The tutor asks questions such as "What did you notice?", "What strategy did you try?", "Why do you think that works?".
• It encourages reflection on mistakes ("What idea from before could help here?").
• Teach-back-Elements can be included where appropriate: children explain to the AI what they have understood, and the AI reflects back, and so on.

„Human in the loop“: Hybrid approaches instead of fully automated solutions

A common shortcoming of current AI tools is the lack of teacher involvement (Guerino et al., 2023). AI must not become a "black box" in the classroom. The most effective scenarios are those in which AI relieves the teacher of some tasks (e.g., through automated differentiation or real-time analysis), allowing them more time for pedagogical interaction (Wezendonk & Veldhuis, 2024; Gonnermann-Müller et al., 2025). Reviews of AI in (mathematical) education emphasize that AI systems should be understood as feedback loops in which data collection, pattern recognition, and adaptive support must always be framed by human decisions (Holmes & Tuomi, 2022; Ninaus & Sailer, 2022). AI can support learning processes, but it cannot replace pedagogical professionalism or the responsibility of teachers (Aru & Laak, 2025; Aufenanger, 2023; Buchholtz et al., 2024).
The meta-analysis by Kaliisa et al. (2025) shows that AI feedback is no less effective than human feedback, but also not systematically superior. In the studies examined—mostly from the field of linguistics—hybrid approaches are particularly promising, combining reliable, direct, and accessible AI feedback with framed feedback from human teachers. Cosentino et al. (2025), in their study on generative AI in embodied learning environments, demonstrate that hybrid feedback models have the potential to reduce cognitive load and support differentiated information processing strategies.
Further studies on hybrid systems confirm this: CoPilot, for example, supports human teachers in real time and leads to significantly better mathematical learning outcomes for younger students – especially where teachers would otherwise provide weaker feedback, for example, due to teaching outside their subject area (Wang et al., 2024). Kestin et al. (2025) note that AI tutors, based on the didactic principles of active learning, can enrich very good face-to-face instruction in certain phases without replacing it. The effective integration in primary schools depends heavily on teachers' attitudes, the available technology, and the involvement of parents and the school community (KMK, 2024; Li, 2024).
However, the involvement of teachers in the design and use of AI tutoring systems often remains insufficient. Guerino et al. (2023) and Wezendonk and Veldhuis (2024) emphasize that teacher-centered design approaches and corresponding AI literacy programs are necessary to ensure practical classroom integration and acceptance, and to avoid using AI as a mere add-on.

Conclusions: AI learning companions should be designed from the outset as Tools and support for teachers to be thought of:

• The generation of feedback must be based on subject-specific didactic information and not left to chance.
• Transparency: Teachers need dashboards to see where students stand and what help the AI has provided.
• AI can suggest tasks, provide support, or offer diagnoses – but the final decision remains with the teacher. Teachers evaluate the quality of AI-supported assistance and decide whether and how AI-based learning support is integrated and in which areas support is beneficial. The "micro-didactic" area of providing support at the task level during problem-solving is particularly promising, as teachers are often unable to offer direct support at crucial points, or can only do so inadequately.
• Professional development and training in the integration and use of AI (AI literacy) are prerequisites for responsible use (Holmes et al., 2018; KMK, 2024; Wang & Nie, 2023) and should therefore be integrated into teacher training and professional development. This should not only extend to knowledge about the technology, but also include pedagogical aspects that address both opportunities and risks.

Motivation and emotion: The tutor as an empathetic partner

Recent reviews emphasize the role of the affective dimension. AI systems that utilize social robots, storytelling, or gamification can fulfill the basic psychological needs for autonomy, competence, and relatedness (Guo et al., 2025; Vitale & Iacono, 2024). Narratives and playful elements, in particular, help maintain motivation even during tedious practice sessions („Enhancing student engagement…“, 2022). Help-seeking research has shown that learners avoid seeking help when it is perceived as public, status-threatening, or embarrassing. Shame, fear of evaluation, and „loss of face“ thus inhibit children from asking questions in class. AI systems can effectively complement teacher support in this regard, as they patiently and personally provide help and feedback without risking the perceived social costs and stigma of seeking help (Aleven et al., 2016).

ConclusionsAI learning support should be a metacognitive and motivational partner:

• Building relationships: Use of friendly, personalized avatars or narratives (Ruan et al., 2020).
• Growth-oriented feedback: Providing feedback that praises effort and framing mistakes as learning opportunities (growth mindset).
• Stimulate reflectionQuestions like "How did you come up with that?" encourage reflection on one's own learning (metacognition).

Ethical aspects: What AI must not do!

Ethical questions are fundamental to learning with genAI – especially when it involves children. Holmes et al. (2021) call for a collaboratively developed ethical framework for AI in education that, beyond data protection, encompasses aspects such as fairness, transparency, agency, and pedagogical responsibility. The Standing Conference of the Ministers of Education and Cultural Affairs (KMK, 2024) explicitly recommends a cautious, research-based use of AI in primary and special education schools, focusing on basic skills, inclusion, equal opportunities, and data protection-compliant, age-appropriate solutions. Scoping reviews on AI and human flourishing show that previous research is strongly performance-oriented and focused on learning outcomes, while ethical, metacognitive, and teacher-related perspectives remain under-researched (Fock & Siller, 2025).
Almheiri et al. (2025) and Cárdenas et al. (2025) identify ethical challenges and scaling problems as key obstacles to the widespread use of AI tutoring systems in their systematic reviews. Furthermore, studies indicate that frequent AI use can be associated with a decline in critical thinking skills, especially when AI is primarily used as an answer-providing machine (Gerlich, 2025). Research on psychological profiling with LLMs demonstrates how accurately models can derive personality and value patterns from texts—thus highlighting the potential for misuse inherent in opaque systems (Rosenfelder et al., 2025). Therefore, the pedagogical pre-structuring and regulation of AI tools is of paramount importance, particularly for younger children.
Gulz et al. (2021) also emphasize the need to combine adaptivity with inclusive pedagogy without stigmatizing learners with special needs – an important aspect that is often neglected.

Conclusions: A responsible AI learning facilitator in mathematics lessons must:

• data-saving to avoid psychological profiling, for example by consistently processing data preferably on the device or in data-secured infrastructures, separating AI evaluations from personal data, which should be limited to the bare minimum.
• be barrier-free: Utilize multimodal interaction (language, text, image) for diverse learning needs (Hocine et al., 2023) and promote equal opportunities by specifically considering disadvantaged learners in the design process.
• to explain its functionality, at least in its basic outlines,
• Students to critical review Stimulate AI responses (Kortenkamp, 2024),
• not control learners, but Strengthening self-reliance.
• be pedagogically pre-structured and controlled.

For the PRIMA-AI project, the SKILL framework model for the use of generative AI in younger children was developed, which links the openness and pre-structured nature of the systems used to the competencies in dealing with AI and can therefore provide important guidance for the design of the use of AI.

AI as a catalyst for our own mathematical discoveries – not as a replacement

AI should not and must not lead to children merely staring at screens. Research on tangible interfaces and social robots shows that AI can also stimulate interaction in the physical world (Ligthart et al., 2023). AI should serve as a catalyst for mathematical activities—for example, to discover patterns that can then be created using tactile materials. There are currently significantly fewer studies for primary education than for secondary and higher education, but the existing results offer cautious optimism: children can benefit from genAI in their learning if learning environments are designed appropriately (Hwang, 2022; Listyaningrum et al., 2024; Mott et al., 2023; Rumbelow & Coles, 2024; Yim & Su, 2025). Some examples:

• Primary school children can understand key AI concepts such as classification and bias when these are addressed in project-based, "unplugged," or playful settings (Yim & Su, 2025; Mott et al., 2023). Such an understanding is important so that children can critically assess how to interact with the scaffolds of AI learning companions—and also that not all assistance is necessarily correct.
• AI-supported object recognition (e.g., for Cuisenaire rods) can help children to increasingly link their actions with abstract mathematical representations (Rumbelow & Coles, 2024).
• AI training can specifically improve arithmetic fluency, but for children with difficulties in arithmetic, it must be carefully combined with other forms of practice (Samuelsson, 2023). Samuelsson shows that AI-supported practice achieves greater fluency gains than memorization-based approaches alone.
• ChatGPT and similar systems show potential for supporting problem-solving, geometric tasks and algebra in primary school, but require high prompt quality and subject-specific filtering by teachers (Harahap, 2024; Listyaningrum et al., 2024; Schneider, 2025).
• Adaptive systems for children with dyscalculia show promising results in maintaining motivation and engagement (Hocine et al., 2023; Holmes, 2024).

Narrative and gamified approaches deserve special attention: Ruan et al. (2020) show that storytelling-based chatbot tutors can promote engagement and learning gains. Sayed et al. (2022) confirm significant improvements, particularly among lower-achieving students, through adaptive, gamified content.

Conclusions: In primary school, AI learning companions should primarily serve as Stimulus for rich mathematical activities They should not serve as a tool to "quickly arrive at a solution." The central task remains to enable children to critically examine, justify, and negotiate mathematical statements—including those from AI (Kortenkamp, 2024; Aufenanger, 2023).

Conclusion: Designing AI-based learning support for mathematics lessons from a subject-specific didactic perspective

Based on the current state of research and previous considerations, the following guiding principles for the design of AI tutors can currently be formulated:

1. Adaptive rather than responsive: Good AI tutors recognize patterns and errors, provide measured assistance, and refrain from giving solutions (Bastani et al., 2025; Bewersdorff et al., 2023; Kuo et al., 2025; Son, 2024).
2. Think before explaining: They are designed so that learners must first become active themselves before explanations and feedback follow (Gisiger, 2025; Kumar et al., 2023).
3. Subject-specific didactic insights as a basis: They are based on explicit models of mathematical learning – not just on linguistic plausibility, which they inherently possess (Cohn et al., 2025; Cononigo, 2024; Holmes & Tuomi, 2022; Makransky et al., 2024).
4. Metacognitive partners: They promote planning, monitoring and reflection instead of mere task completion (Wu et al., 2025; Song et al., 2024).
5. Together instead of isolated: They support teachers rather than replace them and work best in human-framed settings during those learning phases where teachers cannot support all children in the learning process (Holmes et al., 2018; Ninaus & Sailer, 2022; Wang et al., 2024; Wezendonk & Veldhuis, 2024).
6. Ethically justifiable: They take into account data protection, fairness, accessibility and the risk of cognitive „deterioration“ due to excessive relief (Holmes et al., 2021; Fock & Siller, 2025; Gerlich, 2025; KMK, 2024).
7. Pre-structured instead of open: Especially with younger children, an (app- or learning environment-)integrated, pedagogically pre-structured and controlled integration of AI as learning support is necessary, as children are often not yet able to use AI independently as learning support (Gulz et al., 2021).

If we design and further research generative AI learning support based on guiding principles, then it is not a replacement for teaching – but a potential expansion of the didactic repertoire and a tool for more personalized feedback and scaffolding, particularly in primary education. The task for the coming years will be to translate these principles into concrete, empirically tested designs for primary school mathematics instruction. Within the PRIMA-AI project, app-integrated AI learning support tools are currently being developed based on the formulated fundamental principles for AI tutors. These tools are being researched, further developed, and optimized within the framework of design-based research.

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