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Pragmatic AI in education and its role in mathematics learning and teaching

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Figure 1 also indicates the potential for AI (the robot icon) to contribute to the development of the underlying educational goals (SEL development in this example), as well as assisting in mediating both the balancing and reinforcing feedback loops (B1 and R2) associated with emotions. Some of these envisaged points for interaction are autonomous, where the robot icon appears alone, and some are supervised, where the robot and mortarboard coexist. It is important to note that these potential points of AI support are entirely indicative and the examples that are presented here are general suggestions.

Before exploring Fig. 1 in detail, it is important that we emphasise the cyclical nature of this model. Learning does not happen as a one-off event. Rather the objects of education (SEL development in this example) result in a series of changes in other quantities that are then available for use in future cycles. It is also essential to recognise that the system presented in Fig. 1 is incomplete and forms just one sub-system in a much more complex process. That is, there will be other factors in the larger system connected to the nodes of our model that are not represented here (e.g., resilience). For this reason, it is important that students experience both successes in learning and difficulties. Each will cause different emotional responses, and the larger system will respond in different ways potentially developing attributes like perseverance that are not represented here. Any AI implementations that become incorporated into this system need to ensure that they are designed to respond appropriately to both success and difficulty in ways that enhance the underlying educational objectives without disempowering students or their teachers or shortcutting the learning processes.

Working from our conceptual model (Fig. 1), we propose six general areas where AI may be able to provide mechanisms or approaches that support the learning process. From these we have identified specific elements of learning design that may be targeted for research, improvement, or modification. These objects of transformation and their associated design goals are presented in Table 1 along with possible AI application strategies and examples of implementation.

Table 1 Mapping the impact of AI implementation in the learning design

Firstly, supporting teachers to provide mathematical learning activities that are personalised at an appropriate level of complexity to match the cognitive abilities of individual students is essential. The strengths of current approaches to AI lie in their ability to mimic human processes, using vastly larger quantities of data, and with far greater speed that humans can achieve. When an AI is presented with a problem that is similar to ones it has ‘seen’ before, then it is reasonable to expect the algorithm to follow a similar process in generating output. Therefore, the implementation of some form of semi-supervised, or even unsupervised, algorithm to analyse each student’s past and current learning performance and/or mastery data and to suggest learning pathways for them to follow or to dynamically adjust the task demands to an appropriate level would be a potentially effective use for an AI learning support. Such an implementation would appear at in Fig. 1 and provide personalised challenges that maintain an optimal balance between task demand and cognitive quality of instruction. These individualised learning experiences will align with each student’s proficiency level, minimising their frustration and enhancing the likelihood of successful learning outcomes. However, personalisation should not be limited to task difficulty alone. AI can help pinpoint specific moments where students struggle, providing feedback that is not only task-focused but also supports positive appraisals of their efforts. For example, AI-driven systems can identify when a student shows signs of frustration or disengagement and offer supportive feedback that highlights their progress and effort rather than solely focusing on task completion. This can help students reinterpret their experiences as opportunities for learning, thereby fostering a more positive self-concept and increasing their motivation. An algorithm such as this would be best suited for general implementation by resource producers, as they would have ready access to the large amounts of data needed to establish the parameters of the algorithm. However, in a semi-supervised arrangement, some system or process would need to be developed to allow the classroom teacher to provide input and fine tune the algorithm in a straightforward and intuitive way.

Extending the idea of performance monitoring to student self-monitoring, AI algorithms can be used to enhance learners’ perceptions of agency and control and might be utilised at in Fig. 1. Using a large set of learning performance data a resource producer could develop a predictive model that gives students a selection of recommended next steps for their own personalised learning yet remains within the same area of knowledge that the teacher has assigned. In this conception, the AI algorithm essentially creates a decision tree for building learning pathways but leaves the final step of the process, the decision itself, up to the student. Built into such a predictive system would be the opportunity for learning analytics that could build an understanding of each student’s cognitive strengths and weaknesses and provide nudges to assist the student in achieving their own stated goals. AI-enabled tools might also be used in creative learning environments encourage cooperation and thus cultivating positive social interactions. These tools might include interactive and collaborative platforms where students can explore mathematical concepts independently and engage in cooperative problem-solving activities. AI can also contribute to the development of enhanced feelings of control and growth through individualised achievement goal structures and expectations; approaches that are key in reducing maths anxiety.

AI may also assist teachers in enhancing students’ value induction which is an important facet of learning success. AI search engines have access to an almost endless volume of information that could be used to select contexts or situations that highlight the real-world applications and uses of mathematical problems in a way that is relevant to individual students. Such an approach can contribute to students’ understanding of the intrinsic value of mathematical knowledge15.

Chatbots based on large language models (LLMs) have become particularly effective in recent years. While chatbots are still far from perfect, the ability to sideload an LLM with an appropriate set of background data files, does offer educators the possibility to use these algorithms in a safe and closed environment while ensuring that the chatbot has access to only appropriate additional information and not the entire unfiltered web. Adopting such an approach has the added advantage that the LLM itself can be smaller allowing it to run on prosumer level local hardware and removing the need to run on massive cloud infrastructure. The use of an AI approach like this to assist students in moderating feedback loops, such as the one at , has great potential for research and impact16. As noted, there is a reinforcing loop between perceptions of control and maths anxiety (R1 in Fig. 1). In a traditional classroom, this feedback loop might be driven by general reflection on the task and its success criteria analysing what the student got wrong and how to fix this. This type of feedback needs to be carefully supervised to ensure that unhelpful self-talk does not dominate the process. An AI chatbot can help to reframe these reflections to consider how an individual has developed in multiple ways while engaging with the learning activities and reduce the dichotomous focus on success vs. failure.

Furthermore, retraining students’ notions of failure and success becomes feasible through AI interventions that emphasise the iterative nature of learning and the value of the underlying educational goal. Such AI tools placed at could promote the use of personal micro-targets for students and shift the focus of the cognitive process away from the learning activity and onto this deeper learning goal, AI-driven interventions can lead to a shift in student mindset as they learn to view setbacks as opportunities for growth and reduce the anxiety associated with performance.

However, while current AI tools are capable of ‘decision making’ using large amounts of mostly structured data, they lack the capability to genuinely understand and adapt to the emotional and cognitive needs of students. The AI models tend to focus more on the mechanics of teaching rather than the emotional well-being of the learner. That is, currently available AI tools are more focussed on the products of learning than on the human process of learning. To truly harness the potential of AI in transforming mathematics education, we need to prioritise different research goals. Researchers should therefore aim to develop new systems and approaches that foster a deeper, more intuitive understanding of mathematical concepts, rather than just improving the efficiency of content delivery.

For example, we know that self-regulation of emotions is essential in order to manage adverse situations such as maths anxiety. Natural language processing algorithms might be developed to identify the fingerprints of both positive and negative emotional meaning in students’ extended textual responses. This might be supplemented with data gathered through multi-modal learning analytics—such as computer vision and audio analysis—to track non-lingual cues such as facial expressions, tonal variation and gestures17. Together such a dataset might be able to be used to provide support and strategies, both virtual and real-life, that can assist students in developing their self-regulation and emotional moderation. Such a technology might have a place at or in Fig. 1.



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How Ivy League Schools Are Navigating AI In The Classroom

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The widespread adoption and rapid advancement of Artificial Intelligence (AI) has had far-reaching consequences for education, from student writing and learning outcomes to the college admissions process. While AI can be a helpful tool for students in and outside of the classroom, it can also stunt students’ learning, autonomy, and critical thinking, and secondary and higher education institutions grapple with the promises and pitfalls of generative AI as a pedagogical tool. Given the polarizing nature of AI in higher education, university policies for engaging with AI vary widely both across and within institutions; however, there are some key consistencies across schools that can be informative for students as they prepare for college academics, as well as the parents and teachers trying to equip high school students for collegiate study amidst this new technological frontier.

Here are five defining elements of Ivy League schools’ approach to AI in education—and what they mean for students developing technological literacy:

1. Emphasis on Instructor and Course Autonomy

First and foremost, it is important to note that no Ivy League school has issued blanket rules on AI use—instead, like many other colleges and secondary schools, Ivy League AI policies emphasize the autonomy of individual instructors in setting policies for their courses. Princeton University’s policy states: “In some current Princeton courses, permitted use of AI must be disclosed with a description of how and why AI was used. Students might also be required to keep any recorded engagement they had with the AI tool (such as chat logs). When in doubt, students should confirm with an instructor whether AI is permitted and how to disclose its use.” Dartmouth likewise notes: “Instructors, programs, and schools may have a variety of reasons for allowing or disallowing Artificial Intelligence tools within a course, or course assignment(s), depending on intended learning outcomes. As such, instructors have authority to determine whether AI tools may be used in their course.”

With this in mind, high school students should be keenly aware that a particular teacher’s AI policies should not be viewed as indicative of all teachers’ attitudes or policies. While students may be permitted to use AI in brainstorming or editing papers at their high school, they should be careful not to grow reliant on these tools in their writing, as their college instructors may prohibit the technology in any capacity. Further, students should note that different disciplines may be more or less inclined toward AI tolerance—for instance, a prospective STEM student might have a wider bandwidth for using the technology than a student who hopes to study English. Because of this, the former should devote more of their time to understanding the technology and researching its uses in their field, whereas the latter should likely avoid employing AI in their work in any capacity, as collegiate policies will likely prohibit its use.

2. View of AI Misuse as Plagiarism / Academic Dishonesty

Just as important as learning to use generative AI in permissible and beneficial ways is learning how generative AI functions. Many Ivy League schools, including UPenn and Columbia, clearly state that AI misuse—whatever that may be in the context of a particular class or project, constitutes academic dishonesty and will be subject to discipline as such. The more students can understand the processes conducted by large language models, the more equipped they will be to make critical decisions about where its use is appropriate, when they need to provide citations, how to spot hallucinations, and how to prompt the technology to cite its sources, as well. Even where AI use is permitted, it is never a substitute for critical thinking, and students should be careful to evaluate all information independently and be transparent about their AI use when permitted.

Parents and teachers can help students in this regard by viewing the technology as a pedagogical tool; they should not only create appropriate boundaries for AI use, but also empower students with the knowledge of how AI works so that they do not view the technology as a magic content generator or unbiased problem-solver.

Relatedly, prestigious universities also emphasize privacy and ethics concerns related to AI usage in and outside of the classroom. UPenn, for instance, notes: “​​Members of the Penn community should adhere to established principles of respect for intellectual property, particularly copyrights when considering the creation of new data sets for training AI models. Avoid uploading confidential and/or proprietary information to AI platforms prior to seeking patent or copyright protection, as doing so could jeopardize IP rights.” Just as students should take a critical approach to evaluating AI sources, they should also be aware of potential copyright infringement and ethical violations related to generative AI use.

3. Openness to Change and Development in Response to New Technologies

Finally, this is an area of technology that is rapidly developing and changing—which means that colleges’ policies are changing too. Faculty at Ivy League and other top schools are encouraged to revisit their course policies regularly, experiment with new pedagogical methods, and guide students through the process of using AI in responsible, reflective ways. As Columbia’s AI policy notes, “Based on our collective experience with Generative AI use at the University, we anticipate that this guidance will evolve and be updated regularly.”

Just as students should not expect AI policies to be the same across classes or instructors, they should not expect these policies to remain fixed from year to year. The more that students can develop as independent and autonomous thinkers who use AI tools critically, the more they will be able to adapt to these changing policies and avoid the negative repercussions that come from AI policy violations.

Ultimately, students should approach AI with a curious, critical, and research-based mentality. It is essential that high school students looking forward to their collegiate career remember that schools are looking for dynamic, independent thinkers—while the indiscriminate use of AI can hinder their ability to showcase those qualities, a critical and informed approach can distinguish them as a knowledgeable citizen of our digital world.



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In Peru, gangs target schools for extortion : NPR

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Parents drop off their children at the private San Vicente School in Lima, Peru, which was targeted for extortion, in April.

Ernesto Benavides/AFP via Getty Images


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Ernesto Benavides/AFP via Getty Images

LIMA, Peru — At a Roman Catholic elementary school on the ramshackle outskirts of Lima, students are rambunctious and seemingly carefree. By contrast, school administrators are stressing out.

One tells NPR that gangsters are demanding that the school pay them between 50,000 and 100,000 Peruvians sols — between $14,000 and $28,000.

“They send us messages saying they know where we live,” says the administrator — who, for fear of retaliation from the gangs, does not want to reveal his identity or the name of the school. “They send us photos of grenades and pistols.”

These are not empty threats. A few weeks ago, he says, police arrested a 16-year-old in the pay of gangs as he planted a bomb at the entrance to the school. The teenager had not been a student or had other connections with the school.

Schools in Peru are easy targets for extortion. Due to the poor quality of public education, thousands of private schools have sprung up. Many are located in impoverished barrios dominated by criminals — who are now demanding a cut of their tuition fees.

Miriam Ramírez, president of one of Lima’s largest parent-teacher associations, says at least 1,000 schools in the Peruvian capital are being extorted and that most are caving into the demands of the gangs. To reduce the threat to students, some schools have switched to online classes. But she says at least five have closed down.

Miriam Ramierez is wearing a coat while standing in a park.

Miriam Ramírez is president of one of Lima’s largest parent-teacher associations and she says at least 1,000 schools in the Peruvian capital are being extorted and that most are caving into the demands of the gangs.

John Otis for NPR


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John Otis for NPR

If this keeps up, Ramírez says, “The country is going to end up in total ignorance.”

Extortion is part of a broader crime wave in Peru that gained traction during the COVID pandemic. Peru also saw a huge influx of Venezuelan migrants, including members of the Tren de Aragua criminal group that specializes in extortion — though authorities concede it is hard to definitively connect Tren de Aragua members with these school extortions.

Francisco Rivadeneyra, a former Peruvian police commander, tells NPR that corrupt cops are part of the problem. In exchange for bribes, he says, officers tip off gangs about pending police raids. NPR reached out to the Peruvian police for comment but there was no response.

Political instability has made things worse. Due to corruption scandals, Peru has had six presidents in the past nine years. In March, current President Dina Boluarte declared a state of emergency in Lima and ordered the army into the streets to help fight crime.

But analysts say it’s made little difference. Extortionists now operate in the poorest patches of Lima, areas with little policing, targeting hole-in-the-wall bodegas, streetside empanada stands and even soup kitchens. Many of the gang members themselves are from poor or working class backgrounds, authorities say, so they are moving in an environment that they already know.

“We barely have enough money to buy food supplies,” says Genoveba Huatarongo, who helps prepare 100 meals per day at a soup kitchen in the squatter community of Villa María.

Even so, she says, thugs stabbed one of her workers and then left a note demanding weekly “protection” payments. Huatarongo reported the threats to the police. To avoid similar attacks, nearby soup kitchens now pay the gangsters $14 per week, she says.

But there is some pushback.

Carla Pacheco, who runs a tiny grocery in a working-class Lima neighborhood, is refusing to make the $280 weekly payments that local gangsters are demanding, pointing out that it takes her a full month to earn that amount.

Carla Pacheco runs a tiny grocery in Lima and she is refusing to make the $280 weekly payments that local gangsters are demanding.

Carla Pacheco runs a tiny grocery in Lima and she is refusing to make the $280 weekly payments that local gangsters are demanding.

John Otis for NPR


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John Otis for NPR

She’s paid a heavy price. One morning she found her three cats decapitated, their heads hung in front of her store.

Though horrified, she’s holding out. To protect her kids, she changed her children’s schools to make it harder for gangsters to target them.

She rarely goes out and now dispenses groceries through her barred front door rather than allowing shoppers inside.

“I can’t support corruption because I am the daughter of policeman,” Pacheco explains. “If I pay the gangs, that would bring me down to their level.”

After a bomb was found at its front gate in March, the San Vicente School in north Lima hired private security guards and switched to online learning for several weeks. When normal classes resumed, San Vicente officials told students to wear street clothes rather than school uniforms to avoid being recognized by gang members.

“They could shoot the students in revenge,” explains Violeta Upangi, waiting outside the school to pick up her 13-year-old daughter.

Due to the threats, about 40 of San Vicente’s 1,000 students have left the school, says social studies teacher Julio León.

Rather than resist, many schools have buckled to extortion demands.

The administrator at the Catholic elementary school says his colleagues reported extortion threats to the police. But instead of going after the gangs, he says, the police recommended that the school pay them off for their own safety. As a result, the school ended up forking over the equivalent of $14,000. The school is now factoring extortion payments into its annual budgets, the administrator says.

“It was either that,” the administrator explains, “or close down the school.”



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Labour must keep EHCPs in Send system, says education committee chair | Special educational needs

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Downing Street should commit to education, health and care plans (EHCPs) to keep the trust of families who have children with special educational needs, the Labour MP who chairs the education select committee has said.

A letter to the Guardian on Monday, signed by dozens of special needs and disability charities and campaigners, warned against government changes to the Send system that would restrict or abolish EHCPs. More than 600,000 children and young people rely on EHCPs for individual support in England.

Helen Hayes, who chairs the cross-party Commons education select committee, said mistrust among many families with Send children was so apparent that ministers should commit to keeping EHCPs.

“I think at this stage that would be the right thing to do,” she told BBC Radio 4’s Today programme. “We have been looking, as the education select committee, at the Send system for the last several months. We have heard extensive evidence from parents, from organisations that represent parents, from professionals and from others who are deeply involved in the system, which is failing so many children and families at the moment.

“One of the consequences of that failure is that parents really have so little trust and confidence in the Send system at the moment. And the government should take that very seriously as it charts a way forward for reform.

“It must be undertaking reform and setting out new proposals in a way that helps to build the trust and confidence of parents and which doesn’t make parents feel even more fearful than they do already about their children’s future.”

She added: “At the moment, we have a system where all of the accountability is loaded on to the statutory part of the process, the EHCP system, and I think it is understandable that many parents would feel very, very fearful when the government won’t confirm absolutely that EHCPs and all of the accountabilities that surround them will remain in place.”

The letter published in the Guardian is evidence of growing public concern, despite reassurances from the education secretary, Bridget Phillipson, that no decisions have yet been taken about the fate of EHCPs.

Labour MPs who spoke to the Guardian are worried ministers are unable to explain key details of the special educational needs shake-up being considered in the schools white paper to be published in October.

Stephen Morgan, a junior education minister, reiterated Phillipson’s refusal to say whether the white paper would include plans to change or abolish EHCPs, telling Sky News he could not “get into the mechanics” of the changes for now.

However, he said change was needed: “We inherited a Send system which was broken. The previous government described it as lose, lose, lose, and I want to make sure that children get the right support where they need it, across the country.”

Hayes reiterated this wider point, saying: “It is absolutely clear to us on the select committee that we have a system which is broken. It is failing families, and the government will be wanting to look at how that system can be made to work better.

“But I think they have to take this issue of the lack of trust and confidence, the fear that parents have, and the impact that it has on the daily lives of families. This is an everyday lived reality if you are battling a system that is failing your child, and the EHCPs provide statutory certainty for some parents. It isn’t a perfect system … but it does provide important statutory protection and accountability.”



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