Integrating Artificial Intelligence (AI) Platforms into Project-Based Learning (PBL) in High School Mathematics

Essay , 2025 , 40 Pages , Grade: 9 - 12

Didactics - Mathematics

This descriptive information research paper examines the use of Problem-Based Learning (PBL) in high school mathematics, with a particular focus on the emerging integration of Artificial Intelligence (AI) platforms and tools to enhance learning and instruction. Through a comprehensive literature review and analysis of selected PBL math projects, the study explores how real-world, student-centered problem solving can be supported by AI-driven technologies such as intelligent tutoring systems, adaptive learning platforms, and data analysis tools. Observing math projects for high school students as a qualitative research method offers rich, in-depth insights into both student learning and teaching practices, particularly in innovative settings like AI-infused PBL. Findings indicate that PBL fosters critical thinking, collaboration, and deeper conceptual understanding, while AI can provide personalized feedback, scaffold learning, and facilitate data-driven project design. The research also addresses challenges including digital literacy, equitable access, and teacher preparedness. By synthesizing academic research and reviewing practical examples, this study offers insights into how PBL, combined with AI, can transform the teaching and learning of mathematics in secondary education.

Integrating Artificial Intelligence (AI) Platforms into Project-Based Learning (PBL) in High School Mathematics

Duli Pllana,

JMSA High School, Union City, New Jersey

Rudy Baez ,

JMSA High School, Union City, New Jersey

Alma Lama, PhD

UBT Prishtine Kosova

Henry Sanchez,

JMSA High School, Union City, New Jersey

Zahaib Hassan Sain

Superior University

Neril Sandeep

JMSA High School, Union City, New Jersey

Abstract

This descriptive information research paper examines the use of Problem-Based Learning (PBL) in high school mathematics, with a particular focus on the emerging integration of Artificial Intelligence (AI) platforms and tools to enhance learning and instruction. Through a comprehensive literature review and analysis of selected PBL math projects, the study explores how real-world, student-centered problem solving can be supported by AI-driven technologies such as intelligent tutoring systems, adaptive learning platforms, and data analysis tools. Observing math projects for high school students as a qualitative research method offers rich, in-depth insights into both student learning and teaching practices, particularly in innovative settings like AI-infused PBL. Findings indicate that PBL fosters critical thinking, collaboration, and deeper conceptual understanding, while AI can provide personalized feedback, scaffold learning, and facilitate data-driven project design. The research also addresses challenges including digital literacy, equitable access, and teacher preparedness. By synthesizing academic research and reviewing practical examples, this study offers insights into how PBL, combined with AI, can transform the teaching and learning of mathematics in secondary education.

Key Words: AI, PBL, Students, the Teacher, Mathematics Projects, High School Mathematics, Education

1. Introduction to PBL

The teaching method known as project-based learning (PBL) incorporates complex real-world examples to help high school students deepen their learning and better understand concepts and principles. PBL can be applied to any subject, including high school mathematics. By bringing real-life contexts and technology into the curriculum through a PBL approach, students are encouraged to become independent learners, critical thinkers, and lifelong learners (Edutopia, 2007).

Project-based learning enables students to see the application of mathematical concepts, standards, and strategies in real-world situations. In mathematics, PBL can vary in length—from short projects (mini-projects) designed to build understanding of specific concepts, to medium-length projects involving a few standards (such as Common Core State Standards), to long-term projects that span multiple mathematical units. The duration of a PBL project depends on the students' grade level and the intended learning objectives.

However, PBL in high schools does have its drawbacks. While it has been shown to improve student motivation and engagement, it also presents challenges in scaffolding, assessment, and maintaining academic rigor (Thomas, 2000; Bell, 2010). Despite these challenges, there are significant benefits to using PBL in high school mathematics.

1.1 Defining Project Based Learning (PBL)

There are several definitions of problem-based learning (PBL). In general, the application of PBL in mathematics involves students analyzing and solving real-world mathematical problems. A more formal definition of PBL includes specific components. Markham et al. (2003) define PBL as “a systematic teaching method that engages students in learning knowledge and skills through an extended inquiry process structured around complex, authentic questions and carefully designed projects and tasks” (p. 4). This definition emphasizes the word complex, implying that students engage with challenging problems that require thoughtful analysis and structured problem-solving methods. Given the multidimensional benefits of PBL, it is widely implemented in high schools. The value of PBL in the teaching and learning of mathematics is internationally recognized (Ssali et al., 2025). However, the way PBL is used can vary significantly depending on the complexity of the content and the preferences of the teacher—whether the project is short, medium, or long in duration.

Table 1. Preferred PBL length for 10 graders in math high schools

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(Source: Generated from ChatGPT)

1. 2 Pedagogical Foundation

A different definition of Project-Based Learning (PBL) incorporates pedagogical terms. PBL is a student-centered pedagogical framework that engages learners in exploring real-world problems through sustained inquiry and collaborative tasks (Thomas, 2000; Bell, 2010). The term pedagogical foundation refers to the core theories, principles, and approaches that underpin effective teaching and learning. Key elements of pedagogical foundations include learning theories, curriculum design, instructional strategies, classroom management, assessment principles, inclusive and culturally responsive teaching, educational philosophy, and the use of technology in education. PBL stems from a pedagogical tradition that asserts students learn best by experiencing and solving real-world problems (Vega, 2015). It is a student-centered teaching and learning method in which students gain knowledge through experience.

1. 2. 1 Constructivism

Constructivism in education, particularly in high school mathematics, refers to the active contribution of each student based on their personal experiences and individual ideas during lessons or collaborative mathematical projects. The concept of constructivism can vary depending on an individual's perspective. According to Krahenbuhl (2016), constructivism “is an epistemological view of knowledge, arguing that knowledge is derived in a meaning-making process through which learners construct individual interpretations of their experiences and thus, construct meaning in their minds” (p. 4). Although definitions of constructivism may differ in wording or structure, their core meaning remains the same. Simply put, constructivism can be expressed in various forms, but it generally emphasizes that students learn best by actively building (or "constructing") their own understanding and knowledge through experiences, rather than just being told facts by a teacher. In a constructivist mathematics classroom, the teacher acts as a facilitator or guide, encouraging students to ask questions and supporting them in solving problems independently.

1. 2. 2 Inquire Based - Learning

Inquiry-based learning is an approach where students learn by asking questions, exploring, and discovering answers for themselves, rather than simply being told what to know. It is an educational strategy in which students follow methods and practices similar to those of professional scientists to construct knowledge (Keselman, 2003). In high school mathematics, inquiry-based learning encourages students to ask questions, analyze, synthesize, evaluate, and sometimes experiment during mathematical projects. Teachers use student-centered teaching strategies that empower students to take ownership of their learning.

The length of inquiry-based learning (IBL) can vary depending on the complexity of the topic, the students’ age, and the depth of exploration. Typically, IBL can be short-, medium-, or long-term, lasting from one day to several weeks. Long-term IBL often overlaps with project-based learning (PBL). Although there is a subtle difference between IBL and PBL, integrating both in high school mathematics can be complementary. Each has distinct features, but together, they enhance student engagement and deepen understanding.

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Figure 1. General flow work of inquiry - based learning (IBL)

2. Overview of AI in Education

Artificial intelligence (AI) is becoming a powerful tool in education, supporting teachers in delivering more effective instruction, providing students with personalized learning and immediate feedback, and assisting both teachers and students with real-world examples—particularly in project-based learning (PBL). AI-powered tools such as natural language processing (NLP) systems, recommendation engines, and learning analytics dashboards offer new possibilities for differentiated instruction and real-time support (Luckin et al., 2016; Holmes et al., 2019). As AI continues to grow in educational contexts, more secondary school teachers are exploring creative and practical ways to integrate it into student learning (Valenzuela, 2025). Incorporating AI platforms and math solvers into mathematics instruction—especially through real-world applications—equips high school students with the tools they need to develop more effective solutions and achieve better outcomes in their mathematical projects.

2.1 Defining AI in Context of Education

Efforts for consolidating Artificial intelligence (AI) in society started a long time ago. In 1950, English mathematician and computer science pioneer Alan Turing posed the question, “can machines think?” In his paper, “Computing Machinery and Intelligence,” Turing laid out what has become known as the Turing Test, or imitation game, to determine whether a machine is capable of thinking (Lawrence Livermore National Laboratory, n.d.). However, the term AI came six years after Turing raised its famous question on the thinking capacity of computers. The term "artificial intelligence" was actually coined in 1956. In that year, John McCarthy, a Dartmouth College professor, organized a pivotal workshop that coined the term "artificial intelligence" and aimed to create machines capable of reasoning and using human language (University of Iowa, 2024).

Artificial Intelligence (AI) has revolutionized education by enhancing personalized learning experiences, automating administrative tasks, and providing data-driven insights (Emerald Publishing, n.d.). While there are many definitions of AI in education, let’s focus on the simplest one: artificial intelligence is a field of technology that enables machines to think and react like humans (University of Cincinnati Online, n.d.). The scope of AI is vast; even though it is still in the early stages of development, it already incorporates aspects of human activity. Consequently, there is no single, universally accepted definition of AI. Educators and school personnel can tailor the application of AI in educational settings. Some affordable and useful AI platforms in education include ChatGPT-4, MagicSchool, Gemini, Edmentum, GeoGebra, and Desmos.

2. 1. 1 Intelligence Tutoring Systems

Intelligent Tutoring Systems are computer-based programs that assist students in a manner similar to human tutors by providing personalized feedback and instruction. Calvo and D’Mello (2016) write, “Intelligent systems (also known as intelligent tutoring systems) refer to educational software containing an artificial-intelligence component. The software tracks students' work, adjusting feedback and providing hints along the way. By collecting information on a particular student's performance as well as other cognitive and noncognitive variables, the software can make inferences about strengths and weaknesses, and can suggest additional work” (pp. 205–220).

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Figure 2. Basic architecture of an ITS adapted to students' learning styles (Morales-Rodríguez et al., 2012).

Popular intelligent systems that use AI to adapt math instruction based on student performance include Carnegie Learning, Cognitive Tutor, and ALEKS (by McGraw-Hill). Other educational apps, such as Edmentum, incorporate components of ITS by adapting content to students’ academic levels and helping them progress to more advanced material.

2.1.2 NLP Tools

Natural Language Processing (NLP) is a machine learning technology that enables computers to understand and interpret human language. NLP, a subfield of artificial intelligence, focuses on the interaction between computers and human language (TEKsystems, 2024). Through algorithms and models, NLP can analyze unstructured data and convert it into structured formats such as text, tables, graphs, or images. NLP technologies are being applied in various real-world situations, including examples related to high school math projects. One key benefit of NLP is that it allows users to interact with computer systems using everyday, conversational language—eliminating the need for advanced computing or coding knowledge (Hughes, 2025). Table 2 highlights several NLP tools and their key features.

Table 2. Describes several significant characteristics of natural language progressing tools in education.

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(Source: Figure adapted from Lee, 2025)

Natural Language Processing (NLP) tools are becoming valuable assistants for teachers, students, and researchers in the field of education (see Table 2 for examples). Specific tools play crucial roles for each group. For instance, teachers can benefit from tools like Grammarly for writing support, Quillizon for writing and grammar instruction, and Turnitin for plagiarism detection. ChatGPT is a great tool for teachers, students, and educational researchers. The ability for a chatbot to solve higher level mathematical questions is in high demand because it would lead to having less human error when it comes to mathematical calculations and the field of mathematics and artificial intelligence will go a step further (Leonard, 2022). Students have access to NLP-based assistants such as ChatGPT, Readable, AI-powered math solvers, and Homework AI. Educational researchers can use various NLP tools to support their work, including Voyant Tools and the Lexile Analyzer.

2. 1. 3 Analytics

Analytics in AI refers to the application of artificial intelligence techniques and algorithms to analyze large datasets. It involves methods such as machine learning and natural language processing (NLP). As a subset of decision intelligence, AI analytics enhances and automates data analysis using artificial intelligence technologies (Lilliana, 2024). In education, AI analytics is used to improve teaching, learning, and administrative tasks. Key elements of AI analytics in education include personalized student learning, predicting student performance, smart grading and feedback, improving instruction and lesson planning, and assisting with school decision-making.

Ultimately, learning analytics helps instructors make informed decisions. It is crucial for identifying patterns, predicting learner outcomes, and personalizing the learning experience (Digital Learning Institute, n.d.). Also, AI assists students with academic support such as personalized learning, homework help and tutoring, and study for exams.

Despite these benefits, AI analytics also presents challenges. These include difficulties in interpretation, data overload, inconsistent data sources, and concerns around data privacy and ethics. The other challenges concern bias in AI models, overreliance on AI, access to devices, and the internet.

2. 2 General Use of AI

AI is expanding its presence across all branches of education. In general, the use of AI occurs through personalized learning and adaptive tutoring, automated problem-solving and explanation tools, intelligent assessments and feedback, gamification and engagement, teacher support, and promoting equity and accessibility. However, it also presents certain drawbacks, as described in Table 4 (Challenges to Consider in Mathematics Education).

The components of AI activities mentioned above represent the positive aspects—or benefits—of AI in education, while the elements described in Table 4 highlight its negative aspects. As we can see, AI in mathematics education has both strengths and weaknesses. Educators and administrators need to weigh the pros and cons of AI in education as they consider how they and their students will use the technology (Office of Communications, College of Education, 2024). By analyzing and identifying both the advantages and disadvantages of AI in education, educators and administrators can design and select the most suitable AI-integrated programs to meet their educational needs.

Table 3. Impact metrics based on studies and pilot programs.

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(Source: Modified from ChatGPT)

AI platforms identify students' strengths and weaknesses and adapt mathematical problems based on their mistakes and learning pace. Some AI tools that assist students include Khan Academy (Khanmigo)—an AI tutor offering hints and scaffolding; ALEKS (McGraw-Hill)—adaptive math learning software; and Photomath with AI—a tool that provides step-by-step solutions to math problems.

Automated problem-solving and explanation tools are used when students input equations or word problems; the AI solves them while offering explanations. In addition, AI supports the visualization of graphs and geometric figures. Common automated problem-solving tools include Wolfram Alpha, Mathway, and Symbolab.

Intelligent assessments and feedback occur when AI evaluates open-ended math responses and provides targeted feedback. Intelligent tutoring tools—such as EdTech LMS platforms like Squirrel AI, Century Tech, and Edmentum—use diagnostic analytics to detect conceptual misunderstandings, save time for educators, and provide valuable data to improve instruction.

Table 4. Challenges to consider in mathematics education.

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(Source: Modified from ChatGPT)

Math can often feel abstract, repetitive, or intimidating. Gamification makes learning math more enjoyable, while AImakes it adaptive and personalized. Combining gamification with AI increases motivation and persistence, reduces math anxiety, provides real-time, tailored feedback, and encourages exploration and mastery.

Examples of gamified AI tools in mathematics that relate to real-world applications include:

● DreamBox Learning – Uses AI to adapt math content in real time.

● Khan Academy and the Mastery System – AI recommends skills to practice based on past performance.

● Prodigy Math Game – A role-playing game format.

● Mathigon – Interactive math textbooks with puzzles and storytelling.

General AI (or broadly capable AI systems like ChatGPT) can be a powerful tool for supporting math teachers, not just students. AI can enhance teaching effectiveness, reduce workload, and improve outcomes in math education. General AI support for math teachers includes assistance with lesson planning and content creation, assessment design and feedback, differentiation and personalization, administrative support, and classroom engagement.

2. 2. 1 Personalization

AI platforms have the capability to adjust to students' difficulties with mathematics and sequence problems from easier to more difficult examples based on real-time performance. Personalized learning involves tailoring lessons to fit each student’s unique strengths, challenges, and pace (Academic Tips and Resources, n.d.). AI analyzes performance over time and customizes content according to each student’s abilities, weaknesses, learning speed, and interests. For instance, a student who excels in algebra but struggles with functions would receive additional support in that area before progressing to more complex topics such as logarithms.

Personalization also occurs through virtual tutoring, where AI chatbots and virtual tutors explain concepts, guide students through problems step-by-step, and respond to questions using natural language. By leveraging AI in mathematics education, students can become more actively engaged in their learning journey and achieve better academic outcomes (Aina Gbolade Opesemowo & Adewuyi, 2024).

For example, the Socratic AI platform allows students to take photos of mathematical problems and upload them to the chatbot, which then provides detailed explanations. In the case of open-ended questions, platforms like ChatGPT are effective in not only providing answers but also explaining the reasoning behind them.

Most importantly, AI can identify students at risk of failing by analyzing patterns in homework, quiz results, engagement levels, and time spent on tasks. Dashboards generated by these systems highlight which students are falling behind specific standards, enabling timely intervention by both students and teachers to prevent failure in mathematics courses.

2. 2. 2 Assessment

AI transforms assessment in high school mathematics to a higher level by making it more effective and insightful. AI assists teachers assessing students in mathematics through Automated Grading and Instant Feedback, Diagnostic and Formative Assessments, Adaptive Assessments, Learning Analytics and Predictive Insights, Open-Ended and Conceptual Assessment, and Gamified Assessment.

Table 5. Challenges in AI - Based math assessment.

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(Source: Modified from ChatGPT)

A student using an AI math platform completes a diagnostic quiz. The system identifies that the student understands how to solve linear equations but struggles with word problems involving systems. The platform adjusts the learning path, provides targeted practice, and gives teachers a detailed report. After a few sessions, a follow-up assessment confirms improvement.

Despite several challenges of AI assessment described in Table 5, AI scoring has shown great accuracy. The results showed a high degree of consistency between the scores given by teachers and ChatGPT, suggesting the AI’s reliable scoring capability (Yeo & Kim, 2024). Consequently, AI platforms in high school mathematics assessment offer significant benefits for teachers and administrators in evaluating students' academic progress.

2. 2. 3 Feedback

Brisk and MagicSchool are educational platforms that provide significant feedback for high school mathematics students before they take exams. Choose Brisk if you want fast, embedded feedback directly in Google Docs—especially for written math explanations or quick formative assessments. On the other hand, choose MagicSchool if you need more flexible feedback tools for both math and other subjects and are comfortable working in a separate platform. Brisk Teaching functions like a virtual tutor for your classroom, offering multiple tools. It provides personalized comments directly within students’ Google Docs, enhancing the feedback process (Bell, 2025).

Feedback for high school math students can also be delivered through a platform like MagicSchool AI, which typically includes features such as automated reports, progress tracking, and AI-generated insights. For example, MagicSchool AI can generate written feedback on the mathematical problem-solving skills of a specific student group—such as Group P1-G2.

Answer (feedback writing) of MagicSchool AI in the high school math example that is shown in Figure 3.

Areas of Strength:

• Your step-by-step approach to completing the square is methodical and well-organized, showing clear progression from S = πr² + πr to the final form

• You correctly maintained mathematical equivalence throughout each transformation, particularly in handling the π terms

• The isolation of the radius (r) variable demonstrates good algebraic manipulation skills

Areas for Growth:

• While your steps are correct, consider adding brief explanations for each step to show your reasoning

• The final answer in Part B needs to be explicitly calculated using the given surface area value of 3π/4

• Consider drawing a clear conclusion after graphing to show what the radius value means in context

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Figure 3. A high school math example where four students worked collaboratively on solving a mathematical problem using a PBL approach at the technology-focused urban high school in New Jersey.

General Feedback on Writing Mechanics:

• Your mathematical notation is consistent, but adding proper equation alignment would make your work even clearer

• Consider using bullet points or numbering your steps to make your solution path easier to follow

• Add a brief concluding statement for each part to verify that your answer satisfies the original equation

Note to student on Figure 3: Your understanding of completing the square and algebraic manipulation is strong. Focus on making your presentation more complete by adding brief explanations and clearly stating your final answers. This will help demonstrate your full understanding of the problem-solving process.

3. Integration of AI in PBL Contexts

Integrating Artificial Intelligence (AI) with Project-Based Learning (PBL) in high school mathematics is an innovative and powerful approach to deepen conceptual understanding, foster critical thinking, and enhance student engagement. Latrenda Knighten, president of the National Council of Teachers of Mathematics and a former math teacher, said, “We know that children learn math from being able to problem-solve, being able to use reasoning skills, critical thinking, having opportunities to collaborate with each other and talk about what they’re doing” (Prothero, 2025). AI can serve as a tool for educators and students to elevate academic performance in all areas, including PBL. Above all, the integration of AI and PBL in high school mathematics promotes interdisciplinary learning, prepares students for future careers, and makes math more engaging and relevant.

3.1 AI Tools Supporting Phases of PBL

AI tools or mathematics solvers that support project-based learning (PBL) assist both students and teachers in solving mathematical problems, graphing results, and verifying solutions. Some of the most effective AI-powered mathematics solvers used by educators include GeoGebra, Wolfram Alpha, Desmos, PhotoMath, Mathway, and Symbolab. It is important to select the appropriate AI tools for each mathematical project. When used wisely, AI becomes a copilot that supports teachers and students in developing creativity and critical thinking skills (Baez et al., 2025). Technology empowers educators to apply AI tools in a wide range of educational contexts. Applying technology in high school mathematics provides various types of information that can be effectively incorporated into mathematical projects (Pllana et al., 2024). Using the right AI tools in PBL can elevate the quality of student outcomes.

Table 6. Several mathematics tools are empowered by AI that support PBL.

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(Source: Modified from ChatGPT)

3.1.1 Planning

Planning mathematical projects with AI platforms helps teachers improve the quality of their projects and saves time in creating and tailoring them for students. AI also provides initial ideas and supports teachers in developing final projects. Mathematics teachers should take into consideration many factors before assigning math projects. For example, they should consider students' interests when selecting project topics (Baez et al., 2024). It's important to connect the content of mathematics projects to real-world situations in the community, aligning with culturally responsive teaching. Additionally, the complexity of the project should match students' mathematical preparation and grade level. AI can assist by offering preferences for different topics, project length, and appropriate levels of complexity.

Table 7. Sample of mathematics AI project ideas for PBL

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(Source: Modified from ChatGPT)

A teacher at a technology-focused urban high school in New Jersey was interested in creating a mathematics project related to community gardens involving quadratic equations. The teacher used Magic School AI, which was available on the school district’s website. In the chatbot, the teacher requested a math project for 10th-grade Algebra 2 students involving quadratic equations. The Magic School AI platform generated 10 examples based on the given criteria. Table 8 presents three of those examples. If the teacher wishes to generate more examples, they can simply request them and receive results within seconds.

Table 8 presents three examples out of ten PBLs generated by the Magic School AI platform.

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(Source: Generated from Magic School AI)

3.1.2 Execution

Numerous real-world problems can be effectively represented through mathematical models (Pllana, 2023). Any chapter in a mathematics course can be illustrated using real-world situations with the help of AI platforms. Specific examples are presented in Table 8. Moreover, the teacher can refine these examples, express them using mathematical expressions (equations), and enhance them with figures generated or modified by the Gemini AI platform. Project-Based Learning (PBL) can involve interdisciplinary subjects, and mathematics plays a crucial role across multiple fields (Pllana, 2024). However, implementing PBL involves several steps before it is fully developed and assigned to students. Each group then receives an example or question to solve based on the provided scenario. A sample project is depicted in Figure 4, which illustrates the execution of a mini math project in class—specifically, a community garden math PBL.

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Figure 4. A mini math project of students at the technology-focused urban high school in New Jersey.

3.1.3 Reflection

Usually, mathematics teachers assign at least a paragraph at the end of mathematics projects expressing their thoughts about their experience during the project reflection. This concluding paragraph serves to encapsulate their entire project experience, offering insight into their learning process (Baez et al., 2024). Students’ reflection serves as a guidance for improving elements that do not work in mathematics projects and enforce components of the project that work well. On the other hand, students’ reflection on the last paragraph serves them as a metacognitive learning task. Figure 5 presents an example from students at technology-focused urban high school in New Jersey.

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Figure 5. An example that describes students’ reflection of a math project at the technology-focused urban high school in New Jersey.

3.2 Examples of AI Platforms

The classic math modeling problem — rewriting a quadratic equation in vertex form using completing the square— and it’s perfect for introducing AI tools that support algebraic reasoning, visual modeling, and project-based learning on the Table 8. Let analyze the example below by applying AI platforms and tools respectively.

The example in Table 8: A local park is designing a new skateboard ramp. The ramp's cross-section forms a parabola that can be modeled by the equation y = x^2 + 6x + 5, where y is the height and x is the horizontal distance from the left edge of the ramp (both measured in feet). The parks department wants to rewrite this equation in vertex form to easily identify the lowest point of the ramp. Use the completing the square method to help the parks department express the equation in vertex form y = (x - h)^2 + k, where (h, k) represents the vertex of the parabola.

Applying the minimum AI platforms and math solvers empowered by artificial intelligence:

● Use ChatGPT to guide or verify steps for completing the square.

● Use Symbolab to check each algebraic step.

● Use Desmos to visualize the original and vertex-form equation.

General steps on completing the mathematical project:

● Step-by-step guidance for completing the square

● Explanations of vertex form and interpretations of (h, k)

● Project presentation or reflection writing help

ChatGPT - Explains general information for any project including mathematical equations or figuring out errors in mathematical concepts.

● Students can ask ChatGPT to verify their algebra or explain conceptual errors

Example Prompt:

"Help me convert y = x² + 6x + 5 into vertex form using completing the square."

Symbolab - AI-powered step-by-step calculator

● Use for: Automatic algebraic steps, like completing the square or factoring

● How it helps:

1. Students type in the quadratic and select "Convert to vertex form"

2. Symbolab shows each step of completing the square

Desmos Graphing Calculator - Best for graphing and visual and visual math problems

● Use for: Visualizing the standard form vs. vertex form of the parabola

● How it helps:

1. Students can enter both forms of the equation and visually confirm the vertex

2. Experiment with transformations of parabolas to understand vertex shift

● How to use:

1. Input: y = x^2 + 6x + 5 and y = (x + 3)^2 - 4

2. See how they overlap perfectly after completing the square

Students reflect on their experience while they completed the project. For example, students reflect on how (h, k) relates to the ramp design — why the vertex matters. Reflecting on the process and compiling these mathematical projects enables students to engage in deeper, metacognitive thinking (Pllana et al., 2024 ).

3.3 Roles of AI in Scaffolding, Content Generation, Collaboration Enhancement.

Scaffolding refers to the structured support provided to students to help them progress toward a stronger understanding and greater independence in learning. In this context, scaffolding helps students move from guided instruction to independent mastery of completing the square.

Step-by-step guidance breaks down the process:

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AI in Content Generation refers to AI’s ability to generate problems, visual aids, explanations, or even complete project ideas. It enables the creation of rich, engaging materials and alternative problem formats to support diverse learners. AI in Collaboration Enhancement can support and improve group work, communication, and co-construction of knowledge during math projects. The goal is to facilitate meaningful collaboration and deeper mathematical thinking.

For example, a suggested group task breakdown might be:

● Student A: Complete the square

● Student B: Graph the function

● Student C: Interpret the vertex

● Student D: Write recommendations

Table 9. Summary of the roles of AI in scaffolding, content generation, and collaboration enhancement for Table 8 - Example 3.

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(Source: Modified from ChatGPT)

4. Empirical Findings

An empirical study on the integration of Artificial Intelligence (AI) and Problem-Based Learning (PBL) in high school mathematics aims to examine the real-world effects of combining these two powerful educational approaches. The literature contains a significant number of studies demonstrating the effectiveness of AI and PBL in high school mathematics, particularly in improving student learning outcomes, engagement, collaboration, teacher perceptions, and feedback processes. With the advancement of AI education, researchers have initiated empirical studies to explore its implementation in K–12 schools (Liu & Zhong, 2024). Several studies highlight effective practices of integrating AI within PBL across various educational levels from K to 12. AI tools such as ChatGPT and Gemini (among others) are increasingly used in PBL settings across grades 6–12 to support students in refining their final products, enhancing digital media production skills, and expressing their learning creatively (Valenzuela, 2025). These tools significantly contribute to student engagement and collaboration during group work. Educators play a central role in implementing feedback strategies, underscoring the importance of understanding educator-centered perspectives on feedback processes in both K–12 and higher education (Jin et al., 2025). Finally, teachers’ perceptions and students’ feedback collectively shape the core content and instructional strategies adopted within educational districts.

4.1 Studies Showing AI - PBL Effectiveness from K to 12

Although AI has been present since the 1960s, its practical application in education—particularly through the early development of intelligent tutoring systems—has evolved into a significant area of research (Bond et al., 2024). Recently, a growing number of studies have shown that AI-supported problem-based learning (AI-PBL) is highly effective from kindergarten through grade 12. Improving scores on high school math exams remains a challenge for both students and teachers, requiring processes that integrate feedback and enhance the learning experience (Black & Wiliam, 1998; Gamlem & Smith, 2013; Van der Kleij, 2022).

From the perspective of teachers, providing students with meaningful feedback in AI-supported PBL environments can significantly enhance learning outcomes. According to some studies, teachers reported that adaptive feedback and real-time self-assessment tools help reduce student anxiety and increase motivation (Wang et al., 2022). One of the key tasks for teachers is to evaluate both the effectiveness and the drawbacks of integrating AI into PBL. Once teachers recognize the potential of AI in achieving their most challenging instructional goals within their current educational paradigms, their attitudes toward AI are likely to become more positive (Lindner et al., 2019).

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Figure 6. Integration of AI in PBL, illustrating the connection among six components of AI-PBL. The Figure is modified by Gemini AI.

According to teachers, providing meaningful feedback in AI-supported PBL environments has limited impact on student performance. Furthermore, researchers continuously refine AI technologies as they investigate what works and what does not in AI platforms—ultimately aiming to develop more sophisticated tools that support administrators, educators, and students in the educational field.

4.2 Learning Outcomes, Engagement, Collaboration, and Skill Development

AI-powered project-based learning (AI-PBL) makes abstract math concepts tangible by connecting them to real-world data and problems. Teachers and students develop higher-order mathematical skills, make lessons more interactive, and collaborate with one another at any time. Students gain access to mathematical projects even after school or on weekends. AI allows students to take greater ownership of their learning while freeing up teachers to focus on deeper engagement and meaningful feedback (Provenzano, March 2025). The integration of AI into PBL significantly enhances students’ learning outcomes. In addition to fostering critical thinking—an inherent part of project-based learning—AI-PBL also supports preparation for standardized assessments such as the SAT (Moore, 2021). PBL enables students to work in teams to solve mathematical problems in real-world scenarios and helps answer the age-old student question: “When or where am I going to use this mathematical topic in the real world?”

Student engagement with AI in Project-Based Learning (PBL) is an emerging and impactful area in education. As students work on specific mathematical projects and seek assistance from AI platforms, they often receive responses that closely align with—but do not exactly match—their questions. This near-accurate feedback encourages collaboration among students as they work together to find the correct solutions. In this context, AI platforms function as a kind of “pedagogical catalyst,” facilitating a shift from traditional lectures to more engaging, active learning experiences through competitive mathematics projects. This shift is supported by students’ positive reception and notable improvements in learning retention and engagement (Ramos & Condotta, 2024). Within this process, effective group collaboration plays a critical role in determining the level of student engagement and the overall success of their PBL outcomes.

The application of AI in Project-Based Learning (PBL) by mathematics teachers and students shows a positive correlation with the development of key skills in high school mathematics. Incorporating PBL with AI in the classroom is an effective way to engage students in real-world challenges while fostering essential competencies such as critical thinking, collaboration, and creativity (MindSpark Learning, n.d.). AI's flexibility across various topics equips students with powerful tools to tackle complex mathematical problems at the high school level. Since the 1990s, PBL has gained widespread popularity across academic disciplines (Saad & Zainudin, 2022) and continues to play a vital role in the development of students' mathematical skills. Recent findings provide new insights into the literature by offering empirical evidence of PBL's impact on the development of 21st-century skills and student engagement in mathematics (Rehman et al., 2024). The integration of AI with PBL further enhances this effect, showing a strong positive correlation with the skill development of both teachers and students.

4.3 Teacher Perceptions and Student Feedback

The definition of teachers' perceptions suggests that student grading can be subjective. Teacher perceptions refer to the cognitive, emotional, and attitudinal perspectives and beliefs held by educators regarding various aspects of their professional roles, the teaching and learning process, and the educational environment (IGI Global, n.d.). These perceptions—teachers’ thoughts or mental images about their students—are shaped by their background knowledge and life experiences (IRIS Center, n.d.). When teacher perceptions do not align with students’ actual skills in mathematics, it can lead to student demotivation. However, the integration of AI and project-based learning (PBL) can help both teachers and students shift these perceptions. AI tools that provide positive feedback within PBL environments in high school mathematics can motivate students to participate more actively in class. The confidence students gain from AI-generated feedback encourages greater engagement, which, in turn, positively influences teacher perceptions. As a result, this improved perception can lead to more favorable assessments and better academic performance for students.

5. Challenges and Limitations

Integrating AI and project-based learning (PBL) in high school mathematics presents both opportunities and challenges. Key challenges include ethical considerations, algorithmic bias, data privacy concerns, overreliance on AI tools, pedagogical risks, loss of student creativity, potential misuse, inadequate teacher preparedness, and infrastructural gaps. A significant issue lies in the core AI methodologies—such as linear algebra, statistics, and calculus—which are often only partially addressed in high school curricula. As a result, PBL projects involving AI may need to avoid more mathematically intensive topics, potentially limiting their depth and scope.

Additionally, many AI models, particularly complex ones like deep neural networks, function as "black boxes," producing outputs without transparent reasoning (Opesemowo & Ndlovu, 2024). This lack of explainability hinders their utility in mathematical problem-solving, where understanding the reasoning process is crucial. Furthermore, AI tools can sometimes hallucinate—generating incorrect or nonsensical answers—which poses a challenge for both teachers and students. To mitigate these risks, users must critically evaluate AI-generated solutions and verify them using multiple reliable sources before accepting them as accurate.

Another major challenge in integrating AI with project-based learning (PBL) in high school mathematics is teachers’ readiness to effectively use AI tools. According to Li et al. (2024), although many teachers are confident in understanding the basic capabilities of AI, they still face difficulties—particularly in addressing the varying AI skill levels among students. Reducing the gap in teachers' knowledge and confidence in using AI for PBL can significantly improve student performance in mathematics-related projects.

5.1 Ethical Considerations

Ethical considerations surrounding artificial intelligence (AI) platforms in problem-based learning (PBL) involve several issues; however, this paper focuses on three key concerns: bias, data privacy, and overreliance. As AI becomes increasingly embedded in educational environments, it is crucial to establish policies and guidelines that ensure its ethical and effective use (Funa and Gabay, 2025). In the context of AI in education—particularly in high school mathematics—bias can arise from the creators of the technology. Teachers should therefore exercise caution and apply culturally responsive teaching practices when using these tools. AI tools must be designed to accommodate diverse learning needs and backgrounds, enhancing learner-centered approaches and competency assessments, especially for underrepresented groups (University of the Philippines, 2024). According to Berendt et al. (2020) and Crawford et al. (2024), the collection and use of educational data can pose risks to students if not properly managed. Another significant issue is the overreliance on AI by students when completing mathematical projects. This dependence may hinder the development of essential skills such as critical thinking, problem-solving, and effective communication (Zhai et al., 2024). While ethical considerations in AI platforms are multifaceted, this paper will center on the three issues mentioned in Figure 7.

Abb. in Leseprobe nicht enthalten

Figure 7. The three components of ethical considerations: bias, data privacy, and overreliance.

5.1.1 Bias

AI platforms in education are a growing concern in high school mathematics because they may contain algorithmic flaws and rely heavily on the skills of teachers or students to interact effectively with chatbots. If AI algorithms are not developed carefully, they can perpetuate biases present in the training data. In many AI and machine learning models, logarithmic functions are used, and bias can emerge when logarithmic transformations distort feature differences disproportionately—especially when there is poor preprocessing, flawed assumptions about data distributions, or underrepresentation of certain groups, all of which can lead to biased parameter estimation. Additionally, AI chatbots may provide biased responses or inaccurate information (Kasneci et al., 2023; Sedaghat, 2023). Bias may also impact non-native English speakers or students with nonstandard writing styles when communicating with chatbots. As technology advances, AI-powered educational tools are expected to become more sophisticated, delivering more accurate information and offering highly individualized, engaging learning experiences (Labadze et al., 2023). However, whether biases in educational AI platforms will truly diminish or become insignificant in the near future remains uncertain.

5.1.2 Data Privacy

Data privacy is a critical concern when high school students use AI platforms, especially given the sensitivity of minors' personal information. Schools collect a significant amount of data on high school students, and if not managed properly, there is a risk of data breaches that could expose this personal information (McNulty, 2024). Students have the right to protect their privacy—particularly students with disabilities. School districts are obligated to ensure the privacy and security of all students’ data, especially before integrating AI into their curricula. Safeguarding this information helps prevent discrimination, stigmatization, and, in more serious cases, identity theft (Pérez, 2024). When school districts use AI platforms, they should avoid submitting sensitive information in order to protect student privacy and comply with FERPA regulations. According to Hankerson (2024), the following types of student data should not be shared with AI chat tools, along with examples in each category:

● Personally Identifiable Information (PII): Names, addresses, phone numbers, email addresses, Social Security numbers, student ID numbers, birth dates.

● Educational Records: Grades, transcripts, class schedules, disciplinary records, disabilities, Individualized Education Plans (IEPs).

● Health Information: Medical records, health conditions, allergies, medication information, therapy records.

● Financial Information: Family income, financial aid details, bank account information.

● Behavioral or Disciplinary Records: Disciplinary actions, behavior reports, counseling records.

● Photos or Videos: Images or recordings of students without explicit consent.

● Communication Logs: Personal messages, emails, and communications with parents or guardians.

Although AI offers many benefits for students' academic growth, it is essential to integrate it responsibly in school districts. While AI can enhance learning, it also introduces new risks. To use AI safely and appropriately in education, school districts must take the necessary steps to address and eliminate these challenges.

5.1.3 Overreliance

Students' overdependence on AI in project-based learning (PBL) for high school mathematics can lead to surface learning, loss of creativity, diminished academic originality, skill atrophy, and the development of misconceptions. When students use AI to find answers or clues for completing math projects, they often rely on shortcuts and skip the process of deep research or critical thinking. This reliance contributes to a superficial understanding of mathematical concepts. Creativity often emerges through struggle (Orsi, 2025); however, AI removes this struggle by providing instant answers or solutions. As a result, students may experience a decline in creativity. Additionally, in their rush to finish assignments or projects quickly, students might resort to plagiarism or unethical use of AI-generated content. Heavy dependence on AI in PBL may also create an imbalance in student competence, potentially undermining peer collaboration and learning.

Table 10. Describing several issues in overreliance

Illustrations are not included in the reading sample

(Source: Modified from ChatGPT)

Relying entirely on AI to solve mathematical projects may result in high school students becoming less critical thinkers, as they might trust AI-generated solutions without verifying their accuracy. There is a potential risk of diminishing critical thinking skills if students depend too heavily on AI-generated content without proper scrutiny (Garcia, 2025). Students may develop a habit of accepting answers or solutions at face value, without engaging deeply with the underlying concepts. AI errors can occur unpredictably and are not necessarily tied to specific topics (Schneier & Sanders, 2025). When such errors appear during project work, students may unknowingly incorporate them into their final products.

5.2 Pedagogical Risks

Teaching and learning high school mathematics with AI can have both positive and negative impacts on students' learning outcomes. For instance, the article Without Guardrails, Generative AI Can Harm Education, published by the Wharton School, discusses a research study conducted in Turkey involving 1,000 students. According to the paper, the results suggest that the control group relied heavily on the software to solve problems and, as a result, did not learn the underlying mathematical concepts deeply enough to perform well on the exam (Bastani, 2024). The pedagogical risk of integrating AI into any subject, including project-based learning (PBL) in high school mathematics, lies in the fact that, without clear teacher guidance, students may not fully benefit from the use of AI. However, the same study found that students who followed teachers' instructions and used AI appropriately in mathematics were better prepared for their exams.

One issue with using AI platforms in PBL is that AI often lacks the capacity to deeply explain mathematical concepts within projects. For example, while ChatGPT can effectively explain basic concepts like the Pythagorean theorem and provide step-by-step solutions, it struggles to identify and correct misconceptions (Pepin et al., 2025) and lacks robust language for modeling and explaining mathematical problem-solving. A study on mathematics teachers using MagicSchool (Beauchamp & Walkington, 2024) found that teachers believed the tools could support students’ motivation to learn mathematics and increase the efficiency with which teachers generate tasks. Nonetheless, teachers observed that English language learners faced challenges when engaging with real-world examples in mathematics projects.

The effective use of AI in PBL requires not only student readiness but also sufficient teacher preparation. Many math teachers find it challenging to use AI tools in the most effective ways. According to one study, nearly 7 in 10 math teachers reported they had not yet received professional development on using artificial intelligence in their teaching. Of those, 66 percent said they would like to receive such training (Prothero, 2025). These findings, along with other research, suggest that teachers are ready and eager to advance their knowledge of AI in mathematics through professional development opportunities.

5.2.1 Loss of Creativity

Creativity precedes innovation; as a result, mathematics teachers apply creativity in teaching and learning, especially through projects whenever possible. While AI has both positive and negative effects on the teaching of mathematics in the classroom, these tools can help students understand complex concepts and solve problems quickly. However, they can also limit student creativity and lead to overreliance on technology (Holman, 2023). By using AI wisely in project-based learning (PBL), educators and learners can harness its positive aspects in high school mathematics. For example, when proving the Pythagorean Theorem visually as a math project, students used Canva to enhance their Google Slides presentations.

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Figure 8. The student's proof (math project at the technology-focused urban high school in New Jersey) of the Pythagorean theorem, as depicted in the provided images, demonstrates creativity.

The math teacher who assigned the project was interested in determining whether the students’ math project was creative. To evaluate creativity in the project, the teacher posed a question on the Gemini AI platform and uploaded an image of Figure 8. While Gemini offers insights, "the real magic lies in your execution" (Nicholls, 2024). The response from Gemini is described as follows:

The Teacher asked: Does the student's math project show elements of creativity?

The Gemini Answer: Yes, the student's proof of the Pythagorean theorem, as depicted in the provided images, demonstrates creativity.

Why it's Creative

The creativity lies in the visual and dynamic approach to proving the theorem. Instead of a traditional algebraic or geometric proof using static diagrams, the student uses a sequence of transformations on a balance scale to show the equivalence of areas.

Here's a breakdown of the creative elements:

● Balance Scale Analogy: Using a balance scale to represent mathematical equality is an intuitive and visually engaging way to illustrate that the areas on both sides are equivalent. This makes the abstract concept of equality more concrete.

● Decomposition and Recomposition: The proof involves breaking down larger squares and arranging the pieces along with the right triangles to form the squares and . The act of moving and rearranging the pieces on the scale to maintain balance is a creative way to demonstrate the relationship.

● Step-by-Step Visual Progression: The four slides show a clear, logical, and animated progression.

○ Slide 1: Sets up the initial equivalence: plus two triangles on one side, equals plus two triangles on the other. This implicitly shows that + = + where the 2(2​ab) represents the four triangles rearranged.

○ Slide 2: Shows the removal of the four triangles from both sides, leaving and on one side and on the other hand. This step is the most critical in showing the visual cancellation.

○ Slide 3: Rearranges the components more clearly to show and together.

○ Slide 4: Presents the final result with simplified shapes on the balance.

● Intuitive Understanding: This method helps build an intuitive understanding of why the theorem works by visually demonstrating the conservation of area, rather than just abstract symbols.

In the students mathematics project it is obvious students and the teacher used AI platforms wisely. Students proved Pythagorean theorem visually by using Canva only for the visual appeal and ordering slides step by step. On the other hand, the teacher was interested to know whether the students' work contains creative elements or not. The teacher used the Gemini AI to verify students' creativity as it is shown above.

5.2.2 Misuse

Misuse of AI in education occurs when AI tools are used in ways that harm learning, compromise ethics, or create unfair advantages (TSHA Anywhere, n.d.). Educators may misuse AI in project-based learning (PBL) if they rely entirely on AI-generated content without revising, adapting, or verifying the work. Similarly, students can misuse AI in PBL by simply copying and pasting answers without engaging in the learning process. To prevent the misuse of AI in high school mathematics, it is important to avoid shortcuts. Educators and students should use AI platforms as assistants to enhance the quality and clarity of their math projects, not as substitutes for critical thinking and creativity.

5.3 Teacher Preparedness and Infrastructure Gaps

Illustrations are not included in the reading sample

Figure 9. Presents the teachers preparedness gaps and infrastructure gaps modified by Gemini AI and Canva powered by AI.

Addressing teacher preparedness and infrastructure gaps in implementing AI-infused Project-Based Learning (PBL) in high school mathematics is essential for the effective integration of emerging technologies into education. Integrating AI into PBL poses challenges for mathematics teachers due to a lack of adequate professional development on how to apply AI through real-world mathematical examples and effectively implement PBL strategies within math curricula. Several studies have shown that integrating AI in education can help teachers enhance the quality of PBL in mathematics. However, the practical application of AI in certain educational environments is often limited by infrastructure and teacher training challenges (Ruiz et al., 2025). Without sufficient professional development in emerging educational technologies, teachers may struggle to incorporate AI concepts into PBL without disrupting core curriculum goals.

Many schools lack sufficient computing resources or internet bandwidth to support AI experimentation or cloud-based tools. Additionally, schools may not have the necessary licenses or access to AI platforms. To close the gap between teacher preparedness and infrastructure limitations, we must create better conditions for technological infrastructure in schools. AI-based project-based learning (PBL) in high school mathematics holds transformative potential—but only if teacher training and infrastructure development go hand in hand. Building capacity at the system level through policy support, equity-focused resource allocation, and ongoing professional development will be essential for long-term success.

6. Emerging Trends and Research Gaps

While AI holds exciting potential to enhance project-based learning (PBL) in high schools—particularly in personalization and feedback—it also raises critical questions regarding equity, ethics, and effectiveness. Ensuring equitable use of AI will require that educators across all districts have access to high-quality professional learning opportunities, regardless of the zip code in which they teach (Noakes et al., 2024).

It is essential to provide all school districts with equal access to AI tools and offer adequate professional development for teachers to enhance their instructional practices. Ethical considerations in implementing AI in high school mathematics PBL are central to its broader, responsible integration in education. One of the most significant ethical challenges concerns the privacy of both educators and students. Generative artificial intelligence (GAI) models, in particular, raise concerns about students' right to privacy (Adams et al., 2024).

Moreover, the effectiveness of AI in mathematics is not without limitations. For example, as of spring 2024, models like ChatGPT-4.0 have struggled to generate meaningful multiple-choice questions—sometimes producing four incorrect or four correct options—and often fail to create coherent word problems. In some cases, the problems generated were misaligned with the mathematical concepts under consideration (Noakes et al., 2024).

Bridging these research gaps is essential to ensure that AI becomes a meaningful and inclusive tool for 21st-century learning. Addressing the limitations of AI in project-based learning (PBL) can make mathematics projects and real-world problem solving more engaging for high school students, elevate the quality of mathematics teaching and learning, and better prepare students for modern education and emerging technologies.

6.1 AI for Assessment in PBL

Although AI has been increasingly integrated into educational contexts, the design and development of AI systems specifically tailored to support mathematics word problem solving remains underdeveloped (Liu, 2025). It is not only a challenge for AI to support word problems in real-life situations, but it is also limited in assessing students' work in mathematical projects. Using AI as a complementary tool for math teachers in assessing mathematical projects in high schools can enhance their effectiveness and save time when evaluating project-based learning (PBL).

Edmentum is a major player in K–12 EdTech, offering a broad suite of digital curriculum and assessment solutions designed to support personalized, data-driven learning along with educator support. While many districts report positive academic impacts and successful implementations, some student and teacher feedback raises concerns around engagement, efficacy, and working conditions. Nevertheless, Edmentum includes many real-world mathematics word problems. Assessing students based on these examples provides math teachers with insight into students' current understanding and helps inform the design of future mathematics projects.

There are several tools for formative assessment, particularly in the context of assessing mathematical projects. Ross (2025), in his article, highlights several tools for assessing student work. This paper selects three of them:

● Gradescope: Provides detailed feedback and analytics to help educators identify areas where students struggle.

● Socrative: Offers quick quizzes, exit tickets, and other formative assessments with automatic grading and AI-powered performance analytics.

● Kahoot!: Uses AI features to enable adaptive learning paths and real-time performance tracking, making assessments more engaging through gamification.

Gradescope is a powerful tool for grading and analytics, especially for math problem-solving and technical assignments. However, it does not offer dedicated features for the full range of PBL assessment—such as team evaluation, public presentations, or iterative reflection. Socrative and Kahoot! are similar to Gradescope in that they have both strengths and limitations. The table below shows Gradescope’s ability to assess PBL, based on ChatGPT’s analysis.

Table 11. Gradescope support PBL assessment

Illustrations are not included in the reading sample

(Source: Modified from ChatGPT)

6.2 Adaptive Project Scaffolding

Adaptive Project Scaffolding refers to a flexible, dynamic approach to project planning and execution, where the structure of the project evolves based on real-time feedback, changing requirements, and team input. In PBL mathematics, scaffolding involves introducing basic mathematical concepts at the beginning of the project, with increasing complexity as students progress. Various forms of scaffolding may occur during AI-supported PBL, such as assessing what students currently understand during math projects and determining the appropriate next steps. Scaffolding enhances strategic thinking and fosters self-monitoring—an essential component of expert problem-solving (Hendrayana & Mutaqin, 2025).

Illustrations are not included in the reading sample

Figure 10. Mathematics project progression (math project at the technology-focused urban high school in New Jersey) from basic mathematical concepts (linear equations) to more complex ones (exponential equations).

The sequence of projects throughout the academic school year is scaffolded according to the curriculum, following the order of the listed chapters from the first to the last. In the beginning, students are assigned projects containing basic mathematical elements, such as linear equations combined with piecewise functions. As the course progresses to quadratic equations, the next project involves applications of quadratic equations. This is followed by rational functions, accompanied by projects applying these functions to various real-world examples. Finally, students explore the application of exponential functions in real-world contexts related to STEAM. In each project, students use AI as a tool to achieve more accurate and efficient results in their mathematical work.

6.3 Future of Human-AI Collaboration in Learning Environments

The future of human-AI collaboration in learning involves AI platforms that assist both teachers and students in improving instruction and personalizing learning experiences. In particular, integrating AI into Project-Based Learning (PBL) in high school mathematics offers powerful opportunities to personalize, enhance, and modernize math education in alignment with 21st-century learning goals. The rapid development of technology has the potential to significantly expand AI’s capabilities, further transforming teaching and learning at deeper and more effective levels. According to Kim (2024), teachers have suggested that AI and teachers could co-teach by taking turns and sharing instructional responsibilities—both playing active but distinct roles in a lesson (e.g., the teacher introduces a concept, and the AI elaborates, or vice versa). Furthermore, emerging technologies may enhance educational AI platforms by addressing key challenges such as improving algorithm efficiency, reducing AI hallucinations, and protecting the privacy of administrators, educators, students, and parents.

Table 12. Human - AI role in learning PBL in high school mathematics.

Illustrations are not included in the reading sample

(Source: Modified from ChatGPT)

By blending AI's adaptive capabilities with human-led inquiry and collaboration, educators can create math experiences that are deeply personalized, connected to real-world contexts, and future-ready. In the future, AI tutors should be available in every classroom to provide real-time math support during project-based learning (PBL). Next, natural language interfaces will allow students to ask questions about how to apply mathematical concepts within their projects. Additionally, learning analytics dashboards can help teachers monitor student group work and track concept mastery. Mastering multimodal AI tools (text, graphs, speech) will also support students in creating presentations, reports, and models. Above all, educators should receive training on how to effectively integrate AI into the mathematics curriculum.

Conclusion

This paper explores the integration of artificial intelligence (AI) into project-based learning (PBL) in high school mathematics, using a literature review and observations of students' mathematical projects. The study incorporates elements of exploratory and qualitative research methods. When used wisely, integrating AI into PBL in high school mathematics can significantly enhance administrative tasks, instructional practices, and student learning. However, this integration also presents challenges, including ethical considerations, algorithmic bias, data privacy concerns, overreliance on AI tools, pedagogical risks, diminished student creativity, potential misuse, inadequate teacher preparedness, and infrastructural limitations. Additionally, the paper analyzes several mathematical projects from a technology-focused urban high school in New Jersey to examine how AI is being incorporated into PBL. It discusses the benefits of AI integration from a literature-based perspective and presents supporting information through tables and figures that illustrate various properties and findings.

The integration of AI into project-based learning (PBL) offers multifaceted benefits in high school mathematics. It provides teachers with support in brainstorming ideas, planning, executing, and assessing math projects. On the other hand, when students use AI wisely within PBL, they enhance their critical thinking, conceptual understanding, and active classroom engagement.

Teachers can test various mathematical project ideas using their preferred AI platforms and receive diverse suggestions. They might combine, refine, or select the best ideas to develop them into final projects. Depending on the number of student groups, mathematics teachers can also modify the initial conditions for each group to personalize the learning experience.

When students submit their projects, AI helps teachers assess them more efficiently and accurately. Students, in turn, benefit from AI by accessing a wide range of information relevant to their projects. They can combine, modify, and incorporate this information where appropriate. This process allows students to see the real-world application of mathematical concepts learned in class. To reach the best outcomes, students are encouraged to collaborate and engage actively in completing their projects. When both teachers and students integrate AI thoughtfully into PBL, they unlock diverse and meaningful educational benefits.

In addition to the benefits of integrating AI into PBL in high school mathematics, this paper also addresses several challenges. Key challenges include ethical considerations, algorithmic bias, data privacy concerns, overreliance on AI tools, pedagogical risks, loss of student creativity, potential misuse, inadequate teacher preparedness, and infrastructural gaps. Educators and students should be guided on how to overcome these challenges to fully realize the benefits of AI in PBL.

As technology evolves rapidly, AI platforms and AI-powered mathematical solvers are constantly improving. As a result, many of the current challenges associated with integrating AI into PBL are likely to diminish over time. The future of human-AI collaboration in education may involve AI platforms that support both teachers and students in enhancing instruction and personalizing learning experiences. Continued advancements in AI are expected to play an increasingly significant role in teaching and learning, particularly within the context of PBL.

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[...]

• Course: Mathematics
• Grade: 9 - 12
• Authors: Duli Pllana (Author), Rudy Baez et al. (Author)
• Publication Year: 2025
• Pages: 40
• Catalog Number: V1676637
• ISBN (PDF): 9783389169384
• ISBN (Book): 9783389169391
• Language: English
• Tags: AI, PBL, Students, the Teacher, Mathematics Projects, High School Mathematics, Education