Designing a Prompt Framework for Generative AI–Based Critical Thinking Support in SSC Mathematics Learning

As Generative Artificial Intelligence (Generative AI) gains traction, it is poised to offer
innovative solutions for teaching and learning mathematics, particularly in the form of intelligent tutoring systems. But most current AI tutoring systems are designed to output
answers rather than to help students through a sequence of reasoning and problem-solving
steps. For this reason, their contribution to the development of critical thinking is limited,
a very important goal of mathematics education. In addition, current prompt engineering
techniques tend to be optimized for a single prompt rather than offering a complete pedagogical structure based on validated educational theory.
This study aims to develop a structured prompt framework for a Generative AI tutoring
system for facilitating critical thinking in the learning of mathematics in Secondary School
Certificate (SSC). The framework combines the problem solving approach of Pólya with
prompts representing the four stages of the problem solving process: understand the problem, make a plan, execute the plan, look back. Prompts for learners’ guidance, evaluation of
their responses, adaptive feedback, and advancing to the next stage are included as distinct
sections in each stage to facilitate the learners’ active reason and reflective learning.
The study is guided by Design and Development Research (DDR) methodology consisting of four phases namely problem identification by literature review, design of framework,
design of prototype and evaluation by expert opinion. A prototype of AI mathematics tutor based on the proposed framework is built, and the framework is assessed by experts in
computer science and mathematics education through questionnaires and semi-structured
interviews. The assessment is on the clarity, pedagogical relevance, usability and potential
of the framework to support critical thinking.
This inquiry offers a pedagogically informed prompt model incorporating the principles of mathematics learning and of prompt engineering for Generative AI. The proposed
framework offers concrete design considerations for designing AI tutoring systems to support structured mathematical thinking and critical thinking, especially in the context of SSC
mathematics learning.