Using AI to Promote Higher Order Thinking in Math Classrooms
Bret Zheng Yu Xu, LaGuardia Community College
Bio
Bret Xu is a NYC mathematics educator and former quantitative hedge fund manager who leverages his background to incorporate AI in education. Bret designs AI-integrated curricula that foster critical thinking and technical literacy, specifically adopting AI to support ELL students and promote educational equity. By developing custom AI tools for students, he ensures that the next generation, especially multilingual learners, is equipped to lead and navigate an increasingly AI-driven world.
Course Setting
I teach General Psychology at Queens College through the College Now program. My students have a diverse set of interests and cross-disciplinary academic goals.
Problem of Practice
In this pedagogy fellowship, I want to tackle a persistent challenge in my classroom: the wide range of mathematical foundations among my students. While some are ready for college-level Statistics, others struggle with the fundamental concepts needed to access the material. It’s a constant balancing act trying to keep the core curriculum moving without leaving anyone behind. I’m interested in how AI-driven adaptive learning tools can bridge this gap. Specifically, I want to explore leveraging these tools to provide real-time, individualized scaffolds that meet each student exactly where they are. The goal is to offer tailored support that empowers students to catch up on essentials while simultaneously engaging with course content, all without disrupting the collective pace of the class.
Strategy
To address the gap between conceptual understanding and formal notation, I implemented a Recorded Justification Cycle using Snorkl AI. Students first solve a math problem on a digital canvas, then record a short video "thinking out loud" to explain their logic. An AI agent provides instant, multimodal feedback on their verbal reasoning, prompting them to refine their "math talk" or correct logical gaps before final submission.
This strategy creates a low-stakes environment where students use their voice and drawings to demonstrate mastery without being hindered by writing barriers. For my English Language Learners (ELLs), who often possess strong mathematical intuition but lack formal academic vocabulary, this acts as a procedural scaffold. It reduces the anxiety of being "stuck" by providing personalized, real-time guidance.
The rationale is grounded in deepening conceptual clarity and metacognition. By articulating their thought process and responding to AI prompts, students move beyond rote calculation toward higher-order thinking. Research suggests that "explaining the why" helps solidify neural pathways and builds the precise language needed for college-level Statistics and Python programming. This ensures students develop the communication skills necessary to bridge the gap between their native language and formal English mathematical notation.
Documentation
Snorkl AI Question
Page 1 shows a snapshot of the Snorkl AI questions. It is a set of multi-step math problems designed for the Snorkl platform that require students to record verbal and visual justifications for their solutions. These tasks are specifically structured to move students beyond rote calculation and toward higher-order thinking.
Figure #1: Snorkl AI Question Page
Snorkl AI Response Analysis
Page 2 shows their responses, accuracy, reasoning level, and overall class insights.
Figure #2: Snorkl AI Response Analysis Page 2
Measuring Impact
Snorkl’s Assessment of Students’ Responses 1
AI’s assessment on each student’s submission in Material #1, calculating radians.
Figure #3: Snorkl’s Assessment of Students’ Responses 1
Snorkl’s Assessment of Students’ Responses 2
AI’s assessment on each student’s submission in Material #2, graphing trig functions.
Figure #4: Snorkl’s Assessment of Students’ Responses 2
Results Comparison
Box plot analysis of the summative Assessment (exam) result compared to the previous year.
Figure #5: Results Comparison
Analysis
Integrating Snorkl AI into my lessons has been a game-changer for classroom dynamics. By acting as a "digital lab partner," the AI forced students to move beyond rote calculation to actively defending their reasoning. This shift from hunting for "correct" answers to justifying mathematical models leveled up their critical thinking and created a more balanced, student-led environment. The strategy directly addressed my Problem of Practice; because the AI provided instant feedback, I was finally freed from being a human "answer key" and could facilitate deeper, targeted interventions with groups in need.
The impact was clearly reflected in the data, with students scoring 9% higher on their summative assessments compared to last year’s cohort. Their ability to articulate reasoning was significantly more robust, confirming my prediction that multimodal feedback would bridge the gap for my ELLs. However, a remaining challenge is ensuring students don't use the AI as a "help-bot" crutch. To troubleshoot this, I’ve started adapting the strategy to include "thin-slicing" group tasks at the boards, using the AI specifically as a scaffold for incremental challenges. While the processing time for AI feedback can occasionally lag, the real-time guidance has been invaluable in keeping students in the "productive struggle" zone without disrupting the collective pace of the curriculum.
Recommendation
We can no longer prevent AI from entering the classroom, but we can prevent it from eroding student agency. Left to their own devices, students may shift the burden of thinking onto AI to produce quick answers. Our role as educators is to pivot toward intentional implementation, positioning AI as a Socratic partner and scaffolding tool rather than a "help-bot."
For College Now or Early College professors, this strategy is most effective during high-stakes conceptual learning. It requires significant front-end effort to design tasks that demand justifications. I recommend using this approach to foster a "Thinking Classroom" where AI provides the real-time feedback that usually bottlenecks a single instructor. By offloading procedural checks to the AI, you are freed to engage in deeper, high-level discourse. The goal is to keep students in a state of productive struggle, using AI to bridge foundational gaps without bypassing cognitive work.
