Random Groups, Active Voices: The Impact of Visible Thinking in College Algebra
Ronie Mataquel, Queensborough Community College
Bio
Ronie Mataquel began his educational career in the United States in 2002 as a 5th-grade teacher in Sacramento, CA, after immigrating from the Philippines. In 2003, he moved to New York City and joined John Bowne High School, where he transitioned to teaching high school mathematics after a decade of experience in elementary and middle school education. In 2013, Ronie joined Queensborough Community College as an adjunct instructor while continuing to teach in New York City public schools.
Course Setting
John Bowne High School serves more than 3,400 students from diverse cultural and linguistic backgrounds, with over 30 languages spoken in the school community. Known for its inclusive environment and specialized programs, the school also supports English language learners through language development initiatives. The course setting for the fellowship was MA-119 College Algebra and the MA-119 Accelerated Learning Program, a corequisite offered through Queensborough Community College’s College Now Program. Corequisite courses support students who have not met CUNY proficiency benchmarks. They are designed to help students earn college credits while strengthening their mathematical and critical-thinking skills.
Problem of Practice
Over the years, I observed that many students in my College Algebra classes were hesitant to participate actively in discussions and group problem-solving activities. Many remained passive or reluctant to share their thinking due to fear of making mistakes. These experiences highlighted the need to create a more inclusive and collaborative classroom environment where all students feel encouraged to participate.How can I use Visibly Random Groupings (VRGs) and Vertical Non-Permanent Surfaces (VNPS) during warm-up and cooldown activities to ensure the active participation of all students in my College Algebra discussions and group problem-solving tasks?Strategy
I used the Random Minds in Motion Strategy (RMMS) to address limited student participation and varying levels of engagement during class discussions. This strategy combines Visibly Random Groupings (VRGs), Vertical Non-Permanent Surfaces (VNPS), and thinking tasks, where students use whiteboards or blackboards to solve warm-up problems. I also assigned group roles and used low-stakes activities to encourage participation and reduce hesitation.
Documentation
How it Works: Warm-Up & Cooldown Activities
This routine activates thinking, builds collaboration, makes thinking visible, and supports reflection—helping students grow every day.
Student Self-Evaluation and Participation Checklist
Rubrics for student self-assessment (warm-up activity) on the elevator problem/classroom seating puzzle and the student participation checklist.
Measuring Impact
MA-119 College Algebra Average Grades Per Semester
Since I have been teaching MA-119 for some time, I was able to compare average grades from Spring 2025 to Spring 2026, and there is a slight difference in the results.
Performance Level by Rating (0-4)
Analysis of the Spring 2026 course shows that the highest performance levels (3–4) occurred on later assessments (April 1 and April 8), demonstrating increased student confidence and problem-solving independence.
Analysis
The implementation of Visibly Random Groupings (VRGs) and Vertical Non-Permanent Surfaces (VNPS) positively improved student participation, collaboration, and engagement during warm-up and cooldown activities. Students’ scores showed noticeable improvement as they became more actively involved in discussions, board work, and problem-solving tasks. Through random grouping strategies, students were encouraged to work with different classmates, promoting equitable participation and reducing dependence on a few active students.
The use of whiteboards and non-curricular tasks such as “The Elevator Problem” also helped students make their thinking visible and communicate their reasoning more confidently. As students engaged in collaborative conversations, they demonstrated improved communication skills, stronger accountability within groups, and a greater willingness to explain their mathematical thinking. Over time, students became more comfortable participating in discussions and contributing ideas during class activities.
The strategy also created a more inclusive and supportive classroom environment where students learned from one another and developed confidence in sharing their solutions. The gradual increase in assessment scores suggests that the consistent implementation of VRGs and VNPS contributed to improved student understanding, participation, and engagement in mathematics learning.
Recommendation
To further strengthen student participation and academic growth, the consistent use of Visibly Random Groupings (VRGs) and Vertical Non-Permanent Surfaces (VNPS) is highly recommended during warm-up and cooldown activities. Teachers should continue incorporating non-curricular thinking tasks that encourage discussion, collaboration, and problem-solving among students.
Providing students with structured opportunities to explain their reasoning and reflect on their participation may further improve communication skills and confidence during group work. In addition, allowing more time for collaborative discussions and reflection activities may deepen student understanding and encourage more meaningful mathematical conversations.
Teachers may also rotate tasks and groupings regularly to maintain student engagement and ensure equitable participation among all learners. Continued implementation of these strategies may help create a more active, student-centered, and collaborative learning environment that supports both academic achievement and student confidence.
Resources
- Liliedahl, P. (2021). Building thinking classrooms in mathematics: 14 teaching practices for enhancing learning. Corwin.
- Liliedahl, P. & Giroux, M. (2024). Mathematics tasks for the thinking classroom, grades K–5. Corwin.
- National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. NCTM.