At Tranquillity Elementary, a small school in the farming community west of Fresno, California, third through eighth-grade teachers collaborate vertically across grade levels to refine their instruction and improve student outcomes. One key action is embedding reflection into their math instruction to empower students as confident and independent problem solvers.
The Power of Reflection in Learning
Reflection is a cornerstone of effective learning. It enhances metacognition and helps students understand and adapt their strategies for better outcomes. By analyzing their successes and challenges, learners build resilience, refine their problem-solving skills, and strengthen their capacity for independent thinking.
Habit 12: Look in the Mirror from The Project Habit: Making Rigorous PBL Doable by Michael McDowell and Kelley Miller emphasizes the transformative power of reflection in learning. This habit invites learners to critically examine their actions, decisions, and progress by asking reflective questions such as, “What worked well?”, “What didn’t?”, and “What can I improve next time?” Through this process, students cultivate self-awareness, accountability, and a commitment to continuous improvement—key ingredients for personal and academic success.
Reflecting in Math: Empowering Tranquility’s Problem Solvers
With only one teacher per grade level, teachers have had to get creative about how they work together to support and push each other. Alongside Impact Team coach Kristen Eveland, the Tranquility Elementary teachers focused their time and effort on refining their approach to teaching problem-solving.
The teachers decided to use Look in the Mirror to encourage students to revisit problem-solving strategies, identify errors, and refine their approaches. For example, after solving a math problem, students might ask themselves, “Did I use the most efficient strategy?” or “Where did my calculations go wrong?” This reflective practice not only promotes precision and conceptual understanding but also fosters a growth mindset, helping students develop mathematical fluency and confidence.
Early in the process, the educators realized that their students needed clear, easy-to-use, resources to support their reflection. Teachers co-created problem-solving rubrics and developed success criteria with their students, using models and exemplars to clarify expectations. These tools have become central to students assessing their progress, celebrating successes, and identifying areas for growth. Many students even select a specific success criterion to focus on at the beginning of each math session to personalize their learning throughout the period.
When students reflect on their problem-solving processes, they align their efforts with mathematical practices such as making sense of problems, persevering in solving them, and identifying patterns or structures. Developing these math practices supports learners’ ability to transfer strategies from familiar problems to new, more complex situations. Looking back at when and how they made this transfer enables students to understand the problem-solving process and better understand themselves as problem solvers who can build a repertoire of tools and strategies to address more varied and complex problems.
The practice of looking in the mirror becomes a habit when problem solvers begin to self-monitor and reflect as they work; continually evaluating and adjusting their strategies. Regular reflection helps students internalize the problem-solving process, leading to greater independence and confidence in math.
Empowering Mathematicians
By implementing Habit 12, Tranquillity Elementary is fostering a culture of reflection, self-improvement, and empowerment. As students consistently evaluate their problem-solving strategies and set goals for growth, they are becoming Empowered Mathematicians—ready to tackle challenges with resilience, curiosity, and confidence. We can’t wait to hear what they do next!