Reflection: A Powerful Tool in a Math Classroom

"Self-reflection is one of the most underused yet powerful tools for success."
—Richard Carlson

One of the most influential lessons I have learned throughout the course of my career as an educator is how critical self-reflection is to growth.  In reflecting on classroom lessons, we deepen our understanding of students' needs and how we can better support them in their learning journey.  As leaders, we reflect on interactions with colleagues to consider how we can better support others in their growth as they strive to reach their own goals.  We reflect on how we can communicate more clearly, how we can utilize and share resources more effectively, and how we can better manage our time.  But how often do we intentionally provide similar opportunities for reflection for our students related to their math learning?  How do we empower our students to pause, self-assess, and think about how they will propel their own growth?

A student reflects in her
journal about her math thinking.

Reflection in a math classroom is a powerful tool for deepening student understanding, developing flexible thinking, and coming to realize the interconnectedness that embodies the world of mathematics.  Often times, writing in a mathematics classroom is a foreign concept, but it shouldn't be.  Written reflection is one of the most critical ways we can empower our students to take ownership of their learning. 

At a professional development event I attended this past fall, Dr. Yeap Ban Har also emphasized the importance of writing as a critical routine in math classes.  He shared that there are four types of math journaling: 

• Descriptive: "Show and tell me the best method, in your opinion."  This is open-ended, and students have the opportunity to describe any method they think will allow them to solve the problem.  How are students using academic vocabulary?  Is their method viable?  Is it efficient?  Does it build on relevant prior knowledge?
• Evaluative: "Out of these two methods, tell me which is better and why."  This is more structured, and the teacher provides two targeted problem-solving methods to compare.  Do students understand the similarities and differences between the methods?  Can they articulate why one method may be more efficient or precise than another given the problem-solving situation?
• Creative: "What is a story to go with 300 - 125?"  This type of journaling allows our students to put context with computation.  Do students understand a scenario in which the given computation is useful?  If given a similar computation on another occasion, do they understand multiple contexts, or do they continue to go back to the same context for a given type of computation?
• Investigative: "Which method works because the value in the problem is 125?  Which method will work for any value?"  Do students understand the nuances of the different strategies compared in class?  Will they be able to select a viable strategy in a variety of situations?

In addition to the types of journaling above, I also think it is critical to add self-reflection to the list.

• Self-Reflection: "What did you try already?  Was it successful?  Why or why not?  What will you do differently next time?"  Are students able to perceive the most successful aspects of their problem-solving attempt?  More importantly, are they able to identify why unsuccessful attempts did not result in the desired outcome and come up with a revised plan of attack?

Self-reflection can, and should, occur on a regular basis throughout the learning process.  It gives the teacher great insights into how students perceive themselves as mathematicians, what they are taking away from class conversations about what is most important, and if they are able to plan for what they will change as a result of the experience.  Recently after what I thought was a successful debrief of sharing strategies and consolidating learning following a rich task related to capacity, I noticed in some student self-reflections that a few students still did not grasp the key takeaway.  What valuable information for me, as a teacher, so I can revisit the conversation in a different way and plan the next steps for those children according to their actual needs, not what I originally thought they needed.

A student reflects using Seesaw.

Self-reflection can also be a valuable tool for further growth after a summative assessment.  Some of our Lower School teachers have begun using Seesaw as a means for students to reflect on an area of their summative assessment (whether it is a project, presentation, performance task, or test) of which they are particularly proud, as well as an area where they want to continue working to improve in the future.  If it is something like a test, students may explain an error that was made the first time around and what they have since done to re-attempt the problem.  Students are able to do this as a written reflection or as a recorded audio reflection to accompany the photographs of their summative assessment product.  By using a tool like Seesaw or another learning management system, both teachers and parents are able to share in the students' learning journey and self-assessment of their progress.  

A kindergartener shares his
mathematical thinking.

For our youngest learners who may still be learning to write, it is also helpful to encourage an audio component with the self-reflection as well.  After the student "writes" their reflection, an interview where a teacher transcribes the student reflection or an audio recording on a device like an iPad can ensure teachers and parents alike understand what the student is thinking.

Not only will these reflections provide you as the teacher with valuable insights, but it will also begin to build reflective habits of mind within your students to help them grow as mathematicians and overall learners.  What other ideas do you have for building student journaling and reflection into your math classroom?