Reflections

My school is committed to having students reflect on their learning, both in terms of math-specific development and student habits*. The research is pretty strong that reflecting on learning is a huge component of solidifying understanding. As John Dewey wrote, “We do not learn from experience... we learn from reflecting on experience.” Reflection as a skill is something that we intentionally cultivate and assess, but I am always working on making it a more integrated component of my classes and something that students value and appreciate.


Here are some ways that I've worked on doing this over the past few years:

Start of year reflections: establishing relational aspects of class and setting goals

We spend the first two weeks of each course working on open problems and having students read, watch, and discuss ideas that we think are important to setting the tone for the year, establishing classroom norms, and getting buy-in for learning through problem-solving

• Students respond to readings about mathematical practices and/or habits of mind:
• Reflection questions on first chapter of Make It Stick
• Reflection questions on "How to Learn Math" video from Youcubed and excerpt from Mathematical Mindsets
• Math autobiography
• Students reflect on their history as students and mathematicians and set goals for their work in this class

Reflections that emphasize content: after each lesson/assignment and after taking an assessment in order to correct course

We want students actively thinking about their progress in the course, returning to their goals, reflecting on their learning, and fine-tuning strategies in order to make progress.

• At the start of most classes, students summarize the main topics from the last class and homework assignment and reflect on their understanding through this Desmos Activity Builder.
• After most assessments, students reflect on their work in the class, both in terms of content learned and the development of their mathematical practices and student habits
• Typical post-assessment reflection; We realized that having students reflect on ALL mathematical practices was a bit much for a single reflection and tried to pull out a specific practice to reflect on  
• Correct and reflect on errors; plan what to do next

Reflections that emphasize practices and habits of learning: projects, homework, note-taking

• Students reflect on their learning and process on all projects and investigations 
• Menu of write-up reflection options (scroll to the bottom)
• Not strictly reflection, but we are starting to use peer feedback to have students develop specific mathematical practices
• Peer feedback on homework
• Reflection on note-taking
• Peer feedback on note-taking

Things I still need to work on/think about

The reflections were mostly created based on perceived need and don't necessarily spiral and build on each other as clearly as they could. I'd love to spend time going through the prompts and making them more specific - thinking about which mathematical practices should be cultivated at the start of the year, which ones later on, and which ones should be spiraled back to at later times. This would also help make the reflections shorter and more specific, encouraging deeper and more thorough responses. 

I'd love to hear about others' experiences with reflections so please comment or tweet at me with questions or feedback.

*Rubric of mathematical practices and habits of learning