Warning: Helping a butterfly out of the chrysalis will prevent it from ever flying. The butterfly needs the struggle to strengthen its wings.
Ban Har is a math teacher and teacher trainer from Singapore. He worked with the Elementary School of the International School of Prague for 3 days prior to the pre-conference and main conference of CEESA in March. During those days, he worked with the entire staff and with grade level teams following a lesson study format to consider how to structure and manage differentiation, inquiry, challenge, and practice in the maths classroom.
In our whole staff sessions and in the grade level lesson study work, he highlighted what he considers the conditions of learning that are essential in the maths classroom
- Mindset:
- Students need to understand the mindset of math. It is problem solving and figuring things out and not just computation.
- Students need to have a growth mindset that sees that if they put in the time and work, they will figure it out and improve.
- Communication: Maths is communicated through words and in situations that are connected to the real world to which kids can relate. The language of maths is then scaffolded on top.
- Independence: Students need to be able to work independently and have opportunities to independently explore and build understanding. Too much teacher direction robs them of learning. It does not support it.
- Teacher expectations impact learning and have a tremendous affect on how far students will go. High teacher expectations for all is essential.
- The lessons must be organized so that students can go through the phases of learning:
- The opportunity to connect to prior knowledge through a relevant task
- Collection of cognitive resources that will build their conceptual understanding. This is done through interaction in rich tasks that are concrete and allows the learner to explore and build the concept.
- The opportunity to consolidate learning through identifying and explaining what they have done and what they understand.
- Exploration : Students spent time playing with and inquiring into the materials, concepts or ideas before formal learning began.
- Structured learning: Teachers helped to formalizing the learning by demonstrating the conventions that students can not discover.
- Practice: Students had time to independently rehearse what they have learned.
- Journaling: Students had the opportunity to summarize and/or explain what they have learned.
- Reflecting: Students had they opportunity to think about which strategy worked best, or how their strategy was different from their friend's , and/or which strategy was most efficient.
In the grade 5 lesson on place value and decimals, he did this in two clear ways. First, he gave a task with directions that were intentionally ambiguous. Students had to decide for themselves and together the rules of the game based on their understanding. They needed to reason it themselves. Second, he did not allow anyone to ask questions or for help except at designated times when he asked if there were any clarifying questions. This was new for this class, but one could imagine that if this were routine, over time, students would learn there are times when you can ask questions and times when you must figure it out yourselves. They would learn to be responsible to ask when they have the opportunity or suffer the confusion later. It is a powerful strategy that keeps teachers from enabling students not to listen and think when they need to do these things. Allowing students to always ask for and get help at any time robs them of the opportunity to be self-sufficient, self-reliant, and self-directed learners.
If we interfere, if we give them the strategy or procedure before they have built the conceptual understanding themselves, they will learn that math is following steps instead of figuring out. They will learn that they need to wait for the teacher to tell them what to do. They will be butterflies who have not learned to fly.