The 5 Big Ideas In Teaching For Mastery

 

When we teach, we are teaching students with the idea that they will master the material.  Sometimes, we need a reminder of what it involves and ways we can manage it while other times, we stroll along.  For many of us, school has started and we are doing the first of our assessments. So today, I'm looking at the overall picture of teaching for mastery.

First is coherence which is the way topics are taught so they create a coherent learning progression throughout the grades.  They hopefully will end up with a deep understanding of the concepts and topics so they apply math across a large range of contexts.

Second, is carefully selecting representation of the concept or idea to show the structure.  This results in students "seeing" math rather than using it as a way of doing the math. The representations become mental images for students that they can think about as they work on the math and which helps them develop a deeper understanding.

Third, encourage and help students develop mathematical thinking which allows them to make connections, develop conjectures, perform reasoning, and generalize.  When planning any lesson, students should actively be involved in thinking mathematically and communicating using mathematical language. 

Next, all students should have developed fluency of number facts and use of operations so they can spend more time learning the concepts. In addition, fluency also means that students have the flexibility to move between various contexts and representations, be able to make connections as they recognize relationships and choose the best method to solve a problem.

Finally, students need to develop both conceptual and procedural variation.  Conceptual variation is when students are able to vary the way a concept is represented to show a critical feature.  Procedural variation looks at how students "proceed" through a problem. 

These are the 5 big ideas in teaching for mastery and are an overall look.  Over the next few weeks, we'll look at each idea in more detail and see how they can be applied in a post Covid world.  Let me know what you think, I'd love to hear.  Have a great day.