This year in all of my Professional Development sessions three statements seem to have made the biggest difference to teachers. I would like to share these truths with you as well.
1. Understanding cannot be diagnosed with Fluency questions, because when asked routine questions students give only routine answers. To find out if students really “get it”, we need to ask non-routine questions. For some simple examples that will tell you within 5 minutes what your class really Understands (as opposed to what they can repeat back), click here.
2. Support students cannot “catch up” with Fluency questions, because Understanding difficulties cannot be fixed with memorisation. Understanding difficulties arise when students have misconceptions that are undiagnosed and/or untreated. Students cannot remember a procedure if it makes no sense within their existing mathematical structures, no matter how much they practice. Trying to help support students to improve by giving them more and more routine questions and detailed instructions is counter-productive because it does not address their underlying difficulties. Instead, focusing on undoing misconceptions and then on developing mathematical principles that can be always relied on actually works.
Likewise, extension students are not effectively extended with basic Fluency questions, no matter how hard the numbers are. To extend students we want to improve their deep understanding of mathematical principles and their problem-solving capabilities, not just make the numbers bigger. We want students to be able to take a principle and adapt it to any given situation. We want them to be able to solve something that they have never seen before. The best way to challenge and motivate students is to give them something that makes them think creatively and make connections, manipulating mathematical patterns to suit a problem.
3. We need to start measuring our effectiveness by how much students still understand after the Christmas holidays rather than how many boxes we can tick off during the year. Everything that they have forgotten, we have effectively wasted our time on. Think about the teacher who will have the students after you. What the students still retain then is the true measure of your effectiveness. If you could design a class, what would you want them to understand when they began a new year with you? Focus on fixing those problems now as your gift to next year’s teacher.