Watching young children solve mathematical problems certainly looks different than it did just 10 years ago. The use of "tools" whether a ruler or a paper clip is common place in every classroom in my building. As a long time math instructional facilitator, I have had the opportunity to watch students develop mathematical thinking that takes them beyond the numbers and to a level of thinking that challenges the best math student. It is a joy to have students come to my office to "share their strategies". I am often amazed not only at how the problem is solved, but also how it is explained. Taking students beyond the numbers requires dedication, planning and a deep level of mathematical understanding on the part of the teacher. Teachers must be diligent in NO more drill and kill, listening to strategies, asking questions that will scaffold learning, nurturing notation and encouraging risk taking during problem solving. Death of the "Drill and Kill" There is no skill in memorizing math facts. Memorizing does not allow for manipulation of numbers to make them fit patterns or to develop fluency. It is time to do away with the drill and kill of yesterday and embrace the problem solving approach to mathematics. Listen to the Strategy While this may sound odd, it is a vital piece to the mathematical puzzle of taking students beyond the numbers. Looking at a students written work tells a lot about what the child is thinking, but allowing the student to orally explain the strategy he/she chose gives the teacher an insight that the paper pencil version does not. Requiring the student to put into words his thinking helps the teacher develop questions to stretch thinking. Ask Questions Before deep, thought provoking questions can be asked effectively, a no fail environment must be established. Students must gain confidence to explain their thinking with peers in small and large group settings. As they become more comfortable with the process the questions should be strategically asked in an effort to stretch student thinking and scaffold learning. Nurture Notation Helping to move a student from the abstract, direct modeling stage of mathematical thinking to the more concrete notation state requires skilled questioning and a lot of patience. Helping students build a solid foundation in number sense is critical before moving to the notation stage. If students start with solving equations they never truly move past the numbers. The math is not meaningful or relevant. Deep understanding of number sense will allow students to manipulate numbers by composing and decomposing numbers through their daily interaction with mathematics. Watching students solve problems and think beyond the numbers is one of the highlights of this job. `
Until next time, enjoy the view from your own sidewalk! --Karen