Allow me to set the record straight - there is no such thing as 'new' math. Perhaps the greatest noticeable difference is the way in which teachers teach math now. Gone are the days of drill and kill, practicing 30-50 problems per night. Active learning is becoming widely adopted as teachers are now encouraging math talk, math thinking, and modeling through various manipulatives and models. While skeptics may doubt how powerful math talk is, I have witnessed first hand the benefits that talking about your thinking has provided my children.
Learning math, or anything new, is a delicate process. There are so many little nuances and rules to know and follow. However, we handicap students ability to think creatively when we show them only one way to do something. This 'new' math provides students an opportunity to think for themselves and create strategies for learning that will last a life time - to discover when something goes right or when a mistake is made. As students develop their own processes, teachers can begin to bridge gaps that may exist, or question students further to help them create 'shortcuts' in their own processes.
As we encourage students to talk more about their thought process, we also encourage them to make mistakes. Mistakes are an inevitable process of learning, particularly at a young age. The better teachers become at questioning students and their thought process, the easier the transfer of ownership of learning to students becomes. Only then will students be engaged in learning and becoming better mathematicians.
While we may not fully grasp how teachers are teaching today, we must be aware that the world around us is changing. We need students to be able to adapt and think differently than we were ever taught. If you are a parent or a teacher, I encourage you to ask your child or student to share their thinking process with you. Help them discover how much easier learning can be when we talk about what we are doing.