I had the pleasure of attending the 5th International Realistic Mathematics Education (RME) 2015 Conference in Boulder, Colorado at the University of Colorado. Prior to attending the conference I did not know too much about RME. I knew that people that I admired in the field of mathematics education (Lucy West, Toni Cameron, Cathy Fosnot) were greatly influenced by the principles of RME and the Freudenthal Institute (FI). Below is brief history, as posted on the Freudenthal Institute - USA:
In 2003 the Freudenthal Institute - USA (FI-US) was established as a result of the collaboration that had existed for years already between the Wisconsin Center for Education Research at the University of Wisconsin-Madison in the USA and the Freudenthal Institute. In Fall 2005, FI-US relocated to the University of Colorado at Boulder, USA.The Freudenthal Institute for Science and Mathematics Education (FI) aims to improve education in the fields of arithmetic, mathematics, and the sciences, with a focus on primary, secondary and vocational education. FIsme works towards achieving these objectives through research, teaching, curriculum development and services.
What does any of this have to do with developing test-savvy math students, you may inquire? Well the institute is grounded in the belief that learners need to consistently and deliberately experience the application of mathematics in order to learn how to mathematize their world...real and imagined. RME is also grounded in the idea that learning needs to include informal, pre-formal and formal applications. To emphasis this point the researchers at FI use an iceberg as a metaphor. The top of the iceberg is what some people would call, "the math" or the abstractions or mathematic notation. But researchers at FI insist that we need to pay special attention to what in underneath the top of the iceberg. Beneath the iceberg is where conceptual understanding is developed and it is the majority of the iceberg of understanding.
So where does this leave testing and preparing for high-stakes standardized testing? In my opinion...the same place it was before. The concepts of RME are not new and have been influencing classroom instruction for decades. The challenge was and remains to be...knowing that learners need significant time with the informal and pre-formal ideas and structures of mathematics. Time and experiences that help to build towards the formalization of mathematical idea, without letting go of what is beneath the iceberg.
Is it a matter of trust? Trusting that if we spend more time beneath the iceberg, with appropriate tools, models and tasks, that we will not drown. Is it a matter of mindset? Believing that some people can get the math and others cannot, so it does no make sense to focus so much time beneath the iceberg?
I am not sure. I just know that what we have been doing has not produced the results that we are looking for in terms of students being able to see mathematics in their world and use mathematics to describe their world.
What can we do?
- Critically and strategically examine our curriculum programs to note how much of our time is spent beneath the "iceberg" on given topics.
- In teacher teams, vertically and horizontally across grade-levels, develop and examine our "icebergs" to note areas that need additional support and understanding from a teacher content stand-point.
- Expand upon on our notions of assessment to include more experiences that demand the application of mathematical ideas in a realistic and sometimes messy ways.