Principles to Actions, Ensuring Mathematical Success for All, the 2014 groundbreaking publication from the National Council of Teachers of Mathematics (NCTM) lists productive disposition as one of the five interrelated strands that together, constitute mathematical proficiency. The other four strands include:
The National Research Council defines productive disposition as the tendency to see sense in mathematics, to perceive it as both useful and worthwhile, to believe that steady effort in learning mathematics pays off, and to see oneself as an effective learner and doer of mathematics (2001).
While instruction to develop competency in these first four strands are often easier to understand and implement, developing productive disposition in students tends to remain more elusive. A disposition is a person’s inherent qualities of mind and character. Inherent is defined as existing in something as a permanent, essential or characteristic attribute. Productive disposition in mathematics is a combination of a positive attitude toward math and one’s own math identity and perseverance to stay with something until you succeed. As teachers, how do we develop this within our students?
The first step is to address our own, as well as our students’ attitudes about math. We all need to develop positive math identities. Winston Churchill said, “Attitude is a little thing that makes a big difference”. In her book Building Powerful Numeracy in Middle and High School Students, (also a great resource) Pamela Weber Harris’s motto is “math is figure-out-able!” We need our students to truly believe this. We also need them to embrace the quote by American philosopher and psychologist William James, “It is our attitude at the beginning of a difficult task which, more than anything else, will affect its successful outcome."
The best resource I found for helping teachers develop a positive disposition in their students came from the American Psychological Association. Barbara McCombs, PhD from the University of Denver has developed Teacher’s Modules for applying psychological science to practical instructional problems in the classroom. This comprehensive and user friendly resource entitled Developing Responsible and Autonomous Learners: A Key to Motivating Students “provides tools for what teachers of all age groups can do to inspire natural curiosity, creativity and autonomous lifelong learning.” I encourage you to check it out.
Just for fun, a parting thought… Coincidence or not?
This post brought to you by Julie Ace, Elementary Implementation Associate
Enjoy our Blog!
Members of the Elementary C&I team post useful tools, tips, and tricks on a weekly basis to help you help students.