“The world is changing. We no longer need students to just be fast calculators . . . We need students who can think and develop mathematical models and reason and problem solve . . . “
(Jo Boaler, 2014)
Traditional ‘drill and answer’ questions, and closed worded problems such as those used in most textbooks and on online mathematics websites, are usually great for assisting students with understanding of and fluency with maths concepts. However, they don’t necessarily focus students’ learning on higher order mathematical thinking skills.
By contrast, open-ended problems do have greater potential for stimulating higher order mathematical thinking. Open ended problems encourage students to ‘play around with’ different variables in order to generate different solution pathways, to look for new patterns, to trial and error and explore a range of methods, and to apply reasoning to concepts in a range of unfamiliar situations.
In two parts, the attached article puts open-ended problem solving under the spotlight.
How Long Is a Piece of String Part 1 focuses on considering how open-ended problem solving is different from ‘regular’ maths questions or problems, and discusses the significant benefits of using this pedagogical approach to mathematics, for both students and for teachers.
How Long Is a Piece of String Part 2 provides teachers with practical ways to source, develop and implement open-ended problem solving in mathematics lessons.
