Abstract:

There is an increased need to focus on the education of mathematically advanced and gifted children. Research on the characteristics and learning styles of mathematically gifted students over the last two decades shows that when given challenging and engaging materials different from the standard curriculum, these students make significant academic strides. Current reform efforts have moved in the direction of having students solve problems and explain their work, but it is rare for students of any level to be challenged to write their own problems.

This paper describes a two and a half year after-school gifted program created for a group of primary school students when their in-school gifted mathematics program was cut. Over the course of the first year, the group transitioned from problem solving into the more advanced level of problem posing. The curriculum was structured so that the children followed the same process required in mathematics research – understand the material by solving existing problems, formulate an original problem, generate a solution and finally formalize the results through publication and presentation. Successful progress through these stages required creativity, patience, attention to detail during extensive editing and resulted naturally in authentic collaboration. Ultimately, the group wrote a set of problems that was published in the Calendar Problems of the National Council of Teachers of Mathematics journal Mathematics Teacher with an additional problem published in an online mathematics competition website. The project culminated in a seminar held at the University of Hartford giving the children a conference style academic experience on a college campus. Each child prepared a presentation of a problem and solution for an audience of over 45 people.

The instructional materials that developed as a result of this project are based on work with gifted and talented students from early elementary through middle school ages and in conjunction with an ongoing dialogue with teachers, administrators, and parents. Mathematics teachers are provided with guidance on how to best nurture the natural tendencies in their students to develop mathematically creative thinkers. While these materials are designed specifically to address the needs of gifted students in pull-out programs or individualized learning in the classroom, they also have the potential to enhance and enrich the mathematics education of any level student.