Abstract:

Research on the characteristics and learning styles of mathematically gifted students over the last two decades indicates that these students make significant academic strides when given challenging and engaging materials beyond the standard curriculum. There is an increased need to focus on the education of mathematically advanced and gifted children. Current reform efforts have moved in the direction of having students of all levels develop problem solving skills and explain their work. However, it is rare for students to be given the opportunity and challenge to formulate, author, and publish their own problems.

This paper describes an after-school gifted program created for a group of mathematically gifted and talented primary school students when their in-school gifted program was eliminated. Over the course of the first year, the group transitioned from problem solving to the more advanced level of problem posing. 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 gave a presentation of a problem and solution for an audience of over 45 people, completing their research experience.

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. Guidance is provided to mathematics teachers on how to 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.

Keywords:

Mathematics, gifted, elementary.