Academic journal article The Mathematics Enthusiast

Mathematical Creativity for the Youngest School Children: Kindergarten to Third Grade Teachers' Interpretations of What It Is and How to Promote It

Academic journal article The Mathematics Enthusiast

Mathematical Creativity for the Youngest School Children: Kindergarten to Third Grade Teachers' Interpretations of What It Is and How to Promote It

Article excerpt

Introduction

Defining Creativity in Mathematics for Adults and Children

Creativity is critical to mathematics. Professional mathematicians, for instance, create new theories and hypotheses in doing advanced mathematics, and creative advances in mathematics underlie many breakthroughs and advances in other disciplines, including the natural and social sciences. Mathematical creativity at the adult level can be defined as "(a) the ability to produce original work that significantly extends the body of knowledge, and/or (b) the ability to open avenues of new questions for other mathematicians" (Sriraman, 2005, p.23).

However, young children are in the early stages of learning mathematics, and therefore their mathematical creativity must be defined in a different way. Applying the adult definition to young children is inappropriate, but that does not mean they cannot show creativity of other kinds (Adams & Chen, 2012). According to Sriraman (2005), creativity for school learners can be defined as "(a) the process that results in unusual (novel) and/or insightful solution(s) to a given problem or analogous problems, and/or (b) the formulation of new questions and/or possibilities that allow an old problem to be regarded from a new angle requiring imagination" (p.24). This definition applies well even to very young children, aged five to nine years (in kindergarten to grade 3 of public school)-the "emerging mathematicians" who populate the classrooms of the teachers interviewed for this study. Some might assume that there is little room for creativity in early childhood math-after all, children are learning to count, add and subtract, all things that have "right" answers. That assumption is misguided; within the early childhood era, there exists the same potential for flexible and divergent thinking and versatile use of strategies that exists at later grade levels, as opposed to seeking to solve problems in the single most efficient way. Teachers should understand that creativity flourishes when they support children's ability to generate original ideas (Bairaktarova & Evangelou, 2012; Saracho, 2012). Gallenstein (2003) notes that effective teaching models that promote critical thinking in early childhood mathematics and science are less often used in classrooms than in those for older children, but that children aged 3 to 8 are fully capable of creative construction of math and science concepts.

Sriraman's definition of creativity does not require children to invent new mathematical theorems or prove advanced hypotheses. Rather, it points to children transcending mechanically following procedures in order to frame their own questions, see the possibilities in mathematical situations, and/or produce unusual, novel, or insightful answers or strategies. Children can draw on their own inner resources to play with mathematical ideas. Indeed, children encounter possible problems and questions with mathematical elements every day, in and out of school. In approaching these problems, children can display mathematical thinking skills and processes emphasized in various national and state standards and principles for mathematical proficiency, including standards and principles from the National Council of Teachers of Mathematics (NCTM, 2000a), mathematical practice standards from the Common Core State Standards for Mathematics (CCSS-M, CCSS Initiative, 2010), and five strands for mathematical proficiency from the National Research Council (NRC, Kilpatrick, Swafford, & Swindell, 2001). Creativity is evidently considered essential for effective learning of mathematics, no matter the age of the student.

The NCTM (2000b) advocates that students solve problems creatively and resourcefully, but NCTM publications do not give a clear definition of mathematical creativity in school children. In fact, a simple consensus definition is lacking, both for creativity in general (Chen, 2012; Lau, Hui, & Ng, 2004; Sawyer, 2003, 2006) and creativity in the specific area of mathematics (Sriraman, 2005; Sriraman & Freiman, 2007), perhaps because the phenomenon in complex and has multiple facets. …

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