Basic facts and concepts

¶ … Teach Geometry

Dear Parent,

This letter is in response to your question: Why are students in elementary school learning geometry when they do not yet know the basic facts and should be spending their time working on them instead?

There are two parts to the answer. The first is concerned with the learning of math facts. It is an ongoing process for students in the elementary grades. It begins with the development of number sense, which is a child's facility and flexibility in using and manipulating numbers (Chard, Baker, Clarke, Jungjohann, Davis, and Smolkowski, 2008, p. 12). Some students develop number sense in preschool or informally in familial settings before kindergarten; other children do not begin to develop number sense until their formal schooling begins, whether because of opportunity or because of developmental readiness. Developing number sense takes time. It does not happen quickly and it does not happen because a child was drilled with flash cards. Number facts are part of every child's mathematical learning, but there is so much more.

The second part of the answer is concerned with topics of study in the elementary mathematics classroom, including geometry. Research suggests that simultaneously integrating number sense activities with early measurement concepts and simple plain geometry helps reduce subsequent difficulties in mathematics as opposed to teaching these skills separately and sequentially (Chard, et al., 2008, p. 13). In other words, math is not taught in a vacuum. Beginning with the youngest students, math is taught as an amalgamation of skills, strategies and thinking processes. Students need to know their facts but they can be developing greater levels of mathematical thinking as they do so.

American students' performance in mathematics is generally low compared to that of students around the world. There is an achievement gap for students from low-income and minority backgrounds as well as for students with disabilities (Chard, et al., 2008, p. 11). The crisis in math achievement has fostered considerable research of best practices. The National Council of Teachers of Mathematics (NCTM) states that "Communication is an essential part of mathematics and mathematics education" (2000, p. 60, cited in Cooke and Buchholz, 2005, p. 365). Communication during math time gives students and teachers an opportunity to discuss mathematical ideas. Children develop their math vocabulary and learn to use appropriate terms. They have an opportunity to connect new understanding to prior knowledge. Math is not simply rote learning of facts and equations. The Common Core State Standards (CCSS), already adopted by forty-five states, were designed to facilitate higher-order thinking and problem solving skills ("Common core standards adoption by state," 2012). These abilities will better prepare students for the real world. Students will communicate with their teachers and with their peers to figure out different ways to solve problems. There is focus on problem solving as a process, so students will be able to understand where they went wrong and so they will be able to solve similar problems in the future.