From Concrete to Abstract: Teaching for Transfer of Learning when Using Manipulatives

One of the most important uses of manipulatives in a classroom is to aid a learner to make connection from tangible concrete object to its abstraction. In this paper we discuss how teacher educators can foster deeper understanding of how manipulatives facilitate student learning of math concepts by emphasizing the connection between concrete objects and math symbolization with, preservice elementary teachers, the future implementers of knowledge. We provide an example and a model, with specific steps of how teacher educators can effectively demonstrate connections between concrete objects and abstract math concepts.

Undergraduate Engineering Students' Understanding of Heat, Temperature, and Radiation

Difficulty understanding heat and temperature concepts has been recognized in engineering education. Confusion has been shown to persist after instruction. The purpose of this study was to determine whether undergraduate engineering students’ knowledge of four heat transfer concept areas significantly changed with instruction and whether this varied by major and GPA. Two hundred twenty-eight undergraduate engineering students from six institutions were assessed prior to and after instruction. Results showed significant improvement in most concept areas but mean scores were below mastery. Previously documented misconceptions persisted after instruction. Significant differences were found by major and GPA. Suggestions for future research provided.