English Lesson

Concept Maps to Assess Student Teachers’ Understanding

OfMathematical Proof

          Assessment is defined as the process of gathering information so as to monitor student progress and make sound instructional decisions. However, it is not an easy task to assess student understanding of mathematical concepts. Mathematics educators have long used paper and pencil tests as tools to assess learning. However, the need for a better way to represent learners‘ conceptual understanding has led to the development of concept maps as an alternative assessment tool (Novak & Canas, 2006).

          Within the realm of mathematics education, some researchers (Schimittau, 2004; Afamasa-Fuatai, 2004a, 2004b) specifically advocate the use of concept maps to assess mathematical learning. A concept map is an explicit, graphical representation of knowledge. Concept maps can effectively map what is inside the mind to the outside (Tergan, 1988) and reveal those conceptual understandings that are not generally identifiable by other assessment tools (Hasemann & Mansfield, 1995).

          They provide the student with a different mean of demonstrating understanding, and the assessor with an additional opportunity to witness how the student connects ideas and groups or organizes 50 Concept Maps to Assess Understanding of Mathematical Proof information. In other words, concept maps effectively reveal the overall integrated knowledge of the learner.

          The theoretical foundation of concept mapping derives from Ausbel‘s theory of learning. This theory posits that meaningful learning takes place by assimilating new concepts into existing conceptual frameworks held by the learner (Ausbel, 1963; 1968; Ausbel, Novak & Hanesian, 1978). Learners who are asked to draw a concept map must choose visual symbols and/or details to represent concepts and to clarify the nature and relationships among these concepts. Details and connections between concepts can be added in any order. Generally maps are drawn with concepts contained in oval shapes and words noted on the lines connecting concepts/shapes.