On the Assessment of the Van Hiele Levels of Reasoning.
Ángel Gutiérrez, Adela Jaime · Focus on learning problems in mathematics · 1998
There is a scarcity of research related to the van Hiele model of reasoning in which the authors have not needed to assess the students’ van Hiele level. From the beginning of application of the van Hiele model, researchers have felt the necessity of creating instruments of assessment, to be used to identify the level of reasoning of students. Two questions have to be answered: 1) What type of test should be used? 2) How should the students’ responses be evaluated? The aim of this paper is to present our answers to these questions. Different answers to the questions have been given through the time. An early attempt was made by Usiskin (1982), who designed a paper and pencil multiple-choice test in which each item was intended to evaluate a specific level of reasoning. The answers were marked as right or wrong, and students were assigned to a van Hiele level depending on the number of correct answers at each particular level. Some years later, Burger and Shaughnessy (1986) worked at the other end of the spectrum of possibilities by creating a clinical interview test based on a set of problems and semi-structured dialogues. For each problem, each student’s answer was analyzed and a van Hiele level was assigned on the basis of the dominant level evidenced in the answer. Finally, from the levels assigned to a student’s set of answers, an overall van Hiele level was assigned to the student. Other researchers have adopted positions between these two. Most people agree that a clinical interview is the most accurate way of assessment of the van Hiele levels, since it provides more information about the student’s way of reasoning than other procedures. However this procedure is not feasible when many students have to be tested since it is so time consuming. Multiple-choice items, on the other hand, are efficient, as they can be administered in a short time to many people and the scoring can be done by a computer, but they are far from being valid and reliable (see Crowley, 1989, 1990; Wilson, 1990). Aware of the need for a van Hiele test without the limitations mentioned