Supervisors info:
Μισαηλίδου Χριστίνα, Λέκτορας, ΠΤΔΕ, ΕΚΠΑ
Βουδούρη Αγγελική, Καθηγήτρια, ΠΤΔΕ, ΕΚΠΑ
Μπαραλής Γεώργιος, Αναπλ. Καθηγητής, ΠΤΔΕ, ΕΚΠΑ
Summary:
«Area measurement» seems to be a difficult concept for primary as well as secondary school pupils (Outhred & Mitchelmore, 1996; Clements & Ellerton, 1995). A significant number of misconceptions related to this concept is documented in the literature, such as:
«procedural interpretation of the concept of ‘area’»,
«incomplete understanding of the concept of area»,
«lack of understanding of the conservation of area»,
«illusion of proportionality between perimeter and area»,
«illusion of proportionality between dimensions and area»,
«overgeneralization of the parallelogram area type»,
«inability to construct square units»,
«additive rule length + width»,
«idiosyncratic types of area calculation»,
«side-height confusion» and
«area - perimeter confusion».
The aim of the research presented here was to verify whether the misconceptions mentioned in the literature apply to the last year students of the Greek primary school, as well. For such students, the understanding of the concept of «area» is taken for granted. An additional aim was to identify, if possible, new misconceptions, not yet mentioned in the literature. A third, but equally important, aim was the creation of an effective diagnostic tool for all the relevant misconceptions. The administration of a questionnaire was considered the most appropriate method for fulfilling the aims of this study. A questionnaire consisting of 10 items was deemed adequate for the diagnosis of all the known misconceptions. Some of the items were taken from the relevant literature and others were developed based on it. The questionnaire was given to 102 students who completed it within two teaching sessions. The students came from two different suburban schools in Athens. The data were analysed using the Excel software. The results of the analysis confirmed the appearance of all the misconceptions mentioned in the literature. Moreover, 4% of the sample, appeared to have an unknown misconception which was named «area-side confusion». Likewise, another case of the «additive rule length + width» was noticed: 4% of the students calculated a triangle’s area by adding its two sides. This misconception-also unknown to the relevant literature- was named «side + side of a triangle». Overall, this particular questionnaire has proven to be a rather effective diagnostic tool. However, the appearance of many significant misconceptions amongst finishing primary school students is especially alarming. Consequently, it might be useful to reassess the teaching of «area measurement» during the last two primary school years to address the related misconceptions.
