Abstract:

It is a fact that geometric concepts are abstract and rely on students' assumptions. The mathematical properties of these concepts seem complex to students, and they struggle to understand area measurement. However, although area measurement is perceived concretely, it requires flexibility in abstract thinking. If students confuse the concepts of area and perimeter, they may not be able to calculate the area (Anhalt, Fernandes and Civil, 2007; Zacharos, 2005). Some studies have revealed that teachers also make errors because they cannot find the appropriate unit for area and perimeter calculations (Baturo and Nason, 1996; Fuller, 1996). Outhred and Mitchelmore (2000) stated that the errors students make in area calculations stem from their confusion between perimeter and area. The reason for this is that in traditional education, teachers teach the area formula directly as the product of length and width. Thus, the area formula does not go beyond the product of two lengths (Stephan and Clements, 2003). To put an end to this situation, students must first visualise the area in their minds and understand the concept of area. Otherwise, as stated in Yeo's (2008) study, the area will be memorised not as a concept, but merely as Length x Width.

It has been noted that it is important for students to learn the concept of area and the property of ‘covering an area’ using unit squares, and that they struggle with this. It has been observed that they state that the area of a new shape created by dividing a shape into parts and rearranging the same parts is different from the area of the original shape. This indicates that they do not fully grasp the concept of area conservation (Kamii and Kysh, 2006). Haris and Ilma (2011) emphasise the necessity of accessing the algorithm used in area calculation and state that the area is calculated based on the number of pieces used in the area coverage and that the calculated value depends on the length and width.

After reviewing the studies, it is crucial that students can create different geometric shapes themselves and discover the concept of area. To facilitate this discovery, students were first taught the concept of a unit square. They were encouraged to use a square to create rectangles and calculate their areas. This prevented confusion between area and perimeter calculations. Subsequently, a differentiation activity was conducted using Pick's Theorem. This theorem is named after the Austrian mathematician George A. Pick (Corc Ey. Pek) (1859-1942), who discovered it in 1899. This theorem helps to find areas in a different way. In the theorem, the area is calculated by determining the points inside the polygon and the points on the sides of the polygon. Three groups of students were formed. Each group of students was asked to create the shape with the largest area. The pupils created concave and convex shapes. Using this theorem, they easily calculated the areas of all geometric shapes. They analysed the relationships between points, applied mathematical reasoning, solved problems, and made comparisons using the classical area formula. At the end of the study, the students completed the evaluation forms.

Keywords:

Area Calculation, Pick's theorem, Primary Education.