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Feature Analysis and Pattern Classification
Published in Scott E. Umbaugh, Digital Image Processing and Analysis, 2017
The perimeter of the object can help provide us with information about the shape of the object. The perimeter can be found in the original binary image by counting the number of “1” pixels that have “0” pixels as neighbors. Perimeter can also be found by application of an edge detector to the object, followed by counting the “1” pixels. Note that counting the “1” pixels is the same as finding the area, but in this case we are finding the “area” of the border. Since the digital images are typically mapped onto a square grid, curved outlines tend to be jagged, so these methods only give an estimate to the actual perimeter for objects with curved edges. For an irregular shape, an improved estimate to the perimeter can be found by multiplying the results from either of the above methods by π/4. If better accuracy is required, more complex methods, which use chain codes for finding perimeter, can be used (see references). An illustration of perimeter is shown in Figure 6.2-2.
An in-service primary teacher’s implementation of mathematical tasks: the case of length measurement and perimeter instruction
Published in International Journal of Mathematical Education in Science and Technology, 2019
Sumeyra Dogan Coskun, Mine Isiksal Bostan
Furthermore, another missed opportunity in the above task was to use the student’s explanation to make students understand that they can calculate the perimeter of an irregular polygon in a different way. That is, some students calculate the perimeter of an irregular polygon by finding the length of each side individually, then adding all of these lengths together. On the other hand, some others identify the sides whose lengths are equal, then multiply this length by the number of sides equal in length. Finally, they add up the remaining lengths. Hence, if Kubra had told her students that they could discuss these different ways, she could have deepened the students’ knowledge of perimeter, and the students could have considered alternative solutions for a perimeter task given later. Rowland and his colleagues [38] state that making ‘such connections is at the heart of understanding mathematics’ [p.102]. However, making these connections is strictly related to having sufficient mathematical knowledge in teaching considering the connection dimension. Therefore, it may be concluded that although Kubra is quite experienced in elementary education, her limited mathematical knowledge in teaching in terms of connection dimension led to miss opportunities in this incident such as ignoring the student’s idea, not knowing to make the student’s thinking process explicit, and not being able to make connections. On the other hand, if Kubra was able to notice her student’s thinking and to facilitate a discussion on what different ways can be used to calculate the perimeter of an irregular polygon, she could have increased the cognitive demand level of the task. That is, the mathematical knowledge in teaching regarding the connection dimension that Kubra possesses negatively affected the implementation of the task.