Misconceptions in classifying two-dimensional figures
Introduction
Mathematical errors occur due to several diverse reasons which can be student or teacher related. General misconceptions in mathematics vary and are attributed to mathematical complexity, presentational complexity, and translational complexity (Beckmann, 2013). Geometry study in mathematics begins early in school with teachers beginning with two-dimension figures and proceeding with more complex concepts. General misconceptions in study of geometry in a way impact on two-dimension classification misconceptions (Van et al., 2013). Generally, children believe geometry is difficult, confusing, and too broad a topic to comprehend. Misconceptions in classifying two-dimension shapes are to some extent the fault of teachers, learners and learning aids.
Generally, two-dimension figures are grouped as triangles, quadrilaterals, polygons, and circles (Stefan et al., 2012). Triangles include equilateral, isosceles, scalene and right-angled. These triangles are categorized according to length of sides, angles, lines of symmetry, and rotational symmetry among others (Annenberg Learner, 2013). Equilateral triangles have equal sides, equal angles, 3 lines of symmetry, and third order rotation symmetry. Isosceles have two equal sides and angles, one line of symmetry, and no rotation symmetry. Scalene have three sides of unequal length, no line of symmetry, and no rotation symmetry (Learner, 2013).
Generally, when children are introduced to triangles, in most cases proto-typical shapes used in books, posters or worksheets use equilateral triangles as the only type of triangle. Normally, children grow up believing that a triangle has three equal sides and angles. This is because teachers only focus on having children label shapes without providing detailed information. Considering that certain aspects of brain growth and development are best enhanced when children are young, usage of equilateral triangle diagrams in reference to all triangles creates a misconception that all triangles should have equal sides and angles (Beckmann, 2013). Therefore, when children come across isosceles, scalene or right-angled triangles which they are not conversant with, they are likely rule them out from the list of triangles.
Misconception that right-angled triangles do not have lines of symmetry does not apply all the time since a right-angled triangle can have two equal sides hence making it have one line of symmetry and in turn it becomes an isosceles triangle.
Quadrilaterals are any four sided figures and include rectangle, square, parallelogram, trapezium, rhombus, oblong, and kite (Van et al., 2013). These figures are categorized according to equality of sides, angles, lines of symmetry, and rotational symmetry. This classification to some extent overlooks the fact that a square is a special rectangle since it is a quadrilateral with four right-angles which therefore changes the generalization that rectangles have two lines of symmetry and two order rotation symmetry.
Definition of parallelogram as quadrilateral with opposite sides that are parallel and have equal lengths makes square, rectangle, and rhombus parallelograms too (Stefan et al., 2012). However, it is said to have order two rotational symmetry which is not the case for a triangle that has order four rotational symmetry (Laureate Education, 2013).
Recommendations
Teachers need to use more non-prototypical shapes while teaching and include more different shapes as examples. This will rid the misconception that size, orientation, and ratio are integral attributes in classifying two-dimension shapes (Learner, 2013). It will also make children more conversant with all existing shapes in detail hence advanced studies in geometry will not be difficult for them. Teachers also need to expand their teaching methods to ensure that children understand what defines a particular shape category. This will enable them understand and identify integral attributes of a shape and differentiate them from non-integral attributes like size.
References
Annenberg Learner. (2013). Teacher’s lab: Shape and space in geometry. Retrieved from www.learner.org/teacherslab/math/geometry/
Beckmann, S. (2013). Mathematics for elementary teachers with activities (4th ed.). Boston, MA: Pearson.
Laureate Education (Producer). (2013e). Two-dimensional figures [Video file]. Retrieved from https://class.waldenu.edu
Stefan, M. L., McManus, G. E., Dickey, A. L., & Arb, M. S. (2012). Defining supports geometry. Mathematics Teaching in the Middle School, 18(2), 92–98.
Defining supports geometry by Stefan, M. McManus, G., Dickey, A. & Maxwell, S.A., in Mathematics Teaching in the Middle School, Vol.18, Issue 2. Copyright 2012 by National Council of Teachers of Mathematics. Reprinted by permission of National Council of Teachers of Mathematics via the Copyright Clearance Center.
Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2013). Elementary and middle school mathematics: Teaching developmentally (8th ed.). Upper Saddle River, NJ: Pearson.
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