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In mathematics, students are supposed to comprehend the relevant concepts, mathematical relations, and operations. Conceptual understanding ensures that students understand mathematics by developing new knowledge from the prerequisite knowledge and prior experience. The angle concept develops gradually with time as learners recognize deeper and more relationship between physical angle scenarios like using scissors and climbing a slope. When the angle concept is not developed progressively, learners may have difficulties using a protractor. This essay describes the initial activities that can help in understanding the angle concept and the common misconceptions.
Abstract mathematical concepts generally require understanding, fluency, problem solving, and reasoning (Australiancurriculum.edu.au, 2016). One of the initial classroom activities that can help the students in understanding angles is the art of comparison of practical life application of the angle concept. In this case, the students are taken through the concept using similarity. The students should be engaged in comparing different angles before actual measurement with a protractor. In order to understand the angle concept, the students should be made to realize that an angle is a turning as is the case with the hand of a clock. By turning the clock’s hand, the students appreciate practically the concept of an angle (Reys, 2012, p. 411). In addition, the students should be made to appreciate that an angle is an amount of turning by an object. This can be effectively done using a rotogram to help in comparing the amount of turning space (Reys, 2012, p. 411). This device consists of a reference line and two plastic discs.
The other activity that can be used to enhance the conceptual understanding of angles by the students is the introduction of an angle measurement instrument called protractor. This instrument could prove to be a challenge where students do not have a proper foundation on the practical instances where the angle concept is applied in daily life. This learning activity can be followed by a progressive knowledge of unit conversion. The students should be introduced to the equivalent angle measurements such as the equivalence of degrees in radians and the equivalence of minutes in degrees and other similar conversions (Reys, 2012, p. 420). This is because different instruments and devices use different measurement units.
The concept of familiarity is another approach of promoting the angle concept among the learners Using the right angle as a benchmark, the students should be introduced to various shapes such as triangles, rectangles, squares, rhombus, among others by measuring the angles subtended at the corners. This helps them in identifying the common angles such as right angles, 45 degrees (Bobis, Mulligan, & Lowrie, 2004). This concept can be combined with reification where by the learners undertake practical angle operations in daily life such as bends, and corners. Further reification can be enhanced by the use of instruments and devices that involve angles such as scissors, pliers, plumb line, and door.
There are certain common misconceptions about the mathematical concepts. A misconception occurs when learners misunderstand mathematical concepts by incorrect hearing, from incorrect thinking, or use shortcut approaches that interfere with solid mathematical concept development (Education. Vic. Gov. Au, 2016). For example, a learner would read 404 to mean forty-four. In angles, students usually have difficulties in identifying the hypotenuse and the height of a right-angled triangle. Another instance where learners can have a misconception about angles is the space between the lines that subtends an angle. Generally, an angle is the amount of turn by an object and can easily be determined by a geostick (Bobis, Mulligan, & Lowrie, 2004). When forming shapes using angles such as a triangle, the students usually have a misconception that triangles must have one point at the top and two points at the bottom.
In conclusion, learners are required to grasp the pertinent mathematical concepts, relationships, procedures, and operations. A conceptual understanding of mathematical concepts sees to it that learners appreciate mathematics by explicating new knowledge from the prior knowledge and experience acquired. The angle concept evolves systematically with time as students identify deeper correlation between physical angle cases such as using tools like scissors or walking up a slope. When the concept of angles is not built up progressively, students may have problems with using mathematical instruments like a protractor.
Australiancurriculum.edu.au. 2016, Mathematics Foundation to Year 10 Curriculum by rows - The Australian Curriculum v8.2, Available at: https://www.australiancurriculum.edu.au/mathematics/curriculum/f-10?layout=1
Bobis, J, Mulligan, J & Lowrie, T 2004, Mathematics for Children, Sydney, Pearson Prentice Hall.
Education.vic.gov.au. 2016, Common Misunderstandings - Level 3 Multiplicative Thinking. Available at: https://www.education.vic.gov.au/school/teachers/teachingresources/discipline/maths/assessment/Pages/lvl3multi.aspx
Reys, RE, Lindquist, MM, Lambdin, DV, Smith, NL, Falle, J, Frid, S & Bennett, S 2012, Helping children learn mathematics, 1st edn, John Wiley & Sons, Milton, GLD.
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