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Inverses – why we teach and why we need talk more about it more often



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TMME vol5 nos 2 3 p 315 Inverses why we teach and why we need talk more about it more often Woong Lim1 St Agnes Academy Houston Texas Abstract This article examines the key role that the notion of inverses plays in numerous mathematical concepts Keywords Inverse Group Ring Field Binary Operators Introduction The point of inverse gets down to the inverse of which operation Different operations lead different answers about the inverse The main reason why students are confused or make mistakes are that they are not clear which operation teachers refer to In this writing I first discuss the inverse of three types of operations addition its inverse is known as opposite multiplication its inverse is known as reciprocal and composition of maps or functions its inverse is known as inverse Then I introduce the concept of group ring and the field in order to challenge students to utilize their cognitive understanding of inverses in solving equations It was not until I had begun to teach trigonometry that I realized the students understanding 1 of inverse is not so concrete Given sin 30 most students knew csc 30 2 some shouted 2 you flip it That s how you got it It appeared that they understood the reciprocal of sin is csc A few days later when asked the same group about the value of sec 60 a number of 1 students responded sec 60 cos Intrigued by this I did a survey of asking a sophomore 60 1 class about the inverse of 2 Most students answered When asked the same question a number 2 of senior students however responded where is x and y How many inverses are there When it comes to inverses there seems to be a sequential understanding of inverse as students progress from pre algebra to algebra and pre calculus Why are they confused and 1 Secondary Math Teacher St Agnes Academy 9000 Bellaire Blvd Houston TX 77036 wlim st agnes org Acknowledgement I am truly grateful to my advisers Dr Garret Etgen Dr Min Ru and Dr Jennifer Chauvot for their comments suggestions and particularly



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