The Concept Image of Students and Teachers about the Equal Sign

Lia Ardiansari,Dadan Dasari,Didi Suryadi

doi:10.13189/ujer.2020.081240

Abstract

The teacher as an educator plays an important role in the process of forming a concept image of students about the equal sign in learning mathematics. Teachers must have an equal sign meaning in accordance with the capacity, learning experience, and knowledge which is a source for them to compile a certain didactic design. The didactic design that has been compiled becomes a learning environment that triggers students' mental perceptions and actions so that a concept image of the equal sign is formed. This study aims to explore teachers' understanding and confirm that the concept image formed by these students may be the impact of the learning process with didactic designs that have been compiled by the teacher. The investigation was conducted qualitatively using a case study approach involving 6 teachers and 55 elementary and middle school students. The data collection methods included teacher questionnaires and interviews with two selected teachers, as well as students answering a series of questions then six students were deliberately selected to be interviewed based on their responses. The results show that the teachers' concept images about the equal sign are generally difficult to say that they already have a well-developed relational view, in addition, they lack the knowledge and skills to identify, anticipate, reduce, or correct students' misconceptions about the equal sign. As a result, the majority of students do not have a concept image about the equal sign that matches the scientific conception that should be.

Highlights

An important part of mathematics that is used in all kinds of calculation of equations more than any other symbol is the equal sign
Knowledge gained from initial experience if it does not match the information found in future efforts will have a 'top-down' effect so that early learning difficulties become the cause of learning difficulties later in life (Bruner, 1957; McNeil & Alibali, 2004, 2005; Rumelhart, 1980) that students' errors in interpreting the meaning of the equal sign as in the early grades can be the cause of learning difficulties at a later date even at the higher education level (Baiduri 2015; Best, McRoberts, & Goodell, 2001; Flege, Yeni Komshian, & Liu, 1999; Knuth et al, 2006; McNeil & Alibali, 2005)
Some previous researchers mentioned that elementary school students had knowledge of the equal sign as a signal to count, a sign that usually appears at the end of a numeric expression and there is only one number after it (Falkner et al, 1999; Prediger, 2010; Vermeulen & Meyer, 2017)

Summary

Introduction

An important part of mathematics that is used in all kinds of calculation of equations more than any other symbol is the equal sign. Several researchers (e.g, Darr, 2003; Falkner, Levi and Carpenter, 1999) report that one of the main stumbling blocks for students as they move from arithmetic to algebra is their understanding of the equal sign because the meaning of the equal sign is rarely taught to students explicitly (Jones, et al, 2012; Li, et al, 2008) This understanding involves subjective mental action so that each individual can have a different meaning according to their learning experience (Kieran, 1981; McNeil, et al, 2006; Prediger, 2010; Radford, 2000; Sherman & Bisanz, 2009). Knowledge gained from initial experience if it does not match the information found in future efforts will have a 'top-down' effect so that early learning difficulties become the cause of learning difficulties later in life (Bruner, 1957; McNeil & Alibali, 2004, 2005; Rumelhart, 1980) that students' errors in interpreting the meaning of the equal sign as in the early grades can be the cause of learning difficulties at a later date even at the higher education level (Baiduri 2015; Best, McRoberts, & Goodell, 2001; Flege, Yeni Komshian, & Liu, 1999; Knuth et al, 2006; McNeil & Alibali, 2005)

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