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European Journal of Education Studies ISSN: 2501 - 1111 ISSN-L: 2501 - 1111 Available on-line at: www.oapub.org/edu doi: 10.5281/zenodo.1059415 Volume 3 │Issue 11│2017 A SURVEY OF THE ERRORS OF STUDENTS IN GRADES 10 AND 12 WHEN USING VIETA’S FORMULAS TO SOLVE THE ASSOCIATED MATHEMATICAL PROBLEMS Duong Huu Tong1i, Bui Phuong Uyen1, Ha Hoang Quoc Thi1, Nguyen Thi Lai2 1School of Education, Can Tho University, Vietnam 2Master Student, Can Tho University, Vietnam Abstract: Vieta’s formulas have many applications in the general mathematics program in Vietnam. Indeed, they appear in many forms of mathematical problems, ranging from 9th, 10th and 12th grades. The complexity of the mathematical problems makes students commit many errors when using the Vieta’s formulas to solve them. The sample consisted of 246 students in grades 10 and 12, in which they addressed four questionnaires related to Vieta’s formulas. The results were quite unexpected because the errors of tenth graders also existed for 12th grade students for many different reasons. Keywords: Vieta’s formulas, error, reason, quadratic equation 1. Introduction 1.1 Problem solving in mathematics, its errors and reasons Problem solving is a major activity in students’ mathematics learning because it requires them to acquire knowledge and be able to analyze for the solution. The four important steps in solving a problem given by Polya (1973) are as follows: understanding the problem, planning the strategy, implementing the plan, and reviewing the answers. Using these four steps in addressing mathematical problems is Copyright © The Author(s). All Rights Reserved. © 2015 – 2017 Open Access Publishing Group 291 Duong Huu Tong, Bui Phuong Uyen, Ha Hoang Quoc Thi, Nguyen Thi Lai A SURVEY OF THE ERRORS OF STUDENTS IN GRADES 10 AND 12 WHEN USING VIETA’S FORMULAS TO SOLVE THE ASSOCIATED MATHEMATICAL PROBLEMS not easy for many students, resulting in them making undesirable errors. From here, the author, Newman (1977) proposed the error analysis model associated with the following four errors: reading, comprehension, transformation, processing skills, and encoding. Often the errors of students are due to many different causes. Carelessness, limited knowledge, the complexity of mathematical language make it easy for students to make errors (Thuc, 2009). Meanwhile, Herholdt and Sapire (2014) emphasized that particular areas of difficulty are the causes of the common procedural and conceptual errors. In addition, in their research, they put forward a model of error analysis that teachers can use to analyze students' errors when solving mathematical problems. Jupri and Drijvers (2016) divided the difficulties in initial algebra consists of four categories: applying arithmetical operations in numerical and algebraic expressions, understanding the notion of variable, understanding algebraic expressions and understanding the different meanings of the equal sign. Furthermore, in their study, they also revealed that students committed errors in formulating equations, schemas or diagrams when formulating a mathematical model. Sawardi and Shahrill (2014) pointed out that the systematic errors of students were the result of misconceptions. Besides, these errors reflected students’ understanding of a concept, problem or a procedure in mathematics and there were different causes relatet to them as well. One of the causes revealed in their study was maybe a result of inattentiveness on the part of classroom teachers. European Journal of Education Studies - Volume 3 │ Issue 11│ 2017 292