Analysis on students' common algebraic errors

Abstract

Algebra has a wide range of applications that open doors to countless opportunities especially for students who are pursuing Science, Technology, Engineering and Mathematics (STEM) Program. This program in the K 12 Curriculum that was implemented in the Philippines in 2013 aims to produce graduates of secondary level who will take science, research, mathematics and engineering - related courses in tertiary level and thereby add to the scientific and scholarly workforce of the country. The introduction of STEM in the Basic Education paved to the way of putting great effort in enhancing students' performance in mathematics particularly in algebra that is considered as a gateway to higher level STEM - related careers (Adelman, 2006 as cited by Booth, Barbieri, Eyer Biagoev, 2014). These careers include Aircraft Operations Aviation, Aeronautical Engineering, Commerce, Civil Engineering, Actuarial Science, Computer Programming, Computer Science, Computer engineering, Accountancy, Industrial Engineering and Data Analysis and Statistics which are the highest paying jobs in the Philippines based on the 2016 Occupational Wages Survey released by the Department of Labor and Employment (Nucum, 2018). However, despite the efforts exerted to improve learning in algebra, researchers have still observed that this is the most difficult for students to grasp because of its underpinning complexities. Researchers like Rushton (2014), Owusu (2015), Shahrill and Matzin (2015) revealed that this difficulty experienced by the students is greatly influenced by different errors they commit when dealing with algebraic problems. Thus, this study highlights on classifying and analyzing algebraic errors of STEM students which will serve as baseline data to design appropriate intervention plan that aims to enhance mathematics learning and pedagogy. This study generally aimed to classify common algebraic errors committed by students currently enrolled in the Third Trimester of the Academic Year 2018 - 2019 in the University of the Cordilleras - Senior High School under the Science, Technology, Engineering and Mathematics (STEM) Program. Specifically, it sought to answer the following questions: 1. What algebraic errors are committed by students along learning contents on a. Exponent; b. Radical; c. Polynomial; d. Linear Equation; and e. Linear Inequality? 2. What is the difference on the frequency of errors committed by the students along a. Exponent; b. Radical; c. Polynomial; d. Linear Equation; and e. Linear Inequality? Hypothesis: There is a significant difference on the frequency of errors committed by students along learning contents on a. Exponent; b. Radical; c. Polynomial; d. Linear Equation; and e. Linear Inequality. Descriptive survey was employed in this study to classify and describe the algebraic errors committed by the students along learning contents on exponent, radical, polynomial, linear equation and linear inequality. The respondents were purposively selected based on their academic performance in their calculus courses which is fairly satisfactory. Data were gathered through a self-made competency test validated by experts in the field of mathematics. The collected data were then subjected for treatment using frequency count that will determine the number of errors committed per learning area and chi-square goodness-of-fit test at 0.05 level of significance that will measure the difference on the frequency of errors committed by the students. The process of triangulation was also utilized to further analyze and verify the findings of the study. The researcher organized a focus group discussion with the students and calculus teachers of the institution. The salient findings of the study include the following: 1. The students who are specifically taking STEM Strand committed different errors in each learning content which were classified into Conceptual Error, Computational Error and Careless Error. 2. There was a significant difference on the frequency of errors committed by the students along learning contents on exponent, radical, polynomial, linear equation and linear inequality. Based on the aforementioned findings, the researcher framed the following conclusions: 1. Science, Technology, Engineering and Mathematics students are not still prepared to succeed higher mathematics courses necessary in their field. 2. Conceptual error is the most prominent type of error committed by the students followed by computational error and careless error, respectively. In view of the findings and conclusions, the following recommendations are hereby posited: 1. There is a need for a diagnostic assessment to entering grade 11 students so that intervention scheme like learning module can be implemented to alleviate algebraic errors. 2. A training on pedagogical strategies and techniques that can refine and enhance student's conceptual understanding may be provided for teachers. 3. A different sample may be considered specifically in other strands or grade level. 4. Further study may explore the sources of these algebraic errors through a qualitative approach so that a profound analysis will be provided. 5. The proposed module may be evaluated for utilization to lessen students' errors when dealing with algebraic problems.