Abstract:)Mathematics passing rate at Mindanao University of Science and Technology every first semester has always been an issue due to its low turnover. This study reports some of the causes of students’ poor performance in College Algebra. It used a quantitative and qualitative method of research. It used a 24-item test which is a multiple choice of two to three options where the distracters are the misconceptions. The test questions were answered in the classroom to let the students understand why they are wrong. Afterwards, students were asked to write the reasons why they were wrong.

Results revealed that students’ misconceptions are more grievous in absolute value concept where the fundamental operation are done inside the absolute value sign, the application of the laws of exponents, operations of radical numbers , factoring and simplifying rational expressions. Some of the students’ reasons for wrong answers are their inability to remember the concepts, and carelessness.

The research recommends that college teachers should let the students be aware of common misconceptions and emphasize conceptual understanding in teaching the College Algebra. Teachers should give diagnostic test at the start of the classes so that they will be aware of what the students already understood and what their misconceptions are.

Keywords: Misconceptions, College Algebra, basic concept INTRODUCTION

Mathematics achievement has always been regarded as a measure of conceptual understanding on topics covered during instructions. However many students have poor performance especially during the freshmen years in college. This phenomenon has not passed without notice by the mathematics educators in Mindanao University of Science and Technology who have been observing of the many misconceptions that students have been committing. Their erroneous understanding of concepts eventually led them to wrong answers and thus causing failure in the course.

Teachers play a critical role in the concept formation of students. They are the most the important agents of change in the mind of the students. Good and Brephy (1994) suggested that the teachers should know the students’ misconceptions, then correct and help them change their misinterpretation of concepts and mathematical laws. If wrong interpretations are not corrected, the learner recall these interpretations in their minds mathematics tasks are given. Stodlart (1993) believed that the students’ prior knowledge and beliefs influence the ability to learn. When prior knowledge is wrong, this hinders the student’s learning process. According to Labitad (2005), the general error patterns are mostly in conceptual understanding. Misconceptions are caused by insufficient knowledge of the basic concept in lower algebra courses. All of these misconceptions are the problem faced by college mathematics teachers and a study to identify and to correct them is a necessity.

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METHODOLOGY

The study made use of a descriptive survey and qualitative method of research. A 24-item multiple choice teacher made test was given to 80 engineering students at the beginning of the semester. The distracters of the test items were taken from the mistakes committed by students in a previous open ended test. The time allotment of the test is only 15 minutes. The test was answered in the classroom and corrected immediately after they have taken the test so that they will know why they were wrong. Their misconceptions were also pointed out. Afterwards, the students were asked to write the reason why they have committed such misconceptions. The student choices were scored in terms of the wrong answers due to misconceptions. Their mistakes were analyzed using percentage.

RESULTS AND DISCUSSIONS

The questions were grouped by topics for better content analysis.

Table 1 Percentage of Students Misconceptions in Absolute Value Concepts.

Questions Wrong Choice Percentage

4 2

3 − ₄³ ⁻²⁼ ⁻₄⁵ 34%

7

5− ⁵ - ⁷ = -2 26%

x = -2 x = 2 62%

−1

x < 3 x-1< 3, x< 4 42%

x

2 > 1 2x > 1, x > ¹₂ 60%

Table 2 Percentage of Students Misconceptions on Topics of Rational Exponents and Properties of Radicals

16

9+ ⁹ + ¹⁶ 9%

(

^a⁺^b

)

₃¹ ^a ³¹ ^{+ b}³¹ ^38%

3 8 8 ⁶ ⁶⁴ 40%

2 x+1 ²^x⁺² 29%

x9 x³ 37%

1)2

(x−

x − 1

^84%

a 2

−1

+ b 2

−1

_a _b

+

1 58%

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Table 3 Percentage of Students’ Misconception on the Application of the Laws of Integral Exponents

5² 5⁴ 25⁶, 5⁸ 42%

2 6

5

5 1⁴ , 5³ 48%

( 5² )⁶ 5⁸ 17%

(-2) ⁴ -2⁴ 57%

(-5) ⁰ -1 29%

2⁻³ - ₂¹³ 20%

Table 4 Percentage Misconception on Factoring

(x+2)3 + (x+2) y (x+2)3y 54%

3x + 1 3(x + 1) 20%

x³ - y³ (x-y) (x² + y² ) 52%

x³ + 8 not factorable 45%

x² + y² (x + y) (x + y) 42%

4x² -6xy + 9y² (2x – 3y)² 42%

In table 1, it can be seen from the choices that the definition of the concept have been incorrectly applied in the process of obtaining the answer when there is a variable and even when there is a fundamental operation involved. The worst mistake is in ^x = -1 where 62% of the students have chosen the distracter. Teachers need to explain why the answer does not exist. Another question with higher percentage of misconception is ²^x > 1 where the variable has a numerical coefficient. It appears that the inequality relation in absolute in value symbol is erroneously interpreted by students. This concept needs emphasis because this topic was not well discussed in the high school according to the students during interview.

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In table 2, the questions were on rational exponents and properties of radicals. It can be observed that the student’s choices that are wrong are due to the wrong application of the laws of rational exponents and the properties of radicals. Only the question on addition of radicals has the least percentage misconception. The question with highest percentage of student’s misconception is on the expression (x−1)²which is 84% . It is worthy to note that the question seems very easy but many chose the wrong answer. Teachers need to emphasize conceptual understanding on the properties of radicals to promote long term memory of students.

Table 3 shows the questions dealing with applications of the laws of integral exponents. The items were simple applications of the laws but still 57% got wrong in raising a negative integer to an even power. Even in the application of the law of division 48% of the students chose the wrong answer. Students have confusion in the application of the law. The teacher needs to know this misconception so they can remind the students what not to do in applying the laws. In addition students need visualization to strengthen the concept formation in their minds so they will not forget the laws.

Table 4 shows the percentage misconception in factoring. The question which got the highest percentage of students who chose the wrong answer was in common factoring followed by difference of two cubes which are 54% and 52% respectively. Almost all questions in factoring have misconceptions 42% and above, except for 3x + 1 in which only 20% of the respondents got wrong who thought the given expression is not prime. Students need to master factoring as it is always use even in higher mathematics. It is thus necessary that students will be aware of the wrong methods of factoring. In an interview conducted, many of the students said that they were given the laws of factoring. Their problem, however, is they do not know when to use and how to apply them.

From the results of the analysis the researcher found out that some of the causes of student failure in college algebra are 1) wrong application of the definition of absolute value 2) laws of integral and rational exponents 3) properties of radicals and 4) factoring. Based from students’

answers to an interview and their written statements, reasons for their wrong answers are attributed to incomplete understanding of some concepts since they were taking up high school mathematics, inability to remember the discussed concepts, and their misinterpretation and incorrect usage of some of the laws and principles.

CONCLUSION AND RECOMMENDATION

From the analysis and findings it can be inferred that first year college engineering students have poor foundations on the basic concepts of college algebra like the concept on absolute value, laws of integral and rational exponents, properties of radicals and all kinds of factoring. The researcher recommends that all mathematics teachers should diagnose students’ knowledge on the basic concepts of algebra before starting their classes so they can emphasize what the students should not do and consider misconceptions and grave errors as “MORTAL SINS” in mathematics.

The students should be reminded that the more mortal sins they commit, the higher the chance that they will fail in their subject. As for teachers, they should emphasize conceptual understanding in every topic so that students will improve in their retention and be able to apply concepts and laws correctly when tasks are given. Whenever possible, teachers should let students explain, interpret and apply the concepts being discussed to discover their students’ misconception and remedy them accordingly.

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REFERENCES

Good and Brophy (1994) Learning to think mathematically, problem solving metacognition and sense making in mathematics. In D.K. Grous(Ed) Handbook of Research on Mathematics Teaching and Learning. New York.

Labitad, N. (2005) Mathematical readiness and misconceptions of freshmen engineering students in Cagayan de Oro College first semester 2004-2005. Unpublished thesis, CDO.

Stodlart, A. (1993) Moving from arithmetic to algebra under the time pressures of real classroom.

http:dlibrary.aw.edu.au./maths.edu/anne.willias/movingpdf

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