Abstract:$This experimental study evaluated calculation, conceptual, and procedural errors of second year low–achieving students taught using three teaching methods; class instruction with recorded journal writing exercises (RJW), class instruction with unrecorded journal writing exercises(UJW), and class instruction without journal writing exercises(NJW). The study introduced and explored the use of computation journal to assess student’s mathematical understanding, the error patterns, and the effectiveness of journal writing in mathematics instruction.

The multigroup pretest – posttest design was employed in this experimental study conducted at the Palawan State University’s Laboratory High School in the school year 2008- 2009. Thirty – two (32) low achieving second year students who belong to the lowest quartile were selected as the population. Two groups were exposed to computation journal writing exercises – journals were graded for one group and not graded for the other. The third group did not have any journal writing exercise.

Classes exposed to journal writing used computation journal containing the written descriptions of how they solved the problem. The step by step description of student’s solution revealed misconceptions and error patters in solving rational expressions.

A typical low-achieving student committed mostly conceptual and procedural errors. After the experiment, students exposed to recorded and unrecorded journal writing exercises committed significantly less conceptual and procedural errors but not calculation errors resulting from careless solution or answer.

The conclusions drawn from this study strongly justify the use of computation journals as both a teaching and performance-based assessment tool in the mathematics classroom, to supplement regular instruction. This study emphasized that journal writing boosts students’

conceptual understanding and procedural skills.

Introduction

Mathematics has always been a misunderstood and unappreciated subject. It is not only numbers and computations; it is a process that requires analytical thinking and patience for its content to be fully appreciated.

According to the National Research Council (2002), all students can and should achieve proficiency in mathematics. Additionally, mathematical skills are fundamental for individuals seeking occupational and educational advancement. Without proficiency in mathematics, students will likely experience difficulty completing other more advanced branches of mathematics (e.g., algebra) and be unprepared for many occupations. Mathematics education should enable students to understand and apply mathematical concepts. With this emphasis on conceptual understanding and higher-order problem-solving skills, teachers must not ignore computation.

Knowledge of basic computation skills cannot be separated from the overall conceptual understanding and forms the foundation for mathematical thinking (Wu, 1999). The National Council of Teachers of Mathematics (NCTM, 2000) emphasizes computation over overall

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performance in mathematics. According to the NCTM (2000), it is critical for students to know the basic number facts for addition, subtraction, multiplication, and division. Students' fluency and accuracy in methods of computation are equally important.

Over the years, young Filipino students have manifested poor mathematical skills as evidenced in the latest Trends in International Mathematics and Science Study (TIMSS) conducted by the International Association for the Evaluation of Educational Achievement (IEA) in 2003.

Based on the study, the Philippines ranked 41^st among 45 participating countries. Several reasons have been given as causes of the unsatisfactory achievement of students particularly in mathematics. Among these are the lack of textbooks, attitude towards the subject, poor computation skills, and teaching practices. As evident in the published result of TIMSS 2003, among the content domain of mathematics, topics in algebra, equation, and formula garnered the lowest national average score of 23 against the international average score of 45. It only implies that most of the students are having difficulties in algebra lessons.

Teachers can play an important role in helping students immerse themselves in learning; one such way is by using a variety of teaching and learning strategies. They should find appropriate strategies to motivate students’ interest, specially the low achievers of the class. Maqsud (1998) showed that teaching low achieving students using metacognitive strategies such as planning, monitoring, evaluating, and reflecting the acquired learning can lead to increased positive attitude, academic achievement and greater awareness among students.

Another similar study conducted by Ponnusamy (2004) suggested that teachers must improve their students’ metacognitive awareness in order to improve their learning abilities. His study revealed that metacognitive and problem solving strategies have a significant impact on academic achievement. The more students know about effective learning strategies, the higher their classroom achievement is likely to be (Ormrod, 1999).

Research has shown that cognitive skills are determining factors of an individual's learning ability, that weak underlying cognitive skills account for the majority of learning difficulties, and that cognitive skills training is the most successful form of intervention. Burns (1998) suggests that incorporating writing into mathematics classrooms will help students develop their abilities to think about and understand content. Student writing also provides teachers with a better understanding of students’ cognitive processes.

According to Lee – Chua (2007), math anxiety leads to poor mathematical skills. To relieve math anxiety, Kennedy (1995) suggested reflective journal writing as an effective strategy to help the students gain confidence and power in relationship to mathematics.

Journal writing can become one of the most important components of the assessment process because it has the potential to promote critical thinking (Boud, 2001). Also, journal writing helps students understand how they learn and gives a voice to those who are not good at expressing themselves orally.

Similarly, Padrones (2004) reported in his study “Journal Writing and Academic Performance in College-Level Probability and Statistics” that journal writing has significant effect on the academic performance of students in lower cognitive levels such as remembering and understanding but not on the higher cognitive levels such as applying, analyzing, evaluating and creating.

Considering the above situation, this paper aimed to determine the specific errors low–

achieving students commit and to explore how they could do better in solving rational expressions by using computation journal writing as an instructional tool. Specifically, the investigation focused

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on specific errors and patterns committed by second year high school low–achieving students in solving algebraic rational expressions. The study also explored the use of computation journal writing to assess student’s mathematical understanding, to understand the logic of their errors, and to determine if journal writing could be an effective strategy in mathematics instruction.

Methodology

This research is experimental in nature, employing the multigroup pretest – posttest design to assess the effects of computation journal on the students’ number of errors in solving rational algebraic expressions.

The population consisted of thirty – two (32) sophomore students whose average grades for the first and second grading periods of the school year 2008-2009 fall on the lower 25% of the total second year classes.

Each student in the experimental groups was provided a notebook for journal writing exercises. A split – page format was used. Students wrote on the left side of the paper. Writing exercises were done for 5 – 10 minutes and were collected at the end of every math exercise for content and accuracy examination. The researcher commented on any errors, omissions, and inconsistencies that were observed. Researcher’s comments/suggestions were written on the right side of the paper. The exercises were then returned to the students. Using the critiques of the teacher – researcher, students were required to submit a revision of each exercise. The revision was commented upon and rated for accuracy using a rubric which was adapted from the study of Lim &

Pugalee (2005).

Frequency counts and percentage were used to describe the number and error patterns committed in solving algebraic rational expressions.

To test for significance of gain performance in basic calculation and the effectiveness of the experimental treatments (recorded journal writing, unrecorded journal writing, and without journal writing) the Analysis of Covariance or ANCOVA test for related samples was used. This test allowed for the statistical control of the students’ pre-test scores by making it as a covariate, thereby taking out its contribution to their post-test scores.

Findings

The results confirmed that indeed, the low achieving students committed errors that are mostly conceptual and procedural in nature in all the operations – addition, subtraction, multiplication, division – involving rational expressions. Students had almost no chance to commit calculation errors since this type would usually arise only when students know the concept and perform the procedures but arrived at a wrong answer because of carelessness. The errors they committed indicate a general lack of understanding of the concept and procedural skills that are necessary in order to correctly add, subtract, multiply, or divide algebraic rational expressions.

The three groups of students were initially the same in the number of errors committed during the pre-test. However, significant differences were noted during the post-test. Those students with recorded/unrecorded journal writing exercises committed significantly less conceptual and procedural errors during the post-test compared to their initial performance at the start of the experiment. These indicate that there was a significant decrease in the number of student’s conceptual and procedural errors. However, journal writing had no positive effect on the students’

calculation skills. This may be because those students with journal writing exercises have enhanced

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their conceptual and procedural skills but are still impulsive in solving the expressions and therefore, committed more calculation errors. These conclusions are similar to those found by Padrones (2004) and Jurdak & Zein (1998) that the use of journal writing in mathematics class has cognitive benefits in terms of increased conceptual and procedural understanding.

Recommendations

The use of computation journal in mathematics instruction must be strongly considered by teachers as a supplemental teaching activity, in addition to regular classroom instruction.

Additional tasks must be included in the journal so that students would also improve their calculation skills, once they have mastered the concepts and procedural skills. Because journal entries are able to reflect students’ conceptual, procedural understanding and skills, journal writing may be used by teachers as a performance-based assessment tool in secondary mathematics.

Even if this study has not yielded conclusive results on whether it is best to record and include ratings of journal entries in the computation of a student’s grade, it is better that journal writing be graded and allotted a sufficient weight in the computation of the periodic rating since it does reflect achievement. Grading it would also provide greater incentive for students to give time and effort to journal writing.

To improve communication between the teacher and student, computation journals must include not only the student’s written outputs but also the teacher’s feedbacks and responses in the form of comments, questions, and reactions to express feelings and to seek clarifications on the topic.

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