# Errors in Rational Number Operations: A Case of DEBESMSCAT Preservice Teachers

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<ul><li> 1. Errors in Rational Number Operations: A Case of Preservice Teachers Presented by: SHERWIN E. BALBUENA Dr. Emilio B. Espinosa Sr. Memorial State College of Agriculture and Technology (DEBESMSCAT), Masbate, Philippines </li> <li> 2. Contents Rationale Statement of the Problem Objectives Significance of the Study Methods Results and Discussions Conclusions Recommendations </li> <li> 3. Rationale Rational numbers fractions, mixed numbers, integers Rational numbers have different constructs (Behr, Lesh, Post, & Silver ,1983) Taught as early as Grade III Low mastery level of high school graduates, college entrants Preservice teachers understanding of fraction content knowledge is weak (Behr, Khoury, Harel, Post, & Lesh, 1997; Cramer, Post, & del Mas, 2002). </li> <li> 4. Rationale Preservice teachers find it difficult to conceptualize fractions (Ball, 1990) Can hardly explain fractions to children and why computation procedures work (Chinnappan, 2000) Cannot operate fractions correctly, even if they have chosen the correct answer (Becker & Lin, 2005). Future problems posed by this difficulty Diagnosis of procedural errors is imperative </li> <li> 5. Statement of the Problem DEBESMSCAT two teacher education programs Bachelor in Secondary Education (BSEd) Bachelor in Elementary Education (BEEd). Admission process Enrollees are required to pass the college entrance test and screenings to ensure that students are highly qualified to undergo teacher education trainings for four years. However, diversity implies that certain learning difficulties exist among entrants. This study is interested about the learning difficulties exhibited by preservice teachers in understanding rational numbers. </li> <li> 6. Objectives What is the level of performance of DEBESMSCAT preservice teachers in operating rational numbers? Which of the errors exhibited by preservice teachers in dealing with rational number operations are more prevalent? What are the implications for teaching and learning rational numbers? </li> <li> 7. Significance of the Study Information dissemination of results to the basic education teachers Diagnosis of the learning difficulties and research opportunities for tertiary educators Basis for enhancing preservice teachers procedural skills </li> <li> 8. Methods Participants 38 preservice teachers enrolled in their first of four-year BEEd program in DEBESMSCAT Sampling Systematic Random Sampling Profile of Participants 97% are younger than age 25 76% were female, 24% male 87% graduated from secondary schools in the 2nd district of Masbate </li> <li> 9. Methods Instrument Diagnostic pretest with 8 multiple-choice items on adding and multiplying rational numbers Item 1 for identifying errors in adding dissimilar and common fractions, Item 2 in adding dissimilar and uncommon fractions, Item 3 in adding a mixed number and a fraction which are similar and common, Item 4 in adding similar fractions, Item 5 in adding a mixed number and a fraction which are dissimilar and uncommon, Item 6 in multiplying common fractions, Item 7 in multiplying a whole number by a fraction, and Item 8 in multiplying a mixed number by a fraction which are common. </li> <li> 10. Methods Instrument (contd) Example of an item 1/2 + 3/4= A. 4/6 B. 2/3 C. 10/8 D. 5/4 Each distracter has some diagnostic designs to identify students error </li> <li> 11. Results and Discussions </li> <li> 12. Results and Discussions 0 10 20 30 40 50 60 70 80 90 1 2 3 4 5 6 7 8 Percentages of Occurences of Responses in the Item Choices A B C D D A A C B B C D </li> <li> 13. Results and Discussions Total % of errors > Total % of correct responses Only 21.05% of the participants obtained at least 4 marks (50%) Very low performance of the participants in operating rational numbers </li> <li> 14. Correct vs. Wrong Answers 0 10 20 30 40 50 60 70 80 90 1 2 3 4 5 6 7 8 Item Number Percentage of correct responses Percentage of the more prevalent wrong answer </li> <li> 15. More Prevalent Errors </li> <li> 16. Procedural Errors Item 1 Numerator plus numerator Denominator plus denominator Reducing to the lowest term </li> <li> 17. Procedural Errors Item 2 </li> <li> 18. Procedural Errors Item 5 Copying the whole part </li> <li> 19. Procedural Errors Item 8 Copying the whole part </li> <li> 20. Conclusions Preservice teachers knowledge of rational number operations is very weak More prevalent errors were observed in adding dissimilar fractions and in multiplying a mixed number by a fraction Preservice teachers tend to mix up memorized fraction rules Good at adding similar fractions and reducing answers to the lowest terms </li> <li> 21. Conclusions Lack of sufficient knowledge of equivalence of mixed numbers and improper fractions Confirms that preservice teachers procedural knowledge predominates over their conceptual knowledge (Forrester & Chinnappan, 2011) There is a need for students to gain mastery of the processes involved in performing operations on dissimilar fractions Preservice teachers are not ready to learn more advanced topics in mathematics </li> <li> 22. Recommendations Improve the quality of teaching and learning fractions in the elementary and secondary levels Enhance students retention and conceptual understanding of fractions Give preservice teachers more curative interventions and trainings in mathematics Further studies Limitations: Small number of participants Use of fixed questions Emphasis on the procedural knowledge </li> <li> 23. Thank you very much! Madamo nga salamat! </li> </ul>

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