Level of achievement in algebra of grade seven learners
Keywords:
algebraic expression, inequalities, equation, problem solving, error interpretation, simplification, achievement levelAbstract
Utilizing a descriptive research design, this study determined the level of achievement and the common errors in algebra of grade 7 leaners. The respondents consisted of 109 grade 7 Science, Technology and Engineering learners of Leyte National High School in Tacloban City Division in the school year 2018-2019. The findings of this study revealed that the level of achievement of the respondents in the concept of algebraic expressions, specifically under basic knowledge and simplification, did not meet the expectation. In the concept of equations, their achievement level under basic knowledge and manipulation also did not meet the expectation. As to the concept of inequalities, the respondents have a fairly satisfactory achievement level under basic, but their achievement level under manipulation did not meet the expectation. In problem solving, the respondents have a satisfactory achievement level under basic knowledge, but their achievement level under interpretation did not meet the expectation. Errors in basic knowledge are very high under algebraic expressions and equations, high under inequalities, and average under problem solving. Errors in simplification are very high under algebraic expressions. Errors in manipulation are also very high under equations and inequalities. Errors in interpretation are likewise very high in problem solving. It is concluded that the respondents lack mastery of fundamental concepts of algebra in algebraic expressions, inequalities, equations, and problem solving. Conclusively, they have insufficient knowledge and understanding along these concepts. Two or more error types may be observed under any of the abovementioned algebraic concepts. As much as possible, the leaners should be provided with regular feedback on how they perform in algebra because if ignored and left not corrected, there is high tendency for leaners to have difficulty developing conceptual understanding of algebra as well as difficulty learning higher mathematics subjects, particularly when they move up to university level.
References
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Abocejo, F. T., & Padua, R. N. (2010). An econometric model for determining sustainability of basic education development. CNU Journal of Higher Education. 4(1), 40-53. Retrieved from http://www.jhe.cnu.edu.ph/index.php/cnujhe/article/view/39
Adu, E., Assuah, C. K., & Asiedu-Addo, S. K. (2015). Students’ errors in solving linear equation word problems: case study of a Ghanaian senior high school. African Journal of Educational Studies in Mathematics and Sciences, 11, 17-30. Retrieved from https://www.ajol.info/index.php/ajesms/article/view/168996/158459
Barbieri, C., & Booth, J. L. (2016). Support for struggling students in algebra: Contributions of incorrect worked examples. Learning and Individual Differences, 48, 36–44. https://doi.org/10.1016/j.lindif.2016.04.001
Booth, J. L., McGinn, K. M., Barbieri, C., & Young, L. K. (2016). Misconceptions and learning algebra. And the Rest Is Just Algebra, 63–78. https://doi.org/10.1007/978-3-319-45053-7_4
Calmorin, L. (2004). Measurement and Evaluation (3rd Ed.). Mandaluyong City, Philippines: National Book Store.
Cuñado, A. G., & Abocejo, F. T. (2018). Lesson planning competency of English major university sophomore students. European Journal of Education Studies. 5(8), 395-409. http://dx.doi.org/10.5281/zenodo.2538422
Capate, R. & Lapinid, M. (2015). Assessing the mathematics performance of grade 8 students as basis for enhancing instruction and aligning with k to 12 curriculum. Paper presented at the De La Salle University Research Congress, Manila, Philippines.
Dela Cruz, J. K. B., & Lapinid, M. R. C. (2014, March 6-8). Students’ difficulties in translating worded problems into mathematical symbols. Paper presented at the De La Salle University Research Congress, Manila, Philippines. Retrieved from http://www.dlsu.edu. ph/conferences/dlsu_research_congress/2014/_pdf/proceedings/LLI-I-009-FT.pdf
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Egodawatte, G. & Stoilescu, D. (2015). Grade 11 students’ interconnected use of conceptual knowledge, procedural skills, and strategic competence in algebra: a mixed method study of error analysis. European Journal of Science and Mathematics Education, 3(3), 289-305. Retrieved from https://files.eric.ed.gov/fulltext/EJ1107752.pdf
Elia, I., Özel, S., Gagatsis, A., Panaoura, A., & Özel, Z. E. Y. (2016). Students’ mathematical work on absolute value: focusing on conceptions, errors and obstacles. ZDM, 48(6), 895–907. https://doi.org/10.1007/s11858-016-0780-1
El-khateeb, M. M. A. (2016). Errors analysis of solving linear inequalities among the preparatory year students at King Saud University. Journal of Education and Practice, 7(12), 124-133. Retrieved from https://files.eric.ed.gov/fulltext/EJ1099654.pdf
Erabadda, B., Ranathunga, S., & Dias, G. (2017). Automatic identification of errors in multi-step answers to algebra questions. 2017 IEEE 17th International Conference on Advanced Learning Technologies (ICALT). https://doi.org/10.1109/icalt.2017.66
Fernandez, R. C. C., & Abocejo, F. T. (2014). Child labor, poverty and school attendance: Evidences from the Philippines by region. CNU Journal of Higher Education. 8(1), 114-127. Retrieved from http://www.jhe.cnu.edu.ph/index.php/cnujhe/article/view/151
Hadi, S., Retnawati, H., Munadi, S., Apino, E., & Wulandari, N. F. (2018). The difficulties of high school students in solving higher-order thinking skills problems. Problems of Education in the 21st Century, 76(4), 520-532. Retrieved from http://www.scientiasocialis.it/ pec/node/files/pdf/vol76/520-532.Hadi_Vol.76-4_PEC.pdf
Guner, P. (2017). High school students’ achievement of solving quadratic equations. Bartin University Journal of Faculty of Education, 6(2), 447-467. https://doi.org/10.14686/buefad.277494
Jolejole-Caube, C., Dumlao, A. B., & Abocejo, F. T. (2019). Anxiety Towards Mathematics and Mathematics Performance of Grade 7 Learners. European Journal of Education Studies. 6(1), 334-360 http://dx.doi.org/10.5281/zenodo.2694050
Jupri, A. (2016). Student difficulties in mathematizing word problems in algebra. Eurasia Journal of Mathematics, Science & Technology Education, 12(9), 2481-2502. https://doi.org/10.12973/eurasia.2016.1299a
Makonye, J. P., & Khanyile, D. W. (2015). Probing grade 10 students about their mathematical errors on simplifying algebraic fractions. Research in Education, 94(1), 55–70. https://doi.org/10.7227/rie.0022
Mangulabnan, P. A. T. M. (2013). Assessing translation misconceptions inside the classroom: A presentation of an instrument and its result. US-China Education Review A, 3(6), 365–373. Retrieved from https://files.eric.ed.gov/fulltext/ED543811.pdf
McGowen, M. (2016). Examining the role of prior experience in the learning of algebra. And the Rest is Just Algebra, 19–39. https://doi.org/10.1007/978-3-319-45053-7_2
Molina, M., RodrÃguez-Domingo, S., Cañadas, M. C., & Castro, E. (2016). Secondary school students’ errors in the translation of algebraic statements. International Journal of Science and Mathematics Education, 15(6), 1137–1156. https://doi.org/10.1007/s10763-016-9739-5
Mulungye, M. M., O’Connor, M., & Ndethiu, S. (2016). Sources of student errors and misconceptions in algebra and effectiveness of classroom practice remediation in Machakos County- Kenya. Journal of Education and Practice, 7(10), 31-33. Retrieved from https://files.eric.ed.gov/fulltext/EJ1099568.pdf
Naseer, M. S. (2015, September). Analysis of Students’ Errors and Misconceptions in pre-University Mathematics Courses. In M. N. Salleh, & N. F. Z. Abedin, (Eds.), Proceedings: First International Conference on Teaching & Learning 2015 (p. 34-39). Langkawi, Malaysia: MNNF Publisher. Retrieved from https://umexpert.um.edu.my/file/publication/ 00007485_126625.pdf#page=37
Nataraj, M. S., & Thomas, M. (2016). Teaching and learning middle school algebra: valuable lessons from the history of mathematics. And the Rest is Just Algebra, 131–154. https://doi.org/10.1007/978-3-319-45053-7_8
National Council of Teachers of Mathematics (2006). Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence. Association Drive, Reston, VA.
National Council of Teachers of Mathematics (2009). Focus in high school mathematics: reasoning and sense making. Association Drive, Reston, VA.
Nurhayati, D. M., Herman, T., & Suhendra, S. (2017). Analysis of secondary school students’ algebraic thinking and math-talk learning community to help students learn. Journal of Physics: Conference Series, 895, 012054. https://doi.org/10.1088/1742-6596/895/1/012054
Oronce, O. & Mendoza, M. (2010). e-math elementary algebra. Sampaloc, Manila: Rex Book Store, Inc.
Pournara, C., Hodgen, J., Sanders, Y., & Adler, J. (2016). Learners’ errors in secondary algebra: insights from tracking a cohort from grade 9 to grade 11 on a diagnostic algebra test. Pythagoras, 37(1), 1-10. https://doi.org/10.4102/pythagoras.v37i1.334
Ricks, D. D. (2013). Lost in translation: algebraic modelling in the middle school classroom (Master’s thesis, Louisiana State University and Agricultural and Mechanical College, United States of America). Retrieved from https://digitalcommons.lsu.edu/grad school_theses/1501
Rodriguez, K. F. R., & Abocejo, F. T. (2018). Competence vis-Ã -vis performance of special education pre-service teachers. European Academic Research. 6(7), 3474-3498. Retrieved from http://www.euacademic.org/UploadArticle/3707.pdf
Sari, D.P., Darhim, & Rosjanuardi, R. (2018). Errors of students learning with REACT strategy in solving the problems of mathematical representation ability. Journal on Mathematics Education, 9(1), 121-128. Retrieved from https://files.eric.ed.gov/fulltext/EJ1173659.pdf
Tong, D. H. & Loc, N. P. (2017). Students’ errors in solving mathematical word problems and their ability in identifying errors in wrong solutions. European Journal of Education Studies, 3(6), 226-241. https://doi.org/10.5281/zenodo.581482
Trazo, S. P., & Abocejo, F. T. (2019). International phonetic alphabet (IPA) front vowel sound recognition of beginner foreign learners. European Journal of Education Studies. 5(12), 183-196 http://dx.doi.org/10.5281/zenodo.2606194
Trance, N. J. C. (2013). Process inquiry: Analysis of oral problem-solving skills in mathematics of engineering students. US-China Education Review A, 3(2), 73–82. Retrieved from https://files.eric.ed.gov/fulltext/ED540490.pdf
Yahya, N., & Shahrill, M. (2015). The strategies used in solving algebra by secondary school repeating students. Procedia - Social and Behavioral Sciences, 186, 1192–1200. https://doi.org/10.1016/j.sbspro.2015.04.168
Yayen, C. P. (2018). Effectiveness of Marungko approach on the English reading performance and comprehension skills of first grade Thai learners. Asian Journal of Governance and Education, 1(1), 61-74. Retrieved from https://journal.evsu.edu.ph/index.php/ajge/article/view/141/24
Abocejo, F. T. (2017). The impact of international monetary fund (IMF) structural adjustment program policies (SAPs) on the Philippines. Recoletos Multidisciplinary Research Journal. 2(1), 19-28. Retrieved from https://rmrj.usjr.edu.ph/index.php/RMRJ/article/ view/48
Abocejo, F. T., & Padua, R. N. (2010). An econometric model for determining sustainability of basic education development. CNU Journal of Higher Education. 4(1), 40-53. Retrieved from http://www.jhe.cnu.edu.ph/index.php/cnujhe/article/view/39
Adu, E., Assuah, C. K., & Asiedu-Addo, S. K. (2015). Students’ errors in solving linear equation word problems: case study of a Ghanaian senior high school. African Journal of Educational Studies in Mathematics and Sciences, 11, 17-30. Retrieved from https://www.ajol.info/index.php/ajesms/article/view/168996/158459
Barbieri, C., & Booth, J. L. (2016). Support for struggling students in algebra: Contributions of incorrect worked examples. Learning and Individual Differences, 48, 36–44. https://doi.org/10.1016/j.lindif.2016.04.001
Booth, J. L., McGinn, K. M., Barbieri, C., & Young, L. K. (2016). Misconceptions and learning algebra. And the Rest Is Just Algebra, 63–78. https://doi.org/10.1007/978-3-319-45053-7_4
Calmorin, L. (2004). Measurement and Evaluation (3rd Ed.). Mandaluyong City, Philippines: National Book Store.
Cuñado, A. G., & Abocejo, F. T. (2018). Lesson planning competency of English major university sophomore students. European Journal of Education Studies. 5(8), 395-409. http://dx.doi.org/10.5281/zenodo.2538422
Capate, R. & Lapinid, M. (2015). Assessing the mathematics performance of grade 8 students as basis for enhancing instruction and aligning with k to 12 curriculum. Paper presented at the De La Salle University Research Congress, Manila, Philippines.
Dela Cruz, J. K. B., & Lapinid, M. R. C. (2014, March 6-8). Students’ difficulties in translating worded problems into mathematical symbols. Paper presented at the De La Salle University Research Congress, Manila, Philippines. Retrieved from http://www.dlsu.edu. ph/conferences/dlsu_research_congress/2014/_pdf/proceedings/LLI-I-009-FT.pdf
Department of Education. (2010). Discussion paper on the enhanced K to 12 education program. Pasig City: CEAP.
Department of Education (2014). Mathematics learner’s material 7. Pasig City, Philippines: FEP Printing Corporation.
Department of Education (2014). Mathematics learner’s material 9. Pasig City, Philippines: Vibal Group, Inc.
Egodawatte, G. & Stoilescu, D. (2015). Grade 11 students’ interconnected use of conceptual knowledge, procedural skills, and strategic competence in algebra: a mixed method study of error analysis. European Journal of Science and Mathematics Education, 3(3), 289-305. Retrieved from https://files.eric.ed.gov/fulltext/EJ1107752.pdf
Elia, I., Özel, S., Gagatsis, A., Panaoura, A., & Özel, Z. E. Y. (2016). Students’ mathematical work on absolute value: focusing on conceptions, errors and obstacles. ZDM, 48(6), 895–907. https://doi.org/10.1007/s11858-016-0780-1
El-khateeb, M. M. A. (2016). Errors analysis of solving linear inequalities among the preparatory year students at King Saud University. Journal of Education and Practice, 7(12), 124-133. Retrieved from https://files.eric.ed.gov/fulltext/EJ1099654.pdf
Erabadda, B., Ranathunga, S., & Dias, G. (2017). Automatic identification of errors in multi-step answers to algebra questions. 2017 IEEE 17th International Conference on Advanced Learning Technologies (ICALT). https://doi.org/10.1109/icalt.2017.66
Fernandez, R. C. C., & Abocejo, F. T. (2014). Child labor, poverty and school attendance: Evidences from the Philippines by region. CNU Journal of Higher Education. 8(1), 114-127. Retrieved from http://www.jhe.cnu.edu.ph/index.php/cnujhe/article/view/151
Hadi, S., Retnawati, H., Munadi, S., Apino, E., & Wulandari, N. F. (2018). The difficulties of high school students in solving higher-order thinking skills problems. Problems of Education in the 21st Century, 76(4), 520-532. Retrieved from http://www.scientiasocialis.it/ pec/node/files/pdf/vol76/520-532.Hadi_Vol.76-4_PEC.pdf
Guner, P. (2017). High school students’ achievement of solving quadratic equations. Bartin University Journal of Faculty of Education, 6(2), 447-467. https://doi.org/10.14686/buefad.277494
Jolejole-Caube, C., Dumlao, A. B., & Abocejo, F. T. (2019). Anxiety Towards Mathematics and Mathematics Performance of Grade 7 Learners. European Journal of Education Studies. 6(1), 334-360 http://dx.doi.org/10.5281/zenodo.2694050
Jupri, A. (2016). Student difficulties in mathematizing word problems in algebra. Eurasia Journal of Mathematics, Science & Technology Education, 12(9), 2481-2502. https://doi.org/10.12973/eurasia.2016.1299a
Makonye, J. P., & Khanyile, D. W. (2015). Probing grade 10 students about their mathematical errors on simplifying algebraic fractions. Research in Education, 94(1), 55–70. https://doi.org/10.7227/rie.0022
Mangulabnan, P. A. T. M. (2013). Assessing translation misconceptions inside the classroom: A presentation of an instrument and its result. US-China Education Review A, 3(6), 365–373. Retrieved from https://files.eric.ed.gov/fulltext/ED543811.pdf
McGowen, M. (2016). Examining the role of prior experience in the learning of algebra. And the Rest is Just Algebra, 19–39. https://doi.org/10.1007/978-3-319-45053-7_2
Molina, M., RodrÃguez-Domingo, S., Cañadas, M. C., & Castro, E. (2016). Secondary school students’ errors in the translation of algebraic statements. International Journal of Science and Mathematics Education, 15(6), 1137–1156. https://doi.org/10.1007/s10763-016-9739-5
Mulungye, M. M., O’Connor, M., & Ndethiu, S. (2016). Sources of student errors and misconceptions in algebra and effectiveness of classroom practice remediation in Machakos County- Kenya. Journal of Education and Practice, 7(10), 31-33. Retrieved from https://files.eric.ed.gov/fulltext/EJ1099568.pdf
Naseer, M. S. (2015, September). Analysis of Students’ Errors and Misconceptions in pre-University Mathematics Courses. In M. N. Salleh, & N. F. Z. Abedin, (Eds.), Proceedings: First International Conference on Teaching & Learning 2015 (p. 34-39). Langkawi, Malaysia: MNNF Publisher. Retrieved from https://umexpert.um.edu.my/file/publication/ 00007485_126625.pdf#page=37
Nataraj, M. S., & Thomas, M. (2016). Teaching and learning middle school algebra: valuable lessons from the history of mathematics. And the Rest is Just Algebra, 131–154. https://doi.org/10.1007/978-3-319-45053-7_8
National Council of Teachers of Mathematics (2006). Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence. Association Drive, Reston, VA.
National Council of Teachers of Mathematics (2009). Focus in high school mathematics: reasoning and sense making. Association Drive, Reston, VA.
Nurhayati, D. M., Herman, T., & Suhendra, S. (2017). Analysis of secondary school students’ algebraic thinking and math-talk learning community to help students learn. Journal of Physics: Conference Series, 895, 012054. https://doi.org/10.1088/1742-6596/895/1/012054
Oronce, O. & Mendoza, M. (2010). e-math elementary algebra. Sampaloc, Manila: Rex Book Store, Inc.
Pournara, C., Hodgen, J., Sanders, Y., & Adler, J. (2016). Learners’ errors in secondary algebra: insights from tracking a cohort from grade 9 to grade 11 on a diagnostic algebra test. Pythagoras, 37(1), 1-10. https://doi.org/10.4102/pythagoras.v37i1.334
Ricks, D. D. (2013). Lost in translation: algebraic modelling in the middle school classroom (Master’s thesis, Louisiana State University and Agricultural and Mechanical College, United States of America). Retrieved from https://digitalcommons.lsu.edu/grad school_theses/1501
Rodriguez, K. F. R., & Abocejo, F. T. (2018). Competence vis-Ã -vis performance of special education pre-service teachers. European Academic Research. 6(7), 3474-3498. Retrieved from http://www.euacademic.org/UploadArticle/3707.pdf
Sari, D.P., Darhim, & Rosjanuardi, R. (2018). Errors of students learning with REACT strategy in solving the problems of mathematical representation ability. Journal on Mathematics Education, 9(1), 121-128. Retrieved from https://files.eric.ed.gov/fulltext/EJ1173659.pdf
Tong, D. H. & Loc, N. P. (2017). Students’ errors in solving mathematical word problems and their ability in identifying errors in wrong solutions. European Journal of Education Studies, 3(6), 226-241. https://doi.org/10.5281/zenodo.581482
Trazo, S. P., & Abocejo, F. T. (2019). International phonetic alphabet (IPA) front vowel sound recognition of beginner foreign learners. European Journal of Education Studies. 5(12), 183-196 http://dx.doi.org/10.5281/zenodo.2606194
Trance, N. J. C. (2013). Process inquiry: Analysis of oral problem-solving skills in mathematics of engineering students. US-China Education Review A, 3(2), 73–82. Retrieved from https://files.eric.ed.gov/fulltext/ED540490.pdf
Yahya, N., & Shahrill, M. (2015). The strategies used in solving algebra by secondary school repeating students. Procedia - Social and Behavioral Sciences, 186, 1192–1200. https://doi.org/10.1016/j.sbspro.2015.04.168
Yayen, C. P. (2018). Effectiveness of Marungko approach on the English reading performance and comprehension skills of first grade Thai learners. Asian Journal of Governance and Education, 1(1), 61-74. Retrieved from https://journal.evsu.edu.ph/index.php/ajge/article/view/141/24
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2019-06-01
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