Beliefs, Attitudes, and Practices of High School Teachers in Handling Students’ Errors: Implications for Error-Tolerant Mathematics Classrooms

Authors

  • Jemil R. Abay College of Education, Partido State University
  • Michael A. Clores Graduate School, Ateneo de Naga University

DOI:

https://doi.org/10.12928/ijeme.v6i2.23995

Keywords:

Attitudes, Attributes, Beliefs, Error-handling practices, Error-tolerant mathematics classrooms

Abstract

Proper handling of students’ errors in mathematics provides teaching and learning opportunities. Anchored in the Professional Error Competence Model developed by Wuttke and Siefried, this study investigated junior high school teachers’ beliefs, attitudes, and practices in handling students’ errors in their Mathematics class. The study employed a descriptive-correlational design and surveyed one hundred three Mathematics teachers from public secondary schools in Camarines Sur. A researcher-made survey questionnaire was used to gather the necessary data. All statistical analyses on the data collected, such as weighted mean, Pearson’s r, and Canonical Correlation Analysis were done using SPSS (version 21). The findings show that respondents frequently employed error detection, correction, and prevention strategies. It also demonstrates that both beliefs and attitudes correlated significantly with respondents’ error-handling practices. The study further reveals that the respondents’ attributes (age, sex, educational attainment, field of specialization, number of years in teaching mathematics, and seminars attended) contribute to their practices, beliefs, and attitudes in error handling. However, it is noted that as respondents grow older and gain more teaching experiences in Mathematics, certain error-handling practices, beliefs, and attitudes appear to diminish. It is therefore recommended that the frequency of error handling activities that facilitate learning should be increased further in a Mathematics class. School administrators should organize training programs that highlight the critical role of error handling in the learning process. They should also embark on benchmarking activities, mentoring, and coaching to expose teachers to error-handling strategies that promote an error-tolerant mathematics classroom where students have numerous opportunities to learn. Moreover, schools should provide students with opportunities to evaluate their teachers’ practices in handling errors. Finally, future researchers should perform actual observations on error handling practices to learn more about them in the classroom setting. They may also look into how teachers deal with errors in online education.

References

Ager, M. (2019). Senator sounds alarm on deteriorating competence of students, teachers. Philippine Daily Inquirer. https://newsinfo.inquirer.net/1092820/senator-sounds-alarm-on-deteriorating-competence-of-students-teachers

Anthony, G., & Walshaw, M. (2009). Effective Pedagogy in Mathematics. Educational Practices Series-19. UNESCO International Bureau of Education. http://www.ibe.unesco.org/fileadmin/user_upload/Publications/Educational_Practices/EdPractices_19.pdf

Baclig, C. E. (2020). PH’s Grade 4 students lowest in math, science around the world — int’l study. Philippine Daily Inquirer. https://newsinfo.inquirer.net/1370289/phs-grade-4-students-lowest-in-math-science-around-the-world-study

Bargiel-Matusiewicz, K., & Bargiel-Firlit, A. (2009). Correction Techniques Preferred by Students During the Process of Learning a Foreign Language. Psychology of Language and Communication, 13(1), 39–52. https://doi.org/10.2478/v10057-009-0003-8

Barlow, A. T., Watson, L. A., Tessema, A. A., Lischka, A. E., & Strayer, J. F. (2018). Inspection-Worthy Mistakes: Which? And Why?. Teaching Children Mathematics, 24(6), 384-391. https://eric.ed.gov/?id=EJ1174781

Barry, V. J. (2008). Using descriptive feedback in a sixth grade mathematics classroom. https://digitalcommons.unl.edu/mathmidactionresearch/9/

Bentley, B., & Bossé, M. J. (2018). College Students’ Understanding of Fraction Operations. International Electronic Journal of Mathematics Education, 13(3). https://doi.org/10.12973/iejme/3881

Bonney, E. A., Amoah, D. F., Micah, S. A., Ahiamenyo, C., & Lemaire, M. B. (2015). The Relationship between the Quality of Teachers and Pupils Academic Performance in the STMA Junior High Schools of the Western Region of Ghana. Journal of Education and practice, 6(24), 139-150. https://files.eric.ed.gov/fulltext/EJ1078818.pdf

Bray, W. S. (2011). A collective case study of the influence of teachers’ beliefs and knowledge on error-handling practices during class discussion of mathematics. Journal for Research in Mathematics education, 42(1), 2-38. http://jwilson.coe.uga.edu/EMAT7050/articles/Bray.pdf

Brown, J., & Skow, K. (2016). Mathematics: Identifying and addressing student errors. The Iris Center, 179-195.

Capuno, R., Necesario, R., Etcuban, J. O., Espina, R., Padillo, G., & Manguilimotan, R. (2019). Attitudes, Study Habits, and Academic Performance of Junior High School Students in Mathematics. International Electronic Journal of Mathematics Education, 14(3). https://doi.org/10.29333/iejme/5768

Chamundeswari, S. (2014). Conceptual Errors Encountered in Mathematical Operations in Algebra among Students at the Secondary Level. International Journal of Innovative Science, Engineering & Technology, 1(8), 24-38. https://www.ijiset.com/v1s8/IJISET_V1_I8_04.pdf

Damla Gedik, S., Cihan Konyalioglu, A., & Betul Tuncer, E. (2017). Mistake handling activities in mathematics education: Practice in Class. Journal of Education and Human Development, 6(1). https://doi.org/10.15640/jehd.v6n2a9

Dunham, S., Lee, E., & Persky, A. M. (2020). The Psychology of Following Instructions and Its Implications. American Journal of Pharmaceutical Education, 84(8), ajpe7779. https://doi.org/10.5688/ajpe7779

Elbrink, M. K. (2007). Analyzing and addressing common mathematical errors in secondary education: an honors thesis (HONRS 499). https://cardinalscholar.bsu.edu/handle/123456789/202334

Gagani, R.F.M & Diano Jr, F.M. (2019). Characterizing the difficulty in fraction operation. International Journal of Advanced Research and Publications, 3(6), 168-174. https://www.researchgate.net/profile/Ray-Ferdinand-Gagani/publication/340310516_Characterizing_The_Difficulty_In_Fraction_Operation/links/5ecd78f9458515294514661b/Characterizing-The-Difficulty-In-Fraction-Operation.pdf

Gardee, A., & Brodie, K. (2015). A teacher’s engagement with learner errors in her Grade 9 mathematics classroom. Pythagoras, 36(2). https://doi.org/10.4102/pythagoras.v36i2.293

Goldhaber, D., Wolff, M., & Daly, T. (2020). Assessing the Accuracy of Elementary School Test Scores as Predictors of Students’ High School Outcomes. https://caldercenter.org/sites/default/files/CALDER%20WP%20235-0520-2.pdf

Goldman, S. (2021). Can we stop calling them careless mistakes? Edutopia. https://www.edutopia.org/article/can-we-stop-calling-them-careless-mistakes

Hansen, A., Drews, D., Dudgeon, J., Lawon, F., & Surtees, L. (2020), Children’s errors in mathematics. Sage Publishing.

Heinze, A. (2005). Mistake-Handling Activities in the Mathematics Classroom. International Group for the Psychology of Mathematics Education, 3, 105-112. https://www.emis.de/proceedings/PME29/PME29RRPapers/PME29Vol3Heinze.pdf

Heinze, A., & Reiss, K. (2007). Mistake-handling activities in the mathematics classroom: Effects of an in-service teacher training on students’ performance in geometry. In Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 9-16). Seoul: PME. https://www.emis.de/proceedings/PME31/3/9.pdf

Jameel, H. T., & Ali, H. H. (2016). Causes of poor performance in mathematics from the perspective of students, teachers and parents. American Scientific Research Journal for Engineering, Technology, and Sciences, 15(1), 122-136. https://asrjetsjournal.org/index.php/American_Scientific_Journal/article/view/1212

Kavaliauskiene, G., & Anusiene, L. (2012). Case study: Learner attitudes towards the correction of mistakes. Social Technologies, 2(1), 88-101. https://ojs.mruni.eu/ojs/social-technologies/article/view/147

Khalid, M., & Embong, Z. (2019). Sources and Possible Causes of Errors and Misconceptions in Operations of Integers. International Electronic Journal of Mathematics Education, 15(2). https://doi.org/10.29333/iejme/6265

Lai, C. F. (2012). Error Analysis in Mathematics. Technical Report 1012. Behavioral Research and Teaching. https://files.eric.ed.gov/fulltext/ED572252.pdf

Lestiana, H. T., Rejeki, S., & Setyawan, F. (2017). Identifying Students’ Errors on Fractions. JRAMathEdu (Journal of Research and Advances in Mathematics Education), 1(2), 131–139. https://doi.org/10.23917/jramathedu.v1i2.3396

Lim, H. E., Min, J. H., Robles, Y. F. O., & Lapinid, M. R. C. (2019). The “Wrong Answer Note”: An Analysis of Students’ Mistakes. https://www.dlsu.edu.ph/wp-content/uploads/pdf/conferences/research-congress-proceedings/2019/lli-I-005.pdf

Maguire, T. (2012). Investigation of the misconceptions related to the concepts of equivalence and literal symbols held by underprepared community college students. University of San Francisco. https://repository.usfca.edu/diss/40/

Makhubele, Y., Nkhoma, P., & Luneta, K. (2015). Errors displayed by learners in the learning of grade 11 geometry. https://uir.unisa.ac.za/handle/10500/22450

Morallo, M., & Abay, J. (2019). Gaps on Quality Teaching: Assessing Teachers’ Needs Towards the Creation of a Framework for an Extension Program on Teachers’ Professional Development. IOER International Multidisciplinary Research Journal, 1(3), 28-36. https://www.ioer-imrj.com/wp-content/uploads/2019/10/Gaps-on-Quality-Teaching-AssessingTeachers%E2%80 %99-Needs-Mayumi-B.-Morallo-Jemil-R.-Abay.pdf

Noche, J. (2009). Systematic errors in arithmetic of some college students. Kamawotan, 3(1-2),74-86.

O’Dell, S. (2015). Classroom error climate: teacher professional development to improve student motivation. EdD Thesis. Orlando, FL, USA: University of Central Florida. https://stars.library.ucf.edu/etd/704/

Organization for Economic Co-operation and Development. (2009). Professional development of teachers. https://www.oecd.org/berlin/43541636.pdf

Rach, S., Ufer, S., & Heinze, A. (2013). Learning from errors: effects of teachers’ training on students’ attitudes towards and their individual use of errors. PNA, 8(1), 21–30. http://revistaseug.ugr.es/index.php/pna/article/viewFile/6122/5440

Rahman, F., Jumani, N. B., Akhter, Y., Chisthi, S. U. H., & Ajmal, M. (2011). Relationship between training of teachers and effectiveness teaching. International Journal of Business and Social Science, 2(4), 150-160. http://ijbssnet.com/journals/Vol._2_No._4%3B_March_2011/18.pdf

Rezapour, Y., & Taghipour, K. (2013). Effectiveness of simple to complex sequences and composition instructional strategies in learning and retention of concept of experimental science in secondary school. European Online Journal of Natural and Social Sciences, 2(2), 262-272. https://european-science.com/eojnss/article/view/161

Riccomini, P.J. (2016). How to use math error analysis to improve instruction. 1-24.

Rice, J. K. (2003). Teacher quality: Understanding the effectiveness of teacher attributes. Economic Policy Institute, 1660 L Street, NW, Suite 1200, Washington, DC.

Richardson, V. (1996). The role of attitudes and beliefs in learning to teach. Handbook of research on teacher education, 2(102-119), 273-290.

Rocane, M. (2015). The Significance of Teacher`s Beliefs in the Learning Process. Society, Integration, Education. Proceedings of the International Scientific Conference, 2, 165. https://doi.org/10.17770/sie2015vol2.452

Rushton, S. J. (2018). Teaching and learning mathematics through error analysis. Fields Mathematics Education Journal, 3(1), 4. https://doi.org/10.1186/s40928-018-0009-y

Sakinah Nuraini, N. L., Selfi Cholifah, P., & Cahyo Laksono, W. (2018). Mathematics Errors in Elementary School: A Meta-Synthesis Study. Proceedings of the 1st International Conference on Early Childhood and Primary Education (ECPE 2018). https://doi.org/10.2991/ecpe-18.2018.32

SEI-DOST & MATHTED (2011). Mathematics framework for philippine basic education. Manila: SEI-DOST & MATHTED. https://sei.dost.gov.ph/images/downloads/publ/sei_mathbasic.pdf

Shi, G. (2017). Attitudes towards Error Correction, Corrective Moves and Their Effects in College English Classrooms in China. International Journal for Innovation Education and Research, 5(2), 32–39. https://doi.org/10.31686/ijier.vol5.iss2.498

Suleiman, Y., & Hammed, A. (2019). Perceived causes of students’ failure in mathematics in Kwara State Junior Secondary Schools: Implication for educational managers. International Journal of Educational Studies in Mathematics, 6(1), 19-33. https://dergipark.org.tr/tr/pub/ijesim/issue/43715/523993

Voss, T., Kleickmann, T., Kunter, M., & Hachfeld, A. (2013). Mathematics teachers’ beliefs. In Cognitive activation in the mathematics classroom and professional competence of teachers (pp. 249-271). Springer, Boston, MA. https://www.researchgate.net/publication/283996415_Mathematics_Teachers’_Beliefs

Watts, T. W., Duncan, G. J., Clements, D. H., & Sarama, J. (2018). What Is the Long-Run Impact of Learning Mathematics During Preschool? Child Development, 89(2), 539–555. https://doi.org/10.1111/cdev.12713

Watts, T. W., Duncan, G. J., Siegler, R. S., & Davis-Kean, P. E. (2014). What’s Past Is Prologue. Educational Researcher, 43(7), 352–360. https://doi.org/10.3102/0013189X14553660

Wiens, A. (2007). An investigation into careless errors made by 7th grade mathematics students.https://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1036&context=mathmidsummative

Wilmot, E. M., & Otchey, J. E. (2012). The contribution of attitudes of students and teachers to junior high school students’ achievement in mathematics. African Journal of Educational Studies in Mathematics and Sciences, 10, 55-63.https://www.ajol.info/index.php/ajesms/article/view/91956/81415

Wuttke, E., & Seifried, J. (Eds.). (2017). Professional error competence of preservice teachers: evaluation and support. Springer.

Yadav, S. (2019). Role of Mathematics in the Development of Society. IJRAR-International Journal of Research and Analytical Reviews (IJRAR), 6(4), 295-298. https://ijrar.org/papers/IJRAR19S1037.pdf

Yetkin, E. (2003). Student Difficulties in Learning Elementary Mathematics. ERIC Digest. https://eric.ed.gov/?id=ED482727

Zhu, H. (2010). An Analysis of College Students’ Attitudes towards Error Correction in EFL Context. English Language Teaching, 3(4). https://doi.org/10.5539/elt.v3n4p127

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Published

2022-10-31

How to Cite

Abay, J. R., & Clores, M. A. (2022). Beliefs, Attitudes, and Practices of High School Teachers in Handling Students’ Errors: Implications for Error-Tolerant Mathematics Classrooms. International Journal on Emerging Mathematics Education, 6(2), 101–118. https://doi.org/10.12928/ijeme.v6i2.23995