Home / Regular Issue / JSSH Vol. 30 (3) Sep. 2022 / JSSH-8442-2021

 

Assessing Lower Secondary School Students’ Common Errors in Statistics

Lim Hooi Lian, Wun Thiam Yew and Chew Cheng Meng

Pertanika Journal of Social Science and Humanities, Volume 30, Issue 3, September 2022

DOI: https://doi.org/10.47836/pjssh.30.3.26

Keywords: Common error, lower secondary school, statistics, superitem task

Published on: 6 September 2022

Statistical literacy has been emphasised in the school mathematics curriculum, with the growing concern about students’ ability to think critically in solving statistical problem-solving tasks. However, the current studies revealed that secondary school students’ errors mainly involve the problem of basic concepts in statistics, data interpretation, and the selection of an appropriate representation of data. Therefore, this study aimed to analyse the common errors made by students in solving statistics tasks with multi-level complexity. A survey method was applied in this study. The sample of this study consisted of 356 Form One (Grade 7) students from eight secondary schools. The instrument of this study consisted of five superitem tasks, which represented the five content domains: line graph, bar graph, pie chart, dot plot, and histogram. There are four levels of items in each superitem task. Thus, the total number of items is 20. The format of all the 20 items in the five superitem tasks is open-ended. The common errors were then analysed based on all the participants’ solutions shown in their answer script. The findings found that most students could not achieve the highest level of statistical competency. They failed to think qualitatively while justifying data. This study provides a meaningful analysis that assists the teaching and learning of statistics to better link numeracy and literacy. The application of the superitem tasks provides valuable information that enables the teachers to understand their students’ statistical processes better.

  • Angateeah, K. S. (2017). An Investigation on students’ difficulties in solving non-routine word problem at lower secondary. International Journal of Learning and Teaching, 3(1), 46-50.

  • Biggs, J. B., & Collis, K. F. (1982). Evaluating the quality of learning: The SOLO taxonomy (Structure of the Observed Learning Outcome). Academic Press.

  • Bragdon, D., Pandiscio, E., & Speer, N. (2019). University students’ graph interpretation and comprehension abilities. Investigations in Mathematics Learning, 11(4), 275-290. https://doi.org/10.1080/19477503.2018.1480862

  • Capraro, M. M., Kulm, G., & Capraro, R. M. (2005). Middle grades: Misconceptions in statistical thinking. School Science and Mathematics, 105(4), 165-174. https://doi.org/10.1111/j.1949-8594.2005.tb18156.x

  • Chan, S. W., Ismail, Z., & Sumintono, B. (2016). A framework for assessing high school students’ statistical reasoning. PLoS ONE, 11, e0163846. https://doi.org/10.1371/journal.pone.0163846

  • Chin, S. F., & Lim H. L. (2018). The effect of computerized feedback on students’ misconceptions in algebraic expression. Pertanika Journal of Social Sciences & Humanities, 26(3), 1387-1403.

  • Craik, F. I. M., & Lockhart, R. S. (1972). Levels of processing: A framework for memory research. memory, attention, and aging: Selected works of Fergus I. M. Craik. Routledge. https://doi.org/10.4324/9781315440446

  • Erna, H. W., & Budi, M. (2016, March 12). Kesalahan siswa SMP dalam menyelesaikan soal matemaika berbasis PISA pada konten changer and relationship [Middle school students’ mistakes in solving PISA-based math problems on content changers and relationships]. Prosiding Konferensi Nasional Penelitian Matematika dan Pembelajaran, Universitas Muhammadiyah Surakarta, Indonesia.

  • Fitriani, H. N., Turmudi, T., & Prabawanto, S. (2018, December 1). Analysis of students’ error in mathematical problem solving based on Newman’s error analysis. Proceeding of International Conference on Mathematics and Science Education, Universitas Pendidikan Indonesia, Indonesia.

  • Fitriyah, I. M., Lilin, E. P., RofiQoh, S., Nikmarocha, & Aning, W. Y. (2020). Analisis kesalahan siswa dalam menyelesaikan soal cerita koordinat cartesius menurut teori kastolan [Analysis of students’ errors in solving the Cartesian coordinate story problem according to the Kastolan theory]. Al-Khwarizmi: Jurnal Pendidikan Matematika dan Ilmu Pengetahuan Alam, 8(2), 109-122. http://dx.doi.org/10.24256/jpmipa.v8i2.1002

  • Foo, K. K. (2017). Modelling the relationship between the statistical achievement and cognitive determinants among Malaysian diploma students [Unplished Ph.D.’s thesis]. University of Malaya.

  • Friel, S. N., Curcio, F. R., & Bright, G. W. (2001). Making sense of graphs: Critical factors influencing comprehension and instructional implications. Journal for Research in Mathematics Education, 32(2), 124-158.

  • García-García, J., & Dolores-Flores, C. (2021).Pre-university students’ mathematical connections when sketching the graph of derivative and antiderivative functions. Math Education Research Journal, 33, 1-22. https://doi.org/10.1007/s13394-019-00286-x

  • Graham, M., Milanowski, A., & Miller, J. (2012). Measuring and promoting inter-rater agreement of teacher and principal performance ratings. Center for Educator Compensation and Reform.

  • Haryanti, M. D., Herman, T., & Prabawanto, s. (2019). Analysis of students’ error in solving mathematical word problems in geometry. Journal of Physics: Conference Series, 1157, 042084. https://doi.org/10.1088/1742-6596/1157/4/042084

  • Hattie, J., & Brown, G. T. L. (2004). Cognitive processes in asTTle: The SOLO taxonomy (asTTle Technical Report #43). University of Auckland/Ministry of Education. https://dokumen.tips/documents/assessment-tools-for-teaching-and-learning-technical-report-43-.html?page=1

  • Huan, Z. C., & Melissa, N. L. Y. A. (2018). Validity and reliability of the mathematics self-efficacy questionnaire (MSEQ) on primary school students. Pertanika Journal of Social Sciences & Humanities, 26(4), 2161-2177.

  • Khalo, X., & Bayaga, A. (2015). Analysis of errors due to deficient mastery of prerequisite skills, facts and concepts: A case of financial mathematics. The Journal of Teaching and Learning, 10, 98-113.

  • Ibnatul, J. f., Adibah, A. L., & Hawa, S. S. (2021).Assessing statistical literacy level of postgraduate education research students in Malaysian research universities. Turkish Journal of Computer and Mathematics Education, 12(5), 1318-1324.

  • Idehen, F. O. (2020). Assessing Nigerian secondary school students’ misconceptions in five basic statistical concepts. Contemporary Mathematics and Science Education, 1(1), 1-6. https://doi.org/10.30935/conmaths/8448

  • Ishaku, A., & Idris, M. (2017). Analysis of perceived difficult topics by primary school mathematics teachers and pupils in Dutsin-Ma, Katsina State. Abacus, Journal of the Mathematical Association of Nigeria (MAN), 42(1), 164-177. https://www.mannigeria.org.ng/abstract?sid=ABA-EDU-2017-1-17

  • Lynch, E. B., Coley, J. D., & Medin, D. L. (2000). Tall is typical: Central tendency, ideal dimensions, and graded category structure among tree experts and novices. Memory and Cognition, 28(1), 41-50.

  • Kementerian Pendidikan Malaysia. (2015). Kurikulum Standard Sekolah Menengah Matematik – Dokumen Standard Kurikulum dan Pentaksiran – Tingkatan 1 [Mathematics Secondary School Standard Curriculum - Standard Curriculum and Assessment Document - Form 1]. http://bpk.moe.gov.my/index.php/terbitan-bpk/kurikulum-sekolah-menengah/category/16-dskp-tingkatan-1?download=1751:dskp-kssm-tingkatan-1-matematik

  • Kementerian Pendidikan Malaysia. (2016). Kurikulum Standard Sekolah Menengah Matematik – Dokumen Standard Kurikulum dan Pentaksiran – Tingkatan 2 [Mathematics Secondary School Standard Curriculum - Standard Curriculum and Assessment Document - Form 2]. http://bpk.moe.gov.my/index.php/terbitan-bpk/kurikulum-sekolah-menengah/category/43-dskp-tingkatan-2?download=2265:dskp-kssm-tingkatan-2-matematik

  • Nasser, S. N. A., & Lian, L. H. (2021). Development and validation of year five geometrical measurement skills instrument. International Journal of Evaluation and Research in Education, 10(3), 956-965.

  • National Council of Teachers of Mathematics. (2020). Catalysing change in middle school mathematics: Initiating critical conversations. National Council of Teachers of Mathematics.

  • Newman, M. A. (1983). Strategies for diagnosis and remediation. Brace Jovanovich.

  • Ozmen, Z. M., Guven, B., & Kurak, Y. (2020).Determining the graphical literacy levels of the 8th grade students. Eurasian Journal of Educational Research, 86, 269-292.

  • Polit, D. F., Beck, T., & Owen, S. V. (2007). Focus on research methods: Is the CVI an acceptable indicator of content validity. Research in Nursing and Health, 30(4), 459-467.

  • Reaburn, R. (2011). Students’ understanding of statistical inference: Implications for teaching [Doctoral thesis, University of Tasmania, Australia]. https://iase-web.org/documents/ dissertations/11.RobynReaburn.Dissertation.pdf

  • Saidi, S. S., & Siew, N. M. (2019). Assessing students’ understanding of the measures of central tendency and attitude towards statistics in rural secondary schools. International Electronic Journal of Mathematics Education, 14(1), 73-86. https://doi.org/10.12973/iejme/3968

  • Sari, D. R., & Bernard, M. (2020). Analisis kesalahan siswa SMP dalam menyelesaikan soal materi statistika di Bandung Barat [Analysis of junior high school students’ errors in solving statistical problems in West Bandung]. Journal of Mathematics Education IKIP Veteran Semarang, 4(2), 223-232.https://doi.org/10.31331/medivesveteran.v4i2.1060

  • Stemler, S. E., & Tsai, J. (2008). Best practices in interrater reliability: Three common approaches. In J. W. Osborne (Ed.), Best practices in quantitative methods (pp. 29-49). Sage Publication.

  • Smith, T. W., & Colby, S. A. (2007). Teaching for deep learning. The clearing house. A Journal of Educational Strategies, Issues and Ideas, 80(5), 205-210. https://doi.org/10.3200/TCHS.80.5.205-210

  • Thong-oon, M., Maitree, I., & Narumon, C. (2021). Cognitive aspects of students’ mathematical reasoning habits: A study on utilising lesson study and open approach. Pertanika Journal of Social Sciences & Humanities, 29(4), 2591-2614.

  • Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2014). Elementary and middle school mathematics: Teaching developmentally (8th ed.). Pearson.

  • Watson, J. M. (2006). Statistical literacy at school: Growth and goals. Lawrence Erlbaum Associates.

  • Wijaya, A., Panhuizen, M. V. D. H., Doorman, M., & Robitzsch, A. (2014).Difficulties in solving context-based PISA mathematics tasks: An analysis of students’ errors. The Mathematics Enthusiast, 11(3), 555-584.

  • Yayla, G., & Ozsevgec, T. (2015). Ortaokul öğrencilerinin grafik becerilerinin incelenmesi: Çizgi grafikleri oluşturma ve yorumlama [The examination of secondary school students’ graphic skills: Construction and interpretation of line graphs]. Kastamonu Üniversitesi Kastamonu Eğitim Dergisi, 23(3), 1381-1400.

  • Yun, H. J., Ko, E.-S., & Yoo, Y. J. (2016). Students’ misconceptions and mistakes related to measurement in statistical investigation and graphical representation of data. In D. Ben-Zvi & K. Makar (Eds.), The teaching and learning statistics (pp.119-120). Springer.

  • Angateeah, K. S. (2017). An Investigation on students’ difficulties in solving non-routine word problem at lower secondary. International Journal of Learning and Teaching, 3(1), 46-50.

  • Biggs, J. B., & Collis, K. F. (1982). Evaluating the quality of learning: The SOLO taxonomy (Structure of the Observed Learning Outcome). Academic Press.

  • Bragdon, D., Pandiscio, E., & Speer, N. (2019). University students’ graph interpretation and comprehension abilities. Investigations in Mathematics Learning, 11(4), 275-290. https://doi.org/10.1080/19477503.2018.1480862

  • Capraro, M. M., Kulm, G., & Capraro, R. M. (2005). Middle grades: Misconceptions in statistical thinking. School Science and Mathematics, 105(4), 165-174. https://doi.org/10.1111/j.1949-8594.2005.tb18156.x

  • Chan, S. W., Ismail, Z., & Sumintono, B. (2016). A framework for assessing high school students’ statistical reasoning. PLoS ONE, 11, e0163846. https://doi.org/10.1371/journal.pone.0163846

  • Chin, S. F., & Lim H. L. (2018). The effect of computerized feedback on students’ misconceptions in algebraic expression. Pertanika Journal of Social Sciences & Humanities, 26(3), 1387-1403.

  • Craik, F. I. M., & Lockhart, R. S. (1972). Levels of processing: A framework for memory research. memory, attention, and aging: Selected works of Fergus I. M. Craik. Routledge. https://doi.org/10.4324/9781315440446

  • Erna, H. W., & Budi, M. (2016, March 12). Kesalahan siswa SMP dalam menyelesaikan soal matemaika berbasis PISA pada konten changer and relationship [Middle school students’ mistakes in solving PISA-based math problems on content changers and relationships]. Prosiding Konferensi Nasional Penelitian Matematika dan Pembelajaran, Universitas Muhammadiyah Surakarta, Indonesia.

  • Fitriani, H. N., Turmudi, T., & Prabawanto, S. (2018, December 1). Analysis of students’ error in mathematical problem solving based on Newman’s error analysis. Proceeding of International Conference on Mathematics and Science Education, Universitas Pendidikan Indonesia, Indonesia.

  • Fitriyah, I. M., Lilin, E. P., RofiQoh, S., Nikmarocha, & Aning, W. Y. (2020). Analisis kesalahan siswa dalam menyelesaikan soal cerita koordinat cartesius menurut teori kastolan [Analysis of students’ errors in solving the Cartesian coordinate story problem according to the Kastolan theory]. Al-Khwarizmi: Jurnal Pendidikan Matematika dan Ilmu Pengetahuan Alam, 8(2), 109-122. http://dx.doi.org/10.24256/jpmipa.v8i2.1002

  • Foo, K. K. (2017). Modelling the relationship between the statistical achievement and cognitive determinants among Malaysian diploma students [Unplished Ph.D.’s thesis]. University of Malaya.

  • Friel, S. N., Curcio, F. R., & Bright, G. W. (2001). Making sense of graphs: Critical factors influencing comprehension and instructional implications. Journal for Research in Mathematics Education, 32(2), 124-158.

  • García-García, J., & Dolores-Flores, C. (2021).Pre-university students’ mathematical connections when sketching the graph of derivative and antiderivative functions. Math Education Research Journal, 33, 1-22. https://doi.org/10.1007/s13394-019-00286-x

  • Graham, M., Milanowski, A., & Miller, J. (2012). Measuring and promoting inter-rater agreement of teacher and principal performance ratings. Center for Educator Compensation and Reform.

  • Haryanti, M. D., Herman, T., & Prabawanto, s. (2019). Analysis of students’ error in solving mathematical word problems in geometry. Journal of Physics: Conference Series, 1157, 042084. https://doi.org/10.1088/1742-6596/1157/4/042084

  • Hattie, J., & Brown, G. T. L. (2004). Cognitive processes in asTTle: The SOLO taxonomy (asTTle Technical Report #43). University of Auckland/Ministry of Education. https://dokumen.tips/documents/assessment-tools-for-teaching-and-learning-technical-report-43-.html?page=1

  • Huan, Z. C., & Melissa, N. L. Y. A. (2018). Validity and reliability of the mathematics self-efficacy questionnaire (MSEQ) on primary school students. Pertanika Journal of Social Sciences & Humanities, 26(4), 2161-2177.

  • Khalo, X., & Bayaga, A. (2015). Analysis of errors due to deficient mastery of prerequisite skills, facts and concepts: A case of financial mathematics. The Journal of Teaching and Learning, 10, 98-113.

  • Ibnatul, J. f., Adibah, A. L., & Hawa, S. S. (2021).Assessing statistical literacy level of postgraduate education research students in Malaysian research universities. Turkish Journal of Computer and Mathematics Education, 12(5), 1318-1324.

  • Idehen, F. O. (2020). Assessing Nigerian secondary school students’ misconceptions in five basic statistical concepts. Contemporary Mathematics and Science Education, 1(1), 1-6. https://doi.org/10.30935/conmaths/8448

  • Ishaku, A., & Idris, M. (2017). Analysis of perceived difficult topics by primary school mathematics teachers and pupils in Dutsin-Ma, Katsina State. Abacus, Journal of the Mathematical Association of Nigeria (MAN), 42(1), 164-177. https://www.mannigeria.org.ng/abstract?sid=ABA-EDU-2017-1-17

  • Lynch, E. B., Coley, J. D., & Medin, D. L. (2000). Tall is typical: Central tendency, ideal dimensions, and graded category structure among tree experts and novices. Memory and Cognition, 28(1), 41-50.

  • Kementerian Pendidikan Malaysia. (2015). Kurikulum Standard Sekolah Menengah Matematik – Dokumen Standard Kurikulum dan Pentaksiran – Tingkatan 1 [Mathematics Secondary School Standard Curriculum - Standard Curriculum and Assessment Document - Form 1]. http://bpk.moe.gov.my/index.php/terbitan-bpk/kurikulum-sekolah-menengah/category/16-dskp-tingkatan-1?download=1751:dskp-kssm-tingkatan-1-matematik

  • Kementerian Pendidikan Malaysia. (2016). Kurikulum Standard Sekolah Menengah Matematik – Dokumen Standard Kurikulum dan Pentaksiran – Tingkatan 2 [Mathematics Secondary School Standard Curriculum - Standard Curriculum and Assessment Document - Form 2]. http://bpk.moe.gov.my/index.php/terbitan-bpk/kurikulum-sekolah-menengah/category/43-dskp-tingkatan-2?download=2265:dskp-kssm-tingkatan-2-matematik

  • Nasser, S. N. A., & Lian, L. H. (2021). Development and validation of year five geometrical measurement skills instrument. International Journal of Evaluation and Research in Education, 10(3), 956-965.

  • National Council of Teachers of Mathematics. (2020). Catalysing change in middle school mathematics: Initiating critical conversations. National Council of Teachers of Mathematics.

  • Newman, M. A. (1983). Strategies for diagnosis and remediation. Brace Jovanovich.

  • Ozmen, Z. M., Guven, B., & Kurak, Y. (2020).Determining the graphical literacy levels of the 8th grade students. Eurasian Journal of Educational Research, 86, 269-292.

  • Polit, D. F., Beck, T., & Owen, S. V. (2007). Focus on research methods: Is the CVI an acceptable indicator of content validity. Research in Nursing and Health, 30(4), 459-467.

  • Reaburn, R. (2011). Students’ understanding of statistical inference: Implications for teaching [Doctoral thesis, University of Tasmania, Australia]. https://iase-web.org/documents/ dissertations/11.RobynReaburn.Dissertation.pdf

  • Saidi, S. S., & Siew, N. M. (2019). Assessing students’ understanding of the measures of central tendency and attitude towards statistics in rural secondary schools. International Electronic Journal of Mathematics Education, 14(1), 73-86. https://doi.org/10.12973/iejme/3968

  • Sari, D. R., & Bernard, M. (2020). Analisis kesalahan siswa SMP dalam menyelesaikan soal materi statistika di Bandung Barat [Analysis of junior high school students’ errors in solving statistical problems in West Bandung]. Journal of Mathematics Education IKIP Veteran Semarang, 4(2), 223-232.https://doi.org/10.31331/medivesveteran.v4i2.1060

  • Stemler, S. E., & Tsai, J. (2008). Best practices in interrater reliability: Three common approaches. In J. W. Osborne (Ed.), Best practices in quantitative methods (pp. 29-49). Sage Publication.

  • Smith, T. W., & Colby, S. A. (2007). Teaching for deep learning. The clearing house. A Journal of Educational Strategies, Issues and Ideas, 80(5), 205-210. https://doi.org/10.3200/TCHS.80.5.205-210

  • Thong-oon, M., Maitree, I., & Narumon, C. (2021). Cognitive aspects of students’ mathematical reasoning habits: A study on utilising lesson study and open approach. Pertanika Journal of Social Sciences & Humanities, 29(4), 2591-2614.

  • Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2014). Elementary and middle school mathematics: Teaching developmentally (8th ed.). Pearson.

  • Watson, J. M. (2006). Statistical literacy at school: Growth and goals. Lawrence Erlbaum Associates.

  • Wijaya, A., Panhuizen, M. V. D. H., Doorman, M., & Robitzsch, A. (2014).Difficulties in solving context-based PISA mathematics tasks: An analysis of students’ errors. The Mathematics Enthusiast, 11(3), 555-584.

  • Yayla, G., & Ozsevgec, T. (2015). Ortaokul öğrencilerinin grafik becerilerinin incelenmesi: Çizgi grafikleri oluşturma ve yorumlama [The examination of secondary school students’ graphic skills: Construction and interpretation of line graphs]. Kastamonu Üniversitesi Kastamonu Eğitim Dergisi, 23(3), 1381-1400.

  • Yun, H. J., Ko, E.-S., & Yoo, Y. J. (2016). Students’ misconceptions and mistakes related to measurement in statistical investigation and graphical representation of data. In D. Ben-Zvi & K. Makar (Eds.), The teaching and learning statistics (pp.119-120). Springer.

ISSN 0128-7702

e-ISSN 2231-8534

Article ID

JSSH-8442-2021

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