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Copyright (c) 2024 Khairul Bariyah, Wahyu Setyaningrum, Husna Fatwana

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What kinds of mistakes do students make after learning exponential functions online?: A case study
Corresponding Author(s) : Khairul Bariyah
Journal of Teaching and Learning Environments,
Vol. 1 No. 1 (2024): March 2024
Abstract
Due to students' mistakes in comprehending exponential functions, the lifting problem results in low learning outcomes. This study attempts to confirm the accuracy of this and determine the types and reasons for student errors. An approach known as descriptive qualitative is used in this case study research. Data was gathered from the outcomes of tests using the exponential function. 12 of the class's 32 pupils were chosen as the research subjects based on observations. It was discovered, nonetheless, that some pupils also committed errors in the Transformation, Process Skills, and Coding categories. In general, it may be said that students make mistakes because they don't understand the idea of exponential functions and their graphs, as well as because they make blunders while using fractional exponents. Bold education is one of the causes of this problem. Therefore, teachers must really check the results of students' work so that it is clear where the mistakes made by their students are clearly visible so that they can improve the mathematics learning process in the future.
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- Abdullah, A. H., Abidin, N. L. Z., & Ali, M. (2015). Analysis of students’ errors in solving Higher Order Thinking Skills (HOTS) problems for the topic of fraction. Asian Social Science, 11(21), 133–142. https://doi.org/10.5539/ass.v11n21p133
- Adler, J., & Alshwaikh, J. (2019). Theory and practice of lesson study in mathematics: An international perspective. In Journal of Research in Mathematics Education (Vol. 8, Issue 3). https://doi.org/10.17583/redimat.2019.4789
- Agustiani, N. (2021). Analyzing students’ errors in solving sequence and series application problems using newman procedure. International Journal on Emerging Mathematics Education, 5(1), 23–32.
- Aksu, Z., & Kul, Ü. (2016). Exploring mathematics teachers’ pedagogical content knowledge in the context of knowledge of students. Journal of Education and Practice, 7(30), 35–42.
- Alhassora, N. S. A., Abu, M. S., & Abdullah, A. H. (2017). Newman error analysis on evaluating and creating thinking skills. Man In India, 19(97), 413–427.
- Asriyani, R. Y., Handayani, I., & Hadi, W. (2020). Students’ errors in mathematical problem-solving ability on the triangular and quadrilateral materials at Junior High Schools (SMP) Jakarta. Desimal: Jurnal Matematika, 3(2), 125–136. https://doi.org/10.24042/djm.v3i2.5728
- Bayar, N., Darmoul, S., Hajri-Gabouj, S., & Pierreval, H. (2015). Fault detection, diagnosis and recovery using Artificial Immune Systems: A review. Engineering Applications of Artificial Intelligence, 46, 43–57.
- Boss, S., & Larmer, J. (2018). Project based teaching: How to create rigorous and engaging learning experiences. ASCD. https://books.google.com/books?hl=en&lr=&id=TVlxDwAAQBAJ&oi=fnd&pg=PT4&dq=learn+exponentials+and+logarithms+by+looking+at+student+needs&ots=5hRvSOAxYm&sig=Zdbcui-RmZ9I34o0FrohI6QhXxc
- Boyd, P., & Ash, A. (2018). Mastery mathematics: Changing teacher beliefs around in-class grouping and mindset. Teaching and Teacher Education, 75, 214–223.
- Cai, J., Hwang, S., Jiang, C., & Silber, S. (2015). Problem-Posing research in mathematics education: some answered and unanswered questions. In F. M. Singer, N. F. Ellerton, & J. Cai (Eds.), Mathematical Problem Posing (pp. 3–34). Springer New York. https://doi.org/10.1007/978-1-4614-6258-3_1
- Chen, S., Yang, S. J. H., & Hsiao, C. (2016). Exploring student perceptions, learning outcome and gender differences in a flipped mathematics course. British Journal of Educational Technology, 47(6), 1096–1112. https://doi.org/10.1111/bjet.12278
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- Freeman, B., Higgins, K. N., & Horney, M. (2016). How students communicate mathematical ideas: An examination of multimodal writing using digital technologies. Contemporary Educational Technology, 7(4), 281–313.
- Gordon, S. P., & Yang, Y. (2016). Approximating exponential and logarithmic functions using polynomial interpolation. International Journal of Mathematical Education in Science and Technology, 5211(November). https://doi.org/10.1080/0020739X.2016.1254297
- Haans, R. F., Pieters, C., & He, Z.-L. (2016). Thinking about U: Theorizing and testing U-and inverted U-shaped relationships in strategy research. Strategic Management Journal, 37(7), 1177–1195.
- Haji, S. (2019). NCTM ’ s Principles and standards for developing conceptual understanding in mathematics. 01(02), 52–60. https://doi.org/10.32734/jormtt.v1i2.2836
- Hanifah, N. F., Hidayat, W., & Aripin, U. (2020). Gender perspective and newman’s theory in error analysis of students’ answers in ratio and proportion. 5(2), 103–118.
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- Khalo, X., & Bayaga, A. (2015). Analysis of errors due to deficient mastery of prerequisite skills, facts and concepts: A case of financial mathematics. The Independent Journal of Teaching and Learning, 10(1), 98–113.
- Korkmaz, Ö., Çakir, R., & Özden, M. Y. (2017). A validity and reliability study of the computational thinking scales (CTS). Computers in Human Behavior, 72, 558–569.
- Kristianto, E., & Saputro, D. R. S. (2019). Analysis of students’ error in proving convergent sequence using newman error analysis procedure. Journal of Physics: Conference Series, 1180(1), 012001. https://iopscience.iop.org/article/10.1088/1742-6596/1180/1/012001/meta
- Kullberg, A., Runesson Kempe, U., & Marton, F. (2017). What is made possible to learn when using the variation theory of learning in teaching mathematics? ZDM, 49(4), 559–569. https://doi.org/10.1007/s11858-017-0858-4
- Lagos, J. C. (2020). Validation of module on exponential and logarithmic functions using the understanding by design lesson plan for grade 11 mathematics students. African Educational Research Journal, 8(June), 262–271. https://doi.org/10.30918/AERJ.82.20.006
- Li, J., Miller, A. H., Chopra, S., Ranzato, M., & Weston, J. (2017). Learning through Dialogue Interactions by Asking Questions (arXiv:1612.04936). arXiv. http://arxiv.org/abs/1612.04936
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- Naik, N. (2017). The use of GBL to teach mathematics in higher education. Innovations in Education and Teaching International, 54(3), 238–246. https://doi.org/10.1080/14703297.2015.1108857
- Newman, M. A. (1977). An analysis of sixth-grade pupils’ errors on written mathematical tasks. In Victorian Institute for Educational Research Bulletin.
- Nurkamilah, P., & Afriansyah, E. A. (2021). Analisis miskonsepsi siswa pada bilangan berpangkat. Mosharafa: Jurnal Pendidikan Matematika, 10(1), 49-60.
- OECD. (2018). Pisa 2021 mathematics framework (Draft).
- Oktafia, M., Putra, A., & Habibi, M. (2020). The Analysis of students’ error in operation reseach test for linear program topic based on Newman’s Error Analysis (NEA). Edumatika: Jurnal Riset Pendidikan Matematika, 3(2), 103–112.
- Perbowo, K. S., & Anjarwati, R. (2017). Analysis of students’learning obstacles on learning invers function material. Infinity Journal, 6(2), 169–176.
- Priliawati, E., Slamet, I., & Sujadi, I. (2019). Analysis of junior high school students’ errors in solving HOTS geometry problems based on Newman’s error analysis. Journal of Physics: Conference Series, 1321(3), 032131. https://iopscience.iop.org/article/10.1088/1742-6596/1321/3/032131/meta
- Riastuti, N., Mardiyana, M., & Pramudya, I. (2017). Students’ errors in geometry viewed from spatial intelligence. Journal of Physics: Conference Series, 895(1), 012029. https://iopscience.iop.org/article/10.1088/1742-6596/895/1/012029/meta
- Rittle-Johnson, B., Zippert, E. L., & Boice, K. L. (2019). The roles of patterning and spatial skills in early mathematics development. Early Childhood Research Quarterly, 46, 166–178.
- Rohaeti, E. E., Bernard, M., & Primandhika, R. B. (2019). Developing interactive learning media for school level mathematics through open-ended approach aided by visual basic application for excel. Journal on Mathematics Education, 10(1), 59–68.
- Rohmah, M., & Sutiarso, S. (2018). Analysis problem solving in mathematical using theory newman. 14(2), 671–681. https://doi.org/10.12973/ejmste/80630
- Sahin, A., Cavlazoglu, B., & Zeytuncu, Y. E. (2015). Flipping a college calculus course: A case study. Journal of Educational Technology & Society, 18(3), 142–152.
- Salido, A., Suryadi, D., Dasari, D., & Muhafidin, I. (2020). Mathematical reflective thinking strategy in problem-solving viewed by cognitive style. Journal of Physics: Conference Series, 1469(1), 012150. https://iopscience.iop.org/article/10.1088/1742-6596/1469/1/012150/meta
- Schonger, M., & Sele, D. (2021). Intuition and exponential growth: Bias and the roles of parameterization and complexity. https://doi.org/10.1007/s00591-021-00306-7
- Skovsmose, O. (2023). A philosophy of critical mathematics education. In Critical Mathematics Education (pp. 233–245). Springer. https://link.springer.com/chapter/10.1007/978-3-031-26242-5_18
- Son, A. L., Darhim, & Fatimah, S. (2020). Students’ mathematical problem-solving ability based on teaching models intervention and cognitive style. Journal on Mathematics Education, 11(2), 209–222. https://doi.org/10.22342/jme.11.2.10744.209-222
- Sovia, A., & Herman, T. (2019). Slow learner errors analysis in solving integer problems in elementary school. Journal of Engineering Science and Technology, 14(3), 1281–1288.
- Sumule, U., Amin, S. M., & Fuad, Y. (2018). Error Analysis of Indonesian Junior high school student in solving space and shape content PISA Problem using newman procedure. Journal of Physics: Conf. Series 947, 1–7. https://doi.org/10.1088/1742-6596/947/1/012053
- Takači, D., Stankov, G., & Milanovic, I. (2015). Efficiency of learning environment using GeoGebra when calculus contents are learned in collaborative groups. Computers & Education, 82, 421–431.
- Thompson, P. W., & Carlson, M. P. (2017). Variation, covariation, and functions: Foundational ways of thinking mathematically. Compendium for Research in Mathematics Education, 421–456.
- Trapsilasiwi, D., Murtikusuma, R. P., Oktavianingtyas, E., & Wiliandani, I. (2021). Analysis of introverted students ’ error based on newman in solving arithmetic sequences and series problems. 550(Icmmed 2020), 371–375.
- Triana, M., & Zubainur, C. M. (2019). Students’ mathematical communication ability through the brain-based learning approach using autograph. Journal of Research and Advances in Mathematics Education, 4(1), 1–10.
- Van Der Kleij, F. M., Feskens, R. C. W., & Eggen, T. J. H. M. (2015). Effects of feedback in a computer-based learning environment on students’ learning outcomes: A meta-analysis. Review of Educational Research, 85(4), 475–511. https://doi.org/10.3102/0034654314564881
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References
Abdullah, A. H., Abidin, N. L. Z., & Ali, M. (2015). Analysis of students’ errors in solving Higher Order Thinking Skills (HOTS) problems for the topic of fraction. Asian Social Science, 11(21), 133–142. https://doi.org/10.5539/ass.v11n21p133
Adler, J., & Alshwaikh, J. (2019). Theory and practice of lesson study in mathematics: An international perspective. In Journal of Research in Mathematics Education (Vol. 8, Issue 3). https://doi.org/10.17583/redimat.2019.4789
Agustiani, N. (2021). Analyzing students’ errors in solving sequence and series application problems using newman procedure. International Journal on Emerging Mathematics Education, 5(1), 23–32.
Aksu, Z., & Kul, Ü. (2016). Exploring mathematics teachers’ pedagogical content knowledge in the context of knowledge of students. Journal of Education and Practice, 7(30), 35–42.
Alhassora, N. S. A., Abu, M. S., & Abdullah, A. H. (2017). Newman error analysis on evaluating and creating thinking skills. Man In India, 19(97), 413–427.
Asriyani, R. Y., Handayani, I., & Hadi, W. (2020). Students’ errors in mathematical problem-solving ability on the triangular and quadrilateral materials at Junior High Schools (SMP) Jakarta. Desimal: Jurnal Matematika, 3(2), 125–136. https://doi.org/10.24042/djm.v3i2.5728
Bayar, N., Darmoul, S., Hajri-Gabouj, S., & Pierreval, H. (2015). Fault detection, diagnosis and recovery using Artificial Immune Systems: A review. Engineering Applications of Artificial Intelligence, 46, 43–57.
Boss, S., & Larmer, J. (2018). Project based teaching: How to create rigorous and engaging learning experiences. ASCD. https://books.google.com/books?hl=en&lr=&id=TVlxDwAAQBAJ&oi=fnd&pg=PT4&dq=learn+exponentials+and+logarithms+by+looking+at+student+needs&ots=5hRvSOAxYm&sig=Zdbcui-RmZ9I34o0FrohI6QhXxc
Boyd, P., & Ash, A. (2018). Mastery mathematics: Changing teacher beliefs around in-class grouping and mindset. Teaching and Teacher Education, 75, 214–223.
Cai, J., Hwang, S., Jiang, C., & Silber, S. (2015). Problem-Posing research in mathematics education: some answered and unanswered questions. In F. M. Singer, N. F. Ellerton, & J. Cai (Eds.), Mathematical Problem Posing (pp. 3–34). Springer New York. https://doi.org/10.1007/978-1-4614-6258-3_1
Chen, S., Yang, S. J. H., & Hsiao, C. (2016). Exploring student perceptions, learning outcome and gender differences in a flipped mathematics course. British Journal of Educational Technology, 47(6), 1096–1112. https://doi.org/10.1111/bjet.12278
Chinn, S. (2020). The trouble with maths: A practical guide to helping learners with numeracy difficulties. Routledge. https://books.google.com/books?hl=en&lr=&id=YGMPEAAAQBAJ&oi=fnd&pg=PP1&dq=Learning+difficulties+can+be+an+obstacle+to+absorbing+mathematical+information&ots=DwCxchfiG7&sig=1SI1mzH64dkpCDLQh-aNAYeRxuI
Freeman, B., Higgins, K. N., & Horney, M. (2016). How students communicate mathematical ideas: An examination of multimodal writing using digital technologies. Contemporary Educational Technology, 7(4), 281–313.
Gordon, S. P., & Yang, Y. (2016). Approximating exponential and logarithmic functions using polynomial interpolation. International Journal of Mathematical Education in Science and Technology, 5211(November). https://doi.org/10.1080/0020739X.2016.1254297
Haans, R. F., Pieters, C., & He, Z.-L. (2016). Thinking about U: Theorizing and testing U-and inverted U-shaped relationships in strategy research. Strategic Management Journal, 37(7), 1177–1195.
Haji, S. (2019). NCTM ’ s Principles and standards for developing conceptual understanding in mathematics. 01(02), 52–60. https://doi.org/10.32734/jormtt.v1i2.2836
Hanifah, N. F., Hidayat, W., & Aripin, U. (2020). Gender perspective and newman’s theory in error analysis of students’ answers in ratio and proportion. 5(2), 103–118.
Hansen, A., Drews, D., Dudgeon, J., Lawton, F., & Surtees, L. (2020). Children′ s errors in mathematics. Sage. https://books.google.com/books?hl=en&lr=&id=WynoDwAAQBAJ&oi=fnd&pg=PP1&dq=procedural+errors+in+mathematics&ots=ZVT7Rj7rqD&sig=LdO7jMTQ-XP2_Wm50WlFPAfMYOc
Herscovics, N. (2018). Cognitive obstacles encountered in the learning of algebra. Research Issues in the Learning and Teaching of Algebra, 60–86.
İymen, E., & Duatepe-Paksu, A. (2015). Analysis of 8th grade students’ number sense related to the exponents in terms of number sense components. Education & Science/Egitim ve Bilim, 40(177). https://pdfs.semanticscholar.org/72ca/919feafdf132f0dde32315168379bedfba28.pdf
Johnson, R. B., & Chritensen, L. (2014). Educational research: Quantitative, qualitative and mixed approaches. SAGE Publications.
Khalo, X., & Bayaga, A. (2015). Analysis of errors due to deficient mastery of prerequisite skills, facts and concepts: A case of financial mathematics. The Independent Journal of Teaching and Learning, 10(1), 98–113.
Korkmaz, Ö., Çakir, R., & Özden, M. Y. (2017). A validity and reliability study of the computational thinking scales (CTS). Computers in Human Behavior, 72, 558–569.
Kristianto, E., & Saputro, D. R. S. (2019). Analysis of students’ error in proving convergent sequence using newman error analysis procedure. Journal of Physics: Conference Series, 1180(1), 012001. https://iopscience.iop.org/article/10.1088/1742-6596/1180/1/012001/meta
Kullberg, A., Runesson Kempe, U., & Marton, F. (2017). What is made possible to learn when using the variation theory of learning in teaching mathematics? ZDM, 49(4), 559–569. https://doi.org/10.1007/s11858-017-0858-4
Lagos, J. C. (2020). Validation of module on exponential and logarithmic functions using the understanding by design lesson plan for grade 11 mathematics students. African Educational Research Journal, 8(June), 262–271. https://doi.org/10.30918/AERJ.82.20.006
Li, J., Miller, A. H., Chopra, S., Ranzato, M., & Weston, J. (2017). Learning through Dialogue Interactions by Asking Questions (arXiv:1612.04936). arXiv. http://arxiv.org/abs/1612.04936
Mukminah, & Riana. (2020). Analisis Kesalahan newman (newman error analysis-nea ): perbandingan ketelitian antara siswa yang menghafal dan tidak menghafal alqur ’ an. JIKAP PGSD: Jurnal Ilmiah Ilmu Kependidikan, 1, 46–51.
Naik, N. (2017). The use of GBL to teach mathematics in higher education. Innovations in Education and Teaching International, 54(3), 238–246. https://doi.org/10.1080/14703297.2015.1108857
Newman, M. A. (1977). An analysis of sixth-grade pupils’ errors on written mathematical tasks. In Victorian Institute for Educational Research Bulletin.
Nurkamilah, P., & Afriansyah, E. A. (2021). Analisis miskonsepsi siswa pada bilangan berpangkat. Mosharafa: Jurnal Pendidikan Matematika, 10(1), 49-60.
OECD. (2018). Pisa 2021 mathematics framework (Draft).
Oktafia, M., Putra, A., & Habibi, M. (2020). The Analysis of students’ error in operation reseach test for linear program topic based on Newman’s Error Analysis (NEA). Edumatika: Jurnal Riset Pendidikan Matematika, 3(2), 103–112.
Perbowo, K. S., & Anjarwati, R. (2017). Analysis of students’learning obstacles on learning invers function material. Infinity Journal, 6(2), 169–176.
Priliawati, E., Slamet, I., & Sujadi, I. (2019). Analysis of junior high school students’ errors in solving HOTS geometry problems based on Newman’s error analysis. Journal of Physics: Conference Series, 1321(3), 032131. https://iopscience.iop.org/article/10.1088/1742-6596/1321/3/032131/meta
Riastuti, N., Mardiyana, M., & Pramudya, I. (2017). Students’ errors in geometry viewed from spatial intelligence. Journal of Physics: Conference Series, 895(1), 012029. https://iopscience.iop.org/article/10.1088/1742-6596/895/1/012029/meta
Rittle-Johnson, B., Zippert, E. L., & Boice, K. L. (2019). The roles of patterning and spatial skills in early mathematics development. Early Childhood Research Quarterly, 46, 166–178.
Rohaeti, E. E., Bernard, M., & Primandhika, R. B. (2019). Developing interactive learning media for school level mathematics through open-ended approach aided by visual basic application for excel. Journal on Mathematics Education, 10(1), 59–68.
Rohmah, M., & Sutiarso, S. (2018). Analysis problem solving in mathematical using theory newman. 14(2), 671–681. https://doi.org/10.12973/ejmste/80630
Sahin, A., Cavlazoglu, B., & Zeytuncu, Y. E. (2015). Flipping a college calculus course: A case study. Journal of Educational Technology & Society, 18(3), 142–152.
Salido, A., Suryadi, D., Dasari, D., & Muhafidin, I. (2020). Mathematical reflective thinking strategy in problem-solving viewed by cognitive style. Journal of Physics: Conference Series, 1469(1), 012150. https://iopscience.iop.org/article/10.1088/1742-6596/1469/1/012150/meta
Schonger, M., & Sele, D. (2021). Intuition and exponential growth: Bias and the roles of parameterization and complexity. https://doi.org/10.1007/s00591-021-00306-7
Skovsmose, O. (2023). A philosophy of critical mathematics education. In Critical Mathematics Education (pp. 233–245). Springer. https://link.springer.com/chapter/10.1007/978-3-031-26242-5_18
Son, A. L., Darhim, & Fatimah, S. (2020). Students’ mathematical problem-solving ability based on teaching models intervention and cognitive style. Journal on Mathematics Education, 11(2), 209–222. https://doi.org/10.22342/jme.11.2.10744.209-222
Sovia, A., & Herman, T. (2019). Slow learner errors analysis in solving integer problems in elementary school. Journal of Engineering Science and Technology, 14(3), 1281–1288.
Sumule, U., Amin, S. M., & Fuad, Y. (2018). Error Analysis of Indonesian Junior high school student in solving space and shape content PISA Problem using newman procedure. Journal of Physics: Conf. Series 947, 1–7. https://doi.org/10.1088/1742-6596/947/1/012053
Takači, D., Stankov, G., & Milanovic, I. (2015). Efficiency of learning environment using GeoGebra when calculus contents are learned in collaborative groups. Computers & Education, 82, 421–431.
Thompson, P. W., & Carlson, M. P. (2017). Variation, covariation, and functions: Foundational ways of thinking mathematically. Compendium for Research in Mathematics Education, 421–456.
Trapsilasiwi, D., Murtikusuma, R. P., Oktavianingtyas, E., & Wiliandani, I. (2021). Analysis of introverted students ’ error based on newman in solving arithmetic sequences and series problems. 550(Icmmed 2020), 371–375.
Triana, M., & Zubainur, C. M. (2019). Students’ mathematical communication ability through the brain-based learning approach using autograph. Journal of Research and Advances in Mathematics Education, 4(1), 1–10.
Van Der Kleij, F. M., Feskens, R. C. W., & Eggen, T. J. H. M. (2015). Effects of feedback in a computer-based learning environment on students’ learning outcomes: A meta-analysis. Review of Educational Research, 85(4), 475–511. https://doi.org/10.3102/0034654314564881
Vergnaud, G. (2016). The nature of mathematical concepts. In Learning and teaching mathematics (pp. 5–28). Psychology Press. https://www.taylorfrancis.com/chapters/edit/10.4324/9781315784939-2/nature-mathematical-concepts-gerard-vergnaud
Wardhani, T. A. W., & Argaswari, D. P. (2022). High school studentsâ€tm error in solving word problem of trigonometry based on newman error hierarchical model. Infinity Journal, 11(1), 87–102.
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