Mathematical Culture and Thought

Mathematical Culture and Thought

Common Misconceptions and Beliefs About Mathematics: Implications for Teaching and Learning

Document Type : Survey

Authors
A. Nekuei Ghahfarokhi 1
N. Yaftian 2
1 Central Department of Education of the Chaharmahal and Bakhtiari Providence; and Department of Mathematics, Shahid Rajaee Teacher Training University, Iran
2 Department of Mathematics, Shahid Rajaee Teacher Training University, Iran
10.30504/mct.2023.1420.1997
Abstract
Students’ mathematical performance is shaped by cognitive and affective factors, particularly their beliefs—categorized as conscious or unconscious. These beliefs significantly impact learning; for example, viewing mathematics as memorization-based versus comprehension-based affects students’ effort. This study synthesizes research on common student beliefs about mathematics. Some perceive math as a human necessity, while others equate ability with innate talent, assuming only "gifted" individuals can grasp concepts deeply. Many believe math problems have rigid, rule-based solutions, and negative attitudes (e.g., math is difficult or tedious) are widespread. Recognizing these beliefs helps educators design strategies to counter misconceptions and promote engagement.
Keywords
beliefs
beliefs about mathematics
metaphors
Subjects
[۱] احمدی، فاطمه، بررسی تأثیر به‌کارگیریِ نقشه‌های مفهومی به‌عنوان ابزای در فرآیند یاددهی‑یادگیری روی پیشرفت تحصیلی و باورهای ریاضی‌ دانشآموزان پایۀ دوم متوسطه رشته تجربی، پایان نامۀ کارشناسی ارشد آموزش ریاضی، دانشگاه تر بیت دبیر شهید رجائی، تهران، ۱۳۸۸.
[۲] بیک، فرزانه و فرهاد حسین‌زاده لطفی و دیگران، بررسی باور دانش‌آموزان دربارۀ کارِ گروهی برای حل مسئلۀ ریاضی، تحقیق در عملیات و کاربردهای آن، ۲۲ (۱۳۸۸)، ۳۵-۵۰.
[٣] حسام، عبدالله، باورها در آموزش ریاضى، رشد اموزش رباضى، ١٠٦ (١٣٩٥)، ٤-١٥.
[۴] رکاب اسلامی‌زاده، سجاد و فرزانه نوروزی لرکی و دیگران، تدریس به روش حل مسئله بر اساس نظریۀ شونفیلد و سنجش میزان اثربخشی آن، فناوری آموزش، ۶ (۱۳۹۱)، شمارۀ ۴، ۲۷۷-۲۸۵.
[۵] سلیمیان، فاطمه و ابراهیم ریحانی و دیگران، بررسی تأثیر رویکرد آموزشی مبتنی بر مسئلۀ بازپاسخ بر توانایی حل مسئله در دانش‌آموزان پایۀ هفتم، پژوهشهای آموزش و یادگیری، ۱۶ (۱۳۹۸)، شمارۀ ۲، ۱۳-۲۷.
[۶] شعبانی، مصطفی، بررسی باورهای دانش‌آموزان مقاطع متوسطه در بارۀ ر یاضی، پایان‌نامۀ کارشناسی ارشد آموزش ریاضی، دانشگاه تربیت دبیر شهید رجائی، تهران، ۱۴۰۰.
[۷] لیکاف، جرج؛ جانسون، مارک، استعاره‌هایی که با آنها زندگی میکنیم، ترجمۀ هاجر آقاابراهیمی، نشر علم، تهران، ۱۴۰۱.
[۸] یعقوبیان، محمدحسن؛ پورحسن، قاسم، تحلیل و بررسی چیستی باور، معرفت فلسفی، ۶۵ (۱۳۹۸)، ۹۹-۱۱۲.
[9]    Awofala, A. O., Sopekan, O. S., Early-years future teachers’ mathematical beliefs as determinants of performance in primary mathematics, Journal of Research and Advances in Mathematics Education, 5 (2020), no. 1, 54-68.
[10]    Bakar, S. A., Ayub, A. F. M., Gopal, K., Salim, N. R., The influence of students’ beliefs on mathematical problem solving towards mathematics achievement among Malaysian matriculation students, Universal Journal of Educational Research, 7 (2019), no. 10, 2243-2247.
[11]    Can, A. A., İlkokul dördüncü sınıf öğrencilerinin matematik problemi çözmeye ilişkin algılarının metaforlar yoluyla analizi, Uşak Üniversitesi Eğitim Araştırmaları Dergisi [Uşak University Journal of Educational Research], 7 (2021), no. 1, 103-118.
[12]    Chan, K. K., Reynolds, B. L., Metaphoric beliefs of students engaged in dynamic mathematics lessons, EURASIA Journal of Mathematics, Science and Technology Education, 18 (2022), no. 10, em2169.
[13]    Desai, S., Kurtz, B., Safi, F., Mathematics heritage project: An exploration empowering students’ mathematical identities, J. Humanist. Math., 11 (2021), no. 2, 106-122.
[14]    Ertem Akbaş, E., Cancan, M., Metaphors formed by 6th and 7th grade students regarding the difficulties they experienced in the process of learning the subject of circle, International Online Journal of Education and Teaching, 7 (2020), no. 3, 1054-1075.
[15]    González, G., A Geometry teacher’s use of a metaphor in relation to a prototypical image to help students remember a set of theorems, J. Math. Behav., 32 (2013), no. 3, 397-414.
[16]    Habók, A., Magyar, A., Németh, M. B., Csapó, B., Motivation and self-related beliefs as predictors of academic achievement in reading and mathematics: Structural equation models of longitudinal data, International Journal of Educational Research, 103 (2020), 101634.
[17]    Hakim, A. R., Dewi, M. L., Zamrudy, W., Dewajani, H., Ro’isatin, U. A., How student beliefs related to mathematics are influenced by students’ past experiences, Technium, 43 (2023), 97-101.
[18]    Hidayatullah, A., Csíkos, C., Mathematics related belief system and word problem-solving in the Indonesian context, EURASIA Journal of Mathematics, Science and Technology Education, 18 (2022), no. 4, em2094.
[19]    Horzum, T., Yildirim, G., High school students’ metaphors about geometry, Mehmet Akif Ersoy Üniversitesi Eğitim Fakültesi Dergisi [Mehmet Akif Ersoy University Journal of Education Faculty], 40 (2016), 357-374.
[20]    Latterell, C. M., Wilson, J. L., Metaphors and mathematical identity: Math is like a Tornado in Kansas, J. Humanist. Math., 7 (2017), no. 1, 46-61.
[21]    Maasepp, B., Bobis, J., Prospective primary teachers’ beliefs about mathematics, Math. Teach. Educ. Dev., 16 (2014), no. 2, 89-107.
[22]    Markovits, Z., Forgasz, H., “Mathematics is like a lion”: Elementary students’ beliefs about mathematics, Educ. Stud. Math., 9 (2017), no. 1, 49-64.
[23]    McIntosh, R., Jarret, D., Teaching Mathematical Problem Solving: Implementing the Vision, NWREL, Mathematics and Science Education Center, New York, 2000.
[24]    Morali, S., Uğurel, I., Koçyiğit, S., Matematik öğretmen adaylarının matematik ve onun doğasına ilişkin metaforik algıları ve zihinsel imgeleri, Batı Anadolu Eğitim Bilimleri Dergisi [Western Anatolia Journal of Educational Sciences], 13 (2022), no. 1, 27–51.
[25]    Ozturk, T., Guven, B., Evaluating students’ beliefs in problem solving process: A case study, EURASIA Journal of Mathematics, Science and Technology Education, 12 (2016), no. 3, 411-429.
[26]    Pehkonen, E., Pupils’ View of Mathematics: Initial Report for an International Comparison Project, Research Report 152, University of Helsinki, Department of Teacher Education, Helsinki, 1995.
[27]    Philipp, R. A., Mathematics teachers’ beliefs and affect, in Second Handbook of Research on Mathematics Teaching and Learning, F. K. Lester, ed., National Council of Teachers of Mathematics, Reston, VA, 2007, 257-315.
[28]    Prendergast, M., Breen, C., Bray, A., Faulkner, F., Carroll, B., Quinn, D., Carr, M., Investigating secondary students beliefs about mathematical problem-solving, Int. J. Math. Educ. Sci. Technol., 49 (2018), no. 8, 1203-1218.
[29]    Schinck, A. G., Neale Jr, H. W., Pugalee, D. K., Cifarelli, V. V., Using metaphors to unpack student beliefs about mathematics, Sch. Sci. Math., 108 (2008), no. 7, 326-333.
[30]    Schonfeld, A. H., Students’ beliefs about mathematics and their effect on mathematical performance: A questionnaire analysis, in Annual Meeting of the American Educational Research Association, Chicago, 1985.
[31]    Schoenfeld, A. H., Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics, Journal of Education, 196 (2016), no. 2, 1-38.
[32]    Syamsuri, S., Bahtiar, R., Determining the relationship between 11th students’ attitude towards mathematics and their achievement in mathematics, Technium, 39 (2023), 148-154.
[33]    Twohill, A., NicMhuirí, S., Harbison, L., Karakolidis, A., Primary preservice teachers’ mathematics teaching efficacy beliefs: The role played by mathematics attainment, educational level, preparedness to teach, and gender, Int. J. Sci. Math. Educ., 21 (2023), no. 2, 601-622.
[34]    Yin, H., Shi, L., Tam, W. W. Y., Lu, G., Linking university mathematics classroom environments to student achievement: The mediation of mathematics beliefs, Stud. Educ. Eval., 66 (2020), 100905.

  • Receive Date 26 August 2023
  • Revise Date 30 October 2023
  • Accept Date 30 October 2023
  • Publish Date 22 May 2025