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Faculty Members’ Perspectives on Effective Instructional Methods for Teaching Calculus in the UK and Saudi Universities

Article Number: e2025223  |  Available Online: May 2025  |  DOI: 10.22521/edupij.2025.16.223

Mansour Saleh Alabdulaziz , Steve Higgins

Abstract

Background/purpose. The purpose of this study was to elicit faculty members’ perspectives on effective instructional methods for teaching calculus in the UK and Saudi Universities.

Materials/methods. An online questionnaire was administered to 150 UK faculty members and 156 Saudi faculty members specialising in curricula and methods of teaching mathematics and other related areas, such as pure mathematics.

Results. The results revealed that the instructional strategies viewed as most helpful in enabling students to develop a solid understanding of calculus in UK and Saudi Universities were the Flipped Classroom Strategy (FCS) and the GeoGebra program. In addition, a few participants mentioned other tools such as graphing calculators, Desmos, GeoGebra, MATLAB, Maple, WolframAlpha, and Mathematica (a computerised algebra system), along with strategies such as inquiry-based learning, project-based learning, team-based learning, and the Modified Moore method. Regarding the challenges and difficulties encountered when teaching calculus, faculty members stated that students move to university with incorrect beliefs about the best method for teaching the concept of the derivative and the concepts of limit and continuity. For instance, they considered teachers and textbooks to be the sole sources of knowledge. Finally, a common theme that emerged from the results was that all lessons are usually straightforward for students when working with calculus, with the exception of the concept of the derivative and the concept of limit and continuity.

Conclusion. This study concludes by presenting important recommendations for future practice.

Keywords: Faculty members’ perspectives, calculus teaching, UK and Saudi Universities

References

Abbas, M., & al-Absi, M. (2007). Curricula and methods of teaching mathematics for the lower basic stage. Jordan, Dar Al-Masirah

Agyei, E., Darko Agyei, D., & Benning, I. (2022). In-service mathematics teachers’ preparedness, knowledge, skills, and self-efficacy beliefs of using technology in lesson delivery. Cogent Education, 9(1), 2135851. https://doi.org/10.1080/2331186X. 2022.2135851

Akgün, L., Isleyen, T., Tatar, E., Soylu, Y., & Duru, A. (2010). Comprehension test in calculus course. Procedia Social and Behavioural Sciences. 2, 1527–1531. https://doi.org/0.1016/j.sbsp ro.201 0.03.229

Al-Bajalani, F. (2019). Teaching “Academic Debate and Critical Thinking” to Undergraduates in Kurdistan, Iraq. Conference Paper: Challenges and Prospects, At University of Salford, Manchester. https://www.researchgate.net/publication/331481669

Aldridge, A., & Levine, K. (2001). Surveying the social world: Principles and practice in survey research. Open University Press.

Alzahrani, G. (2016). The Availability of Some Critical Thinking Skills and Their Relationship with Some Variables Concerning The Preparatory Year Students for The Faculty of Sciences and Arts at Makhwah - Al Baha University, KSA. International Journal for Talent Development. 7(13), 155- 176. https://doi.org/10.20428/ijtd.7.2.8

Areaya, S., & Sidelil, A. (2012). Students’ difficulties and misconceptions in learning concepts of limit, continuity and derivative. The Ethiopian Journal of Education, 32(2), 1-37.

Artigue, M., Batanero, C., & Kent, P. (2007). Thinking and learning at post-secondary level. In F. Lester (Ed.), Second Handbook of Research on Mathematics Teaching and Learning (pp. 1011-1049). Information Age Publishing.

Aryal, H. P. (2022). The effect of inquiry-based learning on Calculus I students’ math anxiety [Doctoral dissertation, Ohio University].

Ashraf, A. L. A. M. (2020). Challenges and possibilities in teaching and learning of calculus: A case study of India. Journal for the Education of Gifted Young Scientists, 8(1), 407-433. https://doi.org/10.17478/ jegys.660201

Axtell, M. (2006). A two-semester precalculus/calculus sequence: A case study. Mathematics and Computer Education, 40(2), 130-137.

Bell, J. (2005). Doing your research project: A guide for first-time education, health and social science researchers. Open University Press.

Berry, J. S., & Nyman, M. A. (2003). Promoting students‟ graphical understanding of the calculus. The Journal of Mathematical Behavior, 22(4), 479–495. https://doi.org/10.1016/j.jm athb.2003.09.006

Bookman, J. (1993). An expert novice study of metacognitive behavior in four types of mathematics problems. Problems, Resources, and Issues in Mathematics Undergraduate Studies, 3(3), 284-314. https://doi.org/10.1080/10511979308965710

Bookman, J., & Blake, L. (2007). Seven years of Project CALC at Duke University approaching steady state? Problems, Resources, and Issues in Mathematics Undergraduate Studies, 6(3), 221-234. https://doi.org/10.1080/10511979608965825

Borji, V., Alamolhodaei, H., & Radmehr, F. (2018). Application of the APOS-ACE theory to improve students’ graphical understanding of derivative. Eurasia Journal of Mathematics, Science and Technology Education, 14(7), 2947-2967. https://doi.org/10.29333/ejmste/91451

Brame, C. (2013). Flipping the classroom. Center for Teaching, Vanderbilt University. Retrieved Sep. 25, 2024 from: http://cft.vanderbilt.edu/guides-sub-pages/flipping-theclassroom

Branchetti, L., Calza, G., Martani, S., & Saracco, A. (2020). Continuity of real functions in high school: a teaching sequence based on limits and topology. INDRUM.

Braun, B., Bremser, P., Duval, A., Lockwood, E., & White, D. (2017). What Does Active Learning Mean For Mathematicians?. Notices of the AMS, 64(2), 124-129. http://dx.doi. org/10.1090/noti1472

Bressoud, D., Ghedamsi, I., Martinez-Luaces, V., & Törner, G. (2016). Teaching and Learning of Calculus. https://doi.org/10.1007/978-3-319- 32975-8_1

Bressoud, D., Martinez-Luaces, V., Ghedamsi, I., & Törner, G. (2017). Topic Study Group No. 16: Teaching and Learning of Calculus. In Proceedings of the 13th International Congress on Mathematical Education (pp. 447- 452). https://doi.org/10.1007/978-3- 319-62597-3_43

Bryman, A. (2008). Social research methods. Oxford University Press.

Buch, G., & Warren, C. B. (2017). The Flipped Classroom: Implementing Technology To Aid In College Mathematics Student’s Success. Contemporary Issues in Education Research, 10(2), 109-116. https://doi.org/10.19030/cier.v10i2.9921

Carlson, M., Jacobs, S., Coe, E., Larsen, S., & Hsu, E. (2002). Applying covariational reasoning while modeling dynamic events: A framework and a study. Journal for Research in Mathematics Education, 33(5), 352–378. https://doi.org/10.2307/4149958

Clark, J. M., Cordero, F., Cottrill, J., Czamocha, B., Devries, D. J., St. John, D., Tolias, G., & Vidakovic, D. (1997). Constructing a schema: The case of the chain rule? Journal of Mathematical Behavior, 16(4), 345-364. https://doi.org/10.1016/S0732-3123(97) 90012-2

Code, W., Piccolo, C., Kohler, D., & MacLean, M. (2014). Teaching methods comparison in a large calculus class. ZDM-Mathematics Education, 46, 589-601. https://doi.org/10.1007/s11858-014-0582-2

Cohen, L., Manion, L., & Morrison, K. (2004) Research methods in education (6th ed.). Routledge.

Cohen, L., Manion, L., & Morrison, K. (2007). Research methods in education (7th ed.). RoutledgeFalmer. https://doi.org/10.4324/9780203029053

Cornu, B. (1992). Limits. In D. Tall (Ed.), Advanced mathematical thinking (pp. 153-166). Dodrecht, The Netherlands: Kluwer Acdemic.

Cronhjort, M., Filipsson, L., & Weurlander, M. (2018). Improved engagement and learning in flippedclassroom calculus. Teaching Mathematics and its Applications: An International Journal of the IMA, 37(3), 113. https://doi.org/10.1093/teamat/hrx007

Crowl, T. K. (1996). Fundamentals of educational research. Brown & Benchmark.

Dane, A., Çetin, Ö. F., Bas, F., & Sagirli, M. Ö. (2016). A Conceptual and Procedural Research on the Hierarchical Structure of Mathematics Emerging in the Minds of University Students: An Example of Limit-Continuity-Integral-Derivative. International Journal of Higher Education, 5(2), 82 -91. https://doi.org/10.5430/ijhe.v5n2p82

Davis, R., & Vinner, S. (1986). The Notion of Limit: Some Seemingly Unavoidable Misconception Stages. The journal of mathematical behavior, 5(3), 281-303.

Dagley, M. A., Gill, M., Saitta, E., Moore, B., Chini, J., & Li, X. (2018). Using Active Learning Strategies in Calculus to Improve Student Learning and Influence Mathematics Department Cultural Change. Proceedings of the Interdisciplinary STEM Teaching and Learning Conference (2017-2019), 2(8). https://doi.org/10.20429/stem.2018.020108

Delozier, S. J., & Rhodes, M. G. (2016). Flipped classrooms: a review of key ideas and recommendations for practice. Educ. Psychol. Rev. 29, 141–151  https://doi.org/1.1007/s10648-015-9356-9.

Denbel, D. (2015). Some Conceptual Difficulties of Students on Derivation. Journal of Educational and Management Studies, 5(4), 211-214. http://www.science-line.com.

Dubinsky, E., & Schwingendorf, K. (1991). Calculus, concepts and computers. St Paul. West.

El-khateeb, M. (2015). Perceptions and Performance of King Saud University Students' about Concept and Finding Limit of Functions Graphical and Symbolic. Journal of Education and Learning, 4(4), 25–37.

Ellis, J., Kelton, M., & Rasmussen, C. (2014). Student perceptions of pedagogy and associated persistence in calculus. ZDM Mathematics Education, 46, 661-673. https://doi.org/10.1007/s11858-014-0577-z

Engelke, N. (2004). Related rates problems: Identifying conceptual barriers. In D. McDougall (Ed.), Proceedings of the 26th Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 455-462).

Fernández-Plaza, J. A., Rico, L., & Ruiz-Hidalgo, J. F. (2013). Concept of finite limit of a function at a point: Meanings and specific terms. International Journal of Mathematical Education in Science and Technology, 44(5), 699-710. https://doi.org/10.1080/0020739x.2013.805887

Ferrini-Mundy, J., & Graham, K. (1994). Research in calculus learning: Understanding of limits, derivatives, and integrals. MAA notes, 31-46.

Fraenkel, J. R., & Wallen, N. E. (2008). How to design and evaluate research in education. McGraw-Hill Higher Education.

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

Garofalo, J., (1989). Beliefs and their influence on mathematical performance. The Mathematics Teacher, 82(7), 502-505.

Gass, S. M., & Mackey, A. (2007). Data elicitation for second and foreign language research. Lawrence Erlbaum Associates. https://doi.org/10.4324/9780203826102

Gay, L. R., & Airasian, P. (2000). Educational research: Competencies for analysis and application (6th ed.). Prentice Hall.

Gay, L. R., & Airasian, P. W. (2003). Educational research: Competencies for analysis and applications (7th ed.). Mer-rill/Prentice Hall.

Gordon, S. P. (2004). Mathematics for the new millennium. The International Journal of Computer Algebra in Mathematics Education, 11(2), 37-44.

Habre, S., & Abboud, M. (2006). Students’ conceptual understanding of a function and its derivative in an experimental calculus course. The Journal of Mathematical Behavior, 25(1), 57-72. https://doi.org/10.1016/j.jmathb.2005.11.004

Haciomeroglu, E. S., & Andreasen, J. B. (2013). Exploring calculus with dynamic mathematics software. Mathematics and Computer Education, 47(1), 6.

Haciomeroglu, E. S., Aspinwall, L., & Presmeg, N. C. (2010). Contrasting cases of calculus students’ understanding of derivative graphs. Mathematical Thinking and Learning, 12(2), 152-176. https://doi.org/10.1080/10986060903480300

Hart, A., Daucourt, M., & Ganley, C. (2017). Individual differences related to college students’ course performance in calculus II. Journal of Learning Analytics, 4(2), 129– 153. http://dx.doi.org/10 .186 08/jla.2017.42.11

Hauk, S., & Hsu, P. S. (2022). Undergraduate and instructor perspectives on learning in first-year mathematics courses in the United States: A case study in calculus. La Matematica, 1. 583–617.  https://doi.org/10.1007/s44007-022-00022-1

Hegedus, S. J., Dalton, S., & Tapper, J. R. (2015). The impact of technology-enhanced curriculum on learning advanced algebra in US high school classrooms. Educational Technology Research and Development, 63, 203–228. https://doi.org/10.1007/s11423-015-9371-z

Heim, B., Rupp, F., Viet, N., Stockhausen, P. V., Gallenkämper, J., & Kreuzer, J. (2015). Driving studentcentered calculus: results of a comprehensive case study for Kaizen learning in the Sultanate of Oman. International Journal of Mathematical Education in Science and Technology, 46(3), 354–369. https://doi.org/10.80/0020739X.2014.979897.

Hiyam, B., Zoubi, A., & Khataybeh, A. (2019). Utilizing MATHEMATICA software to improve students’ problem solving skills of derivative and its applications. International Journal of Education and Research, 7(11), 57-70.

Hohenwarter, M., Hohenwarter, J., Kreis, Y., & Lavicza, Z. (2008). Teaching and learning calculus with free dynamic mathematics software GeoGebra. Proceedings of conference: 11th International Congress on Mathematical Education (ICME 11) At: Monterrey, Mexico

Hughes-Hallett, D. (1991). Visualization and calculus reform. In W. Zimmermann & S. Cunningham (Eds.), Visualization in teaching and learning mathematics (pp. 121–126). Washington, DC: Mathematical Association of America

Ibrahim, B., & Rebello, N. S. (2012). Representational task formats and problem solving strategies in kinematics and work. Physical Review Special Topics Physics Education Research, 8(1), 010126. https://doi.org/10.1103/PhysRevSTPER.8.010126

Illanes, M. K. G., Breda, A., Manríquez, D. D. C., & Martínez, H. A. A. (2022). Analysis of a teaching learning process of the derivative with the use of ICT oriented to engineering students in Chile. Eurasia Journal of Mathematics, Science and Technology Education, 18(7), em2130. https://doi.org/10.29333/ejmste/12162

Jones, S. R. (2017). An exploratory study on student understandings of derivatives in real-world, nonkinematics contexts. The Journal of Mathematical Behavior, 45, 95-110. https://doi.org/10.1016/j. jmathb.2016.11.002

Jungic, V., Kaur, H., Mulholland, J., & Xin, C. (2015). On flipping the classroom in large first year calculus courses. Int. J. Math. Educ. Sci. Technol., 46, 508–520. https://doi.org/10.1080/0020739x.2014.990529

Juter, K. (2005). Limits of functions: Traces of students’ concept images. Nordic Studies in Mathematics Education, 10(3-4), 65-82.

Kamau, L. M. (2014). Technology adoption in secondary mathematics teaching in Kenya: An explanatory mixed methods study. [Doctoral dissertation, Syracuse University].

Körtesi, P., Simonka, Z., Szabo, Z. K., Guncaga, J., & Neag, R. (2022). Challenging examples of the wise use of computer tools for the sustainability of knowledge and developing active and innovative methods in STEAM and mathematics education. Sustainability, 14(20), 12991. https://doi.org/10.3390/su142012991

Kuh, G. D., Kinzie, J., Schuh, J. H., & Whitt, E. J. (2011). Student success in college: Creating conditions that matter. John Wiley & Sons.

Lang, X. (1999). CAI and the reform of mathematics education in China. International Journal of Mathematical Education in Science and Technology, 30(3), 399–404.  https://doi.org/10.1080/002073999287914

Leng, N. W. (2011). Using an advanced graphing calculator in the teaching and learning of calculus. International Journal of Mathematical Education in Science and Technology, 42(7), 925-938. https://doi.org/10.1080/0020739X.2011.616914

MaciejewskI, W. (2015). Flipping the calculus classroom: an evaluative study. Teach. Math. Appl, 1–15. https://doi.org/10.1093/teamat/hrv019

Maharaj, A., & Wagh, V. (2016). Formulating tasks to develop HOTS for first-year calculus based on Brookhart abilities. South African Journal of Science , 112(11/12), 1- 6. http://orcid.org/0000-0003-4808-551X

Marshall, N., Buteau, C., Jarvis, D., & Lavicza, Z. (2012). Do mathematicians integrate computer algebra systems in university teaching? Comparing a literature review to an international survey study. Computers & Education, 58, 423-434. https://doi.org/10.1016/j.compedu.2011.08.020

Marsitin, R. (2019). Analysis of Differential Calculus in Economics. Journal of Physics Conference Series. 1381(1), 012003. https://doi.org/10.1088/1742-6596/1381/1/012003

Mastorides, E., & Zachariades, T. (2004). Secondary mathematics teachers’ knowledge concerning the concept of limit and continuity. Proceedings of the 28th conference of the international group for the Psychology of mathematics education, 4, 481 – 488.

McLoughlin, M. (2009). Incorporating inquiry-based learning in the calculus sequence: A most challenging endeavor [Paper presentation]. The Annual Joint Meetings of the American Mathematical Society & the Mathematical Association of America.

Mkhatshwa, T. (2018). Business calculus students’ interpretations of marginal change in economic contexts. In Hodges, T. E., Roy, G. J., & Tyminski, A. M. (Eds.), Proceedings of the 40th Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 564-571). Greenville, South Carolina.

Mkhatshwa, T. (2020). Calculus students’ quantitative reasoning in the context of solving related rates of change problems. Mathematical Thinking and Learning, 22(2), 139-161. https://doi.org/10.1080/10986065.2019.1658055

Mkhatshwa, T. (2021). An investigation of students’ content understanding, perception changes, and experiences in a flipped precalculus course. Association for University Regional Campuses of Ohio Journal, 27, 41-73.

Mkhatshwa, T. (2023a). A quantitative and covariational reasoning investigation of students’ interpretations of partial derivatives in different contexts. International Journal of Mathematical Education in Science and Technology, 54(4), 511-533. https://doi.org/10.1080/0020739X.2021.1958941

Mkhatshwa, T. (2023b). Calculus instructors’ perspectives on effective instructional approaches in the teaching of related rates problems. Eurasia Journal of Mathematics, Science and Technology Education, 19(11), 1-15. https://doi.org/10.29333/ejmste/13658

Monk, S., & Nemirovsky, R. (1994). The case of Dan: Student construction of a functional situation through visual attributes. CBMS Issues in Mathematics Education, 4, 139-168. https://doi.org/10.1090/cbmath/004/07

Moru, E. K. (2009). Epistemological obstacles in coming to understand the limit of a function at undergraduate level: A case from the National University of Lesotho. International Journal of Science and Math Education, 7, 431–454. https://doi.org/10.1007/s10763-008-9143-x

Murphy, J., Chang, J. M., & Suaray, K. (2015) Student performance and attitudes in a collaborative and flipped linear algebra course. Intl J. Math. Edu. Sci. Technol. https://doi.org/10.10 80/0020739 X.201 5.1102979

Muzangwa, J., & Chifamba, P. (2012). Analysis of errors and misconceptions in the learning of calculus by undergraduate students. Acta Didactica Napocensia, 5(2), 1–10.

Nabb, K. A. (2010). CAS as a restructuring tool in mathematics education. In Proceedings of the 22nd International Conference on Technology in Collegiate Mathematics (pp. 247-259).

National Council of Teachers of Mathematics (NCTM) (1980). An Agenda for action: Recommendations for school mathematics of the 1980s. Reston, VA: Author.

National Council of Teachers of Mathematics. (1991). Professional standards for teaching mathematics. Reston, VA: Author.

Oppenheim, A. (2001). Questionnaire design, interviewing and attitude measurement. Continuum.

Peters, T., Johnston, E., Bolles, H., Ogilvie, C., Knaub, A., & Holme, T. (2020). Benefits to students of teambased learning in large enrollment calculus. Problems, Resources, and Issues in Mathematics Undergraduate Studies, 30(2), 211-229. https://doi.org/10.1080/10511970.2018.1542417

Piccolo, C., & Code, W. J. (2013). Assessment of students’ understanding of related rates problems. In S. Brown, G. Karakok, K. H. Roh, & M. Oehrtman (Eds.), Proceedings of the 16th Meeting of the MAA Special Interest Group on Research in Undergraduate Mathematics Education (pp. 607-609).

Praslon, F. (1999). Discontinuities regarding the secondary/university transition: The notion of derivative as a specific case. Paper presented at the PME conference.

Ramaglia, H. (2015). The Flipped Mathematics Classroom: A Mixed Methods Study Examining Achievement, Active Learning, And Perception. Dissertation For The Degree Doctor Of Philosophy Of Curriculum And Instruction, College Of Education, Kansas State University, Manhattan, Kansas.

Rasmussen, C., Marrongelle, K., & Borba, M. C. (2014). Research on calculus: what do we know and where do we need to go? ZDM – The International Journal on Mathematics Education, 46, 507–515. https://doi.org/10.1007/s11858-014-0615-x

Renfro, A. (2014). Assessing The Effects Of A Flipped Classroom Approach On Student Achievement, Mathematical Thinking, Attitudes, And Teacher Perceptions In An Undergraduate Calclus Class Using A Participatory Action Research Approach. Dissertation For The Degree Doctor Of Philosophy with a major in Instructional Management and Leadership, Robert Morris University.

Roh, K., & Lee, Y. (2011). The Mayan activity: a way of teaching multiple quantifications in logical contexts. Problems, Resources, and Issues in Mathematics Undergraduate Studies, 21, 685–698. https://doi.org/10.1080/10511970.201 0.485602

Rosly, W. N. S. W. M., Abdullah, S. S. S., & Shukri, F. N. A. (2020). The uses of WolframAlpha in mathematics. Articles of Teaching and Learning in Higher Education, 1, 96-103.

Sahin, A., Cavlazoglu, B., & Zeytuncu, Y. E. (2015). Flipping a College Calculus Course: A Case Study. Educational Technology & Society, 18(3), 142–152.

Sammartino, N. (2023). Teachers’ perspectives of the effects of educational technology tools on high school Algebra I skills [Doctoral dissertation, Saint Peter’s University].

Sari, P., Hadiyan, A., & Antari, D. (2018). Exploring derivatives by means of GeoGebra. International Journal on Emerging Mathematics Education, 2(1), 65 - 78. https://doi.org/10.1 2928/ijeme.v2i1.8670

Schoenfeld, A. H. (1995). A brief biography of calculus reform. UME trends, 6(6), 3-5

Sebsibe, A. S., & Feza, N. N. (2020). Assessment of Students’ Conceptual Knowledge in Limit of Functions. International Electronic Journal of Mathematics Education, 15(2), em0574. https://doi.org/10.29333/iejme/6294

Sepriyanti, N., Fauzan, A., & Arnawa, I. M. (2017). Calculus Based On Contextual Learning Model To Cultivate Student ’ s Activity , Interest And Mathematical Connection Ability. International Journal of Scientific & Technology Research, 6(10), 233–238.

Serkan, C. G. (2013). The good, the bad, and the ugly: The integration of computing technology into calculus classes [Doctoral dissertation, The University of Georgia].

Sevimli, E. (2016). Do calculus students demand technology integration into learning environment? case of instructional differences. International Journal of Educational Technology in Higher Education, 13, 37. https://doi.org/10.1186/s41239-016-0038-6

Siyepu, S. W. (2013). An exploration of students’ errors in derivatives in a university of technology. The Journal of Mathematical Behavior, 32(3), 577-592. https://doi.org/ 10.1016/j.jmathb.2013.05.001

Skemp, P. R. (1976). Relational Understanding and instrumental Understanding. Mathematics Teaching 77, 20-26.

Smith, D. A., & Moore, L. C. (1990). Duke university: Project calc. Priming the calculus pump: Innovations and resources. 51-74.

 Smith, D. A., & Moore, L. C. (1991). Project CALC: An integrated laboratory course. The laboratory approach to teaching calculus. The Mathematical Association of America, Washington, DC, 81-92.

Speer, N. M., Smith III, J. P., & Horvath, A. (2010). Collegiate mathematics teaching: An unexamined practice. The Journal of Mathematical Behavior, 29(2), 99-114. https://doi.org/10.1016/j.jm athb .2010.02.001

Strayer, J., Hart, J., & Bleiler-Baxter, S. (2016). Kick-Starting Discussions With the Flipped Classroom. Mathematics Teacher, 109(9), 662–668 https://doi.org/10.5951/mathteacher.109.9.0662

 Tall, D. (1992). Students’ Difficulties in Calculus. Proceedings of Working Group 3 on Students’ Difficulties in Calculus, ICME-7, Québec, Canada, 13-28.

Tall, D. (1992). The transition to advanced mathematical thinking: Functions, limits, infinity and proof. Handbook of research on mathematics teaching and learning, 495-511.

Tall, D. (2008). The Transition to Formal Thinking in Mathematics. Mathematics Education Research Journal, 20(2), 5-24. https://doi.org/10.1007/BF03217474

Tall, D., & Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics, 12, 151-169. https://doi.org/10.1007/BF00305619

Tall, D., Smith, D., & Piez, C. (2008). Technology and calculus. Research on Technology and the Teaching and Learning of Mathematics, 1, 207-258.

Thompson, P. W. (1994). Images of rate and operational understanding of the fundamental theorem of calculus. Educational Studies in Mathematics 26(2-3), 229-274. https://doi.org/10.1007/ BF01273664

Thompson, P. W., & Harel, G. (2021). Ideas foundational to calculus learning and their links to students’ difficulties. ZDM–Mathematics Education, 53(3), 507–519. https://doi.org/10.1007/s11858-021-01270-1

Tucker, A. C., & Leitzel, J. R. C. (1995). Assessing calculus reform: A report to the community. Washington, DC: Mathematical Association of America.

Tucker, T. W. (Ed.). (1990). Priming the calculus pump: Innovations and resources. Washington, DC: Mathematics Association of America.

Ubuz, B. (2007). Interpreting a graph and constructing its derivative graph: Stability and change in students’ conceptions. International Journal of Mathematical Education in Science and Technology, 38(5), 609-637. https://doi.org/10.1080/00207390701359313

Uwurukundo, M. S., Maniraho, J. F., & Tusiime, M. (2022). Enhancing students’ attitudes in learning 3-Dimension geometry using GeoGebra. International Journal of Learning, Teaching and Educational Research, 21(6), 286–303. https://doi.org/10.26803/ijlter.21.6.17

Viirman, O., & Pettersson, I. (2022). A small-scale implementation of inquiry-based teaching in a single-variable calculus course for first-year engineering students. Hiroshima Journal of Mathematics Education, 15(2), 129-139.

Vincent, B. (2016). First Semester Calculus Students’ Concept Definitions and Concept Images of the Tangent Line and How These Relate to Students’ Understandings of the Derivative. Dissertation Degree of Doctor of Philosophy in Mathematics at West Virginia University

Wassie, Y. A., & Zergaw, G. A. (2019). Some of the potential affordances, challenges and limitations of using GeoGebra in mathematics education. Eurasia Journal of Mathematics, Science and Technology Education, 15(8), em1734. https://doi.org/10.29333/ejmste/108436

White, P., & Mitchelmore, M. (1996). Conceptual knowledge in introductory calculus. Journal for research in mathematics education, 27, 79-95. https://doi.org/10.2307/749199

Wilkinson, D., & Birmingham, P. (2003). Using research instruments: A guide for researchers. RoutledgeFalmer. London: Routledge. https://doi.org/10.4324/9780203422991

Williams, S. R. (1991). Models of Limit Held by College Calculus Students. Journal for Research in Mathematics Education, 22(3), 237–251. https://doi.org/10.2307/749075

Wu, L., & Li, Y. (2017). Project-based learning in calculus on the use of Maple software technology. Journal of Mathematics and System Science, 7, 142-47. https://doi.org/10.17265/2159-5291/2017.05.002

Yerizon, S. F., Tasman, F., & Tasman, F. (2021). Development of a geogebra-assisted calculus worksheet to enhance students’ understanding. International Journal of Information and Education Technology, 11(10), 456–463. https://doi.org/10.18178/ijiet.2021.11.10.1550

Young, G. S. (1987). Present problems and future prospects. Calculus for a new century, 172- 175.

Zachariades, T., Pamfilos, P., Christou, C., Maleev, R., & Jones, K. (2007). Teaching introductory calculus: Approaching key ideas with dynamic software. Paper presented at CETL-MSOR Conference on Excellence in the Teaching and Learning, Stats & OP, University of Birmingham, 10-11 September 2007.

Zbarsky, E. S., Simundza, G., & Henriksen, M. (2021). Teaching calculus as a tool in the twenty-first century. In R. Buckmire, & J. M. Libertini (Eds.), Improving applied mathematics education (pp. 13-25). Springer. https://doi.org/10.1007/978-3-030- 61717-2_2

Zengin, Y. (2017). Investigating the Use of the Khan Academy and Mathematics Software with a Flipped Classroom Approach in Mathematics Teaching. Educational Technology & Society, 20(2), 89–100.

Zengin, Y., Furkan, H., & Kutluca, T. (2012). The effect of dynamic mathematics software geogebra on student achievement in teaching of trigonometry. Procedia-Social & Behavioral Sciences, 31, 183–187. https://doi.org/10.1016/j.sbspro.2011.12.038

Zulnaidi, H., Oktavika, E., & Hidayat, R. (2019). Effect of use of GeoGebra on achievement of high school mathematics students. Education and Information Technologies, 25(1), 51–72. https://doi.org/10.1007/s10639-019-09899-y