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Abstract
Mathematics education and problem-solving are inseparable due to the significance of solving problems with educational implications. This study aims to describe the process of developing and validating a test that measures problem-solving skills in Integral Calculus. This study is done to identify traces of the intended strategy in the answers, style, and quality of the student's responses. Data collection techniques were carried out through mathematical tests using problem-solving questions. The difficulty index, discrimination index, and reliability were calculated to analyze the data for each problem-solving instrument. Based on expert reviews, evaluations, and data analysis tests, five valid problem-solving instrument items with a discrimination index greater than 0.30 and Cronbach's alpha reliability greater than 0.60 have been developed. Therefore, it can be concluded that the developed maths test questions can enhance the problem-solving skills of Ibrahim Sultan Polytechnic students.
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Copyright (c) 2023 Nurul Shida, Abdul Halim Abdullah, Sharifah Osman, Norulhuda Ismail
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References
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- Atteh, E., Andam, E., & Denteh, W. O. (2017) Problem solving framework for mathematics discipline. Asian Research Journal of Mathematics, 4(4), 1–11. https://doi.org/10.9734/ARJOM/2017/32586.
- Bajracharya, R.R. (2014). Student application of the fundamental theorem of calculus with graphical representations in mathematics and physics. Dissertation. The University of Maine. Retrieved from https://digitalcommons.library.umaine.edu/cgi/viewcontent.cgi?article=3238&context=etd.
- Barnett, J., Wong, B. L. W., David, W., Adderley, R., & Smith, M. (2012). Startle reaction: Capturing experiential cues to provide guidelines towards the design of realistic training scenarios. Proceedings of the Human Factors and Ergonomics Society Annual Meeting, 56, 2477-2481. https://doi.org/10.1177/1071181312561504.
- Boadu, A. (2014). Research in problem solving in mathematics education. University of Cape Coast: Department of Science and Mathematics Education.
- Brits, G. P. (2017) University student performance in multiple choice questions : an item analysis of mathematics assessments. Theses. University of Pretoria, pp. 1-215. Retrieved from http://hdl.handle.net/2263/65477.
- Cheng, L. H., Hassan, N. A., & Mustafa, N. Z. (2017). The use of LE-WI techniques to improve PST students' skills in writing wide integral formulas between curves [in Melayu]. Proceedings of the Marticulation Program Research Convention.
- Chirinda, B. (2013). The Development of mathematical problem solving skills of grade 8 learners in a problem-centred teaching and learning environment at a secondary school in Gauteng. Theses. University of South Africa, pp. 1-185. Retrieved from https://www.academia.edu/47018138/.
- Chua, Y. P. (2011). research methods and statistics: Research methods [in Melayu]. Selangor: McGraw-Hill Education.
- Chung, C. H. (2015). A rasch model analysis of critical thinking problem solving test. Dissertation. Universiti Teknologi Malaysia.
- Daud, S. H. S., Yunus, J. N., & Yusor, H. (2017). Validity and reliability of the effective supervision study instrument [in Melayu]. Jurnal Kurikulum & Pengajaran Asia Pasifik, 5(3), 50–61.
- Faizatulhaida, M. I., Azlina, & Hajar, S. (2017). Analysis of errors in basic questions and integration applications of engineering mathematics course 2 [in Melayu]. Politeknik & Kolej Komuniti Journal of Social Sciences and Humanities, 2(1), 198–208.
- Fatimah, S., & Yerizon (2019). Analysis of difficulty learning calculus subject for mathematical education students. International Journal of Scientific and Technology Research, 8(3), 80–84.
- Ghadi, I. N., Bakar, K. A., Alwi, N. H., & Talib, O. (2013) . Measuring critical thinking skills students in Universiti Putra Malaysia. International Journal of Asian Social Science, 3(6), 1458–1466. Retrieved from https://archive.aessweb.com/index.php/5007/article/view/2506.
- Ghazali, Z. A., & Rosli, R. (2017). Analysis of students' errors applying calculations in the topic of integration [in Melayu]. Proceeding of the Seminar Serantau, pp. 247–255
- Gregory, D. (2011). The everywhere war. The Geographical Journal, 177(3), 238–250. http://www.jstor.org/stable/41238044
- Helsdingen, A., van Gog, T., & van Merriënboer, J. (2011). The effects of practice schedule and critical thinking prompts on learning and transfer of a complex judgment task. Journal of Educational Psychology, 103(2), 383–398. http://dx.doi.org/10.1037/a0022370.
- Hohmann, J. W., & Grillo, M. C. (2014). Using critical thinking rubrics to increase academic performance. Journal of College Reading and Learning, 45(1), 35–51. http://dx.doi.org/10.1080/10790195.2014.949551.
- Khalid, S., Alias, M., Razally, W., & Suradi, Z. (2015). The influence of multimedia supported courseware with collaborative learning in algebraic fractions and problem solving skills among Pre-University students. International Journal of Emerging Technologies in Learning, 2(3).
- Kiat, S. E. (2005). Analysis of students’ difficulties in solving integration problems. The Mathematics Educator, 9(1), 39–59.
- Kilpatrick, J. (2014). History of research in mathematics education. In: Lerman, S. (eds) Encyclopedia of mathematics education. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4978-8_71.
- Kuzle, A. (2011). Preservice teachers’ patterns of metacognitive behavior during mathematics problem solving in a dynamic geometry environment. Dissertation. University of Georgia.
- Nitko, A. J. (2004). Educational Assessment of Students. 4th Edition, Pearson Education, Inc., Upper Saddle River, NJ.
- Pallant, J. (2013). SPSS survival manual: A step by step guide to data analysis using IBM SPSS. Open University Press, Berkshire.
- Piaw, C. Y. (2011). Research methods and statistics [in Melayu]. Selangor: McGraw-Hill Education.
- Polya, G. (1978). How To Solve It: A New Aspect Of Mathematical Method Second Edition. New Jersey: Princeton University Press.
- Polya, G. (1977). On solving mathematical problem in high school problem solvinng in mathematic. New Jersey: Princeton University Press.
- Polya, G. (1973). How to solve it. Princeton: Princeton University Press.
- Polya, G. (1962). Mathematical discovery: On understanding, learning, and teaching problem solving. New York: John Wiley.
- Rohani, Riyan, H., & Effandi. (2014). Error Analysis in Integration Learning [in Melayu]. Jurnal Pendidikan Matematik, 2(2), 14–30.
- Saygılı, S. (2017). Examining the problem solving skills and the strategies used by high school students in solving non-routine problems. E-International Journal of Educational Research, 8(2), 91–114.
- Seacrest, D. E. (2011). Children’s voices: Students’ attitudes about routine and nonroutine mathematics. Theses. University of Nebraska-Lincoln.
- Sekaran, U., & Bougie, R. (2016). Research methods for business: A skills development approach [in Bahasa]. Wiley & Sons, West Sussex.
- Setambah, M. A. B., Tajudin, N. M., Adnan, M., & Saad, M. I. M. (2017). Adventure based learning module : Content validity and reliability process. International Journal of Academic Research in Business and Social Sciences, 7(2), 615–623. http://dx.doi.org/10.6007/IJARBSS/v7-i2/2669.
- Spinato, H. J. (2011). The effects of graphing calculator use on high- school students’ reasoning in integral calculus. Dissertation. University of New Orleans. Retrieved from https://scholarworks.uno.edu/td/1346.
- Tiruneh, D. T., De Cock, M., Weldeslassie, A. G., Elen, J., & Janssen, R. (2016). Measuring critical thinking in physics: Development and validation of a critical thinking test in electricity and magnetism. International Journal of Science and Mathematics Education. 15(4), 1–20.
- Veloo, A., Krishnasamy, H., & Abdullah, W. S. W. (2015). Types of student errors in mathematical symbols, graphs and problem-solving. Asian Social Science, 11(15), 324–334. https://doi.org/10.5539/ass.v11n15p324.
- van Velzen, J. H. (2016). Evaluating the suitability of mathematical thinking problems for senior high- school students by including mathematical sense making and global planning. The Curriculum Journal, 27(3), 313–329. https://doi.org/10.1080/09585176.2016.1174140.
- Viechtbauer, W., Smits, L., Kotz, D., Bude, L., Spigt, M., Serroyen, J., & Crutzen, R. (2015). A simple formula for the calculation of sample size in pilot studies. Journal of Clinical Epidemiology, 68(11), 1375–1379. https://doi.org/10.1016/j.jclinepi.2015.04.014.
- Yeo, K. K. J. (2004). Secondary 2 students ’difficulties in solving non-routine problems. International Journal For Mathematics Teaching and Learning, 1–30.
References
Abdullah, M. F. N. L., & Wei, L. T. (2017). Validity and reliability of the first grade geometry learning self-assessment instrument [in Melayu]. Malaysian Journal of Learning and Instruction, 14(1), 211–265. https://doi.org/10.32890/mjli2017.14.1.9.
Atteh, E., Andam, E., & Denteh, W. O. (2017) Problem solving framework for mathematics discipline. Asian Research Journal of Mathematics, 4(4), 1–11. https://doi.org/10.9734/ARJOM/2017/32586.
Bajracharya, R.R. (2014). Student application of the fundamental theorem of calculus with graphical representations in mathematics and physics. Dissertation. The University of Maine. Retrieved from https://digitalcommons.library.umaine.edu/cgi/viewcontent.cgi?article=3238&context=etd.
Barnett, J., Wong, B. L. W., David, W., Adderley, R., & Smith, M. (2012). Startle reaction: Capturing experiential cues to provide guidelines towards the design of realistic training scenarios. Proceedings of the Human Factors and Ergonomics Society Annual Meeting, 56, 2477-2481. https://doi.org/10.1177/1071181312561504.
Boadu, A. (2014). Research in problem solving in mathematics education. University of Cape Coast: Department of Science and Mathematics Education.
Brits, G. P. (2017) University student performance in multiple choice questions : an item analysis of mathematics assessments. Theses. University of Pretoria, pp. 1-215. Retrieved from http://hdl.handle.net/2263/65477.
Cheng, L. H., Hassan, N. A., & Mustafa, N. Z. (2017). The use of LE-WI techniques to improve PST students' skills in writing wide integral formulas between curves [in Melayu]. Proceedings of the Marticulation Program Research Convention.
Chirinda, B. (2013). The Development of mathematical problem solving skills of grade 8 learners in a problem-centred teaching and learning environment at a secondary school in Gauteng. Theses. University of South Africa, pp. 1-185. Retrieved from https://www.academia.edu/47018138/.
Chua, Y. P. (2011). research methods and statistics: Research methods [in Melayu]. Selangor: McGraw-Hill Education.
Chung, C. H. (2015). A rasch model analysis of critical thinking problem solving test. Dissertation. Universiti Teknologi Malaysia.
Daud, S. H. S., Yunus, J. N., & Yusor, H. (2017). Validity and reliability of the effective supervision study instrument [in Melayu]. Jurnal Kurikulum & Pengajaran Asia Pasifik, 5(3), 50–61.
Faizatulhaida, M. I., Azlina, & Hajar, S. (2017). Analysis of errors in basic questions and integration applications of engineering mathematics course 2 [in Melayu]. Politeknik & Kolej Komuniti Journal of Social Sciences and Humanities, 2(1), 198–208.
Fatimah, S., & Yerizon (2019). Analysis of difficulty learning calculus subject for mathematical education students. International Journal of Scientific and Technology Research, 8(3), 80–84.
Ghadi, I. N., Bakar, K. A., Alwi, N. H., & Talib, O. (2013) . Measuring critical thinking skills students in Universiti Putra Malaysia. International Journal of Asian Social Science, 3(6), 1458–1466. Retrieved from https://archive.aessweb.com/index.php/5007/article/view/2506.
Ghazali, Z. A., & Rosli, R. (2017). Analysis of students' errors applying calculations in the topic of integration [in Melayu]. Proceeding of the Seminar Serantau, pp. 247–255
Gregory, D. (2011). The everywhere war. The Geographical Journal, 177(3), 238–250. http://www.jstor.org/stable/41238044
Helsdingen, A., van Gog, T., & van Merriënboer, J. (2011). The effects of practice schedule and critical thinking prompts on learning and transfer of a complex judgment task. Journal of Educational Psychology, 103(2), 383–398. http://dx.doi.org/10.1037/a0022370.
Hohmann, J. W., & Grillo, M. C. (2014). Using critical thinking rubrics to increase academic performance. Journal of College Reading and Learning, 45(1), 35–51. http://dx.doi.org/10.1080/10790195.2014.949551.
Khalid, S., Alias, M., Razally, W., & Suradi, Z. (2015). The influence of multimedia supported courseware with collaborative learning in algebraic fractions and problem solving skills among Pre-University students. International Journal of Emerging Technologies in Learning, 2(3).
Kiat, S. E. (2005). Analysis of students’ difficulties in solving integration problems. The Mathematics Educator, 9(1), 39–59.
Kilpatrick, J. (2014). History of research in mathematics education. In: Lerman, S. (eds) Encyclopedia of mathematics education. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4978-8_71.
Kuzle, A. (2011). Preservice teachers’ patterns of metacognitive behavior during mathematics problem solving in a dynamic geometry environment. Dissertation. University of Georgia.
Nitko, A. J. (2004). Educational Assessment of Students. 4th Edition, Pearson Education, Inc., Upper Saddle River, NJ.
Pallant, J. (2013). SPSS survival manual: A step by step guide to data analysis using IBM SPSS. Open University Press, Berkshire.
Piaw, C. Y. (2011). Research methods and statistics [in Melayu]. Selangor: McGraw-Hill Education.
Polya, G. (1978). How To Solve It: A New Aspect Of Mathematical Method Second Edition. New Jersey: Princeton University Press.
Polya, G. (1977). On solving mathematical problem in high school problem solvinng in mathematic. New Jersey: Princeton University Press.
Polya, G. (1973). How to solve it. Princeton: Princeton University Press.
Polya, G. (1962). Mathematical discovery: On understanding, learning, and teaching problem solving. New York: John Wiley.
Rohani, Riyan, H., & Effandi. (2014). Error Analysis in Integration Learning [in Melayu]. Jurnal Pendidikan Matematik, 2(2), 14–30.
Saygılı, S. (2017). Examining the problem solving skills and the strategies used by high school students in solving non-routine problems. E-International Journal of Educational Research, 8(2), 91–114.
Seacrest, D. E. (2011). Children’s voices: Students’ attitudes about routine and nonroutine mathematics. Theses. University of Nebraska-Lincoln.
Sekaran, U., & Bougie, R. (2016). Research methods for business: A skills development approach [in Bahasa]. Wiley & Sons, West Sussex.
Setambah, M. A. B., Tajudin, N. M., Adnan, M., & Saad, M. I. M. (2017). Adventure based learning module : Content validity and reliability process. International Journal of Academic Research in Business and Social Sciences, 7(2), 615–623. http://dx.doi.org/10.6007/IJARBSS/v7-i2/2669.
Spinato, H. J. (2011). The effects of graphing calculator use on high- school students’ reasoning in integral calculus. Dissertation. University of New Orleans. Retrieved from https://scholarworks.uno.edu/td/1346.
Tiruneh, D. T., De Cock, M., Weldeslassie, A. G., Elen, J., & Janssen, R. (2016). Measuring critical thinking in physics: Development and validation of a critical thinking test in electricity and magnetism. International Journal of Science and Mathematics Education. 15(4), 1–20.
Veloo, A., Krishnasamy, H., & Abdullah, W. S. W. (2015). Types of student errors in mathematical symbols, graphs and problem-solving. Asian Social Science, 11(15), 324–334. https://doi.org/10.5539/ass.v11n15p324.
van Velzen, J. H. (2016). Evaluating the suitability of mathematical thinking problems for senior high- school students by including mathematical sense making and global planning. The Curriculum Journal, 27(3), 313–329. https://doi.org/10.1080/09585176.2016.1174140.
Viechtbauer, W., Smits, L., Kotz, D., Bude, L., Spigt, M., Serroyen, J., & Crutzen, R. (2015). A simple formula for the calculation of sample size in pilot studies. Journal of Clinical Epidemiology, 68(11), 1375–1379. https://doi.org/10.1016/j.jclinepi.2015.04.014.
Yeo, K. K. J. (2004). Secondary 2 students ’difficulties in solving non-routine problems. International Journal For Mathematics Teaching and Learning, 1–30.