Gold Open Access

Structural equation fit test of mathematical connection ability, mathematical reasoning, and mathematics problem-solving ability of junior high school students

Abdurrobbil Falaq Dwi Anggoro(1Mail), Saleh Haji(2), Hari Sumardi(3),
(1) Mathematics Education Study Program, Bengkulu University, Jl. WR. Supratman Bengkulu, 38371A, Indonesia
(2) Mathematics Education Study Program, Bengkulu University, Jl. WR. Supratman Bengkulu, 38371A, Indonesia
(3) Mathematics Education Study Program, Bengkulu University, Jl. WR. Supratman Bengkulu, 38371A, Indonesia

Mail Corresponding Author

Abstract


The purpose of this study was to test the compatibility of theoretical and empirical structural equations on the relationship between mathematical connection skills, mathematical reasoning, and mathematical problem-solving abilities of junior high school students. This is an ex-post facto research at SMP N 1 Bengkulu City. The population of this study was 296 people, and the sample was selected through a simple random technique of 100 people. Data collection techniques through tests with three research instruments. The three instruments are a mathematical problem-solving ability test, a mathematical reasoning ability test, and a mathematical connection ability test that have been valid and reliable based on expert tests and field tests. The data was tested using the Lisrel 8.8 application program. The results of the study are the P-valued of  0.05, RMSEA ≤ 0.08; NFI ≥ 0.90, NNFI ≥ 0.90; CFI ≥ 0.90; IFI ≥ 0.90; RFI ≥ 0.90; RMR ≤ 0.05; SRMR ≤ 0.05; GFI ≥ 0.90; and 0.8≤AGFI≤0.9; then the fit test for the complete structural equation model is good fit. It means that the theoretical structural equation model is compatible with the empirical structural equation model. Thus, the overall fit test of the model shows a fit model, and it can be concluded that the empirical structural equation model is compatible with the theoretical model.


Keywords


Compatibility test; Ability; Problem-solving; Mathematical connection; Mathematical reasoning;

   

Article DOI



DOI: https://doi.org/10.33122/ijtmer.v5i1.117
       

Article Metrics

 Abstract views : 3394 
 PDF views : 333 


   

Article Pages


Pages: 82-93

   

Full Text:

PDF

References


Akuba, SF, Purnamasari, D., & Firdaus, R. (2020). The Influence of Reasoning Ability, Self-Efficacy and Problem-Solving Ability to Mastery of Mathematical Concepts. JNPM (National Journal of Mathematics Education), 4 (1), 44. https://doi.org/10.33603/jnpm.v4i1.2827

Anggo, M. (2011). The involvement of metacognition in mathematical problem solving. Edumatica, 01 (April), 25-32.

Astari, E., & Marsigit. (2019). Mathematical connections process for elementary school students in problem solving of statistics. Journal of Physics: Conference Series, 1280 (4). https://doi.org/10.1088/1742-6596/1280/4/042008

Baiduri, Putri, ORU, & Alfani, I. (2020). Mathematical connection process of students with high mathematics ability in solving PISA problems. European Journal of Educational Research, 9 (4), 1527-1537.
https://doi.org/10.12973/eu-jer.9.4.1527

Baki, A., atlioǧlu, H., Coştu, S., & Birgin, O. (2009). Conceptions of high school students about mathematical connections to the real-life. Procedia - Social and Behavioral Sciences, 1 (1), 1402-1407.
https://doi.org/10.1016/j.sbspro.2009.01.247

Bergqvist, T. (2012). Problem Solving in Mathematics Education Learning. Umeå: Umeå university.

Bradshaw, Z., & Hazell, A. (2017). Developing problem-solving skills in mathematics: a lesson study. International Journal for Lesson and Learning Studies, 6 (1), 32-44. https://doi.org/10.1108/IJLLS-09-2016-0032

Brehmer, D. (2015). Problem solving in mathematics. Sweden: Malardalen University.
https://doi.org/10.1080/0957514860060203

Chan, A., Franke, ML, & Johnson, N. (2017). Mathematical Reasoning and Statistics.

Dostal, J. (2015). Theory of Problem Solving. Procedia - Social and Behavioral Sciences, 174, 2798-2805.
https://doi.org/10.1016/j.sbspro.2015.01.970

Dweck, CS (2002). The Development of Ability Conceptions. Development of Achievement Motivation, 57-88. https://doi.org/10.1016/B978-012750053-9/50005-X

Dwi, N., & Hendikawati, P. (2018). The mathematical problem-solving ability of student on learning with Thinking Aloud Pair Problem Solving (TAPPS) model in term of student learning style. Unnes Journal of Mathematics Education, 7 (1), 1-7. https://doi.org/10.15294/ujme.v7i1.18870

Eccles, PJ (1997). An Introduction to Mathematical Reasoning. An Introduction to Mathematical Reasoning. https://doi.org/10.1017/cbo9780511801136
https://doi.org/10.1017/CBO9780511801136

Evreinov, G. (2017). Skills vs. Abilities Introduction to the Special Thematic Session. dept. of Computer Sciences, University of Tampere. https://doi.org/10.1007/978-3-540-70540-6

Haji, S., & Yumiati. (2018). Ability of students' mathematical connection based on school level in junior high school. Journal of Physics: Conference Series, 1116 (2). https://doi.org/10.1088/1742-6596/1116/2/022047

Haji, S. (2011). Developing Original Thinking Skills Through generative Learning with an Open-Ended Approach. Pasundan Journal of Mathematics Educations, 1 (1), 50-60. Retrieved from http://www.journal.unpas.ac.id/index.php/pjme/article/view/2364

Haji, S. (2007). The Effect of REACT Learning on Students' Reasoning Ability. National Seminar on Mathematics, (December), 1-9.

Haji, S. (2011). Problem Posing Approach in Mathematics Learning in Elementary School. Journal of Triadic Education, 14 (1), 55-63.

Haji, S. (2012). The Influence of Contextual Learning on Mathematics Communication Ability of Bengkulu City Junior High School Students. EXACTA Journal of Mathematics and Science Education, X (2), 115-118.

Haji, S. (2013). Iceberg's Approach in Learning Fraction Division in Elementary School. Infinity Journal, 2 (1), 75. https://doi.org/10.22460/infinity.v2i1.26

Haji, S. (2014). Improving Concept Understanding Ability through Concept-Rich Mathematics Learning. In National Seminar on Mathematics Education, Bengkulu University (pp. 1-12).

Haji, S., & Abdullah, MI (2016). Improving Mathematical Communication Skills Through Realistic Mathematics Learning. Infinity Journal, 5 (1), 42. https://doi.org/10.22460/infinity.v5i1.190

Haji, S., Abdullah, MI, Maizora, S., & Yumiati, Y. (2017). Developing Students' Ability of Mathematical Connection Through Using Outdoor Mathematics Learning. Infinity Journal, 6 (1), 11.
https://doi.org/10.22460/infinity.v6i1.234

Hanifah, LH, & Karyati, K. (2019). The relation between mathematical connection ability and mathematical reasoning ability of senior high school student. …, Engineering and Mathematics …, 310-315. Retrieved from http://digital.library.ump.ac.id/id/eprint/343

Hartati, S., & Ilham, A. (2017). The effect of concept understanding abilities, communications and connection abilities on problem solving ability. Journal of Mathematics Education, Science and Technology, 2 (1), 43-72.
https://doi.org/10.30651/must.v2i1.403

Hasanah, SI, Tafrilyanto, CF, & Aini, Y. (2019). Mathematical Reasoning: The characteristics of students' mathematical abilities in problem solving. Journal of Physics: Conference Series, 1188 (1).
https://doi.org/10.1088/1742-6596/1188/1/012057

Hasbi, M., Lukito, A., Sulaiman, R., Muzaini, M., Negeri Surabaya, U., Lidah Wetan, K., & Lidah Wetan-Surabaya, J. (2019). Improving the Mathematical Connection Ability of Middle-School Students through Realistic Mathematics Approach. Journal of Mathematical Pedagogy, 1 (1), 37-46. Retrieved from https://journal.unesa.ac.id/index.php/JOMP/article/view/7147

Helviyana, G., Susanti, E., Indaryanti, Sari, N., & Simarmata, RH (2020). Students' mathematical reasoning in inquiry learning model. Journal of Physics: Conference Series, 1480 (1). https://doi.org/10.1088/1742-6596/1480/1/012058

Hjelte, A., Schindler, M., & Nilsson, P. (2020). Kinds of mathematical reasoning addressed in empirical research in mathematics education: A systematic review. Education Sciences, 10 (10), 1-15.
https://doi.org/10.3390/educsci10100289

Hodiyanto. (2017). The relationship between mathematical problem-solving ability and mathematical connection ability with student learning achievement. Journal of Informatics and Science Education, 6 (2), 208-218.

Inayah, N. (2016). The effect of mathematical reasoning ability and cognitive style on communication and connection skills in high school students' statistics material. Journal of EST P-ISSN: 2460-1497 e-ISSN:2477-3840, 2 (2), 74-80. https://doi.org/10.26858/est.v2i2.2105

Ismunarti, DH, Zainuri, M., Sugianto, DN, & Saputra, SW (2020). Instrument Reliability Testing on Continuous Variables for Measurement of Chlorophyll-A Concentration in Waters. Marina Oceanography Bulletin, 9 (1), 1-8. https://doi.org/10.14710/buloma.v9i1.23924

Jailani, J., Retnawati, H., Apino, E., & Santoso, A. (2020). High School Students' Difficulties in Making Mathematical Connections when Solving Problems. International Journal of Learning, Teaching and Educational Research, 19 (8), 255-277. https://doi.org/10.26803/ijlter.19.8.14

Jonathan, S. (2010). Basic Understanding of Structural Equation Modeling (SEM). Ukrida Scientific Journal of Business Management, 10 (3), 98528.

Kadir, A., Rochmad, R., & Junaedi, I. (2020). Mathematical Connection Ability of Grade 8th Students' in terms of Self-Concept in Problem Based Learning. Journal of Primary Education, 9 (3), 258-266.
https://doi.org/10.15294/jpe.v9i3.37547

Kyriakides, L., & Gagatsis, A. (2000). Assessing Student Problem-Solving Skills. Structural Equation Modeling, 10 (4), 609-621. https://doi.org/10.1207/S15328007SEM1004_7

Lappan, G., Fey, JT, Fitzgerald, WM, Friel, SN, Phillips, ED, Glenview, I., & Needham, M. (2002). Getting to know Connected mathematics. New Jersey: Prentice Hall. Retrieved from http://enrollment.pps.k12.or.us/.docs/pg/400/rid/13114/f/GettingToKnowCMP1.pdf

Lestari, SAP (2019). Mathematical reasoning ability in relations and function using the problem-solving approach. Journal of Physics: Conference Series, 1188 (1). https://doi.org/10.1088/1742-6596/1188/1/012065
https://doi.org/10.1088/1742-6596/1188/1/012065

Lui, M., Tissenbaum, M., & Slotta, JD (2010). Helping students make mathematics connections: Collaborative visualizations in smart classrooms. Paper Presented at AERA Annual Meeting 05/04/10, Denver, CO., 1-3.

Mainali, B. (2021). Representation in teaching and learning mathematics. International Journal of Education in Mathematics, Science and Technology, 9 (1), 1-21. https://doi.org/10.46328/ijemst.1111
https://doi.org/10.46328/ijemst.1111

Masfinatin, T., Murtafiah, W., & Maharani, S. (2020). Exploration of Creative Mathematical Reasoning in Solving Geometric Problems. Journal of Mathematics Education, 14 (2), 155-168. https://doi.org/10.22342/jpm.14.2.7654.155-168

McCrink, K., & Wynn, K. (2008). Mathematical Reasoning. Encyclopedia of Infant and Early Childhood Development, 1 - 3, 280-289. https://doi.org/10.1016/B978-012370877-9.00098-0

Mhlolo, MK (2012). Mathematical connections of a higher cognitive level: A tool we may use to identify these in practice. African Journal of Research in Mathematics, Science and Technology Education, 16 (2), 176-191. https://doi.org/10.1080/10288457.2012.10740738

Midgett, CW, & Eddins, SK (2001). NCTM's Principles and Standards for School Mathematics: Implications for Administrators. NASSP Bulletin, 85 (623), 43-52. https://doi.org/10.1177/019263650108562306

Moursund, D. (2007). Introduction to Problem Solving in the Information Age. http://Uoregon.Edu/~moursund/Dave/Index.Htm

Mueller, M., Yankelewitz, D., & Maher, C. (2014). Teachers Promoting Student Mathematical Reasoning. Investigations in Mathematics Learning, 7 (2), 1-20. https://doi.org/10.1080/24727466.2014.11790339

NCTM. (2000). Principles and Standards for School Mathematics. USA: The National Council of Teachers of Mathematics, Inc. (www.nctm.org).

NCTM. (2010). Principles and Standards for School Mathematics Overview. National Council of Teachers of Mathematics. https://doi.org/10.1016/S0737-0806(98)80482-6

Nordheimer, S. (2011). Mathematical connections at school. Ann. Maths., 2 (3), 553-574.

Nurjanah, Lutfi, AF, Yuliardi, R., Indonesia, UP, Education, M., Regency, K., & Java, W. (2018). Improving Students' Mathematical Reasoning in. Journal of Mathematics and Natural Sciences Teaching, 23 (2), 94-98. https://doi.org/10.18269/jpmipa.v23i2.13568

OECD/PISA. (2012). Framework for PISA 2012 Problem Solving. Consortium.

OECD/PISA. (2019). PISA 2018 and the EU: Striving for social fairness through education. European Commission: Directorate-General for Education, Youth, Sport and Culture. European Union. Retrieved from https://ec.europa.eu/education/news/pisa-2018_el

OECD. (2019). PISA 2018 Mathematics Framework. https://doi.org/10.1787/13c8a22c-en

OECD. (2021). PISA 2021 Mathematica Framework.

Pambudi, DS, Budayasa, IK, & Lukito, A. (2020). The Role of Mathematical Connections in Mathematical Problem Solving. Journal of Mathematics Education, 14 (2), 129-144.
https://doi.org/10.22342/jpm.14.2.10985.129-144

Piaget, J., & Garcia, R. (1889). Psychology and the History of Science. http://www.Piaget.Org/.

Pitriyani, P., Fitrianna, AY, Malinda, P., & Hajar, MS (2018). Analysis of Mathematic Connection Ability of MTS Students Reviewed From Self Confidence. Journal of Mathematics Research and Learning, 11 (1), 657-666. https://doi.org/10.30870/jppm.v11i1.2989

Polya, G. (1973). How to solve it. A New Aspect of Mathematical Method. New Jersey: Princeton University Press.

Polya, G. (1981). Mathematical Discovery on Understading, Learning, and Teaching Problem Solving. Canada: John Wiley & Sons, Inc.

Posamentier, AS, & Krulik, S. (2009). Problem Solving in Mathematics Grades 3-6. London: Corwin A Sage Company.

Putri, AGE, & Wutsqa, DU (2019). Students' Mathematical Connection Ability in Solving Real-world Problems. Journal of Physics: Conference Series, 1320 (1), 0-7. https://doi.org/10.1088/1742-6596/1320/1/012066

Quirós, NS, & De Gamboa, G. (2016). Extra-mathematical connections: Connecting mathematics and the real world, 1-23. Retrieved from https://ddd.uab.cat/pub/tfg/2016/171342/TFG_Final_NuriaSabate.pdf

Rahmawati, D., Purwanto, Subanji, Hidayanto, E., & Anwar, RB (2017). Process of mathematical representation translation from verbal into graphic. International Electronic Journal of Mathematics Education, 12 (4), 367-381. https://doi.org/10.29333/iejme/618

Reynolds, JM (2019). The meaning of abilities and disabilities. Journal of Speculative Philosophy, 33 (3), 434-447. https://doi.org/10.5325/jspecphil.33.3.0434

Rohendi, D., & Dulpaja, J. (2013). Analysis of Students' Junior High School Mathematical Connection Ability International Journal of Sciences: Analysis of Students' Junior High School Mathematical Connection Ability. Journal of Education and Practice, 4 (4), 1-14.

Rohmah, M., & Sutiarso, S. (2018). Analysis of problem solving in mathematical using Newman's theory. Eurasia Journal of Mathematics, Science and Technology Education, 14 (2), 671-681.
https://doi.org/10.12973/ejmste/80630

Samsuddin, AF, & Retnawati, H. (2018). Mathematical representation: The roles, challenges and implications on instruction. Journal of Physics: Conference Series, 1097 (1). https://doi.org/10.1088/1742-6596/1097/1/012152

Sandy, WR, Inganah, S., & Jamil, AF (2019). The Analysis of Students' Mathematical Reasoning Ability in Completing Mathematical problems on Geometry. Mathematics Education Journals, 3 (1), 72-79.
https://doi.org/10.22219/mej.v3i1.8423

Scheerens, J., Ehren, M., Sleegers, P., & Leeuw, R. de. (2010). OECD review on evaluation and assessment frameworks for improving school outcomes. Ministry of Education of the Netherlands. Retrieved from www.shonamoller.com%0Awww.oecd.org/edu/evaluationpolicy

Schoenfeld, AH (2016). Learning to Think Mathematically: Problem Solving, Metacognition, and Sense Making in Mathematics (Reprint). Journal of Education, 196 (2), 1-38.
https://doi.org/10.1177/002205741619600202

Siregar, R., & Siagian, MD (2019). Mathematical connection ability: Teacher's perception and experience in learning. Journal of Physics: Conference Series, 1315 (1). https://doi.org/10.1088/1742-6596/1315/1/012041

Smit, R., Bachmann, P., Blum, V., Birri, T., & Hess, K. (2017). Effects of a rubric for mathematical reasoning on teaching and learning in primary school. Instructional Science, 45 (5), 603-622.
https://doi.org/10.1007/s11251-017-9416-2

Sokolowski, A. (2018). The effects of using representations in elementary mathematics: Meta-analysis of research. IAFOR Journal of Education, 6 (3), 129-152. https://doi.org/10.22492/ije.6.3.08

Solso, RL (1995). Cognitive Psychology. Boston: Allyn and Bacon.

Son, AL, Sudirman, S., & Widodo, SA (2020). Association of Mathematical Connections and Problem-Solving Ability: Cross-Sectional in West Timor. AKSIOMA: Journal of Mathematics Education Study Program, 9 (2), 326-337. https://doi.org/10.24127/ajpm.v9i2.2742

Sugiyono. (2010). Quantitative, Qualitative Research and R&D. Bandung: Alpha Beta.

Sugiyono. (2013). Educational Research Methods Quantitative Approach. Qualitative, and R&D. Bandung: Alphabeta.

Sukirwan, Darhim, D., & Herman, T. (2018). Analysis of students' mathematical reasoning. Journal of Physics: Conference Series, 948 (1). https://doi.org/10.1088/1742-6596/948/1/012036

Sulianto, J., Sunardi, S., Anitah, S., & Gunarhadi, G. (2020). Classification of Student Reasoning Skills in Solving Mathematics Problems in Elementary School. JPI (Jurnal Pendidikan Indonesia), 9 (1), 95.
https://doi.org/10.23887/jpi-undiksha.v9i1.23103

Sundstrom, T. (2003). Mathematical reasoning: writing and proof. Choice Reviews Online, 40 (09), 40-5255-40-5255. https://doi.org/10.5860/CHOICE.40-5255

Sundstrom, T. (2016). Mathematical Reasoning: Writing and Proof. Grand Valley: Pearson Education, Inc. Change.

Tambychik, T., & Meerah, TSM (2010). Students' difficulties in mathematics problem-solving: What do they say? Procedia - Social and Behavioral Sciences, 8, 142-151. https://doi.org/10.1016/j.sbspro.2010.12.020

Tisngati, U., & Genarsih, T. (2021). Reflective thinking process of students in completing mathematical problems based on mathematical reasoning ability. Journal of Physics: Conference Series, 1776 (1).
https://doi.org/10.1088/1742-6596/1776/1/012035

Yuanita, P., Zulnaidi, H., & Zakaria, E. (2018). The effectiveness of Realistic Mathematics Education approach: The role of mathematical representation as a mediator between mathematical belief and problem solving. PLoS ONE, 13 (9), 1-20. https://doi.org/10.1371/journal.pone.0204847

Zakir, M. (2015). Description of Logical Reasoning in Solving Mathematics Problems Based on Students' Thinking Style of Students at SMPN 2 Pinrang. Journal of Mathematical Power, 3 (2), 152. https://doi.org/10.26858/jds.v3i2.3229


Refbacks

  • There are currently no refbacks.


Copyright (c) 2022 Abdurrobbil Falaq Dwi Anggoro, Saleh Haji & Hari Sumardi

International Journal of Trends in Mathematics Education Research (IJTMER)

E-ISSN 2621-8488

Published by the SAINTIS Publishing
Homepage: http://ijtmer.saintispub.com/index.php/ijtmer/index
Editor E-mail : ijtmer@saintispub.com; ijtmer@gmail.com

Creative Commons License  IJTMER is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.