Training Egyptian undergraduate mathematics students to implement REACT strategies: An approach to strengthen their conceptual and procedural knowledge of rational numbers and capability to create contextual situations

Samah Gamal Ahmed Elbehary

Abstract


Background: The quality of instruction significantly influences students' understanding of school mathematics, highlighting the importance of initial teacher education. Concerns about how to enhance prospective teachers' pedagogical skills remain significant. This study addresses the scarcity of national investigations on employing REACT strategies in preparing pre-service mathematics teachers.
Aim: This study aims to strengthen the conceptual and procedural knowledge of rational numbers among undergraduate mathematics students and develop their abilities to create contextual situations that align with the five interpretations of rational numbers: part-whole, operator, quotient, ratio, and measure.
Method: An embedded design was employed, selecting a convenient sample of thirty undergraduates from the mathematics teacher preparation program at the Faculty of Education, Tanta University in Egypt, during the academic year 2022-2023. Data collection involved administering a test to assess participants' conceptual and procedural knowledge and a survey to explore their capabilities in creating contextual situations. The data were analyzed using descriptive and inferential statistics, coupled with qualitative analysis of participants' answers.
Results: The adapted training significantly enhanced participants' knowledge of rational numbers, evidenced by a large effect size (Cohen’s d = 2.71). Furthermore, participants' ability to generate contextual scenarios improved, demonstrated by the diversity of contexts and the inclusion of all interpretations of rational numbers in their scenarios.
Conclusion: The study demonstrates the effectiveness of REACT strategies in improving prospective mathematics teachers' knowledge and skills. Future research should evaluate the quality of contextual scenarios proposed by prospective teachers across various domains of mathematics.


Keywords


Context; Rational numbers; REACT strategies; Teacher education

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References


Abd Elmalak, M. M. (2021). A program based on the Mathematical Knowledge for Teaching (MKT) Framework to develop the professional noticing skills of student thinking among pre-service mathematics teachers [برنامج قائم علي المعرفة الرياضية للتدريس MKT لتنمية مهارات الملاحظة المهنية لتفكير الطلاب لدى معلمي الرياضيات قبل الخدمة]. Mathematics Education Journal, 24 (12), 49-95. https://doi.org/10.21608/armin.2022.230991

Abdou, H. (2020). Using Context-based Learning Approach in Science Education and its Impact on Developing Problem-Solving Skills and Imaginative Thinking for Prep Students [استخدام مدخل التعلم القائم على السياق في تدريس العلوم وأثره على تنمية مهارات حل المشكلات والتفكير التخيلي لدى تلاميذ المرحلة الإعدادية]. Egyptian Journal of Science Education, Ain Shams University, 32(5), 51-96. https://mktm.journals.ekb.eg/article_113523.html?lang=en

Abdul Karim, S. (2017). The effect of using the REACT strategy (linking - experience - application - cooperation - transportation) on developing successful intelligence abilities, understanding concepts, and level of ambition of first-grade students with negative attitudes towards learning chemistry [أثر استخدام إستراتيجية REACT(الربط – الخبرة – التطبيق – التعاون – النقل) في تنمية قدرات الذكاء الناجح وفهم المفاهيم ومستوى الطموح لدى طالبات الصف الأول الثانوي ذوات الاتجاه السلبي نحو تعلم الكيمياء]. Journal of Scientific Research in Education, the Faculty of Women for Arts, Science, and Education, Ain Shams University, 18, 231-274. https://jsre.journals.ekb.eg/article_8299.html

Abd Elsaied, S. M. (2022). The Effectiveness of a Suggested Program Based on Using Interactive Mathematics Software in Developing Teaching Performance and Professional Self-Efficacy for Students/Teachers in the Faculties of Education [فاعلية برنامج تدريبي مقترح قائم علي استخدام البرمجيات الرياضية التفاعلية في تنمية الأداء التدريسي والكفاءة الذاتية المهنية لدى الطلاب المعلمين بكليات التربية]. Mathematics Education Journal, 25(4), 107-158. https://doi.org/10.21608/armin.2022.251034

Abebe, W. K., Tafari, H. W., & Faris, S. B. (2023). Effect of context based REACT strategy on students’ conceptual understanding of heredity. Cogent Education, 11(1). https://doi.org/10.1080/2331186x.2023.2290104

Adamu, L. E. (2018). The effect of contextual teaching-learning approach on senior secondary school students’ attitude to mathematics in Kaduna state. Journal of the Nigerian Council of Educational Psychologists, 12(1), 7-14. https://journals.ezenwaohaetorc.org/index.php/NCEP/article/view/1118

Akperov, N., Tuyakov, Y., & Zhadrayeva, L. (2023). Review of research results on the effectiveness of teaching mathematics using contextual tasks. Collection of Scientific Papers “SCIENTIA,” May 19, 2023; Berlin, Germany, 104–107. https://previous.scientia.report/index.php/archive/article/view/975

Al-Mutawah, M. A., Thomas, R., Eid, A., Mahmoud, E. Y., & Fateel, M. J. (2019). Conceptual Understanding, Procedural Knowledge and Problem-Solving Skills in Mathematics: High School Graduates Work Analysis and Standpoints. International Journal of Education and Practice, 7(3), 258–273. https://eric.ed.gov/?id=EJ1239165

Altay, K. M., Erhan, K. G., & Bati, E. (2020). Contexts used for real life connections in mathematics textbook for 6th graders. İlköğretim online, 310–323. Https://doi.org/10.17051/ilkonline.2020.656880

Anderson, L. W. and Krathwohl, D. R., et al (Eds..). (2001). A Taxonomy for Learning, Teaching, and Assessing: A Revision of Bloom’s Taxonomy of Educational Objectives. Allyn & Bacon. Boston, MA (Pearson Education Group).

Ball, D. L. (1990). The Mathematical Understandings That Prospective Teachers Bring to Teacher Education. The Elementary School Journal, 90(4), 449–466. https://www.jstor.org/stable/1001941

Behr, M., Lesh, R., Post, T., & Silver, E. (1983). Rational number concepts. In R. Lesh & M. Landau (Eds.), Acquisition of mathematics concepts and processes, pp. 91–125, Academic Press, New York, NY.

Berns, R. G., & Erickson, P. M. (2001). Contextual Teaching and Learning: Preparing Students for the New Economy. The Highlight Zone: Research @ Work No. 5. In ERIC. For full text: http://www. https://eric.ed.gov/?id=ED452376

Boaler, J. (1993). The Role of Contexts in the Mathematics Classroom: Do They Make Mathematics Mor. For the Learning of Mathematics, 13(2), 12–17. https://eric.ed.gov/?id=EJ473508

Bowie, L., Venkat, H., & Askew, M. (2019). Pre-service Primary Teachers’ Mathematical Content Knowledge: An Exploratory Study. African Journal of Research in Mathematics, Science and Technology Education, 23(3), 286–297. https://doi.org/10.1080/18117295.2019.1682777

Byrnes, J. P., & Wasik, B. A. (1991). Role of conceptual knowledge in mathematical procedural learning. Developmental Psychology, 27(5), 777–786. https://doi.org/10.1037/0012-1649.27.5.777

Cheng, L. P. (2013). The design of a mathematics problem using real-life context for young children. Journal of Science and Mathematics Education in Southeast Asia, 36(1), 23-43.

Chinnappan, M., & Forrester, T. (2014). Generating procedural and conceptual knowledge of fractions by pre-service teachers. Mathematics Education Research Journal, 26(4), 871–896. https://doi.org/10.1007/s13394-014-0131-x

Chirove, M., & Ogbonnaya, U. I. (2021). The relationship between grade 11 learners’ procedural and conceptual knowledge of algebra. JRAMathEdu (Journal of Research and Advances in Mathematics Education), 6(4), 368–387. https://doi.org/10.23917/jramathedu.v6i4.14785

Christou, K. P., & Vamvakoussi, X. (2021). Natural number bias on evaluations of the effect of multiplication and division: The role of the type of numbers. Mathematics Education Research Journal. https://doi.org/10.1007/s13394-021-00398-3

Cabbar, G. B., & Şenel, H. (2020). Content Analysis of Biology Education Research That Used Context-Based Approaches: The Case of Turkey. Journal of Educational Issues, 6(1), 203. https://doi.org/10.5296/jei.v6i1.16920

Clarke, D., & Roche, A. (2009). Using Mathematical Tasks Built around “Real” Contexts: Opportunities and Challenges for Teachers and Students. Australian Primary Mathematics Classroom, 14(2), 24–31. https://search.informit.org/doi/10.3316/informit.985957394685023

Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.). Hillsdale, NJ: Lawrence Erlbaum Associates, Publishers.

Common Core State Standards Initiative. (2010). Common Core State Standards for Mathematics. Washington, DC: National Governors Association Center for Best Practices and the Council of Chief State School Officers. https://learning.ccsso.org/wp-content/uploads/2022/11/ADA-Compliant-Math-Standards.pdf

Crawford, L.M. (2001) Teaching Contextually: Research, Rationale, and Techniques for Improving Student Motivation and Achievement. CCI Publishing, Inc., Texas.

Creswell, J. W. (2012). Educational research: Planning, conducting, and evaluating quantitative and qualitative research (4th ed.). Boston, MA: Pearson.

Crooks, N. M., & Alibali, M. W. (2014). Defining and measuring conceptual knowledge in mathematics. Developmental Review, 34(4), 344–377. https://doi.org/10.1016/j.dr.2014.10.001

Doğan, A., & Işik tertemiz, N. (2020). Fraction models used by primary school teachers. İlköğretim Online, 1888–1901. https://doi.org/10.17051/ilkonline.2020.762538

Elbehary, S., & Aboseira, F. (2022). Portraying mathematics teachers’ knowledge for teaching the addition of fractions through representations. International Journal of Research in Educational Sciences., 5(4), 303 - 342. Retrieved from https://iafh.net/index.php/IJRES/article/view/372

Elfouly. E. (2022). Teaching Biology through the contextual-based strategy REACT to develop the conceptual structure and self-regulation skills among agricultural secondary education students [تدريس مادة البيولوجي باستخدام استراتيجية REACT القائمة على مدخل السياق لتنمية البنية المعرفية ومهارات التنظيم الذاتي لدى طلاب التعليم الثانوي الزراعي ] Journal of the Faculty of Education, Beni Suef University, 19(115), 200-249. https://jfe.journals.ekb.eg/article_270658.html

Freudenthal, H. (1971). Geometry between the devil and the deep sea. Educational Studies in Mathematics, 3(3-4), 413–435. https://doi.org/10.1007/bf00302305

Gad. E. (2021). The Effectiveness of Teaching Biology Using REACT Strategy in Developing Achievement, Genetic Problem Solving Skills, and Motivation to Learn among Secondary Stage Students. [فاعلية تدريس الاحياء باستخدام استراتيجية REACTفي تنمية التحصيل ومهارات حل المسائل الوراثية والدافعية للتعلم لدى طالبات المرحلة الثانوية]. Journal of Education, Sohag University, 84(84), 761-805. https://edusohag.journals.ekb.eg/article_150734.html

Govender, S. (2021). Investigating the teaching of fractions across the Intermediate Phase (Grade 4 to Grade 6): What range of sub-constructs is made available, and how are these connected? [Dectoral Dissertation]. https://wiredspace.wits.ac.za/server/api/core/bitstreams/839fdad3-fbf2-4e96-ad5d-4933d2dc40b5/content

Graumann, G. (2011). Mathematics for problem in the everyday world. In J. Maasz & J. O ́Donghue (Eds.), Real-world problems for secondary school mathematics students: case studies (pp. 113-122). Rotterdam: Sense Publishers.

Herlina, E., & Ilmadi. (2022). The Implementation of REACT Strategy in Training Students’ Higher Order Thinking Skills (HOTS). TA’DIB JOURNAL, 25 (1), 47-57.

Hiebert, J. (Ed.). (2013). Conceptual and Procedural Knowledge. Routledge. https://doi.org/10.4324/9780203063538

Hiebert, J., & Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: An introductory analysis. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 1-27). Hillsdale, NJ: Erlbaum.

Hurrell, D. (2021). Conceptual Knowledge OR Procedural Knowledge or Conceptual Knowledge AND Procedural Knowledge: Why the Conjunction is Important to Teachers. Australian Journal of Teacher Education, 46(2), 57–71. https://doi.org/10.14221/ajte.2021v46n2.4

Inci, A. M., Peker, B., & Kucukgencay, N. (2023). Realistic mathematics education. In O. Cardak & S. A. Kiray (Eds.), Current Studies in Educational Disciplines 2023 (pp. 66-83). ISRES Publishing

Jazuli, A., Setyosari, P., Sulthon, & Kuswandi, D. (2017). Improving conceptual understanding and problem-solving in mathematics through a contextual learning strategy. Global Journal of Engineering Education, 19(1), 49–53. http://www.wiete.com.au/journals/GJEE/Publish/vol19no1/07-Jazuli-A.pdf

Jelatu, S., Sariyasa, S., & Ardana, I. M. (2018). Effect of GeoGebra-Aided REACT Strategy on Understanding of Geometry Concepts. International Journal of Instruction, 11(4), 325–336. https://doi.org/10.12973/iji.2018.11421a

Kadir, K., Kodirun, E. Cahyono, Hadi, A. L., Sani, A., & Jafar. (2020). The ability of prospective teachers to pose contextual word problem about fractions addition. Journal of Physics: Conference Series, 1581(1), 012025–012025. https://doi.org/10.1088/1742-6596/1581/1/012025

Kainulainen, M., McMullen, J., & Lehtinen, E. (2016). Early Developmental Trajectories Toward Concepts of Rational Numbers. Cognition and Instruction, 35(1), 4–19. https://doi.org/10.1080/07370008.2016.1251287

Khashan, D. K. H. (2014). Conceptual and Procedural Knowledge of Rational Numbers for Riyadh Elementary School Teachers. Journal of Education and Human Development, 3(4). https://doi.org/10.15640/JEHD.V3N4A17

Kashim, R. M. (2016). The conceptual and procedural knowledge in rational numbers in primary school teachers. International Journal of Educational and Pedagogical Sciences, 10, (3).

Kent, L. B. (2000). Connecting integers to meaningful contexts. Mathematics Teaching in the Middle School, 6(1), 62-66.

Khatimah, H., & Fatmah. (2021). REACT Strategy Aided by Cabri 3D to Improve Students’ Mathematical Connection Ability. Www.atlantis-Press.com; Atlantis Press. https://doi.org/10.2991/aer.k.211215.043

Kieren, T. E. (1976). On the mathematical, cognitive and instructional foundations of rational numbers. In R. A. Lesh (Ed.), Number and Measurement (pp. 101–144). Fonte: ERIC Document Reproduction Service No. ED 120 027.

Kieran, C. (2013). The false dichotomy in mathematics education between conceptual understanding and procedural skills: An example from algebra. In K. Leatham, Vital directions for mathematics education research. New York: Springer. https://doi.org/10.1007/978-1-4614-6977-3

Komalasari, K. (2010). Pembelajaran Kontekstual: Konsep dan Aplikasi. Bandung: Refika Aditama.

Kolar, V. M., Hodnik Čadež, T., & Vula, E. (2018). Primary Teacher Students’ Understanding of Fraction Representational Knowledge in Slovenia and Kosovo. Center for Educational Policy Studies Journal, 8(2), 71–96. https://doi.org/10.26529/cepsj.342

Komarudin, K., Mutia, M., Putri, D. P., Masykur, R., Suherman, S., & Astuti, A. D. (2022). Effect of REACT learning strategy on creative thinking and mathematical communication skills. Jurnal Math Educator Nusantara: Wahana Publikasi Karya Tulis Ilmiah Di Bidang Pendidikan Matematika, 8(1), 48-61. https://doi.org/10.29407/jmen.v8i1.16839

Laurens, T., Batlolona, F., Batlolona, J., & Leasa, M. (2017). How Does Realistic Mathematics Education (RME) Improve Students’ Mathematics Cognitive Achievement? Eurasia Journal of Mathematics, Science and Technology Education, 14(2). https://doi.org/10.12973/ejmste/76959

Lee, J.-E. (2012). Prospective elementary teachers’ perceptions of real-life connections reflected in posing and evaluating story problems. Journal of Mathematics Teacher Education, 15(6), 429–452. https://doi.org/10.1007/s10857-012-9220-5

Lemonidis, C., & Pilianidis, N. (2020). The 8th Grade Students’ Competencies in Alternating Different Symbolic Representations of Rational Numbers. International Electronic Journal of Mathematics Education, 15(3). https://doi.org/10.29333/iejme/7865

Lenz, K., & Wittmann, G. (2021). Individual Differences in Conceptual and Procedural Fraction Knowledge: What Makes the Difference and What Does It Look Like? International Electronic Journal of Mathematics Education, 16(1). https://eric.ed.gov/?id=EJ1291620

Lin, C.-Y., Becker, J., Byun, M.-R., Yang, D.-C., & Huang, T.-W. (2013). Preservice Teachers’ Conceptual and Procedural Knowledge of Fraction Operations: A Comparative Study of the United States and Taiwan. School Science and Mathematics, 113(1), 41–51. https://doi.org/10.1111/j.1949-8594.2012.00173.x

Ma, L. (1999). Knowing and Teaching Elementary Mathematics: Teacher’s Understanding of Fundamental Mathematics in China and the United States. In ERIC. Lawrence Erlbaum Associates, Inc. https://eric.ed.gov/?id=ED477840

Mack, N. K. (2001). Building on informal knowledge through instruction in a complex content domain: partitioning, units, and understanding multiplication of fractions. Journal for Research in Mathematics Education, 32(3), 267-295.

Marlan. (2017). The “REACT “ strategy application in the study of mathematics. Asian Journal of Natural & Applied Sciences, 6(4), 123-127.

Mehawed, H. A. (2021). Technological Pedagogical Content Knowledge (TPACK) of Pre-service Mathematics Teachers: An Exploratory Developmental Study [كفايات المعرفة البيداغوجية والتكنولوجية للمحتوى لدى معلمي الرياضيات قبل الخدمة: "دراسة ميدانية تطويرية"]. Mathematics Education Journal, 24 (10), 55-113. https://doi.org/10.21608/armin.2021.212901

Meyer, M., Dekker, T., & Querelle, N. (2001). Contexts in Mathematics Curriculum. Mathematics Teaching in the Middle School, 6(9), 522–527.

Mishra, R. K. (2014). Social Constructivism and Teaching of Social Science. Journal of Social Studies Education Research, 5(2). https://doi.org/10.17499/jsser.22283

Mohamed, R. (2019). The Effectiveness of Using REACT Strategy in Developing Future Thinking Skills and Academic Achievement Motivation Among Preparatory Second-Grade Students [فاعلية استخدام استراتيجية REACTفي تنمية مهارات التفكير المستقبلي ودافعية الإنجاز الاكاديمي لدى تلاميذ الصف الثاني الاعدادي]. Journal of Faculty of Education, Benha University, 30 (119), 81-128. https://search.mandumah.com/Record/1011208

Musyadad, M. A., & Avip, B. (2020). Application of react (relating, experiencing, applying, cooperating, transferring) strategy to improve mathematical communication ability of junior high school students. Journal of Physics: Conference Series, 1521, 032048. https://doi.org/10.1088/1742-6596/1521/3/032048

Nahdi, S. D., & Jatisunda, G. M. (2020). Conceptual Understanding and Procedural Knowledge: A Case Study on Learning Mathematics of Fractional Material in Elementary School. Journal of Physics: Conference Series, 1477, 042037. https://doi.org/10.1088/1742-6596/1477/4/042037

Nosehy, Sh. (2021). The effectiveness of the REACT strategy (Relating-Experiencing-Applying- Cooperating-- Transferring) in developing twenty-first-century skills and science learning enjoyment for primary school students [فاعلية استراتيجية REACT(الربط- الخبرة- التطبيق- التعاون- النقل) في تنمية مهارات القرن الحادي والعشرين ومتعة تعلم العلوم لدى تلاميذ المرحلة الابتدائية ]. Journal of Faculty of Education, Ain Shams University, 45, 1, 221-288. https://jfees.journals.ekb.eg/article_187901_964a076055cecf6df0d0f45a16ba8037.pdf

Nurzannah, N., Muliana, M., Herizal, H., Fajriana, F., & Mursalin, M. (2021). The effect of REACT strategy assisted by GeoGebra software on students’ mathematical representation ability. Malikussaleh Journal of Mathematics Learning (MJML), 4(2), 90. https://doi.org/10.29103/mjml.v4i2.5709

Omoruan, B. E., & Osadebe, P. U. (2020). Models Connecting Points on Pupils’ Achievement in Rational Numbers. Journal of Educational and Social Research, 10(4), 1. https://doi.org/10.36941/jesr-2020-0059

Olanoff, D., Lo, J.-J., & Tobias, J. (2014). Mathematical Content Knowledge for Teaching Elementary Mathematics: A Focus on Fractions. The Mathematics Enthusiast, 11(2), 267–310. https://scholarworks.umt.edu/tme/vol11/iss2/5/

Organisation for Economic Co-operation and Development. (2003). The PISA 2003 assessment framework. Mathematics, reading, science and problem solving knowledge and skills. OECD.

Organisation for Economic Co-Operation and Development (2009). Learning mathematics for life: A perspective from PISA. Paris: Organisation for Economic Co-operation and Development. Retrieved March 12, 2014, from http://browse.oecdbookshop.org/oecd/pdfs/free/9809111E.PDF

Paredes, S., Cáceres, M. J., Diego-Mantecón, J. M., Blanco, T. F., & Chamoso, J. M. (2020). Creating Realistic Mathematics Tasks Involving Authenticity, Cognitive Domains, and Openness Characteristics: A Study with Pre-Service Teachers. Sustainability, 12(22), 9656. https://doi.org/10.3390/su12229656

Putra, Z. H. (2018). A praxeological analysis of pre-service elementary teachers’ knowledge of rational numbers. Recherches En Didactique Des Mathematiques, 38(3), 315–364.

Putra, Z. H. (2019). Danish Pre-service Teachers’ Mathematical and Didactical Knowledge of Operations with Rational Numbers. International Electronic Journal of Mathematics Education, 15(1). https://doi.org/10.29333/iejme/5775

Putra, Z. H. (2019). Elementary Teachers’ Knowledge on Fraction Multiplication: An Anthropological Theory of the Didactic Approach. JOURNAL of TEACHING and LEARNING in ELEMENTARY EDUCATION (JTLEE), 2(1), 47. https://doi.org/10.33578/jtlee.v2i1.6964

Putra, Z. H., Sari, I. K., & Dahnilsyah, D. (2023). Online Formative Assessment in Mathematics Education: Prospective Primary Teachers’ Understanding of Rational Numbers. Journal of Elementary Education, 16(2), 1232–1232. https://doi.org/10.18690/rei.16.2.1232

Qadri, L., Ikhsan, M., & Yusrizal, Y. (2019). Mathematical Creative Thinking Ability for Students Through REACT Strategies. International Journal for Educational and Vocational Studies, 1(1), 58. https://doi.org/10.29103/ijevs.v1i1.1483

Qetesh, M. I., AlFayez, M. Q., & Saadh., M. J (2020). Conceptual and Procedural Knowledge in Mathematics and Its Relationship to Mathematical Thinking Among Jordanian Teachers. Multicultural education, 6(4), 27-32. https://doi.org/10.5281/zenodo.4180107

Raslan, M. (2018). Using of contextual teaching and learning approach (CTL)‎ to develop some non-routine mathematical problems solving skills and learning engagement of gradual levels achievement pupils at the primary stage [استخدام مدخل التدريس والتعلم السياقيCTLلتنمية بعض مهارات حل المشكلات الرياضية غير الروتينية والانخراط في التعلم لدي التلاميذ متدرجي المستويات التحصيلية بالمرحلة الابتدائية]. Journal of Faculty of Education, Kafrelsheikh University, 3(2), 2, 1413-1480. https://www.kfsedu.xyz/2018/06/issue-2-v3-2018-e2.html

Reitz-Koncebovski, K., Kuzle, A., & Kortenkamp, U. (2022). Is there a number in-between, and if so, how many? Analysis of pre-service primary teachers’ knowledge of rational numbers. Twelfth Congress of the European Society for Research in Mathematics Education (CERME12), Feb 2022, Bozen-Bolzano, Italy. ffhal-03744858f. https://hal.science/hal-03744858/document

Rejeki, S., Meidina, R. A., Hapsari, M. P., Setyaningsih, R., & Azura, R. N. F. (2021). Context-based tasks in mathematics textbooks for vocational high school students. Journal of Physics: Conference Series, 1776(1), 012030. https://doi.org/10.1088/1742-6596/1776/1/012030

Rittle-Johnson, B., & Schneider, M. (2015). Developing conceptual and procedural knowledge of mathematics. In R. C. Kadosh & A. Dowker (Eds.), The Oxford handbook of numerical cognition (pp. 1118–1134). Oxford University Press. https://doi.org/10.1093/oxfordhb/9780199642342.013.014

Rittle-Johnson, B., Siegler, R. S., & Alibali, M. W. (2001). Developing conceptual understanding and procedural skill in mathematics: An iterative process. Journal of Educational Psychology, 93(2), 346–362. https://doi.org/10.1037/0022-0663.93.2.346

Rittle-Johnson, B., Schneider, M., & Star, J. R. (2015). Not a One-Way Street: Bidirectional Relations Between Procedural and Conceptual Knowledge of Mathematics. Educational Psychology Review, 27(4), 587–597. https://doi.org/10.1007/s10648-015-9302-x

Rizos, I., & Adam, M. (2022). Mathematics students’ conceptions and reactions to questions concerning the nature of rational and irrational numbers. International Electronic Journal of Mathematics Education, 17(3), em0686. https://doi.org/10.29333/iejme/11977

Roth, W.-M. (1996). Where Is the Context in Contextual Word Problems?: Mathematical Practices and Products in Grade 8 Students’ Answers to Story Problems. Cognition and Instruction, 14(4), 487–527. https://www.jstor.org/stable/3233784

Saleh, A. (2018). The Effect of REACT Strategy Based on Contextual Approach in Developing Learning Transferring, Deep Understanding, and Academic Self-Efficacy in Biology for Secondary Students [اثر استراتيجية REACTالقائمة على مدخل السياق في تنمية انتقال اثر التعلم والفهم العميق والكفاءة الذاتية الاكاديمية في مادة الاحياء لطلاب المرحلة الثانوية]. Egyptian Journal of Science Education, Ain Shams University, 21(6). 1-68. https://doi.org/10.21608/mktm.2018.113712

Salifu, A. S. (2021). Pre-Service Teachers’ Conceptual and Procedural Knowledge of Rational Numbers in E. P. College of Education, Bimbilla, Ghana. Education Journal, 10(4), 126-137. https://doi.org/10.11648/j.edu.20211004.13

Samritin, S., Natsir, S. R., Abdul Manaf, & Sari, E. R. (2023). The effect of realistic mathematics education implementation in mathematics learning in elementary school. Formatif: Jurnal Ilmiah Pendidikan MIPA, 13 (1), 81-88. http://dx.doi.org/10.30998/formatif.v13i1.16522

Sari, D. P., & Darhim, D. (2020). Implementation of react strategy to develop mathematical representation, reasoning, and disposition ability. Journal on Mathematics Education, 11(1), 145–156. https://doi.org/10.22342/jme.11.1.7806.145-156

Schneider, M., Rittle-Johnson, B., & Star, J. R. (2011). Relations among conceptual knowledge, procedural knowledge, and procedural flexibility in two samples differing in prior knowledge. Developmental Psychology, 47(6), 1525–1538. https://doi.org/10.1037/a0024997

Schneider, M., & Stern, E. (2010). The developmental relations between conceptual and procedural knowledge: A multimethod approach. Developmental Psychology, 46(1), 178–192. https://doi.org/10.1037/a0016701

Selvianiresa, D., & Prabawanto, S. (2017). Contextual Teaching and Learning Approach of Mathematics in Primary Schools. Journal of Physics: Conference Series, 895, 012171. https://doi.org/10.1088/1742-6596/895/1/012171

Siegler, R. S., & Lortie-Forgues, H. (2017). Hard lessons: Why rational number arithmetic is so difficult for so many people. Current Directions in Psychological Science, 26(4), 346–351. https://doi.org/10.1177/0963721417700129

Siemon, D., Beswick, K., Brady, K., Clark, J., Faragher, R., & Warren, E. (2015). Teaching Mathematics: Foundations to Middle Years (2nd Edition). South Melbourne, Victoria: Oxford University Press.

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

Slattery, J., & Fitzmaurice, O. (2014). Ours is not to reason why, just invert and multiply: an insight into Irish prospective secondary teachers' conceptual understanding of the division of fractions. Irish Educational Studies, 33(4), 467-488.

Spitzer, M., Ruiz-Garcia, M., Strittmatter, Y., & Moeller, K. (2023, July 7). On the difficulty of rational number formats. https://doi.org/10.31234/osf.io/7qebn

Standards for the Preparation of Middle Level Mathematics Teachers National Council of Teachers of Mathematics Developed by the Standards Revision Task Force. (2020). https://www.nctm.org/uploadedFiles/Standards_and_Positions/NCTM_Middle_School_2020_Final.pdf

Star, J. R., & Stylianides, G. J. (2013a). Procedural and Conceptual Knowledge: Exploring the Gap Between Knowledge Type and Knowledge Quality. Canadian Journal of Science, Mathematics and Technology Education, 13(2), 169–181. https://doi.org/10.1080/14926156.2013.784828

Suastika, I. K., & Tri Wahyuningtyas, D. (2018). Developing Module of Fractional Numbers using Contextual Teaching and Learning Approach. Pancaran Pendidikan, 7(1). https://doi.org/10.25037/pancaran.v7i1.132

Supandi, S., Waluya, S. B., & Rochmad, R. (2016). Analysis Of Mathematical Representation by React Strategy On The Realistic Mathematics Education. Anatolian Journal of Education, 1(2). https://doi.org/10.29333/aje.2016.121a

Taley, B. I. (2022). Teacher and student views of mathematics word problem-solving task at senior high school level. Faculty of Natural and Applied Sciences Journal of Mathematics and Science Education, 3(2), 33-43.

The Egyptian Ministry of Education and Technical Education. (2020). Mathematics for first preparatory grade, first term. Book Sector.

The National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. Reston, Va.: NCTM.

Thurtell, E., Forrester, P., & Chinnappan, M. (2019). Building conceptual knowledge of fraction operations among pre-service teachers: Effect of a representation-based teaching approach within a teacher education program. Faculty of Social Sciences - Papers (Archive), 100–124. https://ro.uow.edu.au/sspapers/4473/

Tobias, J. (2009). Preservice Elementary Teachers’ Development of Rational Number Understanding through the Social Perspective and the Relationship Among Social and Individual Environments. Electronic Theses and Dissertations. https://stars.library.ucf.edu/etd/3967/

Van Steenbrugge, H., Lesage, E., Valcke, M., & Desoete, A. (2014). Preservice elementary school teachers’ knowledge of fractions: a mirror of students’ knowledge? JOURNAL of CURRICULUM STUDIES, 46(1), 138–161. https://biblio.ugent.be/publication/5671645

Vergnaud, G. (1983). Multiplicative structures. In R. Lesh and M. Landau (Eds). Acquisition of mathematics concepts and processes. 92-126. New York: Academic Pres.

Vygotsky, L. S., & Cole, M. (1978). Mind in Society. Harvard University Press. http://books.google.ie/books?id=RxjjUefze_oC&printsec=frontcover&dq=Mind+in+Society:+The+Development+of+Higher+Psychological+Processes&hl=&cd=3&source=gbs_api

Westwood, P. (2008). What Teachers Need to Know about Numeracy. In Google Books. Aust Council for Ed Research. https://books.google.com.eg/books/about/What_Teachers_Need_to_Know_about_Numerac.html?id=b5E3uHTT1l0C&redir_esc=y

Widada, W., Herawaty, D., Mundana, P., Agustina, M., Putri, F. R., & Anggoro, A. F. D. (2019). The REACT strategy and discovery learning to improve mathematical problem solving ability. Journal of Physics: Conference Series, 1318(1), 012081. https://doi.org/10.1088/1742-6596/1318/1/012081

Wijaya, A., van den Heuvel-Panhuizen, M., & Doorman, M. (2015). Opportunity-to-learn context-based tasks provided by mathematics textbooks. Educational Studies in Mathematics, 89(1), 41–65. https://doi.org/10.1007/s10649-015-9595-1

Yang, X., & Wang, Y. (2022). People’s preferences for different types of rational numbers in linguistic contexts. Quarterly Journal of Experimental Psychology, 174702182210763. https://doi.org/10.1177/17470218221076398

Zakaria, E., & Zaini, N. (2009). Conceptual and procedural knowledge of rational numbers in trainee teachers. European Journal of Social Sciences, 9(2), 202-217.

Zakaryan, D., & Ribeiro, M. (2018). Mathematics teachers’ specialized knowledge: a secondary teacher’s knowledge of rational numbers. Research in Mathematics Education, 21(1), 25–42. https://doi.org/10.1080/14794802.2018.1525422




DOI: http://dx.doi.org/10.24042/ajpm.v15i1.21420

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