Examining the effect primary school teachers’ preferred teaching method has on primary school students’ mathematics achievement is important. In this context, the purpose of the research is to determine whether the worked example method is effective on students’ ability to learn fundamental knowledge about fractions and their success in solving mid- and high-difficulty fraction problems compared to the traditional teaching method. The research uses the experimental design with a pretest-posttest control group. The experimental group has 36 students, and the control group has 37 students. While teaching fractions was conducted in accordance with the traditional teaching method in the control group, the worked example method was applied in the experimental group. The research results from the research determined the worked example method to be more effective than the traditional teaching method in learning the fundamental knowledge about fractions and developing student success in solving mid- and high-difficulty fraction problems. The traditional teaching method was not effective at developing students’ success in solving high-difficulty fraction problems. Because problem solving is a skill that develops slowly, teachers should not prefer time-consuming methods in developing problem-solving skills. Using the worked example method is suggested in primary school as it has been revealed to develop problem-solving skills in a short time and these skills’ foundations are laid in primary school.

Keywords: Primary school, mathematics, worked example method, fraction, problem solving.


Abdul-Rahman, S. S., & Du Boulay, B. (2014). Learning programming via workedexamples: Relation of learning styles to cognitive load. Computers in Human Behavior, 30, 286–298.

Ardeleanu, R. (2019). Traditional and modern teaching methods in mathematics. Journal of Innovation in Psychology, Education and Didactics, 23(2), 133-140.

Altun, M. (2005). Matematik öğretimi [Teaching mathematics]. Bursa: Alfa Aktüel Publications.

Arise, N. (2018). The effectiveness of small group discussion method in the teaching of reading comprehension, (Unpublished doctoral dissertation). UIN Alauddin Makassar, Indonesia.  

Ashman, G., Kalyuga, S., & Sweller, J. (2020). Problem-solving or explicit instruction: Which should go first when element interactivity is high? Educational Psychology Review32(1), 229-247.

Atkinson, R. K., Derry, S. J., Renkl, A., & Wortham, D. (2000). Learning from examples: Instructional principles from the worked examples research. Review of Educational Research, 70, 181–214.

Atkinson, R.K., Renkl, A., & Merrill, M. M. (2003). Transitioning from studying examples to solving problems: Effects of self-explanation prompts and fading worked-out steps. Journal of Educational Psychology, 95(4), 774-783.

Ayvaz Can, A., & Türer, C. (2018). 4. sınıf öğrencilerinin kesirler konusundaki bilgi düzeylerinin incelenmesi, [Investigation of 4th grade students’ fractional knowledge]. In 17th International Primary School Teacher Education Symposium Abstract Book, 387-388.

Ayvaz Can, A. (2018). İlkokul 4. sınıf öğrencilerinin problem çözme başarılarına çözülmüş örnekler yönteminin etkisi [The effect of worked examples method on problem solving achievement of fourth grade primary school students], (Unpublished doctoral dissertation).  Marmara University, Turkey.

Baars, M., Van Gog, T., de Bruin, A., & Paas, F. (2017). Effects of problem solving after worked example study on secondary school children’s monitoring accuracy. Educational Psychology, 37(7), 810-834.

Behlol, M. G., Akbar, R. A., & Sehrish, H. (2018). Effectiveness of problem solving method in teaching mathematics at elementary level. Bulletin of Education and Research, 40(1), 231-244.

Behr, M. J., Wachsmuth, I., & Post T. (1985). Construct a sum: a measure of children’s understanding of fraction size. Journal for Research in Mathematics Education, 16(2), 120-131.

Berthold, K., Eysink, T. H. S., & Renkl, A. (2009). Assisting self-explanation prompts are more effective than open prompts when learning with multiple representations. Instructional Science, 37(4), 345-363.

Bokosmaty, S., Sweller, J., & Kalyuga, S. (2015). Learning geometry problem solving by studying worked examples: Effects of learner guidance and expertise. American Educational Research Journal, 52(2), 307-333.

Booker, G. (1998). Children’s construction of initial fraction concepts, Proceedings of the 22nd Conference of the International Group for the Psychology of Mathematics Education, 2, 128-135, Stellenbosh: South Africa.

Booth, J. L., Lange, K. E., Koedinger, K. R., & Newton, K. J. (2013). Example problems that improve student learning in algebra: Differentiating between correct and incorrect examples. Learning and Instruction, 25, 24-34.

Bourne, L. E., Goldstein, S., & Link, W. E. (1964). Concept learning as a function of availability of previously learned information. Journal of Experimental Psychology, 67, 439-448.

Brewer, W. F., & Nakamura, G. V. (1984). The nature and function of schemas. In R. S. Wyer & T. K. Srull (Eds.), Handbook of Social Cognition (pp. 119-160). Hillsdale, NJ: Erlbaum.

Brooks, C. D. (2009). Effects of process-oriented and product-oriented worked examples and prior knowledge on learner problem solving and attitude: A study in the domain of microeconomics. Electronic Theses, Treatises and Dissertations, Florida State University, USA.

Brooks, D. W., & Crippen K. J. (2005). Understanding why worked examples work. Retrieved on April, 21 2020 from

Bruner, J. S., Goodnow, J., & Austin, G. (1956). A study of thinking. New York: Wiley.

Budé, L., Van De Wiel, M. W., Imbos, T., & Berger, M. P. (2012). The effect of guiding questions on students’ performance and attitude towards statistics. British Journal of Educational Psychology, 82(2), 340-359.

Carraher, D. W., & Schliemann, A. D. (1991). Children’s understanding of fraction as expressions of relative magnitude. In F. Fringhetti (Ed.) Proceedings of the Fifteenth PME Conference, Asisi, Italy, 1, 184-191.

Carroll, W. M. (1994). Using worked examples as an instructional support in the algebra classroom. Journal of Educational Psychology, 86, 360–367.

Catrambone, R. (1996). Generalizing solution procedures learned from examples. Journal of Experimental Psychology: Learning, Memory, and Cognition, 22(4), 1020-1031.

Catrambone, R., & Holyoak, K. J. (1989). Overcoming contextual limitations on problem-solving transfer. Journal of Experimental Psychology: Learning, Memory, and Cognition, 15, 1147-1156.

Chen, O., Retnowati, E., & Kalyuga, S. (2020). Element interactivity as a factor influencing the effectiveness of worked example–problem solving and problem solving–worked example sequences. British Journal of Educational Psychology, 90, 210-223.

Chi, M. T., Feltovich, P. J., & Glaser, R. (1981). Categorization and representation of physics problems by experts and novices. Cognitive Science, 5, 121-152.

Chi, M. T., Glaser, R., & Rees, E. (1982). Expertise in problem solving. In R. Sternberg (Ed.), Advances in the psychology of human intelligence (pp. 7-75). Hillsdale, NJ: Erlbaum.

Clark, R. C., & Mayer, R.E. (2011). E-learning and the science of instruction: Proven guidelines for consumers and designers of multimedia learning, (3nd ed), CA: John Wiley & Sons, Pfeiffer.

Clark, R., Nguyen, F., & Sweller, J. (2006). Efficiency in learning: Evidence-based guidelines to manage cognitive load. San Francisco: Pfeiffer.

Clarke, T., Ayres, P., & Sweller, J. (2005). The impact of sequencing and prior knowledge on learning mathematics through spreadsheet applications. Educational Technology Research and Development, 53(3), 15-24.

Cohen J. (1988). Statistical power analysis for the Behavioral Sciences (3th edition). Lawrence Erlbaum Associates, New Jersey.

Compañ-Rosique P., Molina-Carmona R., & Satorre-Cuerda R. (2020) Impact of constant work on the students’ academic performance. In: Zaphiris P., Ioannou A. (Eds) Learning and collaboration technologies. Designing, developing and deploying learning experiences. HCII 2020. Lecture Notes in Computer Science, 12205. Springer, Cham.

Cooper, G., & Sweller, J. (1987). Effects of schema acquisition and rule automation on mathematical problem-solving transfer. Journal of Educational Psychology, 79(4), 347 -362.

Corral, D., Quilici, J. L., & Rutchick, A. M. (2020). The effects of early schema acquisition on mathematical problem solving. Psychological Research, 84(6), 1495–1506.

Crissman, J. K. (2006). The design and utilization of effective worked examples: A meta-analysis. The University of Nebraska-Lincoln. A dissertation.

Crocker, L., & Algina, J. (1986). Introduction to classical and modern test theory. Toronto: Holt, RineHart, and Winston, Inc.

D’Ambrosio, B., & Mewborn, D., (1994). Children’s constructions of ımplications for classroom instruction, Journal for Research in Childhood Education, 8(2), 150-161.

Da Costa, B., & Seok, S. (2010). Managing cognitive load in the design of assistive technology for those with learning disabilities. In Seok, S., Meyen, E. L. and DaCosta, (Eds.), Handbook of Research on Human Cognition and Assistive Technology: Design, Accessibility and Transdisciplinary Perspectives (pp.21-42). Hershey, PA: IGI Global.

Darabi, A. A., Nelson, D. W., & Paas, F. (2007). Learner involvement in instruction on a complex cognitive task: Application of a composite measure of performance and mental effort. Journal of Research on Technology in Education, 40(1), 39-48.

Davis, E. G. (2003). Teaching and classroom experiments dealing with fractions and proportional reasoning. Journal of Mathematical Behavior, 22, 107-111.

Faulkner, D. R. (1999). A Comparison of worked-examples and problem-based learning on the achievement and retention of middle school science student team, (Unpublished doctoral dissertation). The University of South Alabama.

Fraenkel, J. R., & Wallen, N. E. (2009). How to design and evaluate research in education (7th ed). New York: McGraw-Hill.

Gerjets, P., Scheiter, K., & Catrambone, R. (2006). Can learning from molar and modular worked examples be enhanced by providing instructional explanations and prompting self-explanations? Learning and Instruction, 16, 104-121.

Gerven, P. V., Paas, F., Merrienboer, J. V., & Schmidt, H. (2002). Cognitive load theory and aging: Effects of worked examples on training efficiency. Learning and Instruction, 12, 87-105.

Gholami, M., Moghadam, P. K., Mohammadipoor, F., Tarahi, M. J., Sak, M., Toulabi, T., & Pour, A. H. H. (2016). Comparing the effects of problem-based learning and the traditional lecture method on critical thinking skills and metacognitive awareness in nursing students in a critical care nursing course. Nurse education today, 45, 16-21.

Gick, M. L., & Holyoak, K. J. (1983). Schema induction and analogical transfer. Cognitive Psychology, 15, 1-38.

Glover, L. (2019). The effects of using schema-based instruction in math word problems on student performance in third grade. Master of Education. Goucher College. America.

Goffin, S. G., & Tull, C. Q. (1985). Problem solving: Encouraging active learning. Young Children, 40, 28-32.

Gupta, U. & Zheng, R. Z. (2020). Cognitive load in solving mathematics problems: validating the role of motivation and the ınteraction among prior knowledge, worked examples, and task difficulty. European Journal of STEM Education, 5(1), 5.

Hart, K. M. (1993). Fractions. In K. M. Hart (Ed.,) Children’s Understanding of Mathematics: 11-16, (66-81). John Murray: London.

Haslam, F., & Treagust, D. F. (1987). Diagnosing secondary students' misconceptions of photosynthesis and respiration in plants using a two-tier multiple choice instrument. Journal of biological education, 21(3), 203-211.

Hinsley, D. A., Hayes, J. R., & Simon, H. A. (1977). From words to equations meaning and representation in algebra word problems. In M. A. Just & P. A. Carpenter (Eds.), Cognitive Processes in Comprehension (pp. 89-106). Hillsdale, NJ: Erlbaum.

Hollender, N., Hofmann, C., Deneke, M., & Schmitz, B. (2010) Integrating cognitive load theory and concepts of human–computer interaction. Computers in Human Behavior, 26(6), 1278–1288.

Hoogerheide, V., Renkl, A., Fiorella, L., Paas, F., & van Gog, T. (2019). Enhancing example-based learning: Teaching on video increases arousal and improves problem-solving performance. Journal of Educational Psychology, 111(1), 45–56.

Hsin, C. T., & Wu, H. K. (2011). Using scaffolding strategies to promote young children’s scientific understandings of floating and sinking. Journal of Science Education and Technology20(5), 656-666.

Hurioğlu, L., & Efendioğlu, A. (2017). İki farklı tür çalışan örnek: Öğretmen adaylarının ölçme ve değerlendirme dersindeki problem çözme becerilerinin incelenmesi. [Two different types of worked example: enhancing problem solving skills of teacher candidates in measurement and evaluation course]. Electronic Turkish Studies, 12(6), 403-422.

İltüzer, Y. (2016). Öz açıklamalı çözümlü örneklerle desteklenmiş çevrimiçi öğrenme sürecinin karar kurallarını uygulama becerilerine etkisi [The impact of an online learning process supported with self-explained worked examples on applying decision rules skills], (Unpublished Master Thesis). Hacettepe University. Turkey.

Jitendra, A. K., Griffin, C. C., Buchman, A. D., & Sczesniak, E. (2007). Mathematical problem solving in third-grade classrooms. The Journal of Educational Research, 100(5), 282-302.

Jones, E. C. (2014). Cognitive load theory and collage composition: Can worked examples help novice writers learn argumentation?, (Unpublished doctoral dissertation). Capella University, USA.

Kalyuga, S. (2008). When less is more in cognitive diagnosis: A rapid online method for diagnosing learner task-specific expertise. Journal of Educational Psychology, 100, 603–612.

Karasel, N., Ayda, O., & Tezer, M. (2010). The relationship between mathematics anxiety and mathematical problem solving skills among primary school students. Procedia Social and Behavioral Sciences, 2, 5804–5808.

Keijzer, R., & Terwel, J., (2003). Learning for mathematical insight: a longitudinal comparative study on modelling. Learning and Instruction, 13, 285-304.

Khan, I., Mehmood, A., & Jumani, N. B. (2020). Classroom practices of teacher educators: Constructivist versus traditional approach. Journal of Research in Social Sciences, 8(1), 20-34.

Kim, R. S., Weitz, R., Heffernan, N. T., & Krach, N. (2009). Tutored problem solving vs.―pure‖ worked examples. In Proceedings of the 31st annual conference of the cognitive science society (3121 - 3126). Cognitive Science Society Austin, TX.

Krulik S., & Reys R E (1980). Problem solving in school mathematics. National Council of Teachers of Mathematics 1980 Yearbook. Reston Va: NCTM.

Kusuma, I. A., & Retnowati, E. (2021). Designs of faded-example to increase problem solving skills and procedural fluency in algebraic division. Journal of Physics: Conference Series, 1806(1), IOP Publishing.

Kyriakides, A.O. (2006). Modelling fractions with area: The salience of vertical partitioning. In J. Novotná, H. Moraová, M. Krátká & N. Stehlíková (Eds.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education, Vol. 4, (pp. 17-24). Prague: PME.

Lee, K. M., Nicoll, G., & Brooks, D. W. (2004). A comparison of inquiry and worked example web-based instruction using physlets. Journal of Science and Technology, 13(1), 81-88.

Leinhardt, G., & Smith, D. A. (1985). Expertise in mathematics instruction: Subject matter knowledge. Journal of Educational Psychology, 77, 247-271.

Lesh, R., & Zawojewski, J. (2007). Problem solving and modeling. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (Vol. 2, pp. 763-804). Charlotte, NC: Information Age Pub.

Lesnussa, Y. A. (2019). Realistic mathematics education (RME) provides great benefits for students in Indonesia. Jurnal Aplikasi Multidisiplinari Filsafat & Sains, 1(1), 1-6.

Lessani, A., Yunus, A., & Bakar, K. (2017). Comparison of new mathematics teaching methods with traditional method. People: International Journal of Social Sciences, 3(2), 1285-1297.

Lockwood, E., Ellis, A. B., & Lynch, A. G. (2016). Mathematicians’ example-related activity when exploring and proving conjectures. International Journal of Research in Undergraduate Mathematics Education, 2(2), 165-196.

Ma, L. (2010). Knowing and teaching elementary mathematics: Teachers' understanding of fundamental mathematics in China and the United States. New York: Routledge.

Mayer, R. E., Sims, V., & Tajika, H. (1995). Brief note: A comparison of how textbooks teach mathematical problem solving in Japan and the United States. American Educational Research Journal, 32(2), 443-460.

Morrison, G. R., & Anglin, G. J. (2005). Research on cognitive load theory: Application to e-learning. Educational Technology Research and Development, 53(3), 94-104.

Mutrofin, M., Degeng, I., Ardhana, I. W., & Setyosari, P. (2019). The effect of instructional methods (lecture-discussion versus group discussion) and teaching talent on teacher trainees student learning outcomes. Journal of Education and Practice, 8(9), 203-209.

Nafees, M. (2011). An experimental study on the effectiveness of problem-based versus lecture-based instructional strategy on achievement, retention and problem solving capabilities in secondary school general science students, (Unpublished doctoral dissertation). International Islamic University, Islamabad.

Nainan, M., Balakrishnan, B., & Mohamad Ali, A. Z. (2020). Design of worked examples for learning programming:  Literature review. International Journal of Instruction, Technology, and Social Sciences, 1(3), 8-16.

Nelson, D. W. (2006). Effects of practice sequence variations on the transfer of complex cognitive skills practiced in computer-based instruction, (Unpublished doctoral dissertation). Florida State University, USA.

Newstead, K., & Murray, H., (1998). Young student’s construction of fractions. Proceedings of the 22nd Conference of the International Group for the Psychology of Mathematics Education, 3, 295-302, Stellenbosh: South Africa.

Nguyen, H. A., Guo, Y., Stamper, J., & McLaren, B. M. (2020). Improving students’ problem-solving flexibility in non-routine mathematics. In International Conference on Artificial Intelligence in Education (pp. 409-413). Springer, Cham.

Nurutdinova, A. R., Perchatkina, V. G., Zinatullina, L. M., Zubkova, G.  I., & Galeeva, F.  T. (2016). Innovative teaching practice: Traditional and alternative methods (challenges and implications). International journal of environmental and science education, 11(10), 3807-3819.

Oliveira, I., & Ramalho, G. (1994). Rational numbers: Strategies and misconceptions in sixth grade students. Lisbon: Portugal: Proceedings PME XVIII.

Olkun, S., & Toluk Uçar, Z. (2014). İlköğretimde etkinlik temelli matematik öğretimi (6. baskı) [Activity based mathematics teaching in primary education (6th ed.)]. Ankara: Eğiten Kitap.

Orton, A., & Frobisher, L. (1996). Insights into teaching mathematics. London: Cassell.

Özcan, Z. Ç., Kılıç, Ç., & Obalar, S. (2018). Öğrencilerin matematikteki hatalarını belirleme ve gidermede açıklayıcı ipuçlarıyla desteklenmiş çözümlü örnekler [Worked-out questions supported with self-explanation prompts for determination and elimination of students mistakes in mathematics], Mehmet Akif Ersoy University Journal of Education Faculty, 45, 1-22.

Paas, F. G. (1992). Training strategies for attaining transfer of problem-solving skill in statistics: A cognitive-load approach. Journal of Educational Psychology, 84, 429-434.

Paas, F. G., & Van Merriënboer, J. J. G. (1994). Variability of worked examples and transfer of geometrical problem-solving skills: A cognitive-load approach. Journal of Educational Psychology, 86(1), 122–133.

Paas, F., Renkl, A., & Sweller, J. (2004). Cognitive load theory: Instructional implications of the interaction between information structures and cognitive architecture. Instructional Science, 32(1-2), 1-8.

Pachman, M., Sweller, J., & Kalyuga, S. (2014). Effectiveness of combining worked examples and deliberate practice for high school geometry. Applied cognitive psychology, 28(5), 685-692.

Pawley, D. M. (2004). A cognitive load approach to instruction in formation of algebraic equations, (Unpublished doctoral dissertation). Available from ProQuest Dissertations and These database. (UMI No. 0807623)

Pease, R. S. (2012). Using elaborative interrogation enhanced worked examples to improve chemistry problem solving, (Unpublished doctoral dissertation). The University of Maryland.

Petit, M., & Zawojewski, J. S. (1997). Teachers and students learning together about assessing problem solving. The Mathematics Teacher, 90(6), 472.

Pillay, H. K. (1994). Cognitive load and mental rotation: Structuring orthographic projection for learning and problem solving. Instructional Science, 22, 91-113.

Polya, G. (1945). How to solve it. New Jersey, NJ: Princeton University Pres.

Reed, S. K. (1993). A schema-based theory of transfer. In D. K. Detterman & R. J. Sternberg (Eds.), Transfer on trial: Intelligence, cognition, and instruction (pp. 39-67). Norwood, NJ: Ablex

Renkl, A. (1997). Learning from worked-out examples: A study on individual differences. Cognitive Science, 21(1), 1-29.

Renkl, A. (1999). Learning mathematics from worked-out examples: Analyzing and fostering self-explanations. European Journal of Psychology of Education, 14, 477-488.

Renkl, A. (2002). Worked-out examples: Instructional explanations support learning by self-explanations. Learning and Instruction, 12, 529-556.

Renkl, A. (2005). The worked-out examples principle in multimedia learning. In Mayer, R. E. (Ed.), The Cambridge handbook of multimedia learning (pp. 229–245). New York: Cambridge University Press.

Renkl, A., & Atkinson, R. K. (2010). Learning from worked-out examples and problem solving. In Cognitive load theory. Cambridge University Press.

Richards, K. A. R., & Graber, K. C. (2019). Retention in PETE: Survey results and discussion. Journal of Teaching in Physical Education, 38(1), 53-60.

Rodiawati, A., & Retnowati, E. (2019). How to design worked examples for learning patterns in mathematics. In Journal of Physics: Conference Series, 1320(1), p. 012045. IOP Publishing.

Rosenthal, J. S. (1995). Active learning strategies in advanced mathematics classes, Studies in Higher Education, 20(2), 223-228.

Rourke, A., & Sweller, J. (2009). The worked-example effect using ill-defined problems: Learning to recognise designers’ styles. Learning and Instruction, 19, 185-199.

Rumelhart, D. E., & Ortony, A. (1977). The representation of knowledge in memory. In R. C. Anderson, R. J. Spiro, & W. E. Montague (Eds.), Schooling and the acquisition of knowledge. Hillsdale, NJ: Erlbaum.

Saira, N. Z., & Hafeez, M. (2021). A critical review on discussion and traditional teaching methods. Psychology and Education Journal, 58(1), 1871-1886.

Samuelsson, J. (2008). The impact of different teaching methods on students’ arithmetic and self‐regulated learning skills. Educational Psychology in Practice, 24(3), 237-250,

Seeley, C. L. (2017).  Turning teaching upside down. Educational Leadership, 75(2), 32-36.

Senemoğlu, N. (2020). Gelişim, öğrenme ve öğretim [Development, learning, and instruction]. Ankara: Anı Publishing.

Shen, C. (2004). The effectiveness of worked examples in a game-based problem-solving task, (Unpublished doctoral dissertation). Available from ProQuest Dissertations and These database. (UMI No. 3196889)

Silver, E. A. (1979). Student perceptions of relatedness among mathematical verbal problems. Journal for Research in Mathematics Education, 10, 195-210.

Silver, E. A., & Marshall, S. P. (1990). Mathematical and scientific problem solving: Findings, issues and instructional implications. In B. F. Jones & C. Idol (Eds.), Dimensions of thinking and cognitive instruction. Hillsdale, NJ: Erlbaum.

Stonewater, J. K. (2005). Inquiry teaching and learning: The best math class study. School Science and Mathematics, 105(1), 36 - 47.

Sweller, J. (1988). Cognitive load during problem solving: effects on learning. Cognitive Science, 12, 257-285.

Sweller, J. (2006). The worked example effect and human cognition. Learning and instruction, 16(2), 165-169.

Sweller, J. (2011). Cognitive load theory and E-learning. In International Conference on Artificial Intelligence in Education. Springer, Berlin, Heidelberg.

Sweller, J. (2020). Cognitive load theory and educational technology. Educational Technology Research and Development68(1), 1-16.

Sweller, J., & Cooper, G. A. (1985). The use of worked examples as a substitute for problem solving in learning algebra. Cognition and Instruction, 2(1), 59-89.

Sweller, J., & Levine, M. (1982). Effects of goal specificity on means–ends analysis and learning. Journal of experimental psychology: Learning, memory, and cognition, 8(5), 463-474.

Sweller, J., Ayres, P., & Kalyuga, S. (2011). The worked example and problem completion effects. In Cognitive load theory (pp. 99–109). Springer New York.

Tamir, P. (1989). Some issues related to the use of justifications to multiple-choice answers. Journal of Biological Education, 23(4), 285-292.

Tennyson, R. D., & Cocchiarella, M. J. (1986). An empirically based instructional design theory for teaching concepts. Review of Educational Research, 56, 40-71.

Tennyson, R. D., Wooley, F. R., & Merrill, M. D. (1972). Exemplar and nonexemplar variables which produce correct concept classification behavior and specified classification errors. Journal of Educational Psychology, 63, 144-152.

Tobias, J. (2013). Prospective elementary teachers’ development of fraction language for defining the whole. Journal of Mathematics Teacher Education, 16(2), 85-103.

Treagust, D. F. (1988). Development and use of diagnostic tests to evaluate students’ misconceptions in science. International journal of science education, 10(2), 159-169.

Treagust, D. F., & Chandrasegaran, A. L., (2007), The Taiwan national science concept learning study in an international perspective. International Journal of Science Education, 29(4), 391-403.

Tuovinen, J. E. (1997). Cognitive load and discovery learning.

Tüker, B. G. (2013). Near and far transfer of learning in mathematics lesson designed based on cognitive load theory principles: A case study, (Unpublished doctoral dissertation). Orta Doğu Teknik University. Ankara.

Van  Gog,  T.,  Rummel,  N.,  &  Renkl,  A.  (2019). Learning how to solve problems by studying examples.  In J. Dunlosky &  K.  A.  Rawson (Eds.) The Cambridge Handbook of Cognition and Education (183–208). Cambridge University.

Van de Walle, J. A., Karp, K., & Bay-Williams, J. M. (2019). Elementary and middle school mathematics: Teaching developmentally (10nd ed.). Boston: Pearson.

Van Gerven, P. W. M., Paas, F. G. W. C., Van Merriënboer, J. J. G., & Schmidt, H. G. (2002). Cognitive load theory and aging: Effects of worked examples on training efficiency. Learning and Instruction, 12(1), 87-105.

Van Gog, T., & Rummel, N. (2010). Example-based learning: Integrating cognitive and social-cognitive research perspectives. Educational Psychology Review, 22(2), 155-174. 

Van Gog, T., Paas, F., & Van Merriënboer, J. J. (2006). Effects of process-oriented worked examples on troubleshooting transfer performance. Learning and Instruction, 16(2), 154-164.

Van Gog, T., Paas, F., & Van Merriënboer, J. J. G. (2004). Process-oriented worked examples: Improving transfer performance through enhanced understanding. Instructional Science, 32(1-2), 83-98.

Van Gog. T., Kester, L., & Paas, F. (2011). Effects of worked examples, example problem, and problem-example pairs on novices’ learning. Contemporary Educational Psychology, 36(3), 212-218.

Van Hoof, J., Engelen, A. S., & Van Dooren, W. (2021). How robust are learners’ misconceptions of fraction magnitude? An intervention study comparing the use of refutation and expository text. Educational Psychology, 1-20.

Van Merriënboer, J. J., & Sweller, J. (2005). Cognitive load theory and complex learning: Recent developments and future directions. Educational psychology review, 17(2), 147-177.

VanLehn, K. (1990). Problem solving and cognitive skill acquisition. In M. I. Posner (Ed.), Foundations of Cognitive Science (pp. 527-579). Cambridge, MA: MIT Press.

Venkateswarlu, T., & Kumar, M. S. (2020). The role of English language teacher as a facilitator- a critical study in the undergraduate context of Acharya Nagarjuna University, Guntur, Research Journal of English, 5(1), 30-38.

Ward, M., & Sweller, J. (1990). Structuring effective worked examples. Cognition and Instruction, 7(1), 1-39.

Widyastuti, B. W., & Retnowati, E. (2021). Effects of worked example on experts’ procedural skills in solving geometry problems. In 7th ICRIEMS, 338-343. Atlantis Press.

Wood, D., Bruner, J. S., & Ross, G. (1976). The role of tutoring in problem solving. Journal of Child Psychology Psychiatry, 17(2), 89-100.

Yeo, D. J., & Fazio, L. K. (2019). The optimal learning strategy depends on learning goals and processes: Retrieval practice versus worked examples. Journal of Educational Psychology, 111(1), 73-90.

Yeo, L. M., & Tzeng, Y. T. (2020). Cognitive effect of tracing gesture in the learning from mathematics worked examples. International Journal of Science and Mathematics Education, 18(4), 733-751.

Zhao, J., & Li, M. (2020). Teaching methods reform of “algorithm design and analysis” course. In 2020 6th International Conference on Social Science and Higher Education (ICSSHE 2020) (pp. 49-53). Atlantis Press.

Zhu, X., & Simon, H. A. (1987). Learning mathematics from examples and by doing. Cognition and Instruction, 4(3), 137-166.






Research Article