MATH TEXTBOOKS AND LEARNING ALGEBRAIC CONTENT THROUGH DISCOVERY-BASED LEARNING

Proceedings of 2nd International Scientific Conference Teaching, Learning and Teacher Education (TLTE 2025) (pp. 101-112)

AUTOR(I) / AUTHOR(S): Sanja Anđelković , Nela Malinović Jovanović , Aleksandra Milanović

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DOI: https://doi.org/10.46793/2TLTE.093A

SAŽETAK / ABSTRACT:

Starting from the position that algebra teaching in primary mathematics education should be based on students’ independent discovery, construction and generation of knowledge, the authors emphasize the importance of studying algebraic content in primary mathematics education as well as the methodological design of algebra teaching aimed at students’ active participation in the learning process. In this context, taking into account the key role of textbooks in teachers’ teaching practice, a content analysis of the textbook was carried out with the aim of investigating its role in creating conditions for discovery-based learning of algebraic content. The study was conducted on a sample of 45 first to fourth grade primary school mathematics textbooks. The elements that form the basis for discovery-based learning of algebraic content were analyzed, i.e. those that stimulate students’ thinking activity, direct their attention, initiate the drawing of conclusions and contribute to the construction of knowledge at a satisfactory level. The results obtained show that in the mathematics textbooks for the first four grades of primary school, the expository approach dominates, in which the new content is presented explicitly, without any special requirements that would stimulate students’ thinking activity. On the other hand, on average only a third of the tasks provide a basis for discovery-based learning. It can be concluded that examples that encourage students to discover new algebraic content are insufficiently represented in mathematics textbooks, which means that textbooks in general do not provide adequate conditions for discovery learning of algebraic content. Specifically, the research findings point to aspects that should be improved in the design of textbooks. They can help to improving the quality of textbooks through an appropriate didactic design of mathematical content and the creation of a stimulating environment for students.

KLJUČNE REČI / KEYWORDS:

algebraic content, discovery-based learning, elementary mathematics teaching, textbook

LITERATURA / REFERENCES:

  • Blanton, L.M. and Kaput, J. J. (2005). Characterizing a classroom practice that promotes algebraic reasoning. Journal for Research in Mathematics Education, 36, 412–446. https://www.jstor.org/stable/30034944
  • Bozalo, J., Samardžić, B. (2016). Udžbenik matematike u funkciji problemske nastave. U: A. Pešikan (ur.), Nastava i učenje – udžbenik u funkciji nastave i učenja, 365–376. Užice: Učiteljski fakultet. https://pfu.kg.ac.rs/wp-content/uploads/2022/03/Nastava-ucenje-Udzbenik-u-funkciji-nastave-i-ucenja-  2016.pdf
  • Carpenter, T., Franke, M. L. (2001). Developing algebraic reasoning in the elementary school: Generalization and proof. In: H. Chick, K. Stacey, J. Vincent and J. Vincent (Eds.), Proceedings of the 12th ICMI Study Conference: The Future of the Teaching and Learning Algebra, 155–162. Australia: The University of Melbourne.
  • Cai, J. (2004). Developing Algebraic Thinking in the Earlier Grades: A Case Study of the Chinese Elementary School Curriculum, The MathematicsEducator, 8(1), 107–130.
  • Carraher, W. D., Schliemann, D. A., Brizuela, M. B., Earnest, D. (2006). Arithmetic and Algebra in Early Mathematics Education. Journal for Research in Mathematics Education, 37 (2), 87–115. https://www.researchgate.net/publication/298917525_Arithmetic_and_algebra_in_early_mathematics_educati on
  • Carraher, D. W., Schliemann, A. (2007). Early algebra and algebraic reasoning. In: F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning, 669–705. Greenwich, CT: Information Age Publishing.https://www.researchgate.net/publication/292696143_Early_algebra_and_algebraic_reasoning
  • Hammer, D. (1997). Discovery learning and discovery teaching. Cognition and instruction,      15 (4), 485–529. Ivić, I., Pešikan, A. i Antić, S. (2008). Vodič za dobar udžbenik – opšti standardi kvaliteta udžbenika. Novi Sad: Platoneum.
  • Kalathaki, M. (2015). Evaluation Tool for the Application of Discovery Teaching Method in the Greek Environmental School Projects. World Journal of Education, 5 (2), 40–51. https://files.eric.ed.gov/fulltext/EJ1158417.pdf
  • Kieran, C. (1981). Concepts associated with the equality symbol. Educational Studies in Mathematics, 12, 317–326. Kieran, C. (2004). Algebraic thinking in the early grades: What is it? Mathematics Educator, 8 (1), 139–151. https://www.researchgate.net/publication/228526202_Algebraic_thinking_in_the_early_grades_What_is_it
  • Knuth, E., Stephens, A., McNeil, N. & Alibali, M. W. (2006). Does Understanding the Equal Sign Matter? Evidence from Solving Equations. Journal for Research in Mathematics Education, 36 (4), 297–312. https://www.researchgate.net/publication/234007126_Does_understanding_the_equal_sign_matter_Evidence_ from_solving_equations
  • Kovačević, Z. (2011). Instrukcije za samostalno učenje u udžbenicima za mlađe razrede. Beograd: Učiteljski fakultet.
  • Lew, H. S. (2004). Developing Algebraic Thinking in Early Grades: Case Study of Korean Elementary School Mathematics, The Mathematics Educator 2004, 8(4),     88–106. https://www.researchgate.net/publication/228786238_Developing_algebraic_thinking_in_early_grades_Case_ study_of_Korean_elementary_school_mathematics
  • Lott, J. W. (ed.) (2000). Algebra? A gate? A barrier? A mystery! Mathematics Education Dialogues, 3(2), 1–12. https://eric.ed.gov/?id=ED439926
  • Maričić, S., Milinković, N. (2017). Udžbenik u stvaranju uslova za kontekstualni pristup učenju sadržaja algebre u početnoj nastavi matematike, Zbornik radova Pedagoškog fakulteta u Užicu, 19, 117–130. https://scindeks-clanci.ceon.rs/data/pdf/2560-550X/2017/2560-550X1719117M.pdf
  • Moses, R. P. and C. E. Cobb (2001). Radical Equations: Math Literacy and Civil Rights. Boston: Beacon Press. National Council of Teachers of Mathematics (2000). Principles and Standards of School Mathematics. Reston, VA: NCTM.
  • Pravilnik o nastavnom planu i programu za prvi, drugi, treći i četvrti razred osnovnog obrazovanja i vaspitanja (2006). Prosvetni glasnik, Službeni glasnik Republike Srbije, br. 15/2006.
  • Pravilnik o programu nastave i učenja za prvi razred osnovnog obrazovanja i vaspitanja (2017). Prosvetni glasnik, Službeni glasnik Republike Srbije, br. 10/2017.
  • Pravilnik o programu nastave i učenja za drugi razred osnovnog obrazovanja i vaspitanja (2018). Prosvetni glasnik, Službeni glasnik Republike Srbije, br. 16/2018.
  • Pravilnik o programu nastave i učenja za treći razred osnovnog obrazovanja i vaspitanja (2019).
  • Prosvetni glasnik, Službeni glasnik Republike Srbije, br. 5/2019.
  • Pravilnik o programu nastave i učenja za četvrti razred osnovnog obrazovanja i vaspitanja (2019).
  • Prosvetni glasnik, Službeni glasnik Republike Srbije, br. 11/2019.
  • Pedagoški leksikon (1996). Beograd: Zavod za udžbenike i nastavna sredstva.
  • Romano, D. A. (2009). Šta je algebarsko mišljenje? MAT-KOL Banja Luka, XV (2) 19–29. http://www.imvibl.org/dmbl/meso/mat_kol_15_2_2009/mat_kol_152_2009_19-29.pdf
  • Sfard, A. & Linchevski, L. (1994). Between arithmetic and algebra: In the search of a missing link the case of equations and inequalities. Rendiconti Del Seminario Matematico, 52, 279–307.
  • Svinicki, D. M. (1998). A theoretical foundation for discovery learning. ADVANCES IN PHYSIOLOGY EDUCATION, 20 (1), 4–7. https://doi.org/10.1152/advances.1998.275.6.s4
  • Van Stiphout, I., Drijvers, P. H. M., & Gravemeijer, K. P. E. (2013). The development of students’ algebraic proficiency. Mathematics Education, 8 (2–3), 62–80. https://www.iejme.com/download/the-development-of- students-algebraic-proficiency.pdf
  • Vlahović, B. (2009). Udžbenik u susret sutrašnjici obrazovanja. U: N. Potkonjak (ur.), Buduća škola – Zbornik radova sa naučnog skupa II deo (1090–1110). Beograd: Srpska akademija obrazovanja. http://www.sao.org.rs/documents/ZBORNIK%20RADOVA%20SKOLA%20BUDUCNOSTI%20%20II%20 DEO.pdf
  • Španović, S. (2008). Teorijske pretpostavke za didaktičko oblikovanje udžbenika. Naša škola, 3–4, 63– 87.