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\u00a0<\/p>

\u041f\u0440\u0435\u0443\u0437\u043c\u0438\u0442\u0435 \u043a\u043e\u043c\u043f\u043b\u0435\u0442\u0430\u043d \u0440\u0430\u0434\/Download<\/a><\/p>

\u0410\u0443\u0442\u043e\u0440\u0438: \u0411\u043e\u0458\u0430\u043d \u0414. \u041b\u0430\u0437\u0438\u045b, \u041c\u0430\u0440\u0438\u043d\u0430 \u0411. \u041c\u0438\u043b\u043e\u0448\u0435\u0432\u0438\u045b, \u041a\u0440\u0438\u0441\u0442\u0438\u043d\u0430 \u0420. \u0421\u0430\u0431\u043e<\/p>

DOI 10.5937\/ZRPFU2224141L<\/a><\/p>

\u0423\u0414\u041a 37.091.3::51-028.31<\/p>

\u00a0<\/p>

\u0417\u0410\u0414\u0410\u0426\u0418 \u041e\u0422\u0412\u041e\u0420\u0415\u041d\u041e\u0413 \u0422\u0418\u041f\u0410 \u0423 \u0424\u0423\u041d\u041a\u0426\u0418\u0408\u0418 \u041f\u041e\u0414\u0421\u0422\u0418\u0426\u0410\u040a\u0410 \u041b\u041e\u0413\u0418\u0427\u041a\u041e\u0413 \u041c\u0418\u0428\u0409\u0415\u040a\u0410\u00a0 \u0423 \u041f\u041e\u0427\u0415\u0422\u041d\u041e\u0408 \u041d\u0410\u0421\u0422\u0410\u0412\u0418 \u041c\u0410\u0422\u0415\u041c\u0410\u0422\u0418\u041a\u0415<\/p>

\u0410\u043f\u0441\u0442\u0440\u0430\u043a\u0442: \u041b\u043e\u0433\u0438\u0447\u043a\u043e \u043c\u0438\u0448\u0459\u0435\u045a\u0435 \u0458\u0435 \u0432\u0430\u0436\u0430\u043d \u043f\u0440\u043e\u0446\u0435\u0441 \u0440\u0430\u0441\u0443\u0452\u0438\u0432\u0430\u045a\u0430 \u0438 \u043e\u0441\u043d\u043e\u0432\u043d\u0430 \u0432\u0435\u0448\u0442\u0438\u043d\u0430 \u0443 \u0438\u0437\u0433\u0440\u0430\u0434\u045a\u0438 \u0437\u043d\u0430\u045a\u0430 \u0438 \u0438\u0441\u043a\u0443\u0441\u0442\u0432\u0430 \u0443\u0447\u0435\u043d\u0438\u043a\u0430 \u043a\u043e\u0458\u0430 \u0442\u0440\u0435\u0431\u0430 \u0434\u0430 \u043f\u0440\u0430\u0442\u0438 \u043f\u0440\u043e\u0446\u0435\u0441 \u0443\u0447\u0435\u045a\u0430 \u0438 \u0440\u0430\u0437\u0432\u0438\u0458\u0430 \u0443\u0447\u0435\u043d\u0438\u0447\u043a\u0435 \u043f\u043e\u0442\u0435\u043d\u0446\u0438\u0458\u0430\u043b\u0435 \u043d\u0430 \u0441\u0432\u0438\u043c \u043d\u0438\u0432\u043e\u0438\u043c\u0430 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u045a\u0430. \u041f\u0440\u043e\u00ad\u0433\u0440\u0430\u043c \u043d\u0430\u0441\u0442\u0430\u0432\u0435 \u0438 \u0443\u0447\u0435\u045a\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043ae \u0437\u0430 \u043e\u0441\u043d\u043e\u0432\u043d\u0443 \u0448\u043a\u043e\u043b\u0443 \u0443 \u0421\u0440\u0431\u0438\u0458\u0438 \u0441\u0430\u0434\u0440\u0436\u0438 \u0432\u0435\u043b\u0438\u043a\u0438 \u0431\u0440\u043e\u0458 \u0442\u0435\u043c\u0430 \u043a\u043e\u0458\u0435 \u043f\u043e\u0434\u0440\u0436\u0430\u0432\u0430\u0458\u0443 \u0446\u0438\u0459 \u0443\u0447\u0435\u045a\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0435, \u0430\u043b\u0438 \u043f\u043e\u0441\u0442\u043e\u0458\u0438 \u043f\u0440\u043e\u0441\u0442\u043e\u0440 \u0438 \u0437\u0430 \u043f\u043e\u0431\u043e\u0459\u0448\u0430\u045a\u0435\u043c.<\/p>

\u0420\u0430\u0434 \u0441\u0435 \u0431\u0430\u0432\u0438 \u0441\u0430\u0433\u043b\u0435\u0434\u0430\u0432\u0430\u045a\u0435\u043c \u043c\u043e\u0433\u0443\u045b\u043d\u043e\u0441\u0442\u0438 \u043f\u0440\u043e\u043f\u0435\u0434\u0435\u0432\u0442\u0438\u043a\u0435 \u043b\u043e\u0433\u0438\u043a\u0435 \u0438 \u043f\u043e\u0434\u0441\u0442\u0438\u00ad\u0446\u0430\u045a\u0430 \u043b\u043e\u0433\u0438\u0447\u043a\u043e\u0433 \u043c\u0438\u0448\u0459\u0435\u045a\u0430, \u043f\u0440\u0438\u043c\u0435\u043d\u043e\u043c \u0437\u0430\u0434\u0430\u0442\u0430\u043a\u0430 \u043e\u0442\u0432\u043e\u0440\u0435\u043d\u043e\u0433 \u0442\u0438\u043f\u0430 \u0443 \u043f\u043e\u0447\u0435\u0442\u043d\u043e\u0458 \u043d\u0430\u0441\u0442\u0430\u0432\u0438 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0435. \u0420\u0435\u0441\u043f\u0435\u043a\u0442\u0438\u0432\u043d\u043e \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u0441\u043a\u0438\u043c \u0441\u0430\u0434\u0440\u0436\u0430\u0458\u0438\u043c\u0430 \u0440\u0430\u0437\u0440\u0435\u0434\u043d\u0435 \u043d\u0430\u0441\u0442\u0430\u0432\u0435 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0435, \u043f\u0440\u0438\u043a\u0430\u0437\u0430\u043d\u0438 \u0441\u0443 \u043f\u0440\u0438\u043c\u0435\u0440\u0438 \u0437\u0430\u0434\u0430\u0442\u0430\u043a\u0430 \u043e\u0442\u0432\u043e\u0440\u0435\u043d\u043e\u0433 \u0442\u0438\u043f\u0430, \u043a\u0430\u043e \u043f\u043e\u0434\u0440\u0448\u043a\u0430 \u0438 \u0430\u043d\u0430\u043b\u043e\u0433\u043e\u043d \u0443\u0447\u0438\u0442\u0435\u0459\u0438\u043c\u0430 \u0443 \u043a\u0440\u0435\u0438\u0440\u0430\u045a\u0443 \u043d\u0430\u0441\u0442\u0430\u0432\u043d\u0435 \u043f\u0440\u0430\u043a\u0441\u0435, \u0443 \u0446\u0438\u0459\u0443 \u043f\u043e\u0441\u043f\u0435\u0448\u0438\u0432\u0430\u045a\u0430 \u0440\u0430\u0437\u0432\u043e\u0458\u0430 \u043b\u043e\u0433\u0438\u0447\u043a\u043e\u0433 \u043c\u0438\u0448\u0459\u0435\u045a\u0430 \u0443\u0447\u0435\u043d\u0438\u043a\u0430, \u043a\u0430\u043e \u0431\u0438\u0442\u043d\u0435 \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u0435 \u0438\u0441\u0445\u043e\u0434\u0430 \u0443\u0447\u0435\u045a\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0435.<\/p>

\u041a\u0459\u0443\u0447\u043d\u0435 \u0440\u0435\u0447\u0438: \u043b\u043e\u0433\u0438\u0447\u043a\u043e \u043c\u0438\u0448\u0459\u0430\u045a\u0435, \u0440\u0430\u0437\u0440\u0435\u0434\u043d\u0430 \u043d\u0430\u0441\u0442\u0430\u0432\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0435, \u0437\u0430\u0434\u0430\u0446\u0438 \u043e\u0442\u0432\u043e\u0440\u0435\u043d\u043e\u0433 \u0442\u0438\u043f\u0430.<\/p>

<\/a>\u00a0<\/p>

OPEN-ENDED TASKS AS A MEANS OF ENCOURAGING\u00a0 LOGICAL THINKING IN INITIAL TEACHING OF MATHEMATICS<\/p>

Summary: Logical thinking represents an important process of reasoning and a basic skill in building students\u02bc knowledge and experience which should accompany the learning process and develop students\u2019 potential at all levels of education. The program of teaching and learning mathematics in primary education in Serbia contains a large number of topics that support the goal of learning mathematics, but there is also room for improvement.<\/p>

The paper deals with the possibility of propaedeutics of logic and the encouragement of logical thinking, the application of open-ended tasks in the initial teaching of mathematics. Respectively to the program contents of the mathematics class, examples of open-ended tasks are presented, as support and analog to teachers in creating teaching practice, in order to promote the development of students\u02bc logical thinking, as an important component of mathematics learning outcomes.<\/p>

Keywords: logical thinking, mathematics classroom teaching, open-ended tasks.<\/p>

\u041b\u0438\u0442\u0435\u0440\u0430\u0442\u0443\u0440\u0430<\/p>

Aini, N., Juniati, D. & Siswono, T. (2020). Exploring the combinatorial reasoning of high school students with reflective and impulsive cognitive style in solving problems. Journal for the Education of Gifted Young Scientists, 8(3), 1113\u20131124. DOI 10.17478\/jegys.768023.<\/p>

Ani\u0107, I. & Pavlovi\u0107 Babi\u0107, D. (2015). How we can support success in solving mathematical problems?. Teaching Innovations, 28(3), 36\u201349.<\/p>

Gordi\u0107, S., Milo\u0161evi\u0107, M. & Sabo, K. (2019). Solving combinatorial problems in lower grades of primary school. Proceedings of the ATEE Winter Conference \u2018Science and mathematics education in the 21st century\u2019, 107\u2013115.<\/p>

Dyer, M. & Moynihan, C. (2000). Open-ended question in elementary mathematics: instruction & assessment. Larchmont, New York: Eye on Education<\/p>

Zapata-Cardona, L. (2018). Supporting Young Children to Develop Combinatorial Reasoning. In Leavy A., Meletiou-Mavrotheris M. & Paparistodemou E. (\u0435ds.), Statistics in Early Childhood and Primary Education (257\u2013272). Singapore: Springer. DOI 10.1007\/978-981-13-1044-7_15.<\/p>

Incikabi, L., Tuna, A. & Cagri Biber, A. (2013). An Analysis Of Mathematics Teacher Candidates Critical Thinking Dispositions And Their Logical Thinking Skills. Journal of International Education Research<\/a>, 9(3), 257\u2013266.<\/p>

\u0408\u043e\u0432\u0430\u043d\u043e\u0432\u0438\u045b, \u0420. \u0418. \u0438 \u0412\u0443\u043b\u043e\u0432\u0438\u045b, \u0420. \u041d. (2021). \u0423\u043e\u0447\u0430\u0432\u0430\u045a\u0435 \u0437\u0430\u043a\u043e\u043d\u0438\u0442\u043e\u0441\u0442\u0438 \u0438 \u043f\u0440\u0430\u0432\u0438\u043b\u0430 \u0443 \u043f\u043e\u0447\u0435\u0442\u043d\u043e\u0458 \u043d\u0430\u0441\u0442\u0430\u0432\u0438 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0435. \u0423\u0437\u0434\u0430\u043d\u0438\u0446\u0430, XVIII(1), 325\u2013338.<\/p>

Kadum, V. (2005). Utjecaj u\u010denja rje\u0161avanjem problemskih zadataka na obrazovni u\u010dinak u elementarnoj nastavi matematike.\u00a0Metodi\u010dki ogledi, 12(2), 31\u201360.<\/p>

\u041a\u0440\u0435\u043a\u0438\u045b, \u0412. (2007). \u0421\u0430\u0432\u0440\u0435\u043c\u0435\u043d\u0435 \u043c\u0435\u0442\u043e\u0434\u0438\u0447\u043a\u0435 \u0442\u0440\u0430\u043d\u0441\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u0458\u0435 \u0435\u043b\u0435\u043c\u0435\u043d\u0430\u0442\u0430 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0442\u043e\u0440\u0438\u043a\u0435 \u0443 \u043f\u043e\u0447\u0435\u0442\u043d\u043e\u0458 \u043d\u0430\u0441\u0442\u0430\u0432\u0438 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0435 (\u0434\u043e\u043a\u0442\u043e\u0440\u0441\u043a\u0430 \u0434\u0438\u0441\u0435\u0440\u0442\u0430\u0446\u0438\u0458\u0430). \u0411\u0435\u043e\u0433\u0440\u0430\u0434: \u0423\u0447\u0438\u0442\u0435\u0459\u0441\u043a\u0438 \u0444\u0430\u043a\u0443\u043b\u0442\u0435\u0442.<\/p>

Kreki\u0107-Pinter, V., Ivanovi\u0107, J., Namestovski, \u017d. & Major, L. (2015). Strategy and Methods for Solving Combinatorial Problems in Initial Instruction of Mathematics. International Journal of Modern Education Research, 2(6), 77\u201387.<\/p>

\u00a0Kwon O. N., Park J. S. & Park J. H. (2006). Cultivating divergent thinking in mathematics through an open-ended approach. Asia Pacific Education Review, 7(1), 1, 51\u201361.<\/p>

Major, J. & Major, M. (2015). Developing Combinatorial Thinking. Acta Mathematica Nitriensia, 1(2), 29\u201334.<\/p>

Mandak, A. & Pavli\u010di\u0107, Z. (2016). Uloga problemskih zadataka iz obasti kvadra i kocke na razvoj matemati\u010dkih sposobnosti u\u010denika. Zbornik radova U\u010diteljskog fakulteta, 10, 85\u201399.<\/p>

Mari\u010di\u0107, S., \u0160pijunovi\u0107, K. & Lazi\u0107, B. (2016). The Influence of Content on the Development of Students\u2019 Critical Thinking in the Initial Teaching of Mathematics. Croatian Journal of Education, 18(1), 11\u201340. DOI 10.15516\/cje.v18i1.1325.<\/p>

Mari\u010di\u0107, S., \u0160pijunovi\u0107, K., Coti\u010d, M. & Felda, D. (2017). Matemati\u010dko mi\u0161ljenje u po\u010detnoj nastavi matematike. Koper: Zalo\u017eba Univerze na Primorskem.<\/p>

M\u0430\u0440\u0438\u0447\u0438\u045b, \u0421. (2011). \u041f\u043e\u0447\u0435\u0442\u043d\u0430 \u043d\u0430\u0441\u0442\u0430\u0432\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0435 \u0438 \u0440\u0430\u0437\u0432\u0438\u0458\u0430\u045a\u0435 \u043a\u0440\u0438\u0442\u0438\u0447\u043a\u043e\u0433 \u043c\u0438\u0448\u0459\u0435\u045a\u0430 \u0443\u0447\u0435\u043d\u0438\u043a\u0430 (\u0434\u043e\u043a\u0442\u043e\u0440\u0441\u043a\u0430 \u0434\u0438\u0441\u0435\u0440\u0442\u0430\u0446\u0438\u0458\u0430). \u0423\u0436\u0438\u0446\u0435: \u0423\u0447\u0438\u0442\u0435\u0459\u0441\u043a\u0438 \u0444\u0430\u043a\u0443\u043b\u0442\u0435\u0442<\/p>

Maricic, S., Lazic, B. & Petojevic, A. (2016). Mathematics textbooks for enabling students to solve problems in elementary mathematics education. In D. Petrovic & M. Antolovic (eds.), Education and the Social Challenges at the Beginning of the 21st Century (136\u2013151). Sombor: Faculty of Education.<\/p>

Melusova, \u0408. & Vidermanova, \u041a. (2015). Upper-secondary Students\u2019 Strategies for Solving Combinatorial Problems. Procedia \u2013 Social and Behavioral Sciences, 197, 1703-1709. DOI 10.1016\/j.sbspro.2015.07.223.<\/p>

\u041c\u0438\u043b\u0438\u043d\u043a\u043e\u0432\u0438\u045b, J. \u0438 \u041b\u0430\u0437\u0438\u045b, \u0411. (2018). \u041f\u043e\u0441\u0442\u0438\u0433\u043d\u0443\u045b\u0435 \u0443\u0447\u0435\u043d\u0438\u043a\u0430 \u043d\u0430 \u0422\u0418\u041c\u0421\u0421 \u0438 \u041f\u0418\u0421\u0410 \u0438\u0441\u043f\u0438\u0442\u0438\u0432\u0430\u045a\u0443 \u043a\u0430\u043e \u0441\u043c\u0435\u0440\u043d\u0438\u0446\u0430 \u0437\u0430 \u0438\u0437\u043c\u0435\u043d\u0435 \u0443 \u043d\u0430\u0441\u0442\u0430\u0432\u043d\u043e\u043c \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u0443 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0435. \u0418\u043d\u043e\u0432\u0430\u0446\u0438\u0458\u0435 \u0443 \u043d\u0430\u0441\u0442\u0430\u0432\u0438, 31(3), 74\u201387.<\/p>

\u041c\u0438\u043b\u0438\u043d\u043a\u043e\u0432\u0438\u045b, J. (2007). \u041c\u0435\u0442\u043e\u0434\u0438\u0447\u043a\u0438 \u0430\u0441\u043f\u0435\u043a\u0442\u0438 \u0443\u0432\u043e\u0434\u0430 \u0443 \u0432\u0435\u0440\u043e\u0432\u0430\u0442\u043d\u043e\u045b\u0443 \u0438 \u0441\u0442\u0430\u0442\u0438\u0441\u0442\u0438\u043a\u0443. \u0411\u0435\u043e\u0433\u0440\u0430\u0434: \u0423\u0447\u0438\u0442\u0435\u0459\u0441\u043a\u0438 \u0444\u0430\u043a\u0443\u043b\u0442\u0435\u0442.<\/p>

\u041c\u0438\u0445\u0430\u0458\u043b\u043e\u0432\u0438\u045b, A. \u0438 \u0415\u0433\u0435\u0440\u0438\u045b, M. (2012). \u041a\u0440\u0435\u0430\u0442\u0438\u0432\u043d\u043e\u0441\u0442 \u0443 \u043d\u0430\u0441\u0442\u0430\u0432\u0438 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0435. \u041d\u0435\u043a\u0435 \u0441\u0442\u0440\u0430\u0442\u0435\u0433\u0438\u0458\u0435 \u043a\u0440\u0435\u0438\u0440\u0430\u045a\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u043a\u0438\u0445 \u043f\u0440\u043e\u0431\u043b\u0435\u043c\u0430 \u043e\u0442\u0432\u043e\u0440\u0435\u043d\u043e\u0433 \u0442\u0438\u043f\u0430. \u0423 \u041d. \u0412\u0443\u043b\u043e\u0432\u0438\u045b (\u0443\u0440.): \u041c\u0435\u0442\u043e\u0434\u0438\u0447\u043a\u0438 \u0430\u0441\u043f\u0435\u043a\u0442\u0438 \u043d\u0430\u0441\u0442\u0430\u0432\u0435 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0435 II (23\u201331). \u0408\u0430\u0433\u043e\u0434\u0438\u043d\u0430: \u0424\u0430\u043a\u0443\u043b\u0442\u0435\u0442 \u043f\u0435\u0434\u0430\u0433\u043e\u0448\u043a\u0438\u0445 \u043d\u0430\u0443\u043a\u0430 \u0423\u043d\u0438\u0432\u0435\u0440\u0437\u0438\u0442\u0435\u0442\u0430 \u0443 \u041a\u0440\u0430\u0433\u0443\u0458\u0435\u0432\u0446\u0443.<\/p>

Nunes, T. & Csap\u00f3, B. (2011). Developing and Assessing Mathematical Reasoning. In B. Csap\u00f3 & M. Szendrei (eds.), Framework for Diagnostic Assessment of Mathematics (17\u201356). Budapest: Nemzeti Tank\u00f6nyvkiad\u00f3.<\/p>

Pehkonen, E. (1997a). Introduction to the concept \u201copen-ended\u201d problem, Use of openended problems in mathematics classroom, Research report 176, Helsinki Univ., Dept. of Teacher Education, 8\u201311.<\/p>

Rakic, D., Lazic, B. & Maric, M. (2021). The influence of differentiated mathematical tasks on students logical-combinatorial thinking in elementary mathematics teaching. Slavonic Pedagogical Studies Journal, 10(1), 78\u201392. DOI 10.18355\/pg.<\/p>

\u0421\u0430\u0431\u043e, K. (2020). \u041b\u043e\u0433\u0438\u0447\u043a\u043e \u0440\u0430\u0437\u043c\u0438\u0448\u0459\u0430\u045a\u0435 \u0443 \u0440\u0430\u0437\u0440\u0435\u0434\u043d\u043e\u0458 \u043d\u0430\u0441\u0442\u0430\u0432\u0438 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0435 (\u043c\u0430\u0441\u0442\u0435\u0440 \u0440\u0430\u0434). \u0421\u043e\u043c\u0431\u043e\u0440: \u041f\u0435\u0434\u0430\u0433\u043e\u0448\u043a\u0438 \u0444\u0430\u043a\u0443\u043b\u0442\u0435\u0442.<\/p>

Sullivan, P. (2011). Teaching Mathematics: Using Research-informed Strategies. Australian Education Review, 59.\u00a0<\/p>

Foong, P. Y. (2002). Using short open-ended mathematics questions to promote thinking and understanding, In A. Rogerson (ed.), Proceedings of the International Conference: The Humanistic Renaissance in Mathematics Education, Retrieved February 2009, 135\u2013140, http:\/\/math.unipa.it\/~grim\/SiFoong.pdf.<\/p>

Hidayati, Y., Sa\u2019dijah, C. & Qohar, S. (2019). Combinatorial Thinking to Solve the Problems of Combinatorics in Selection Type.\u00a0International Journal of Learning, Teaching and Educational Research, 18(2), 65\u201375. DOI org\/10.26803\/ijlter.18.2.5.<\/p>

Hiebert, \u0408. & Wearne, D. (1993). Instructional Tasks, Classroom Discourse and Students\u2019 Learning in Second-Grade Arithmetic. American Educational Research Journal, 30(2), 393\u2013425.<\/p>

Clarke, D. & Roche, A. (2017). Using contextualized tasks to engage students in meaningful and worthwhile mathematics learning. Journal of Mathematical Behavior, 51, 95\u2013108. DOI 10.1016\/j.jmathb.2017.11.006.<\/p>

Clarke, D. (2011). Open-Ended Tasks and Assessment: The Nettle or the Rose. In B. Kaur & K. Y. Wong (\u0435ds.): Assessment in the mathematics classroom: 2011 Association of Mathematics Educators Yearbook (237\u2013256). Singapore: World Scientific Publishing.<\/p>

Ciernikova, D. (2020). Effects of the application of the open-ended tasks in mathematics teaching. Norma, 25(2), 187\u2013197.<\/p>

Chan, C. M. E. (2007). Using open-ended mathematics problems: A classroom experience (Primary). In C. Shagar & R. B. A. Rahim (\u0435ds.): Redesigning pedagogy: Voices of practitioners (129\u2013146). Singapore: Pearson Education South Asia.<\/p>

Yan, Z. & Fong, T. (2005). An analysis of Singapore secondary students\u2019 performance on one authentic open-ended mathematics task, ICMI Regional Conference: The 3rd East Asia Regional Conference on Mathematics Education, paper printed in its entirety, 7\u201312 august 2005, Shanghai, Nanjing, and Hangzhou, China.<\/p>

\u0428\u043f\u0438\u0458\u0443\u043d\u043e\u0432\u0438\u045b, K. \u0438 \u041c\u0430\u0440\u0438\u0447\u0438\u045b, \u0421. (2016). \u041c\u0435\u0442\u043e\u0434\u0438\u043a\u0430 \u043f\u043e\u0447\u0435\u0442\u043d\u0435 \u043d\u0430\u0441\u0442\u0430\u0432\u0435 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0435. \u0423\u0436\u0438\u0446\u0435: \u0423\u0447\u0438\u0442\u0435\u0459\u0441\u043a\u0438 \u0444\u0430\u043a\u0443\u043b\u0442\u0435\u0442.<\/p>

\u00a0<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"

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