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Аутор/Authors: Рада М. Шћепановић, Јасмина В. Милинковић

DOI: 10.5937/ZRPFU2123127S

УДК: 37.091.3::51


ФОРМАТИВНО ВРЕДНОВАЊЕ ПОСТИГНУЋА У МАТЕМАТИЦИ И ОДАБИР ЗАДАТАКА

Апстракт: Вредновање математичких знања засновано је на вишеструким изворима информација. У савременоj наставној пракси посебно место има формативно вредновање математичких постигнућа ученика као интегрални део наставе, који подржава учење и пружа корисне информације наставницима и ученицима. Рад је посвећен анализи иновативних техника за вредновање у настави математике, које одсликавају промењену парадигму математичког образовања. Циљ рада је да истражи особености и импликације аутентичних техника вредновања и, у складу са тим, прављења избора задатака као инструмента вредновања. Методом теоријске анализе резултата истраживања аутентичних метода процена математичких знања, вештина и ставова утврђујемо критеријуме за избор задатака за вредновање математичких постигнућа ученика (усмереност за продубљену и проширену примену постојећих знања у различитом контекстима, више начина решавања, могућност истраживања). Дискурс је затим усмерен ка разматрању оригиналности критеријума вредновања задатака. У завршним разматрањима указујемо да се одабиром математичких задатака, ствара прилика за примену широког спектра аутентичних техника у вредновању математичких постигнућа ученика, и шире и дубље планира даљи ток наставе у когнитивном и мотивационом развоју ученика. 

Кључне речи: дијагностичко вредновање, критеријуми вредновања, технике вредновања,  инструменти вредновања, математички задатак.


FORMATIVE ASSESSMENT OF ACHIEVEMENTS IN MATHEMATICS AND SELECTION OF TASKS

Abstract: The evaluation of mathematical knowledge is based on multiple sources of information. In modern teaching practice, a special place has a formative evaluation of mathematical achievements of students as an integral part of teaching that supports learning and provides useful information to teachers and students. The paper is dedicated to the analysis of innovative evaluation techniques in mathematics teaching that reflect the changed paradigm of mathematics education. The aim of this paper is to explore the features and implications of authentic evaluation techniques and, accordingly, to make the choice of tasks as evaluation instruments. Using the method of theoretical analysis of research results of authentic methods for assessing mathematical knowledge, skills and attitudes, we determine the criteria for selecting tasks for evaluating students’                            mathematical achievements (focus on in-depth and extended application of existing knowledge in different contexts, multiple solutions, research possibilities). The discourse is then directed towards considering the originality of the task evaluation criteria. In the final considerations, we point out that the selection of mathematical tasks creates an opportunity to apply a wide range of authentic techniques in evaluating students ‘mathematical achievements, and broader and deeper plans the further course of teaching in students’ cognitive and motivational development. We point out that by choosing      mathematical tasks, it creates an opportunity to apply a wide range of authentic techniques in evaluating students’ mathematical achievements, and broader and deeper plans the further course of teaching in the cognitive and motivational development of students.

Keywords: diagnostic evaluation, evaluation criteria, evaluation techniques, evaluation instruments, mathematical task.


Литература/References:

Andersson, C. (2017). Formative assessment – and the component of adjusted teacher instruction. In T. Dooley and G. Gueudet (еds.): Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education;CERME10 (3419–3426), February 1–5, 2017, Dublin, Ireland: DCU Institute of Education and ERME.

Balan, A. (2012). Assessment for learning, A case study in mathematics education (doctoral dissertation in education). Malmö: Malmö University.

Barmby, P. (2019). Using a variety of methods for mathematics education research. In J. Milinković and Z. Kadelburg (eds.), Research in Mathematics Education (16–30). Scientific Conference Research in Mathematics Education, May 10–11, 2019. Belgrade: Mathematical Society of Serbia.

Bisson, M. J., Gilmore, C., Inglis, M. & Jones, I. (2016). Measuring conceptual understanding using comparative judgement. International Journal of Research in Undergraduate Mathematics Education, 2(2), 141−164.

Black, P. & Wiliam, D. (1998). Assessment and Classroom Learning. Assessment in Education: Principles, Policy and Practise, 5(1), 7−74.

Blum, W. & Niss, M. (1991). Applied mathematical problem solving, modelling, applications, and links to other subjects – State, trends and issues in mathematics instruction. Educational Studies in Mathematics, 22(1), 37–68.

Chanudet, М. (2017). Teachers’ formative assessment practices: The case of an IBME-centered course. In T. Dooley and G. Gueudet (eds.), Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education; CERME10 (3436–3444), February 1–5, 2017, Dublin, Ireland: DCU Institute of Education and ERME.

Cusi, A., Morselli, F. & Sabena, C. (2017). Designing and analysing the role of digital resources in supporting formative assessment processes in the classroom: The helping worksheets. In T. Dooley and G. Gueudet (eds.), Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education;              CERME10 (3452–3460), February 1–5, 2017, Dublin, Ireland: DCU Institute of Education and ERME.

Davies, B. (2017). A case for a new approach to establishing the validity of comparative judgement as an assessment tool for mathematics. In T. Dooley and G. Gueudet  (eds.), Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education; CERME10 (3476–3484), February 1–5, 2017, Dublin,  Ireland: DCU Institute of Education and ERME.

Grapin, N. & Sayac, N. (2017). Using external assessments for improving assessment practice of primary school teachers: A first study and some methodological questions.  In T. Dooley and G. Gueudet (eds.), Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education; CERME10 (3508–3516), February 1–5, 2017, Dublin, Ireland: DCU Institute of Education and ERME.

Henningsen, М. & Stein, М. К. (1997). Mathematical Tasks and Student Cognition: Classroom-Based Factors That Support and Inhibit High-Level Mathematical Thinking and Reasoning. Journal for Research in Mathematics Education, 28(5), 524–549.

Jones, J. C. (2012). Visualizing Elementary and Middle School Mathematics Methods. Hoboken: John Wiley & Sons.

Jones, I. & Inglis, M. (2015). The problem of assessing problem solving: can comparative judgement help?. Educational Studies in Mathematics, 89, 337–355.

Kwek, M. L. (2015). Using Problem Posing as a Formative Assessment Tool. In M. F. Singer, F. N. Ellerton and J. Cai (еds.), Mathematical Problem Posing (From Research to Effective Practice) (273–293). New York: Springer Reference. DOI 10.1007/978-1-4614-6258-3.

Lester, F. K. (2013). Thoughts about research on mathematical problem − solving instruction. The Mathematics Enthusiast, 10(1–2), 245−278.

Mellone, М., Ribeiro, М. & Jakobsen, А. (2018). Characterizing prospective teachers’ knowledge in/for interpreting students’ Solutions. Retrieved May 27, 2020 from the World Wide Web https://www.researchgate.net/publication/331604369.

Milinković, D. & Pikula, M. (2015). Matematički zadaci u kontekstu evaluacije učeničkih postignuća u razrednoj nastavi. U S. Marinković i J. Stamatović (ur.): Nastava i učenje – evaluacija vaspitno-obrazovnog rada (373–386). Užice: Učiteljski fakultet.

Milinković, J. (2013). Autentične tehnike praćenja napretka učenika u procesu nastave matematike. U R. Nikolić (ur.), Nastava i učenje − kvalitet vaspitno obrazovnog procesa (513–522). Međunarodni naučni skup Nastava i učenje, 13. 11. 2013, Užice. Užice: Učiteljski fakultet.

Milinković, J. (2015а). Postavljanje problema – nova oblast u metodici nastave matematike. U J. Milinković i B. Trebješanin (ur.): Implementacija inovacija u obrazovanju i vaspitanju – izazovi i dileme (561–571). Beograd: Učiteljski fakultet.

Pešikan, A. (2015). Školski zadaci za efikasno učenje. U S. Marinković i J. Stamatović  (ur.):  Nastava i učenje – evaluacija vaspitno-obrazovnog rada (13–28). Užice: Učiteljski fakultet.

Pilet, Ј. & Horoks, Ј. (2017). Assessment in mathematics as a lever to promote students’ learning and teachers’ professional development. In T. Dooley and G. Gueudet (eds.), Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education; CERME10 (3572–3579), February 1–5, 2017, Dublin. Ireland: DCU Institute of Education and ERME.

Pollitt, A. (2012). The method of adaptive comparative judgement. Assessment in Education: Principles, Policy & Practice, 19(3), 281−300.

Pravilnik o načinu ocjenjivanja učenika u osnovnoj školi (2019), Službeni list CG, br. 062/19 od 12. 11. 2019. Retrieved December 14, 2020 from the World Wide Web www.skolskiportal.edu.me.

Reit, X. R. (2017). Towards an empirical validation of mathematics teachers’ intuitive assessment practice exemplified by modelling tasks. In T. Dooley and G. Gueudet (eds.), Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education; CERME10 (3588–3596), February 1–5 2017, Dublin. Ireland: DCU Institute of Education and ERME.

Silver, E. A. (1994). On Mathematical Problem Posing. For the Learning of Mathematics, 14(1), 19−28.

Silver, E. A. & Cai, J. (2005). Assessing students’ mathematical problem posing.Teaching Children Mathematics, 12(3), 129–135.

Spasić, R. (2013). Ocenjivanje. U W. Anderson (ed.): Nastava orijentisana na učenje (161–189). Beograd: Centar za demokratiju i pomirenje u jugoistočnoj Evropi.

Stoyanova, E. N. (1997). Extending and exploring studentsʼ problem solving via problem posing (doctoral dissertation). Retrieved Маy 27, 2019 from the World Wide Web https://ro.ecu.edu.au/theses/885.

Špijunović, K. & Maričić, S. (2015). Ocenjivanje u početnoj nastavi matematike usmereno na razvoj i napredovanje učenika. U S. Marinković i J. Stamatović (ur.). Nastava i učenje – evaluacija vaspitno-obrazovnog rada (347–356). Užice: Učiteljski fakultet.

Zhao, X., Heuvel-Panhuizen, M. & Veldhuis, M. (2017). Using classroom assessment techniques in Chinese primary schools: Effects on student achievement. In T. Dooley and G. Gueudet (eds.), Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education; CERME10 (3604–3612), February 1–5, 2017, Dublin. Ireland: DCU Institute of Education and ERME.

Wiliam, D. (2011). What is assessment for learning?. Studies in Educational Evaluation. 37(1), 3–14. DOI 10.1016/j.stueduc.2011.03.001.