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Teachers’ reflection on PISA items and why they are so hard for students in Serbia

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Abstract

The study explores how teachers perceive and go about students’ thinking in connection to particular mathematical content and how they frame the notion of applied mathematics in their own classrooms. Teachers’ narratives are built around two released PISA 2012 mathematics items, the ‘Drip rate’ and ‘Climbing Mount Fuji’ (will be referred to as the Fuji item). Teachers show concordance as to the reasons that could make either of the items difficult for students and are able to provide more examples justifying their reasoning for the ‘Fuji’ item. Suggestions linked to making the items more familiar to the students mostly relate to de-contextualization of the items’ content towards a more formal mathematical record. The teachers agree that students need only basic mathematical knowledge, at a level learned during elementary school, in order to solve these problems. Yet, at the same time, many teachers have difficulty clearly verbalising which procedures students are expected to follow to be able to solve the tasks. Disagreement among the teachers is noticeable when labelling the most difficult part(s) of each of the selected items. Mathematics teachers show openness for learning on how to create math problems we examined in this study, but question the purpose and meaning in incorporating more such problems in their own teaching.

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Notes

  1. We distinguish here between the concepts of teacher cognition linked to particular teachers’ self-reflections and knowledge about their teaching, subject matter and/or students; and an understanding of beliefs as propositions, which may be consciously or unconsciously held, are evaluative in nature, as such held true by the individual, and are therefore saturated with emotive commitment serving as a guide to thought and behaviour. (Borg 2001, p. 186).

  2. Here we refer to interaction between a student and a teacher, irrespective of the actual mode of teaching (e.g. inquiry based, whole class).

  3. Considered as the minimal level of functional literacy.

  4. Serbia did not partake in the PISA 2015 cycle.

  5. According to our own analysis the share of Serbian student at highest levels (5th and 6th) should be about 7% and this is less than 5%

  6. In the sense of appropriating factual knowledge, not building on students’ competences and problem solving strategies.

  7. e.g. Rule book on teaching plan and programme for grammar school - Official Gazette: 5/1990–1, 3/1991–1, 3/1992–1, 17/1993–106, 2/1994–59, 2/1995–1, 8/1995–1, 23/1997–1, 2/2002–4, 5/2003–1, 10/2003–1, 11/2004–1, 18/2004–1, 24/2004–2, 3/2005–1, 11/2005–163, 2/2006–1, 6/2006–129, 12/2006–2, 17/2006–6, 1/2008–1, 8/2008–3, 1/2009–1, 3/2009–24, 10/2009–64, 5/2010–1, 7/2011–12, 4/2013–175, 14/2013–2, 17/2013–1, 18/2013–8, 5/2014–6, 4/2015–5, 18/2015–1, 11/2016–563, 13/2016–10 (correction); Rule book on teaching plan and programme for educational profile of electrical engineer in telecommunications - Official Gazette: 9/2007–1, 5/2011–133, 10/2014–1, 10/2014–140, 8/2015–46. The rule books for array of educational profiles in electrical engineering, economy and law were inspected for the purpose of this text. Above listed are given as examples.

  8. Compulsory primary education starts at the age of 7, lasting 8 years. Upper secondary education takes part through different vocational education profiles or in grammar schools, for age groups 15 to 19.

  9. Taught by subject area teachers in grades 5 to 8 of elementary school and all grades at upper secondary level.

  10. Conclusion is drawn based on syllabus analyses for mathematics teacher programme at the undergraduate and master level, as well as other mathematics programmes offered by Faculties of Mathematics at different universities in Serbia. Current analyses included syllabuses from Faculty of Mathematics (University of Belgrade), Faculty of Sciences (University of Novi Sad) and Faculty of Sciences and Mathematics (University of Nis). According to the Serbian bylaws and rulebooks, a person is allowed to apply for a position of a mathematics subject teacher after graduating from any of the accredited programmes in mathematics.

  11. VET schools with such educational programs were contacted as they represent the majority of VET schools in Serbia, when observed across the span of possible education fields.

  12. Full overview is available at: https://www.oecd.org/pisa/pisaproducts/pisa2012-2006-rel-items-maths-ENG.pdf

  13. PISA items in mathematics include the following content area: change and relationships, space and shape, quantity, and uncertainty and data. The Contexts include: personal occupational, societal and scientific.

  14. This suggestion is not in accord with the official instructions given for the item as part of the translation procedures followed in the PISA Survey.

  15. The game says that starting from the knuckle on your pinky finger one can calculate the number of days in the month. Each knuckle represents 31 days and an indent in between them 30 days. The game is usually taught already in Grade 1 of elementary school by the class teachers.

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Funding

Study was partially funded by Ministarstvo Prosvete, Nauke i Tehnološkog Razvoja (grant number 179018).

Author information

Authors and Affiliations

  1. Department of Teacher Education and School Research, Faculty of Educational Sciences, University of Oslo, Postboks 1099, Blindern, 0317, Oslo, Norway

    Jelena Radišić

  2. Faculty of Philosophy, University of Belgrade, Belgrade, Serbia

    Aleksandar Baucal

Authors
  1. Jelena Radišić
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  2. Aleksandar Baucal
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Corresponding author

Correspondence to Jelena Radišić.

Additional information

Jelena Radišić. Department of Teacher Education and School Research, Faculty of Educational Sciences, University of Oslo. E mail: jelena.radisic@ils.uio.no

Current Themes of Research:

Jelena Radišić is a postdoc researcher at the Department of Teacher Education and School Research, Faculty of Educational Sciences, University of Oslo. In her research, she examines the following topics: student, teacher and school characteristics affecting academic achievement; assessing the quality and efficacy of the education system (secondary analysis of PISA and TIMSS results); teacher beliefs and practices and their impact on student learning; motivation for learning; mathematics anxiety; emergent literacy.

Most relevant publications in the field of Psychology of Education:

Marković, J., Radišić, J., Jovanović, V. & Ranković, T. (2017). Developing a model for dropout prevention and intervention in primary and secondary schools in Serbia: Assessing the Model Effectiveness. Psihološka istraživanja, 20(1), 145–169.

Radišić, J. & Baucal, A. (2016). Using video-stimulated recall to understand teachers’ perceptions of teaching and learning in the classroom setting. Psihološka istraživanja, 19(2), 165–183.

Kovač Cerović, T., Radišić, J., & Stanković, D. (2015). Bridging the gap between teachers’ initial education and induction through student teachers’ school practice: case study of Serbia. Croatian Journal of Education, 17(2), 43–70.

Radišić, J. & Jošić, S. (2015). Challenges, obstacles and outcomes of applying inquiry method in primary school mathematics: example of an experienced teacher. Teaching Innovations, 28(3), 99–115.

Radišić, J., Videnović, M., & Baucal, A. (2015). Math anxiety – contributing school and individual level factors. European Journal of Psychology of Education, 30(1), 1–20

Aleksandar Baucal. Faculty of Philosophy, University of Belgrade. E mail: abaucal@f.bg.ac.rs

Current Themes of Research:

Aleksander Bauca, PhD is a professor at the Department of Psychology at the University of Belgrade. His main field of interest is the socio-cultural developmental psychology and studies of development of new competencies through symmetric (collaborative peer learning) and asymmetric (learning with adults) social interaction. The author’s work is also related to improvement of traditional pre-post test research design by integration with the item response theory (IRT) and involvement of qualitative case studies.

Most relevant publications in the field of Psychology of Education:

Budjevac, N., Arcidiacono, F., & Baucal, A. (2017). Reading together: the interplay between social and cognitive aspects in argumentative and non-argumentative dialogues. In: F. Arcidiacono and A. Bova (Eds), Interpersonal argumentation in educational and professional contexts. Springer

Tartas, V., Perret-Clermont, A. N. & Baucal, A. (2016). Experimental micro-histories, private speech and a study of children’s learning and cognitive development. Infancia y Aprendizaje, 39(4), pp. 772–811

Radišić, J., Videnović, M., & Baucal, A. (2015). Math anxiety – contributing school and individual level factors. European Journal of Psychology of Education, 30(1), 1–20

Baucal, A. (2013). Two instead of one ZPD: Individual and joint construction in the ZPD. In S. Phillipson, K. Ku, & S. Phillipson (Eds.), Constructing educational achievement: a sociocultural perspective (pp. 161–173). Routledge, London.

Baucal, A. (2012). Ključne kompetencije mladih u Srbiji u PISA 2009 ogledalu [Youth in Serbia: Key competencies in the PISA 2009 mirror]. Belgrade: Institute of Psychology.

Baucal, A., Arcidiacono, F. & Budjevac, N. (2011). Studying interaction in different contexts: a qualitative view. Belgrade: Institute of Psychology.

Appendix 1. The interview guide

Appendix 1. The interview guide

Introductory section provided the participants with the study aims and some basic information relative to the country participation in the PISA programme.

Now we will show you two cards with math items and we will discuss each and how they can be solved, as well as how you perceive these problems. These items were chosen by examining students’ achievement in the cycle 2012 and comparing it with the achievement of students in other participating countries.

Here is the first item. Please take a look at it.

  1. 1.

    What is your general impression about this item? Is this a math item? Is the picture accompanying the item appropriate and explains the math item?

  2. 2.

    Is the instruction given in the problem clear enough? In your experience what kind of students might have difficulty to understand instructions for this math item (e.g. language difficulties)?

  3. 3.

    Would you suggest some modifications that would make instruction for this problem more understandable to the students (language, presentation, information...)

  4. 4.

    Do you find all parts of the item easy or difficult for our students? Which part of the items do you find more difficult?

  5. 5.

    What kind of competencies do the students need to solve this item?

  6. 6.

    What students need to know previously and to be able to do in order to solve this math item?

  7. 7.

    How would you explain to the students to think about this math problem while solving it? What is it you expect students to do while solving this math item?

  8. 8.

    To what extent you think our students deal with such items at their math lessons? (if answered they do not deal enough what might facilitate the change towards dealing with them more often in class)

    [Questions 1 to 8 were asked for each item. The ‘Drip rate’ was the first item and ‘Fuji’ the second]

  9. 9.

    If you look at your in-service training and seminars organised by the mathematical association are these kind of problems something you tackle in these?

  10. 10.

    Do you feel you as a teacher might need additional support to introduce more problems like these in you mathematics lessons or do you believe their amount in your teaching is enough? (If the answer is yes what kind of support you think would enable you to introduce more of this kind of math problems in your teaching? Should the support come from actors at the school level, mathematics teachers’ associations or the policy makers?)

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Radišić, J., Baucal, A. Teachers’ reflection on PISA items and why they are so hard for students in Serbia. Eur J Psychol Educ 33, 445–466 (2018). https://doi.org/10.1007/s10212-018-0366-0

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