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Educational Studies in Mathematics

, Volume 102, Issue 2, pp 275–288 | Cite as

The credit system and the summative assessment splitting moment

  • Tânia C. B. CabralEmail author
  • Roberto Ribeiro Baldino
Article
  • 223 Downloads

Abstract

By using Shlomo Vinner’s credit system concept, we show that summative assessment is a rather vague and underrepresented notion in mathematics education literature. The emotional drive behind this article is expressed in the following questions: How is it possible to look for concrete exclusionary school practices that qualify some and disqualify others without realizing that promotion/exclusion only becomes effective when a certain symbol is officially attached to the name of a student? How is it possible not to notice that promotion/exclusion can only be based on assessment-evaluation of mathematical content ability? How is it possible that mathematics education literature never broaches the consequences of assessment-evaluation on the lives of the students? We argue that these are not due to a temporary blindness of mathematics education research, but, rather, that we are dealing with a symptom. We focus on the dichotomous aspect of summative assessment as potentially loaded with anguish for students and teachers; we call it the splitting moment and endeavor to discuss its consequences for students and teachers.

Keywords

Summative assessment Formative assessment School credit system Symptom 

Notes

References

  1. Allal, L. (2008). Evaluation des apprentissages. In Dictionnaire de l’éducation (pp. 311–314). Presses Universitaires de France – PUF.Google Scholar
  2. Baldino, R. R., & Cabral, T. C. B. (1998). Lacan and the school credit system. In A. Olivier & K. Newstead (Eds.), Proceedings of 22 ndConference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 56–63). South Africa: Stellenbosch.Google Scholar
  3. Baldino, R. R., & Cabral, T. C. B. (2006). Inclusion and diversity from the Hegel-Lacan point of view: do we desire our desire for change? International Journal of Science and Mathematics Education, 4, 19–43.  https://doi.org/10.1007/s10763-005-9004-9 CrossRefGoogle Scholar
  4. Baldino, R. R., & Cabral, T. C. B. (2008). I love maths anxiety. In T. Brown (Ed.), The psychology of mathematics education: a psychoanalytic displacement (pp. 61–92). Rotterdam, the Netherlands: Sense publishers.Google Scholar
  5. Baldino, R. R., & Cabral, T. C. B. (2013). The productivity of students’ schoolwork: an exercise in Marxist rigor. The Journal of Critical Education Policy Studies, 11, 70–84.Google Scholar
  6. Baldino, R. R., & Cabral, T. C. B. (2015). Profitability of qualified-labour-power production. The Journal of Critical Education Policy Studies, 13, 61–82.Google Scholar
  7. Baldino, R. R., & Cabral, T. C. B. (2017). From Hegel to Lacan or from ego to agora. International Journal of Žižek Studies, 11(2), 8.Google Scholar
  8. Black, P., & Wiliam, D. (1998). Assessment and classroom learning. Assessment in Education: Principles, Policy & Practice, 5(1), 7–74.Google Scholar
  9. Boaler, J. (2014). Ability grouping in mathematics classrooms. In S. Lerman (Ed.), Encyclopedia of mathematics education. Dordrecht, the Netherlands: Springer.Google Scholar
  10. Buchholtz, N. F., Krosanke, N., Orschullk, A. B., & Vorhölter, K. (2018). Combining and integrating formative and summative assessment in mathematics teacher education. ZDM Mathematics Education, 50, 715–728.  https://doi.org/10.1007/s11858-018-0948-y CrossRefGoogle Scholar
  11. Bullock, E. (2017). Beyond “ism” groups and figure hiding: Intersectional analysis and critical mathematics education. In A. Chronaki (Ed.), Proceedings of the Ninth International Mathematics Education and Society Conference (Vol. 1, pp. 29–44). Volos, Greece: University of Thessaly Press.Google Scholar
  12. Burkhardt, H., & Schoenfeld, A. (2018). Assessment in the service of learning: challenges and opportunities or plus ça change, plus c’est la même chose. ZDM Mathematics Education, 50, 571–585.  https://doi.org/10.1007/s11858-018-0937-1 CrossRefGoogle Scholar
  13. Cabral, T. C. B. (1993) Vicissitudes da aprendizagem em um curso de cálculo (Unpublished master’s theses, State University of São Paulo – UNESP, Brazil).Google Scholar
  14. Cabral, T. C. B. (1998) Contribuições da Psicanálise à Educação Matemática. A lógica da intervenção didática em processos de aprendizagem (Unpublished doctoral dissertation, University of São Paulo – USP, Brazil).Google Scholar
  15. Cabral, T. C. B., & Baldino, R. R. (2019). The social turn and its big enemy: a leap forward. In J. Subramanian (Ed.), Proceedings of the Tenth International Mathematics Education and Society Conference (p. 15). Hyderabad, India: Printed by Sri Satya Sai Designing Studio Pvt Ltd.Google Scholar
  16. Cabral, T. C. B., Pais, A., & Baldino, R. R. (2019). Mathematics education’s solidarity assimilation methodology. In U. T. Jankvist, M. Van den Heuvel-Panhuizen, & M. Veldhuis (Eds.), Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education. Utrecht, the Netherlands: Freudenthal Group & Freudenthal Institute, Utrecht University and ERME (to appear).Google Scholar
  17. Chanudet, M. (2017). Teachers’ formative assessment practice: the case of a IBME – centered course. In T. Dooley & G. Gueudet (Eds.), Proceedings of 10 thCongress of European Research in Mathematics Education. DCU Institute of Education & ERME: Dublin.Google Scholar
  18. Cusi, A., Morselli, F., & Sabena, C. (2017). Designing and analyzing the role of digital resources in supporting formative assessment process in the classroom: the helping worksheet. In T. Dooley & G. Gueudet (Eds.), Proceedings of 10 thCongress of European Research in Mathematics Education. DCU Institute of Education & ERME: Dublin.Google Scholar
  19. D’Souza, R. (2017). Ableism in mathematics education: Ideology, resistance and solidarity. In A. Chronaki (Ed.), Proceedings of the Ninth International Mathematics Education and Society Conference (Vol. 2, pp. 463–470). Volos, Greece: University of Thessaly Press.Google Scholar
  20. Davies, B. (2017). A case for a new approach to establishing the validity of comparative judgment as assessment tool for mathematics. In T. Dooley & G. Gueudet (Eds.), Proceedings of 10 thCongress of European Research in Mathematics Education. DCU Institute of Education & ERME: Dublin.Google Scholar
  21. Gellert, U. (2017). Revisiting mathematics for all: a commentary to Pais’s critique. In H. Straehler-Pohl, N. Bohlmann, & A. Pais (Eds.), The disorder of mathematics education. Challenging the sociopolitical dimensions of research (pp. 67–87).  https://doi.org/10.1007/978-3-319-34006-7_5 CrossRefGoogle Scholar
  22. Gifford, B. R., & O’Connor, M. C. (Eds.). (1992). Changing assessment. Boston, MA: Kluwer Academic Press.Google Scholar
  23. Gomes da Silva, M. R. (1997). Avaliação e trabalho em grupo em Assimilação Solidária: Análise de uma intervenção. (Unpublished doctoral dissertation, UNESP, Brazil).Google Scholar
  24. Grapin, N., & Sayac, N. (2017). Using external assessment for improving assessment of primary school teachers: a first study and some methodological questions. In T. Dooley & G. Gueudet (Eds.), Proceedings of 10 thCongress of European Research in Mathematics Education. DCU Institute of Education & ERME: Dublin.Google Scholar
  25. Gutiérrez, R. (2013). The sociopolitical turn in mathematics education. Journal for Research in Mathematics Education, 44(1), 37–68.Google Scholar
  26. Harari, Y. N. (2015). Homo Deus. London, UK: Vintage.Google Scholar
  27. Jablonka, E. (2017). Gamification, standards and surveillance in mathematics education: an illustrative example. In A. Chronaki (Ed.), Proceedings of the Ninth International Mathematics Education and Society Conference (Vol. 2, pp. 544–553). Volos, Greece: University of Thessaly Press.Google Scholar
  28. Jackson, C. (2017). ‘Sets 4 and 5 were stuffed full of pupil premium1 kids’: two teachers experiences of ‘ability’ grouping. In A. Chronaki (Ed.), Proceedings of the Ninth International Mathematics Education and Society Conference (Vol. 2, pp. 554–568). Volos, Greece: University of Thessaly Press.Google Scholar
  29. Kollosche, D. (2018). Social functions of mathematics education: a framework for socio-political studies. Educational Studies in Mathematics, 98(3), 287–303.  https://doi.org/10.1007/s10649-018-9818-3 CrossRefGoogle Scholar
  30. Leder, G. C. (Ed.). (1992). Assessment and learning of mathematics. Camberwell, UK: AECER.Google Scholar
  31. Lerman, S. (2000). The social turn in mathematics education research. In J. Boaler (Ed.), Multiple perspectives on mathematics education and learning. Westport, CT: Ablex Publishing.Google Scholar
  32. Lesh, R., & Lamon, S. J. (Eds.). (1992). Assessment of authentic performance n school mathematics. Washington, DC: AAAS Press.Google Scholar
  33. Moomaw, S. (2017). Teddy bear pre-school assessment: validation of a constructivist game - and story- based measure. In T. Dooley & G. Gueudet (Eds.), Proceedings of 10 thCongress of European Research in Mathematics Education. DCU Institute of Education & ERME: Dublin.Google Scholar
  34. Morgan, C. (2017). From police to practice: discourses of mastery and “ability” in England. In A. Chronaki (Ed.), Proceedings of the Ninth International Mathematics Education and Society Conference (Vol. 2, pp. 717–727). Volos, Greece: University of Thessaly Press.Google Scholar
  35. Niss, M. (Ed.). (1992). Investigations into assessment in mathematics education. Dordrecht, the Netherlands: Kluwer Academic Press.Google Scholar
  36. Niss, M. (Ed.). (1993). Cases of assessment in mathematics education. Dordrecht, the Netherlands: Kluwer Academic Press.Google Scholar
  37. Nortvedt, G. A., & Buchholtz, N. (2018). Assessment in mathematics education: responding issues regarding methodology, policy and equity. ZDM Mathematics Education, 50(4), 555–570.Google Scholar
  38. Pais, A. (2011). Criticisms and contradictions of ethnomathematics. Educational Studies in Mathematics, 76, 209–230.  https://doi.org/10.1007/s10649-010-9289-7 CrossRefGoogle Scholar
  39. Pais, A. (2013). An ideology critique of the use-value of mathematics. Educational Studies in Mathematics, 84, 15–34.  https://doi.org/10.1007/s10649-013-9484-4 CrossRefGoogle Scholar
  40. Pais, A. (2014). Economy: the absent center of mathematics education. ZDM Mathematics Education, 46, 1085–1093.  https://doi.org/10.1007/s11858-014-0625-8 CrossRefGoogle Scholar
  41. Pais, A. (2015). Symbolizing the real of mathematics education. Educational Studies in Mathematics, 89, 375–391.  https://doi.org/10.1007/s10649-015-9602-6 CrossRefGoogle Scholar
  42. Pais, A. (2016). At the intersection between the subject and the political: a contribution to on ongoing discussion. Educational Studies in Mathematics, 92, 347–359.  https://doi.org/10.1007/s10649-016-9687-6 CrossRefGoogle Scholar
  43. Pais, A. (2017). The narcissism of mathematics education. In H. Straehler-Pohl, N. Bohlmann, & A. Pais (Eds.), The disorder of mathematics education. Challenging the sociopolitical dimensions of research (pp. 53–63). New York, NY: Springer.Google Scholar
  44. Pais, A., & Costa, M. (2017). An ideology critique of global citizenship. Critical Studies in Education, 1–16.  https://doi.org/10.1080/17508487.2017.1318772
  45. Popkewitz, T. (2002). Whose heaven and whose redemption? The alchemy of the mathematics curriculum to save (please check one or all of the following): (a) the economy, (b) democracy, (c) the nation, (d) human rights, (d) the welfare state, (e) the individual). In MES 3 Proceedings of the Third International Mathematics and Education and Society Conference. Helsingør. http://mes3.learning.aau.dk/Plenaries/Popkewitz.pdf
  46. Povey, H. (2019). How might the practice of pre-service mathematics tutor contribute to social justice? A consideration of a possible approach. In U. T. Jankvist, M. Van den Heuvel-Panhuizen, & M. Veldhuis (Eds.), Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education. Utrecht, the Netherlands: Freudenthal Group & Freudenthal Institute, Utrecht University and ERME (to appear).Google Scholar
  47. Powell, A. B., & Frankenstein, M. (Eds.). (1997). Ethnomathematics: challenging eurocentrism in mathematics education. Albany, NY: State University of New York Press.Google Scholar
  48. Reit, X.-R. (2017). Towards an empirical validation of mathematics teachers’ intuitive assessment practice exemplified by modeling tasks. In T. Dooley & G. Gueudet (Eds.), Proceedings of 10 thCongress of European Research in Mathematics Education. DCU Institute of Education & ERME: Dublin.Google Scholar
  49. Romberg, T. A. (Ed.). (1992). Mathematics assessment and evaluation. Albany, NY: State University of New York Press.Google Scholar
  50. Ruthven, K. (1994). Better judgement: rethinking assessment in mathematics education. Educational Studies in Mathematics, 27(4), 433–450.Google Scholar
  51. Sadafule, V., & Berntsen, M. (2017). Mathematics learning and social background: studying the context of learning in a secondary school in a semi-rural area of Maharashtra. In A. Chronaki (Ed.), Proceedings of the Ninth International Mathematics Education and Society Conference (Vol. 2, pp. 834–845). Volos, Greece: University of Thessaly Press.Google Scholar
  52. Sangwin, C. J., & Jones, I. (2017). Asymmetry in student achievement on multiple-choice and constructed-response items in reversible mathematics processes. Educational Studies in Mathematics, 94(2), 205–222.Google Scholar
  53. Scriven, M. (1967). The methodology of evaluation. In R. Tyler, R. Gagne, & M. Scriven (Eds.), Perspectives on curriculum evaluation, AERA monograph series – Curriculum evaluation. Chicago, IL: Rand McNally and Co..Google Scholar
  54. Shavelson, R. J. (2006). On the integration of formative assessment in teaching and learning with implications for teacher education. In Paper prepared for the Stanford Education Assessment Laboratory and the University of Hawaii Curriculum Research and Development Group. https://web.stanford.edu/dept/SUSE/SEAL/Reports_Papers/On the Integration of Formative Assessment_Teacher Ed_Final.doc
  55. Straehler-Pohl, H. & Gellert, U. (2015). Pathologie oder Struktur: Selektive Einsichten zur Theorie und Empirie des Mathematikunterrichts. Springer.  https://doi.org/10.1007/978-3-658-07272-8_2 Google Scholar
  56. Subramanian, J. (2017). Beyond poverty and development: Caste dynamics and access to mathematics education in India. In A. Chronaki (Ed.), Proceedings of the Ninth International Mathematics Education and Society Conference (Vol. 2, pp. 924–935). Volos, Greece: University of Thessaly Press.Google Scholar
  57. Suurtamm, C., et al. (2016). Assessment in mathematics education. In Assessment in mathematics education. ICME-13 topical surveys. Cham: Springer.  https://doi.org/10.1007/978-3-319-32394-7_1 CrossRefGoogle Scholar
  58. Taras, M. (2005). Assessment – summative and formative – some theoretical reflections. British Journal of Educational Studies, 53(4), 466–478.  https://doi.org/10.1111/j.1467-8527.2005.00307.x CrossRefGoogle Scholar
  59. Vinner, S. (1997). From intuition to inhibition mathematics education and other endangered species. In E. Pehkonen (Ed.), Proceedings of the 21th Conference of the International Group for Psychology of Mathematics Education (Vol. 1, pp. 63–78). Helsinki, Finland: Lahti Research and Training Centre, University of Helsinki.Google Scholar
  60. Wilson, M. (2004). Assessment, accountability and the classroom community of judgement. Yearbook of the National Society for the Study of Education., 103(2), 20–50.Google Scholar
  61. Žižek, S. (1999). The sublime object of ideology. London, UK: Verso.Google Scholar

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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.State University of Rio Grande do Sul - Campus Guaíba (UERGS)GuaíbaBrazil
  2. 2.Pontifical University of Rio Grande do Sul (PUCRS)Porto AlegreBrazil

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