Abstract
This study explored what kind of mathematics is needed in cabinetmakers’ everyday work and how problem solving is intertwined in it. The informants of the study were four Finnish cabinetmakers and the data consisted of workshop observations, interviews, photos, pictures and sketches made by the participants during the interviews. The data was analysed using different qualitative techniques. Even though the participants identified many areas of mathematics that could be used in their daily work, they used mathematics only if they were able to. The cabinetmakers’ different mathematical skills and knowledge were utilized to their skill limit. Cabinetmakers were found to constantly face problem solving situations along with the creative processes. Being able to use more advanced mathematics helped them to solve those problems more efficiently, without wasting time and materials. Based on the findings, the paper discusses the similarities and differences between problem solving and creative processes. It is suggested that the combination of craftsmanship, creativity, and efficient problem solving skills together with more than basic mathematical knowledge will help cabinetmakers in adapting and surviving in future unstable labour markets.
Similar content being viewed by others
Change history
12 March 2018
Unfortunately, the original version of this article was published online with error. The Figures and Pictures was mixed up.
References
Atkinson, P., & Delamont, S. (2005). Analytic Perspectives. In N. Denzin & Y. Lincoln (Eds.), The Sage Handbook of Qualitative Research (3rd ed., pp. 821–840). Thousand Oaks, Canada: SAGE.
Arminen, I. (2001). Workplace Studies: The Practical Sociology of Technology in Action. Acta Sociologica, 44(2), 183–189. https://doi.org/10.1080/000169901300346918.
Barton, B. (1997). Anthropological Perspectives on Mathematics and Mathematics Education. In A. J. Bishop, K. Clements, C. Keitel, J. Kilpatrick, & C. Laborde (Eds.), International Handbook of Mathematics Education (Vol. 2, pp. 1035–1054). Dordrecht: Kluwer.
Bessot, A. (2000). Visibility of Mathematical Objects present in Professional Practice. In A. Bessot & J. Ridgway (Eds.), Education for Mathematics in the Workplace (pp. 225–238). Dordrecht: Kluwer. https://doi.org/10.1007/0-306-47226-0.
Blake, K., & Stalberg, E. (2009). Me and my shadow: observation, documentation, and analysis of serials and electronic resources workflow. Serials Review, 35(4), 242–252. https://doi.org/10.1016/j.serrev.2009.08.018.
Bodner, G. M. (1987). The role of algorithms in teaching problem solving. Journal of Chemical Education, 64(6), 513–514. https://doi.org/10.1021/ed064p513.
Bruner, J. (1964). Bruner on knowing. Cambridge: Harvard University Press.
Cockcroft, W. H. (1982). Mathematics counts: Report of the Committee of Inquiry into the Teaching of Mathematics in Schools under the chairmanship of W.H. Cockcroft. London: H.M.S.O.
Cornish, F., Gillespie, A., & Zittoun, T. (2014). Collaborative analysis of qualitative data. In U. Flick (Ed.), The SAGE handbook of qualitative data analysis (pp. 79–93). London: SAGE. https://doi.org/10.4135/9781446282243.
Csapó, B., & Funke, J. (Eds.). (2017). The Nature of Problem Solving: Using Research to Inspire 21 st Century Learning. Paris: OECD. Retrieved from: http://publicatio.bibl.u-szeged.hu/11201/1/2017_Csapo_Funke_NatureOfProblemSolving.pdf.. https://doi.org/10.1787/9789264273955-en.
Duncker, K. (1945). On problem solving. Psychological Monographs, 58(5), i-113. https://doi.org/10.1037/h0093599.
Finnish National Board of Education. (2013). Vocational Qualification in Wood Processing 2010, Study Programme/Specialisation in Industrial Joinery, Joiner, Requirements for Vocational Qualifications, Regulations 33/011/2010. Retrieved from Finnish National Agency for Education website: http://www.oph.fi/download/158842_Wood_Processing_2010.pdf.
FitzSimons, G. E. (2014). Commentary on vocational mathematics education: where mathematics education confronts the realities of people's work. Educational Studies in Mathematics, 86, 291–305. https://doi.org/10.1007/s10649-014-9556-0.
Frey, C. B., & Osborne, M. A. (2017). The future of employment: How susceptible are jobs to computerization? Technological Forecasting and Social Change, 114, 254–280. https://doi.org/10.1016/j.techfore.2016.08.019.
Gainsburg, J. (2006). The mathematical modelling of structural engineers. Mathematical Thinking and Learning, 8(1), 3–36. https://doi.org/10.1207/s15327833mtl0801_2.
Greiffenhagen, C., & Sharrock, W. (2008). School mathematics and its everyday other? Revisiting Lave’s ‘Cognition in Practice’. Educational Studies in Mathematics, 69(1), 1–21. https://doi.org/10.1007/s10649-008-9115-7.
Hadamard, J. (1945). The psychology of invention in the mathematical field. New York: Dover.
Hayes, J. R. (1980). The complete problem solver. Philadelphia: Franklin Institute Press.
Hodson, R. (2004). A Meta-Analysis of Workplace Ethnographies: Race, Gender, and Employee Attitudes and Behaviours. Journal of Contemporary Ethnography, 33(1), 4–38. https://doi.org/10.1177/0891241603259808.
Hogan, J., & Morony, W. (2000). Classroom teachers doing research in the workplace. In A. Bessot & J. Ridgway (Eds.), Education for Mathematics in the Workplace (pp. 101–113). Dordrecht: Kluwer. https://doi.org/10.1007/0-306-47226-0.
Hoyles, C., Noss, R., & Pozzi, S. (2001). Proportional reasoning in nursing practice. Journal for Research in Mathematics Education, 32(1), 4–27. https://doi.org/10.2307/749619.
Koestler, A. (1964). The act of creation. New York: Macmillan.
Leikin, R., & Pitta-Pantazi, D. (2013). Creativity and mathematics education: the state of the art. ZDM Mathematics Education, 45(2), 159–166. https://doi.org/10.1007/s11858-012-0459-1.
Liljedahl, P. (2004). The AHA! experience: Mathematical contexts, pedagogical implications (Doctoral dissertation). Simon Fraser University, Burnaby.
Liljedahl, P. (2009). In the words of the creators. In R. Leikin, A. Berman, & B. Koichu (Eds.), Mathematical creativity and the education of gifted children (pp. 51–70). Rotterdam: Sense.
Liljedahl, P. (2013). Illumination: an affective experience? The International Journal on Mathematics Education, 45(2), 253–265. https://doi.org/10.1007/s11858-012-0473-3.
Liljedahl, P., & Allen, D. (2013). Mathematical discovery. In E. G. Carayannis (Ed.), Encyclopedia of creativity, invention, innovation, and entrepreneurship. New York: Springer. https://doi.org/10.1007/978-1-4614-3858-8.
Liljedahl, P., & Sriraman, B. (2006). Musings on mathematical creativity. For the Learning of Mathematics, 26(1), 20–23.
Lubart, T. (2001). Models of the Creative Process: Past, Present and Future. Creativity Research Journal, 13(3/4), 295–308. https://doi.org/10.1207/S15326934CRJ1334_07.
Magajna, Z., & Monaghan, J. (2003). Advanced mathematical thinking in a technological workplace. Educational Studies in Mathematics, 52(2), 101–122. https://doi.org/10.1023/A:1024089520064.
Malloch, M., Cairns, L., Evans, K., & O'Connor, B. N. (Eds.) (2011). The sage handbook of workplace learning. Retrieved from https://ebookcentral-proquest-com.libproxy.helsinki.fi.
Mason, J., Burton, L., & Stacey, K. (1982). Thinking mathematically. London: Addison-Wesley.
Mayer, R. E. (1990). Problem solving. In W. M. Eysenk (Ed.), The Blackwell Dictionary of Cognitive Psychology (pp. 284–288). Oxford: Basil Blackwell.
Milroy, W. L. (1992). An ethnographic study of the mathematical ideas of a group of carpenters. Journal for Research in Mathematics Education, Monograph, 5, 1–201.
Ministry of Economic Affairs and Employment. (2015). Pula- ja ylitarjonta-ammatit nyt netissä. Retrieved from http://tem.fi/artikkeli/-/asset_publisher/pula-ja-ylitarjonta-ammatit-nyt-netissa.
Ministry of Education and Culture’s working group on increasing the competence of and educational opportunities for the unemployed. (2017). Competence development during unemployment. Publications of the Ministry of Education and Culture, 17, Finland. Retrieved from the Ministry of Education and Culture website: http://urn.fi/URN:ISBN:978-952-263-463-4.
Moreira, D., & Pardal, E. (2012). Mathematics in Masons’ Workplace. Adults Learning Mathematics: An International Journal, 7(1), 32–48.
Noss, R., Hoyles, C., & Pozzi, S. (2002). Abstraction in expertise: A study of nurses’ conceptions of concentration. Journal for Research in Mathematics Education, 33(3), 204–229. https://doi.org/10.2307/749725.
Occupational Barometer. (2018). Retrieved from https://www.ammattibarometri.fi/info.asp?kieli=en. Accessed 29 Jan 2018.
Opetushallitus. (2016). Puualan perustutkinto, Määräyksen diaarinumero 74/011/2014. Retrieved from Finnish National Agency for Education website: http://www.oph.fi/download/176202_puuala_maarays.pdf.
Paavola, P. J., & Ilonen, K. (1981). Manual on jigs for the furniture industry. New York: Unido.
Pajarinen, M., Rouvinen, P., & Ekeland, A. (2015, April 22). Computerization Threatens One-Third of Finnish and Norwegian Employment. ETLA Brief, 34. Retrieved from http://pub.etla.fi/ETLA-Muistio-Brief-34.pdf.
Perkins, D. (2000). Archimedes' bathtub: The art of breakthrough thinking. New York: W.W. Norton & Company.
Poincaré, H. (1952). Science and method. New York: Dover.
Pólya, G. (1957). How to solve it (2nd ed.). Princeton: Princeton University Press.
Pozzi, S., Noss, R., & Hoyles, C. (1998). Tools in practice, mathematics in use. Educational Studies in Mathematics, 36, 105–122. https://doi.org/10.1023/A:1003216218471.
Quinlan, E. (2008). Conspicuous Invisibility: Shadowing as a Data Collection Strategy. Qualitative Inquiry, 14, 1480–1499.
Rapley, T. J. (2001). The art(fullness) of open-ended interviewing: some considerations on analysing interviews. Qualitative Research, 1(3), 303–323. https://doi.org/10.1177/146879410100100303.
Resnick, L. B., & Glaser, R. (1976). Problem solving and intelligence. In L. B. Resnick (Ed.), The nature of intelligence (pp. 205–230). Hillsdale: Lawrence Erlbaum Associates.
Riall, R., & Burghes, D. (2000). Mathematical needs of young employees. Teaching Mathematics and its Applications, 19(3), 104–113. https://doi.org/10.1093/teamat/19.3.104.
Saló i Nevado, L., Holm, G., & Pehkonen, L. (2011). Farmers do use mathematics: The case of animal feeding. Nordic Studies in Mathematics Education, 16(3), 43–63.
Saxe, G. B. (1991). Culture and cognitive development: Studies in mathematical understanding. Hillsdale: Laurence Erlbaum Associates.
Schoenfeld, A. H. (1983). The wild, wild, wild, wild, wild world of problem solving: A review of Sorts. For the Learning of Mathematics, 3, 40–47.
Sriraman, B. (2004). The characteristics of mathematical creativity. The Mathematics Educator, 14(1), 19–34. https://doi.org/10.1007/s11858-008-0114-z.
Stanic, G., & Kilpatrick, J. (1988). Historical Perspectives on Problem Solving in the Mathematics Curriculum. In R. I. Charles & E. A. Silver (Eds.), The teaching and assessing of mathematical problem solving (pp. 1–22). Reston: National Council of Teachers of Mathematics.
Straesser, R. (2000). Mathematical Means and Models for Vocational Contexts. In A. Bessot & J. Ridgway (Eds.), Education for Mathematics in the Workplace (pp. 65–80). Dordrecht: Kluwer. https://doi.org/10.1007/0306-47226-0.
Taylor, S. (2012). The Meanings and Problems of Contemporary Creative Work. Vocations and Learning, 5(1), 41–57. https://doi.org/10.1007/s12186-011-9065-6.
Thomas, D. R. (2006). A General Inductive Approach for Analyzing Qualitative Evaluation Data. American Journal of Evaluation, 27(2), 237–246. https://doi.org/10.1177/1098214005283748.
Tuomaala, M. (2016). Kysynnän ja tarjonnan kohtaanto nykyisillä ja tulevilla työmarkkinoilla - Tilannetta ja näkymiä keväällä 2016, TEM raportteja, 19. Retrieved from Ministry of employment and the economy website: https://julkaisut.valtioneuvosto.fi/bitstream/handle/10024/74901/TEMrap_19_2016.pdf?sequence=1.
Van Harpen, X. Y., & Sriraman, B. (2013). Creativity and mathematical problem posing: an analysis of high school students’ mathematical problem posing in China and the USA. Educational Studies in Mathematics, 82, 201–221. https://doi.org/10.1007/s10649-012-9419-5.
Virolainen, M. (2007). Workplace learning and higher education in Finland: reflections on current practice. Education +Training, 49(4), 290–309. https://doi.org/10.1108/00400910754444.
Wallas, G. (1926). The art of thought. New York: Harcourt Brace.
Wimmer, L. (2016). Problem solving as a sufficient condition of the creative process: a case for closer cooperation of creativity research and problem solving research. Frontiers in Psychology, 7, 488. https://doi.org/10.3389/fpsyg.2016.00488.
Williams, J., & Wake, G. (2007). Black boxes in workplace mathematics. Educational Studies in Mathematics, 64, 317–343. https://doi.org/10.1007/s10649-006-9039-z.
Zevenbergen, R., & Zevenbergen, K. (2009). The Numeracies of Boatbuilding: New Numeracies Shaped by Workplace Technologies. International Journal of Science and Mathematics Education, 7(1), 183–206. https://doi.org/10.1007/s10763-007-9104-9.
Author information
Authors and Affiliations
Corresponding author
Additional information
The original version of this article was revised: The Figures and Pictures was mixed up in the published online paper.
Rights and permissions
About this article
Cite this article
Saló i Nevado, L., Pehkonen, L. Cabinetmakers’ Workplace Mathematics and Problem Solving. Vocations and Learning 11, 475–496 (2018). https://doi.org/10.1007/s12186-018-9200-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12186-018-9200-8