Mathematical understanding and reasoning of vocational school students in agriculture-based mathematical tasks

Year 2020, , 771 - 782, 15.06.2020

Ai Tusi Fatımah , Sufyani Prabawanto

https://doi.org/10.17478/jegys.702884

Cited By: 1

Abstract

Mathematical understanding and reasoning are important in solving agriculture problems. This study aims to describe students' mathematical understanding and reasoning in agriculture-based mathematical tasks. This research is a case study of vocational students in food crops and horticulture agribusiness of 11th graders students'. Data collected through tasks and interviews. Analysis of data to determine students' understanding (coherence, correspondence, and connection) and reasoning (algorithmic or creative). The results show students' mathematical understanding and reasoning was influenced by the design of tasks and students' experiences. Both algorithmic and creative reasoning, should by the plausibility of the reality of workplace practice in agriculture to affects the ability of coherence and correspondence of students' mathematical representations. Mathematical knowledge and experience affect the whole process of solving the tasks.

Keywords

agriculture, mathematical understanding, mathematical reasoning, mathematical task

References

• Bakker, A., Hoyles, C., Kent, P., & Noss, R. (2006). Improving work processes by making the invisible visible. Journal of Education and Work, 19(4), 343–361. https://doi.org/10.1080/13639080600867133
• Bakker, A. (2014). Characterizing and developing vocational mathematical knowledge. Educational Studies in Mathematics, 86(2), 151–156. https://doi.org/10.1007/s10649-014-9560-4
• Bakker, A., Groenveld, D., Wijers, M., Akkerman, S. F., & Gravemeijer, K. P. E. (2014). Proportional reasoning in the laboratory: an intervention study in vocational education. Educational Studies in Mathematics, 86(2), 211–221. https://doi.org/10.1007/s10649-012-9393-y
• Bakker, A. & Akkerman, S. F. (2014). A boundary-crossing approach to support students’ integration of statistical and work-related knowledge. Educational Studies in Mathematics, 86(2), 223–237. https://doi.org/10.1007/s10649-013-9517-z
• Cai, J., & Ding, M. (2017). On mathematical understanding: perspectives of experienced Chinese mathematics teachers. Journal of Mathematics Teacher Education, 20(1), 5–29. https://doi.org/10.1007/s10857-015-9325-8
• C., N. (1923). Mathematics for students of agriculture. Nature, 112, 128–129. https://doi.org/10.1038/112128c0
• Coben, D., & Weeks, K. (2014). Meeting the mathematical demands of the safety-critical workplace: medication dosage calculation problem-solving for nursing. Educational Studies in Mathematics, 86(2), 253–270. https://doi.org/10.1007/s10649-014-9537-3
• FitzSimons, G. E., & Björklund Boistrup, L. (2017). In the workplace mathematics does not announce itself: towards overcoming the hiatus between mathematics education and work. Educational Studies in Mathematics, 95(3), 329–349. https://doi.org/10.1007/s10649-017-9752-9
• FitzSimons, G. E. (2014). Commentary on vocational mathematics education: where mathematics education confronts the realities of people’s work. Educational Studies in Mathematics, 86(2), 291–305. https://doi.org/10.1007/s10649-014-9556-0
• Greeno, J. G. (1978) Understanding and procedural knowledge in mathematics instruction. Educational Psychologist. 12(3), 262-283. https://doi.org/10.1080/00461527809529180.
• Hershkowitz, R., Tabach, M., & Dreyfus, T. (2017). Creative reasoning and shifts of knowledge in the mathematics classroom. ZDM Mathematics Education, 49(6), 25–36. https://doi.org/10.1007/s11858-016-0816-6.
• Ikram, M., Purwanto, Parta, I.N., & Susanto, H. (2020). Exploring the potential role of reversible reasoning: cognitive research on inverse function problems in mathematics. Journal for the Education of Gifted Young Scientists, 8(1), 591-611. https://doi.org/10.17478/jegys.665836
• Johnson, H. L., Coles, A., & Clarke, D. (2017). Mathematical tasks and the student: navigating “tensions of intentions” between designers, teachers, and students. ZDM Mathematics Education, 49(6), 813–822. https://doi.org/10.1007/s11858-017-0894-0.
• Johnson, H. L., McClintock, E., & Hornbein, P. (2017). Ferris wheels and filling bottles: a case of a student’s transfer of covariational reasoning across tasks with different backgrounds and features. ZDM Mathematics Education, 49(6), 851–864. https://doi.org/10.1007/s11858-017-0866-4
• LaCroix, L. (2014). Learning to see pipes mathematically: preapprentices’ mathematical activity in pipe trades training. Educational Studies in Mathematics, 86(2), 157-176. https://doi.org/10.1007/s10649-014-9534-6.
• Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding It Up-Helping Children Learn Mathematics. Washington: National Academy Press.
• Lithner, J. (2000). Mathematical reasoning in school task. Educational Studies in Mathematics, 41(2), 165–190. https://doi.org/10.1023/A:1003956417456
• Lithner, J. (2003). Students’ mathematical reasoning in university text book exercises. Educational Studies in Mathematics, 52(1), 29–55. https://doi.org/10.1023/A:1023683716659.
• Lithner, J. (2008). A research framework for creative and imitative reasoning. Educational Studies in Mathematics, 67(3), 255–276. https://doi.org/10.1007/s10649-007-9104-2.
• Lithner, J. (2017). Principles for designing mathematical tasks that enhance imitative and creative reasoning. ZDM Mathematics Education, 49(6), 937–949. https://doi.org/10.1007/s11858-017-0867-3.
• Maass, K., & Engeln, K. (2019). Proffesional development on connection to world of work in mathematics and science education. ZDM Mathematics Education, 51(6), 967-978. https://doi.org/10.1007/s11858-019-01047-7.
• 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%3A1024089520064.
• Muhrman, K. (2015). Mathematics in agriculture and vocational education for agriculture. Proceedings of the Ninth Congress of European Society for Research in Mathematics Education. Prague, Czech Republic, 1669-1670. https://hal.archives-ouvertes.fr/hal-01287937
• National Council of Teachers of Mathematics. (2000). Principle and Standards for School Mathematics. Reston, VA: The Council.
• Nunes, T. A., Schliemann, D., & Carraher, D. W. (1993). Street mathematics and school mathematics. Cambridge: Cambridge University Press.
• Piere, S., & Martin, L. (2000). The role of collecting in the growth of mathematical understanding. Mathematics Education Research Journal, 12(2), 127-146.
• Piere, S. E. B., & Kiere, T. (1989). A recursive theory of mathematical understanding. For the Learning Mathematics, 9(3), 7-11.
• Piere, S. E. B., & Schwarzenberg, R. L. E. (1988). Mathematical discussion and mathematical understanding. Educational Studies in Mathematics, 19(4), 459-470. https://doi.org/10.1007/BF00578694
• Pozzi, S., Noss, R., & Hoyles, C. (2003). Tools in practice, mathematics in use. Educational Studies in Mathematics, 32(2), 105–122. https://doi.org/10.1023/A%3A1003216218471
• Rezat, S., & Sträßer, R. (2012). From the didactical triangle to the socio-didactical tetrahedron: artifacts as fundamental constituents of the didactical situation. ZDM Mathematics Education, 44(6), 641–651. https://doi.org/10.1007/s11858-012-0448-4
• Ross, K. A. (1998). Doing and proving: the place of algorithms and proofs in school mathematics, American Mathematical Monthly, 105(3), 252–255. https://doi.org/10.1080/00029890.1998.12004875
• Roth, W. (2014). Rules of bending, bending the rules: the geometry of electrical conduit bending in college and workplace. Educational Studies in Mathematics, 86(2), 177-192. https://doi.org/10.1007/s10649-011-9376-4
• Sáenz, C. (2009). The role of contextual, conceptual and procedural knowledge in activating mathematical competencies (PISA). Educational Studies in Mathematics, 71(2), 123–143. https://doi.org/ https://doi.org /10.1007/s10649-008-9167-8
• Skemp, R. R. (1976). Relational understanding and instrumental understanding. Mathematics teaching, 77(1), 20-26.
• Swanson, D. (2014). Making abstract mathematics concrete in and out of school. Educational Studies in Mathematics, 86(2), 193–209. https://doi.org/10.1007/s10649-014-9536-4
• Thanheiser, E. (2017). Commentary on mathematical tasks and the Student: coherence and connectedness of mathematics, cycles of task design, and context of implementation. ZDM Mathematics Education, 49(6), 965–969. https://doi.org/10.1007/s11858-017-0895-z
• Triantafillou, C., & Potari, D. (2010). Mathematical practices in a technological workplace: the role of tools. Educational Studies in Mathematics, 74(3), 275–294. https://doi.org/ 10.1007/s10649-010-9237-6
• Williams, J. S., & Wake, G. D. (2007). Black boxes in workplace mathematics. Educational Studies in Mathematics, 64(3), 317–343.
• Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27(4), 458–477.
• Yeo, J. B. W. (2017). Development of a framework to characterise the openness of mathematical tasks. International Journal of Science and Mathematics Education, 15, 175–191. https://doi.org/ 10.1007/s10763-015-9675-9.