Procedural mathematical knowledge and use of technology by senior high school students

Christian Dorner; Christoph Ableitinger

doi:10.29333/ejmste/12712

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Christian Dorner ¹ ^* , Christoph Ableitinger ²

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¹ Institute for Secondary Teacher Education, University College of Teacher Education Styria, Graz, AUSTRIA² Faculty of Mathematics, University of Vienna, Vienna, AUSTRIA^* Corresponding Author

Abstract

The article at hand deals with students’ procedural knowledge, the frequency of technology use (CAS, graphics calculators) during mathematics education in upper secondary level and their self-assessed technology knowledge. In this study, the participating students (representative sample of Austrian high school students in the final year, n=455) had to solve procedural, curriculum-related tasks without any aids (neither technology nor formula booklets). We examined how the frequency of technology use in the classroom affects the students’ success rate on procedural tasks. On average, GeoGebra or graphic calculators with CAS are used once a week by the teacher and the students in class, respectively, and unexpectedly, there is no significant correlation between the frequency of technology use during mathematics education in upper secondary level and the procedural knowledge acquired. Regardless of the success in solving the procedural tasks, the students rate their technology knowledge for solving the procedural tasks as rather high.

Keywords

procedural knowledge
technology use
technology knowledge
mathematics education

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, 2022, Volume 18, Issue 12, Article No: em2202

https://doi.org/10.29333/ejmste/12712

Publication date: 12 Dec 2022

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References

Altieri, M. (2016). Erfolg in Mathematikklausuren ingenieurwissenschaftlicher Studiengänge unter besonderer Berücksichtigung prozeduralen Wissens [Success in mathematics exams in engineering courses with a special focus on procedural knowledge] [PhD dissertation, Technical University of Dortmund. https://doi.org/10.17877/DE290R-17417
Bartok, L., & Steinfeld, J. (2015). Stichprobenziehung. Ein Kommentar zur aktuellen und Vorschläge zur weiteren Vorgehensweise [Sampling. A comment on the current procedure and suggestions for the further procedure]. BIFIE.
Bergqvist, E. (2007). Types of reasoning required in university exams in mathematics. The Journal of Mathematical Behavior, 26(4), 348-370. https://doi.org/10.1016/j.jmathb.2007.11.001
Bergsten, C., Engelbrecht, J., & Kågesten, O. (2017). Conceptual and procedural approaches to mathematics in the engineering curriculum–comparing views of junior and senior engineering students in two countries. EURASIA Journal of Mathematics, Science and Technology Education, 13(3), 533-553. https://doi.org/10.12973/eurasia.2017.00631a
BMBWF. (2022). SRP Mathematik (AHS): 3-Stufen-Plan zur Weiterentwicklung des Mathematik-Unterrichts und der Mathematik-Matura [Mathematics in high schools for general education: 3-step plan for the further development of the school leaving exam]. https://www.matura.gv.at/index.php?eID=dumpFile&t=f&f=4812&token=570ef569b2950dfbcc89d7633d94112dc1cc631c
Bosse, M. J., & Bahr, D. L. (2008). The state of balance between procedural knowledge and conceptual understanding in mathematics teacher education. International Journal for Mathematics Teaching and Learning.
Cambridge Assessment Admissions Testing. (2019). Test of mathematics of university admission trail: Durham University 2015. Cambridge Assessment. https://www.admissionstesting.org/Images/536431-tmua-trial-durham-2015-2019-report.pdf
Cheung, A. C. K., & Salvin, R. E. (2013). The effectiveness of educational technology applications for enhancing mathematics achievement in K-12 classrooms: A meta-analysis. Educational Research Review, 9, 88-113. https://doi.org/10.1016/j.edurev.2013.01.001
Concept SRP. (2021). Die standardisierte schriftliche Reifeprüfung in Mathematik (AHS) [The standardized school leaving exam in mathematics (AHS)]. https://www.matura.gv.at/index.php?eID=dumpFile&t=f&f=4826&token=4574fed24b889f914a68a7411172dbce06459c69
Curriculum. (2021). Bundesrecht konsolidiert: Gesamte Rechtsvorschrift für Lehrpläne — allgemeinbildende höhere Schulen [Consolidated federal law: Entire legal regulation for curricula — high schools for general education]. https://www.ris.bka.gv.at/GeltendeFassung.wxe?Abfrage=Bundesnormen&Gesetzesnummer=20007850
Di Martino, P., & Gregorio, F. (2019). The mathematical crisis in secondary–tertiary transition. International Journal of Science and Mathematics Education, 17(4), 825-843. https://doi.org/10.1007/s10763-018-9894-y
Die Presse. (2015). Mathe-Auffrischung für 2000 Studienanfänger an der TU [Math refresher for 2000 first-year students at the TU]. https://www.diepresse.com/4820682/mathe-auffrischung-fur-2000-studienanfanger-an-der-tu
Drijvers, P., Ball, L., Barzel, B., Heid, M. K., Cao, Y., & Maschietto, M. (2016). Uses of technology in lower secondary mathematics education. Springer. https://doi.org/10.1007/978-3-319-33666-4
Engelbrecht, J., Bergsten, C., & Kågesten, O. (2009). Undergraduate students’ preference for procedural to conceptual solutions to mathematical problems. International Journal of Mathematical Education in Science and Technology, 40(7), 927-940. https://doi.org/10.1080/00207390903200968
Ericsson, K. A., & Simon, H. A. (1980). Verbal reports as data. Psychological Review, 87(3), 215-251. https://doi.org/10.1037/0033-295X.87.3.215
Ericsson, K. A., & Simon, H. A. (1993). Protocol analysis: Verbal reports as data. The MIT Press. https://doi.org/10.7551/mitpress/5657.001.0001
Greefrath, G., Hoever, G., Kürten, R., & Neugebauer, C. (2015). Vorkurse und Mathematiktests zu Studienbeginn — Möglichkeiten und Grenzen [Preparatory courses and mathematics tests at the beginning of the course — possibilities and limits]. In J. Roth, T. Bauer, H. Koch, & S. Prediger (Eds.), Übergänge konstruktiv gestalten [Design transitions constructively] (pp. 19-32). Springer. https://doi.org/10.1007/978-3-658-06727-4
Grønmo, L. S., Lindquist, M., & Arora, A. (2014). TIMSS advanced 2015 assessment frameworks. In I. V. S. Mullis, & M. O. Martin (Eds.), TIMSS advanced 2015 assessment frameworks (pp. 9-16). TIMSS & PIRLS International Study Center.
Hallett, D. (2006). What have we learned from calculus reform? The road to conceptual understanding. In N. Hastings (Ed.), A fresh start for collegiate mathematics: Rethinking the courses below calculus (pp. 43-45). Mathematical Association of America. https://doi.org/10.5948/UPO9781614443025.008
Heinze, A., Neumann, I., Ufer, S., Rach, S., Borowski, A., Buschhüter, D., Greefrath, G., Halverscheid, S., Kürten, R., Pustelnik, K., & Sommerhoff, D. (2019). Mathematische Kenntnisse in der Studieneingangsphase — Was messen unsere Tests? [Mathematical knowledge in the introductory phase — what do our tests measure?] In A. Frank, S. Krauss, & K. Binder (Eds.), Beiträge zum Mathematikunterricht 2019 [Contributions to mathematics education 2019] (pp. 345-348). WTM-Verlag. https://doi.org/10.17877/DE290R-20862
Hiebert, J., & Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: An introductory analysis. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 1-28). Lawrence Erlbaum Associates, Inc.
Hoever, G. (2018). Erhebungsbogen und Test zum Studienbeginn [Questionnaire and test at the beginning of the course]. FH Aachen.
Hoever, G., & Greefrath, G. (2018). Vorkenntnisse von Studienanfänger/innen, Vorkursteilnahme und Studienerfolg — Untersuchungen in Studiengängen der Elektrotechnik und der Informatik an der FH Aachen [Previous knowledge of first-year students, pre-course participation and study success — examinations in electrical engineering and computer science courses at the FH Aachen]. In Fachgruppe Didaktik der Mathematik der Universität Paderborn (Eds.), Beiträge zum Mathematikunterricht 2018 [Contributions to mathematics education 2018] (pp. 803-806). WTM-Verlag. https://doi.org/10.17877/DE290R-19409
Ingelmann, M. (2009). Evaluation eines Unterrichtskonzeptes für einen CAS-gestützten Mathematikunterricht in der Sekundarstufe I [Evaluation of a teaching concept for a CAS-supported mathematics instruction on lower secondary level]. Logos-Verlag.
Jordan, A., Ross, N., Krauss, S., Baumert, J., Blum, W., Neubrand, M., Löwen, K., Brunner, M., & Kunter, M. (2006). Klassifikationsschema für Mathematikaufgaben. Materialien aus der Bildungsforschung [Classification scheme for mathematics tasks. Materials from educational research]. Max-Planck-Institut. https://pure.mpg.de/rest/items/item_2100753_3/component/file_2197661/content
Kieran, C. (2013). The false dichotomy in mathematics education between conceptual understanding and procedural skills: An example from algebra. In K. Leatham (Ed.), Vital directions for mathematics education research (pp. 153-171). Springer. https://doi.org/10.1007/978-1-4614-6977-3_7
Kieran, C., & Drijvers, P. (2006). The co-emergence of machine techniques, and theoretical reflection: A study of CAS use in secondary school algebra. International Journal of Computers for Mathematical Learning, 11(2), 205-263. https://doi.org/10.1007/s10758-006-0006-7
Kieran, C., & Yerushalmy, M. (2004). Research on the role of technological environments in algebra learning and teaching. In K. Stacey, H. Chick, & M. Kendal (Eds.), The future of the teaching and learning of algebra (pp. 99-152). Springer. https://doi.org/10.1007/1-4020-8131-6_6
Knospe, H. (2008). Der Mathematik-Eingangstest an Fachhochschulen in Nordrhein-Westfalen [The mathematics entrance test at technical colleges in North Rhine-Westphalia]. In Proceedings of the 6^th Workshop Mathematics for Engineers (pp. 6-11).
Kopńaska-Bródka, D., Dudzińska-Baryła, R., & Michalska, E. (2015). An evaluation of the selected mathematical competence of the first-year students of economic studies. Didactics of Mathematics, 12(16), 69-84. https://doi.org/10.15611/dm.2015.12.08
Kurier. (2018). Mathematik: “Man müsste früher in der Schule ansetzen” [Mathematics: “You should start earlier in school”]. https://kurier.at/chronik/oesterreich/mathe-studiendekan-man-muesste-frueher-in-der-schule-ansetzen/400037467
Lenz, K., Dreher, A., Holzäpfel, L., & Wittmann, G. (2019). Entwicklung und Validierung eines Testinstruments zur Erfassung von konzeptuellem und prozeduralem Wissen zu Brüchen [Development and validation of a test instrument for capturing conceptual and procedural knowledge about fractions.]. In A. Frank, S. Krauss, & K. Binder (Eds.), Beiträge zum Mathematikunterricht 2019 [Contributions to mathematics education 2019] (pp. 481-484). WTM-Verlag. https://doi.org/10.17877/DE290R-20498
Li, Q., & Ma, X. (2010). A meta-analysis of the effects of computer technology on school students’ mathematics learning. Educational Psychology Review, 22(3), 215-243. https://doi.org/10.1007/s10648-010-9125-8
Liebscher, M., Breyer, G., Fürst, S., Heugl, H., Kraker, M., Preis, C., Svecnik, E., Liegl, I., & Plattner, G. (2013). Praxishandbuch Mathematik AHS Oberstufe — Auf dem Weg zur standardisierten kompetenzorientierten Reifeprüfung. Teil 1 [Handbook of best practice for mathematics AHS upper level — on the way to the standardized competence-based school-leaving exam. Part 1]. BIFIE.
Matyas, K., & Drmota, M. (2018). Das “M” in MINT: TU Wien beobachtet Absinken der Mathematikkenntnisse von Studienanfänger_innen. Offener Brief an Bundesminister Heinz Faßmann [The “M” in STEM: TU Vienna observes a decrease in the mathematics knowledge of first-year students. Open letter to Federal Minister Heinz Faßmann]. https://www.tuwien.at/tu-wien/aktuelles/news/news/das-m-in-mint-tu-wien-beobachtet-absinken-der-mathematikkenntnisse-von-studienanfaenger-innen
OECD. (2015). Students, computers and learning: Making the connection. OECD Publishing. https://doi.org/10.1787/9789264239555-en
OECD. (2018). PISA 2022 mathematics framework (draft). https://pisa2022-maths.oecd.org/files/PISA%202022%20Mathematics%20Framework%20Draft.pdf
ÖMG. (2019). Stellungnahme der ÖMG zur Zukunft der standardisierten Reife- und Diplomprüfung im Fach Mathematik (AHS, BHS) [Statement of the ÖMG on the future of the standardized final school leaving examination in mathematics (AHS, BHS)]. http://www.oemg.ac.at/Mitteilungen/2019-06-13-Zukunft-SRDP.pdf
Open Letter. (2017). Mathematikunterricht und Kompetenzorientierung — ein offener Brief [Mathematics teaching and competence orientation — an open letter]. http://www.tagesspiegel.de/downloads/19549926/2/offener-brief.pdf
Österman, T., & Bråting, K. (2019). Dewey and mathematical practice: Revisiting the distinction between procedural and conceptual knowledge. Journal of Curriculum Studies, 51(4), 457-470. https://doi.org/10.1080/00220272.2019.1594388
Pederson, I. F. (2015). What characterizes the algebraic competence of Norwegian upper secondary school students? Evidence from TIMSS advanced. International Journal of Science and Mathematics Education, 13(1), 71-96. https://doi.org/10.1007/s10763-013-9468-y
Provasnik, S., Malley, L., Stephens, M., Landeros, K., Perkins, R., & Tang, J. H. (2016). Highlights from TIMSS and TIMSS advanced 2015: Mathematics and science achievement of U.S. students in grades 4 and 8 and in advanced courses at the end of high school in an international context (NCES 2017-002). U.S. Department of Education, National Center for Education Statistics. http://nces.ed.gov/pubsearch
Qetrani, S., Ouailal, S., & Achtaich, N. (2021). Enhancing students’ conceptual and procedural knowledge using a new teaching approach of linear equations based on the equivalence concept. EURASIA Journal of Mathematics, Science and Technology Education, 17(7), em1978. https://doi.org/10.29333/ejmste/10938
Rakes, C. R., Valentine, J. C., McGatha, M. B., & Ronau, R. N. (2010). Methods of instructional improvement in algebra: A systematic review and meta-analysis. Review of Educational Research, 80(3), 372-400. https://doi.org/10.3102/0034654310374880
Rittle-Johnson, B., & Schneider, M. (2014). Developing conceptual and procedural knowledge of mathematics. In R. Kadosh, & A. Dowker (Eds.), Oxford handbook of numerical cognition (pp. 1118-1134). Oxford University Press. https://doi.org/10.1093/oxfordhb/9780199642342.013.014
Rolfes, T., Lindmeier, A., & Heinze, A. (2021). Mathematikleistungen von Schülerinnen und Schülern der gymnasialen Oberstufe in Deutschland: Ein Review und eine Sekundäranalyse der Schulleistungsstudien seit 1995 [Mathematical achievements of upper secondary school students in Germany: A review and a secondary analysis of large scale assessment studies since 1995]. Journal für Mathematik-Didaktik [Journal for Didactics of Mathematics], 42(2), 395-429. https://doi.org/10.1007/s13138-020-00180-1
Ronau, R. N., Rakes, C. R., Bush, S. B., Driskell, S. O., Niess, M. L., & Pugalee, D. K. (2014). A survey of mathematics education technology dissertation scope and quality: 1968-2009. American Educational Research Journal, 51(5), 974-1006. https://doi.org/10.3102/0002831214531813
Star, J. R. (2005). Reconceptualizing procedural knowledge. Journal for Research in Mathematics Education, 36(5), 404-411.
Star, J. R., Pollack, C., Durkin, K., Rittle-Johnson, B., Lynch, K., Newton, K., & Gogolen, C. (2015). Learning from comparison in algebra. Contemporary Educational Psychology, 40, 41-54. https://doi.org/10.1016/j.cedpsych.2014.05.005
Wynands, A. (1984). Rechenfertigkeit und Taschenrechner [Numeracy and calculator]. Journal für Mathematik-Didaktik [Journal for Didactics of Mathematics], 5(1), 3-32. https://doi.org/10.1007/BF03339239
Yao, X., & Zhao, J. (2022). Chinese mathematics teachers’ use of digital technologies for instruction: A survey study. EURASIA Journal of Mathematics, Science and Technology Education, 18(8), em2135. https://doi.org/10.29333/ejmste/12209
Zerr, R. J. (2009). Promoting students’ ability to think conceptually in calculus. Primus, 20(1), 1-20. https://doi.org/10.1080/10511970701668365

How to cite this article

APA

Dorner, C., & Ableitinger, C. (2022). Procedural mathematical knowledge and use of technology by senior high school students. Eurasia Journal of Mathematics, Science and Technology Education, 18(12), em2202. https://doi.org/10.29333/ejmste/12712

Vancouver

Dorner C, Ableitinger C. Procedural mathematical knowledge and use of technology by senior high school students. EURASIA J Math Sci Tech Ed. 2022;18(12):em2202. https://doi.org/10.29333/ejmste/12712

AMA

Dorner C, Ableitinger C. Procedural mathematical knowledge and use of technology by senior high school students. EURASIA J Math Sci Tech Ed. 2022;18(12), em2202. https://doi.org/10.29333/ejmste/12712

Chicago

Dorner, Christian, and Christoph Ableitinger. "Procedural mathematical knowledge and use of technology by senior high school students". Eurasia Journal of Mathematics, Science and Technology Education 2022 18 no. 12 (2022): em2202. https://doi.org/10.29333/ejmste/12712

Harvard

Dorner, C., and Ableitinger, C. (2022). Procedural mathematical knowledge and use of technology by senior high school students. Eurasia Journal of Mathematics, Science and Technology Education, 18(12), em2202. https://doi.org/10.29333/ejmste/12712

MLA

Dorner, Christian et al. "Procedural mathematical knowledge and use of technology by senior high school students". Eurasia Journal of Mathematics, Science and Technology Education, vol. 18, no. 12, 2022, em2202. https://doi.org/10.29333/ejmste/12712