Adults’ Use of Mathematics and Its Influence on Mathematical Competence

  • Christoph Duchhardt
  • Anne-Katrin Jordan
  • Timo Ehmke
Article

Abstract

The Programme for the International Assessment of Adult Competencies (PIAAC) has recently drawn additional attention to “mathematical literacy” as an important influential factor for individuals’ life chances. High levels of mathematical literacy have thereby been linked to using mathematics in daily and working life frequently. In this paper, based on the data from Germany, we focus on the construct “use of mathematics” in two ways: First, we analyze in depth how it can be utilized to describe different groups of adults. Second, we investigate its role as predictor of mathematical competence and mediator of other relevant background variables. Results show that three groups of adults can be distinguished that use mathematics differently in daily and working life. However, the construct can sensibly be described as unidimensional. In a path model, “use of mathematics” turns out to be the strongest predictor of mathematical competence. In addition, it mediates effects of the mathematical requirements of the job, duration of education, and gender.

Keywords

Adults Mathematical competence Mathematical literacy Mathematical requirements of the job Use of mathematics 

Supplementary material

10763_2015_9670_MOESM1_ESM.docx (21 kb)
ESM 1(DOCX 21 kb)
10763_2015_9670_MOESM2_ESM.docx (58 kb)
ESM 2(DOCX 57 kb)

References

  1. Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In B. N. Petrov & F. Csaki (Eds.), 2nd International Symposium on Information Theory (pp. 267–281). Budapest, Hungary: Akademiai Kiado.Google Scholar
  2. Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19(6), 716–723.CrossRefGoogle Scholar
  3. Barton, D., Ivanic, R., Appleby, Y., Hodge, R. & Tusting, K. (2004). Adult Learners’ Lives project: Setting the scene. London, England: National Research and Development Centre for Adult Literacy and Numeracy.Google Scholar
  4. Blossfeld, H.-P., Schneider, T. & Doll, J. (2009). Methodological advantages of panel studies: Designing the New National Educational Panel Study (NEPS) in Germany. Journal for Educational Research Online, 1(2), 10–32.Google Scholar
  5. Blossfeld, H.-P., Roßbach, H.-G., & von Maurice, J. (Eds.). (2011). Education as a lifelong process: The German National Educational Panel Study (NEPS). Zeitschrift für Erziehungswissenschaft, 14 [Special Issue]. Google Scholar
  6. Brooks, G., Heath, K. & Pollard, A. (2005). Assessing adult literacy and numeracy. A review of assessment instrument. London, England: National Research and Development Centre for Adult Literacy and Numeracy.Google Scholar
  7. Burnham, K. P. & Anderson, D. R. (2002). Model selection and multimodel inference: A practical information-theoretic approach (2nd ed.). New York, NY: Springer.Google Scholar
  8. Bynner, J. & Parsons, S. (1998). Use It or Lose It? The Impact of Time out of Work on Literacy and Numeracy Skills. London, England: Basic Skills Agency.Google Scholar
  9. Carpentieri, J. C., Lister, J. & Frumkin, L. (2010). Adult numeracy: A review of research. London, England: National Research and Development Centre for Adult Literacy and Numeracy.Google Scholar
  10. Coben, D. (2003). Adult numeracy: Review of research and related literature. London, England: National Research and Development Centre for Adult Literacy and Numeracy.Google Scholar
  11. Desjardins, R. & Warnke, A. (2012). Ageing and skills: A review and analysis of skill gain and skill loss over the lifespan and over time. (OECD Education Working Papers, No. 72). Paris, France: OECD Publishing.CrossRefGoogle Scholar
  12. Ehmke, T., Duchhardt, C., Geiser, H., Grüßing, M., Heinze, A. & Marschick, F. (2009). Kompetenzentwicklung über die Lebensspanne - Erhebung von mathematischer Kompetenz im Nationalen Bildungspanel [Skills development across the lifespan - collection of mathematical competence in the National Educational Panel]. In A. Heinze & M. Grüßing (Eds.), Mathematiklernen vom Kindergarten bis zum Studium. Kontinuität und Kohärenz als Herausforderung für den Mathematikunterricht (pp. 313–327). Münster, Germany: Waxmann.Google Scholar
  13. Embretson, S. E. & Reise, S. P. (2000). Item response theory for psychologists. Mahwah, NJ: Erlbaum.Google Scholar
  14. Evans, J., Wedege, T. & Yasukawa, K. (2013). Critical perspectives on adults’ mathematics education’. In M. A. Clements, A. Bishop, C. Keitel, J. Kilpatrick & F. Leung (Eds.), Third International Handbook of Mathematics Education (pp. 203–242). New York, NY: Springer.Google Scholar
  15. Gal, I. (Ed.). (2000). Adult numeracy development: Theory, research, practice. Cresskill, NJ: Hampton.Google Scholar
  16. Gal, I., van Groenestijn, M., Manly, M., Schmitt, M. J. & Tout, D. (2005). Adult numeracy and its assessment in the ALL survey: A conceptual framework and pilot results. In S. T. Murray, Y. Clermont & M. Binkley (Eds.), Measuring adult literacy and life skills: New frameworks for assessment (pp. 137–191). Ottawa, Canada: Statistics Canada.Google Scholar
  17. Green, D. A. & Riddel, W. C. (2001). Literacy, Numeracy and Labor Market Outcomes in Canada (International Adult Literacy Survey). Ottawa, Canada: Statistics Canada.Google Scholar
  18. Hector-Mason, A., Safford-Ramus, K. & Coben, D. (2006). Numeracy is not just an aspect of literacy. Reflect, 6, 28.Google Scholar
  19. Hertzog, C., Kramer, A. F., Wilson, R. S. & Lindenberger, U. (2008). Enrichment effects on adult cognitive development can the functional capacity of older adults be preserved and enhanced? Psychological Science in the Public Interest, 9(1), 1–65.Google Scholar
  20. Hoyles, C., Wolf, A., Molyneux-Hodgson, S. & Kent, P. (2002). Mathematical skills in the workplace: Final report to the Science, Technology and Mathematics Council. London, England: Institute of Education, University of London.Google Scholar
  21. Hu, L. T. & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling: A Multidisciplinary Journal, 6(1), 1–55.CrossRefGoogle Scholar
  22. Hultsch, D. F., Hertzog, C., Small, B. J. & Dixon, R. A. (1999). Use it or lose it: engaged lifestyle as a buffer of cognitive decline in aging? Psychology and Aging, 14(2), 245.CrossRefGoogle Scholar
  23. Hurvich, C. M. & Tsai, C. L. (1995). Model selection for extended quasi-likelihood models in small samples. Biometrics, 51(3), 1077–1084.CrossRefGoogle Scholar
  24. Kanfer, R. & Ackerman, P. L. (2004). Aging, adult development, and work motivation. Academy of Management Review, 29(3), 440–458.Google Scholar
  25. Krahn, H. & Lowe, G. S. (1998). Literacy utilization in Canadian workplaces. Ottawa, Canada: Statistics Canada and Human Resources Development Canada.Google Scholar
  26. Lazarsfeld, P. F. & Henry, N. W. (1968). Latent structure analysis. Boston, MA: Houghton Mifflin Co.Google Scholar
  27. Masters, G. N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47, 149–174.CrossRefGoogle Scholar
  28. Mincer, J. & Ofek, H. (1982). Interrupted work careers: Depreciation and restoration of human capital. Journal of Human Resources, 17(1), 3–24.CrossRefGoogle Scholar
  29. Murray, T. S., Kirsch, I. S. & Jenkins, L. (Eds.). (1997). Adult Literacy in OECD Countries: Technical Report on the First International Adult Literacy Survey. Washington, DC: United States Department of Education.Google Scholar
  30. Muthén, L. K., & Muthén, B. O. (1998–2012). Mplus User’s Guide. Seventh Edition. Los Angeles, CA: Muthén & Muthén.Google Scholar
  31. National Educational Panel Study (2014). Research Data – Starting Cohort Adults. Retrieved from https://www.neps-data.de/tabid/323/language/en-US/.
  32. Neumann, I., Duchhardt, C., Grüßing, M., Heinze, A., Knopp, E. & Ehmke, T. (2013). Modeling and assessing mathematical competence over the lifespan. Journal for Educational Research Online, 5(2), 80–109.Google Scholar
  33. O’Donoghue, J. (2000). Assessing Numeracy. In D. Coben, J. O’Donoghue & G. E. Fitzsimons (Eds.), Perspectives on adults learning mathematics (pp. 271–287). London, England: Kluwer.Google Scholar
  34. Organisation for Economic Co-operation and Development & Human Resources Development Canada (1997). Highlights from the Second Report of the International Adult Literacy Survey. Retrieved from http://www.nald.ca/library/research/nls/ials/ialsreps/ialsrpt2/ials2/coverh.htm.
  35. Organisation for Economic Co-operation and Development. (2003). The PISA 2003 assessment framework—mathematics, reading, science and problem solving knowledge and skills. Paris, France: Author.Google Scholar
  36. Organisation for Economic Co-operation and Development. (2013a). Skilled for Life? Key findings from the survey of adult skills. Paris, France: Author.Google Scholar
  37. Organisation for Economic Co-operation and Development. (2013b). OECD Skills Outlook 2013: First results from the survey of adult skills. Paris, France: Author.Google Scholar
  38. Organisation for Economic Co-operation and Development. (2013c). PISA 2012 Assessment and Analytical Framework: Mathematics, reading, science, problem solving and financial literacy. Paris, France: Author.Google Scholar
  39. Organisation for Economic Co-operation and Development. (2013d). Technical Report of the Survey of Adult Skills (PIAAC). Paris, France: Author.Google Scholar
  40. Organisation for Economic Co-operation and Development, & Statistics Canada (1995). Literacy, economy and society: Results of the first International Adult Literacy Survey. Paris, France: OECD.Google Scholar
  41. Organisation for Economic Co-operation and Development, & Statistics Canada (1997). Literacy skills for the knowledge society: further results from the International Adult Literacy Survey. Paris, France: OECD.Google Scholar
  42. Organisation for Economic Co-operation and Development, & Statistics Canada (2005). Learning a Living. First Results of the Adult Literacy and Life Skills Survey. Paris, France: OECD.Google Scholar
  43. Osberg, L. (2000). Schooling, Literacy and Individual Earnings. Ottawa, Canada: Statistics Canada.Google Scholar
  44. Payne, J. (2002). Basic skills in the workplace: A research review. Brighton, UK: Learning and Skills Development Agency.Google Scholar
  45. PIAAC Numeracy Expert Group (2009). PIAAC numeracy: A conceptual framework. (OECD Education Working Paper, No. 35). Paris, France: OECD.CrossRefGoogle Scholar
  46. Rammstedt, B. (Ed.). (2013). Grundlegende Kompetenzen Erwachsener im internationalen Vergleich: Ergebnisse von PIAAC 2012 [Basic Adult Competences in international comparison: Results from PIAAC 2012]. Münster, Germany: Waxmann.Google Scholar
  47. Rasch, G. (1960/1980). Probabilistic models for some intelligence and attainment tests. (Copenhagen, Danish Institute for Educational Research), expanded edition (1980) with foreword and afterword by B.D. Wright. Chicago, IL: The University of Chicago Press.Google Scholar
  48. Reder, S. (1994). Practice engagement theory: A sociocultural approach to literacy across languages and cultures. In B. Ferdman, M. Weber & A. Ramirez (Eds.), Literacy across languages and cultures (pp. 33–74). Albany, NY: SUNY-Albany Press.Google Scholar
  49. Reder, S. (2009a). The development of adult literacy and numeracy in adult life. In S. Reder & J. Bynner (Eds.), Tracking adult literacy and numeracy skills: Findings from longitudinal research (pp. 59–84). New York, NY: Routledge.Google Scholar
  50. Reder, S. (2009b). Scaling up and moving in: connecting social practices views to policies and programs in adult education. Literacy and Numeracy Studies, 16(2), 35–50.CrossRefGoogle Scholar
  51. Rubin, D. B. (1987). Multiple imputations for non-response in surveys. New York, NY: Wiley.CrossRefGoogle Scholar
  52. Salthouse, T. (2006). Mental exercise and mental aging. evaluating the validity of the “use it or lose it” hypothesis. Perspectives on Psychological Science, 1(1), 68–87.CrossRefGoogle Scholar
  53. Salthouse, T. (2007). Reply to Schooler. Consistent is not conclusive. Perspectives on Psychological Science, 2(1), 30–32.CrossRefGoogle Scholar
  54. Salthouse, T. (2010). Major issues in cognitive aging. New York, NY: Oxford University Press.Google Scholar
  55. Schafer, J. L. (1997). Analysis of incomplete multivariate data. London, England: Chapman & Hall.CrossRefGoogle Scholar
  56. Schooler, C. (2007). Use it—and keep it, longer, probably. A reply to Salthouse (2006). Perspectives on Psychological Science, 2(1), 24–29.CrossRefGoogle Scholar
  57. Schooler, C., Mulatu, M. S. & Oates, G. (1999). The continuing effects of substantively complex work on the intellectual functioning of older workers. Psychology and Aging, 14(3), 483–506.CrossRefGoogle Scholar
  58. Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics, 6(2), 461–464.CrossRefGoogle Scholar
  59. Sewell, B. (1981). Use of mathematics by adults in daily life. Leicester, England: Advisory Council for Adult and Continuing Education (ACACE).Google Scholar
  60. Stine-Morrow, E. A. (2007). The Dumbledore hypothesis of cognitive aging. Current Directions in Psychological Science, 16(6), 295–299.CrossRefGoogle Scholar
  61. Swain, J., Baker, E., Holder, D., Newmarch, B. & Coben, D. (2005). Beyond the daily application: making numeracy teaching meaningful to adult learners. London, England: Institute of Education.Google Scholar
  62. The Bureau of Labor and Statistics. (2014). ISCO-08 – SCO 2010 Crosswalk Table [Excel Spreadsheet]. Retrieved from http://www.bls.gov/soc/ISCO_SOC_Crosswalk.xls.
  63. Wang, J. & Wang, X. (2012). Structural equation modeling. Applications using Mplus. Chichester, England: Wiley.CrossRefGoogle Scholar
  64. Warm, T. A. (1989). Weighted likelihood estimation of ability in item response models. Psychometrika, 54, 427–450.CrossRefGoogle Scholar
  65. Wu, M. L. (2005). The role of plausible values in large-scale surveys. Studies in Educational Evaluation (SEE), 31(2-3) [Special issue], 114–128.Google Scholar
  66. Wu, M. L., Adams, R. J., Wilson, M. R. & Haldane, S. A. (2007). ACER ConQuest Version 2: Generalised item response modelling software. Camberwell, England: Australian Council for Educational Research.Google Scholar

Copyright information

© Ministry of Science and Technology, Taiwan 2015

Authors and Affiliations

  • Christoph Duchhardt
    • 1
  • Anne-Katrin Jordan
    • 1
  • Timo Ehmke
    • 2
  1. 1.University of BremenBremenGermany
  2. 2.Leuphana University of LüneburgLüneburgGermany

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