MODELLING OF FORGETTING CURVES IN EDUCATIONAL E-ENVIRONMENT
AbstractModelling of the didactical process by using educational network needs network representation of learning and forgetting curves known from the literature. The learning and forgetting curves are the solution of differential equations. The differential equations can be represented in the form of a network of connected elements in a similar way to the electrical circuits and represented in the form of an intuitive schematic. The network can be simulated using a microsystems simulator. Such an approach enables the easy creation of the macro models and their analysis. It enables the use of many advanced simulation algorithms. The use of analogy enables defining the educational environment by defining network variables and giving them meaning relative to generalized variables. In the paper, examples of representation of forgetting curves as the above-mentioned network are presented. Parameters of elements were selected in the deterministic optimisation process. The obtained results were compared with the forgetting curves known from the literature. The appropriate time constants were identified in the systems and their values were given. Time constants have their equivalents in the appropriate values in the formulas describing the forgetting curves. Based on the results, appropriate conclusions were drawn. The work also shows the concept of a model that uses behavioural modelling and variable parameters of elements depending on the state and time. The model has been used in practice. The presented approach enables a much more accurate determination of the parameters of the forgetting curves. The models can be used in the simulation of the forgetting process. The paper can be interesting for those who deal with modelling of the didactical process, especially on the e-learning platforms.
H. Ebbinghaus, “Memory: A contribution to experimental psychology”, 1913, original work published 1885. [online]. Available: https://web.archive.org/web/20051218083239/http://psy.ed.asu.edu:80/~classics/Ebbinghaus/index.htm
M. Jaap, J. Murre, and J. Dros, “Replication and analysis of Ebbinghaus’ forgetting curve”,Plus One, vol. 2, pp. 396–408, July 2015. [online]. Available:http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0120644
W. Gerstner and W.Kistler, Spiking Neuron Models. Cambridge University Press, 2002.
J. Deutch and A. Newton, “Data-flow based behavioral-level simulation and synthesis”,Proc. IEEE ICCAD, Sept1983.
H. Mantooth and M. Fiegenbaum, Modelling with an analog hardware description language. Norwell, Massachusetts 02061, USA: Kluwer Academic Publishers, 1995.
J. Ogrodzki and D. Bukat, “Compact modelling in circuit simulation: the general purposeanalyzer OPTIMA 3”,ISCAS 94 PROCEEDINGS, pp. 383–386,1994.
P.Plaskuraand and J. Ogrodzki, “Event-driven circuit simulator with AHDL input,” MIXDES 99 Proceedings, 1999.
P. Plaskura, Symulator mikrosystemów Dero v4. Metody i algorytmy obliczeniowe, modelowanie behawioralne, przykłady.(Microsystems simulator Derov4. Computational methods and algorithms, behavioural modelling, examples.).AIVA, 2013.
E. Christen and K. Bakalar, “VHDL-AMS - a hardware description language for analog and mixed-signal applications”, Circuits and Systems II: Analog and Digital Signal Processing, vol. 46, pp. 1263–1272, Oct 1999.
I. Miller and T. Cassagnes, “Verilog-ams eases mixed mode signal simulation”,Technical Proceedings of the 2000 International Conference on Mode ling and Simulation of Microsystems, pp. 305–308, 2000. [online]. Available: https://web.archive.org/web/20070927051749/http://www.nsti.org/publ/MSM2000/T31.01.pdf
P. Woźniak, E. Gorzelańczyk, and J. Murakowski, “The two-component model of long-term memory.Symbolicformula describing the increase in memory stability for varying levels of recall”,Cybernetic Modelling of Biological Systems, 2005.
P. Woźniak, E. Gorzelańczyk, and J. Murakowski, “Two components of long-term memory”, Act a Neurobiologiae Experimentalis, vol. 55, pp. 301–305, 1995.
J. Murre, M.Meeter, and A.Chessa, Statistical and Process Models for Neuroscience and Aging. Mahwah ,NJ: Lawrence Erlbaum,2007,ch.Modelingamnesia:Connectionist and mathematical approaches,pp.119–162.
J. Mazur and R. Hastie, “Learning as accumulation: a re-examination of the learning curve”, Psychol. Bull., vol. 85, pp. 1256–1274,1978.
D.Towill,“Forecasting learning curves”, International Journal of Forecasting,vol.6(1),pp.25–38,1990.
A. Badiru, “Computational survey of univariate and bivariate learning curve models”, IEEE Trans. Eng. Manage., vol. 39, pp. 176–188, 1992.
E.McIntyre, “Cost-volume-profit analysis adjusted for learning”, Manage.Sci., vol.24, pp.149–160,1977.
N. Womer, “Learning curves, production rate and program costs”, Management Science, vol. 25 (4), pp. 312–319, 1979.
(2017) SuperMemo. [online]. Available:https://www.supermemo.com/
(2017) Anki. [online]. Available:https://apps.ankiweb.net/
W. Wickelgren, “Single-trace fragility theory of memory dynamics”, Memory and Cognition, vol. 2, pp. 775–780, 1974.
O. Heller, W. Mack, and J. Seitz, “Replikation der Ebbinghaus’schen Vergessenskurve mit der Ersparnis-methode: Das Behalten und Vergessen als Function der Zeit”, Zeitschrift für Psychologie, no.199, pp.3–18,1991.
D. Rubin, S. Hinton, and A. Wenzel, “The precise time course of retention”,Journal of Experimental Psychology: Learning, Memory, and Cognition, pp. 1161–1176, 1999.
C. Ho, A. Ruehli, and P.Brennan, “The modified nodal approach to network analysis”,IEEE Trans. Circuits Syst., vol. CAS-22, no. 6, pp. 504–509, Jun1975.
J. Ogrodzki, Circuit simulation methods and algorithms.Boca Raton, USA: CRC Press, 1994.
P. Plaskura, Quela - a platform for managing the didactical process. Połtawa, Ukraina: Poltava V.G. Korolenko National Pedagogical University, 2016, pp.337–340.
Authors who publish in this journal agree to the following terms:
- Authors hold copyright immediately after publication of their works and retain publishing rights without any restrictions.
- The copyright commencement date complies the publication date of the issue, where the article is included in.
- Authors grant the journal a right of the first publication of the work under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License (CC BY-NC-SA 4.0) that allows others freely to read, download, copy and print submissions, search content and link to published articles, disseminate their full text and use them for any legitimate non-commercial purposes (i.e. educational or scientific) with the mandatory reference to the article’s authors and initial publication in this journal.
- Original published articles cannot be used by users (exept authors) for commercial purposes or distributed by third-party intermediary organizations for a fee.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) during the editorial process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (see this journal’s registered deposit policy at Sherpa/Romeo directory).
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Post-print (post-refereeing manuscript version) and publisher's PDF-version self-archiving is allowed.
- Archiving the pre-print (pre-refereeing manuscript version) not allowed.