Fraction Subtraction and Addition Assessment Item Responses

Source: R/fraction-data.R

Fraction Subtraction and Addition Assessment Item Responses

items_fractions

Format

An object of class matrix (inherits from array) with 536 rows and 20 columns.

Details

The subjects answered the following assessment items:

  • Item01: \(\frac{5}{3}-\frac{3}{4}\)

  • Item02: \(\frac{3}{4}-\frac{3}{8}\)

  • Item03: \(\frac{5}{6}-\frac{1}{9}\)

  • Item04: \(3\frac{1}{2}-2\frac{3}{2}\)

  • Item05: \(4\frac{3}{5}-3\frac{4}{10}\)

  • Item06: \(\frac{6}{7}-\frac{4}{7}\)

  • Item07: \(3-2\frac{1}{5}\)

  • Item08: \(\frac{2}{3}-\frac{2}{3}\)

  • Item09: \(3\frac{7}{8}-2\)

  • Item10: \(4\frac{4}{12}-2\frac{7}{12}\)

  • Item11: \(4\frac{1}{3}-2\frac{4}{3}\)

  • Item12: \(\frac{11}{8}-\frac{1}{8}\)

  • Item13: \(3\frac{3}{8}-2\frac{5}{6}\)

  • Item14: \(3\frac{4}{5}-3\frac{2}{5}\)

  • Item15: \(2-\frac{1}{3}\)

  • Item16: \(4\frac{5}{7}-1\frac{4}{7}\)

  • Item17: \(7\frac{3}{5}-2\frac{4}{5}\)

  • Item18: \(4\frac{1}{10}-2\frac{8}{10}\)

  • Item19: \(4-1\frac{4}{3}\)

  • Item20: \(4\frac{1}{3}-1\frac{5}{3}\)

References

Data originated from:

  • Tatsuoka, C. (2002). Data analytic methods for latent partially ordered classification models. Journal of the Royal Statistical Society: Series C (Applied Statistics), 51(3), 337–350. doi:10.1111/1467-9876.00272

  • Tatsuoka, K. K. (1984), Analysis of errors in fraction addition and subtraction problems (Final Report for Grant No. NIE-G-81-0002). Urbana: University of Illinois, Computer-Based Education Research Laboratory (CERL).

Data used in:

  • Chen, Y., Liu, Y., Culpepper, S. A., & Chen, Y. (2021). Inferring the number of attributes for the exploratory DINA model. Psychometrika, 86(1), 30–64. doi:10.1007/s11336-021-09750-9

  • Chen, Y., Culpepper, S. A., & Liang, F. (2020). A sparse latent class model for cognitive diagnosis. Psychometrika, 1–33. doi:10.1007/s11336-019-09693-2

  • Culpepper, S. A. (2019). Estimating the cognitive diagnosis \(Q\) matrix with expert knowledge: Application to the fraction-subtraction dataset. Psychometrika, 84(2), 333–357. doi:10.1007/s11336-018-9643-8

  • Culpepper, S. A., & Chen, Y. (2019). Development and application of an exploratory reduced reparameterized unified model. Journal of Educational and Behavioral Statistics, 44(1), 3–24. doi:10.3102/1076998618791306

  • Chen, Y., Culpepper, S. A., Chen, Y., & Douglas, J. (2018). Bayesian estimation of the dina q matrix. Psychometrika, 83(1), 89–108. doi:10.1007/s11336-017-9579-4