qmatrix_fractions | R Documentation |
Fraction Subtraction and Addition Assessment Expert-Derived Q Matrix
qmatrix_fractions
An object of class matrix
(inherits from array
) with 20 rows and 8 columns.
Each entry in the matrix is either 1
, if the Item uses the Trait, or 0
, if
the Item does not use the Trait. The traits identified by this matrix
are:
Trait1
: Convert a whole number to a fraction,
Trait2
: Separate a whole number from fraction,
Trait3
: Simplify before subtraction,
Trait4
: Find a common denominator,
Trait5
: Borrow from the whole number part,
Trait6
: Column borrow to subtract the second numerator from the first,
Trait7
: Subtract numerators,
Trait8
: Reduce answers to simplest form.
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}
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. \Sexpr[results=rd]{tools:::Rd_expr_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. \Sexpr[results=rd]{tools:::Rd_expr_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. \Sexpr[results=rd]{tools:::Rd_expr_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.
\Sexpr[results=rd]{tools:::Rd_expr_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. \Sexpr[results=rd]{tools:::Rd_expr_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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s11336-017-9579-4")}
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