qmatrix_fractions {edmdata} R Documentation

## Fraction Subtraction and Addition Assessment Expert-Derived Q Matrix

### Description

Fraction Subtraction and Addition Assessment Expert-Derived Q Matrix

### Usage

```qmatrix_fractions
```

### Format

An object of class `matrix` (inherits from `array`) with 20 rows and 8 columns.

### Details

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`: 5/3 - 3/4

• `Item02`: 3/4 - 3/8

• `Item03`: 5/6 - 1/9

• `Item04`: 3*1/2 - 2*3/2

• `Item05`: 4*3/5 - 3*4/10

• `Item06`: 6/7 - 4/7

• `Item07`: 3 - 2*1/5

• `Item08`: 2/3 - 2/3

• `Item09`: 3*7/8 - 2

• `Item10`: 4*4/12 - 2*7/12

• `Item11`: 4*1/3 - 2*4/3

• `Item12`: 11/8 - 1/8

• `Item13`: 3*3/8 - 2*5/6

• `Item14`: 3*4/5 - 3*2/5

• `Item15`: 2 - 1/3

• `Item16`: 4*5/7 - 1*4/7

• `Item17`: 7*3/5 - 2*4/5

• `Item18`: 4*1/10 - 2*8/10

• `Item19`: 4 - 1*4/3

• `Item20`: 4*1/3 - 1*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., 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

[Package edmdata version 1.1.0 Index]