fractarithm: Arithmetic Problems with Fractions

In pks: Probabilistic Knowledge Structures

Arithmetic Problems with Fractions

Description

Responses of 191 participants presented with 23 arithmetic problems with fractions. The participants were first-level middle school students (about 11 to 12 years old). A subset of 13 problems is included in Stefanutti and de Chiusole (2017).

Usage

data(fractarithm)

Format

A list consisting of a single component:

R

a person-by-problem indicator matrix representing the responses of 191 persons to 23 problems. The responses are classified as correct (0) or incorrect (1).

The 23 problems were:

• p01 % \big(\frac{1}{3} + \frac{1}{12}\big) : \frac{2}{9} = ?

• p02 % \big(\frac{3}{2} + \frac{3}{4}\big) \times \frac{5}{3} - 2 = ?

• p03 % \big(\frac{5}{6} + \frac{3}{14}\big) \times \big(\frac{19}{8} - \frac{3}{2}\big) = ?

• p04 % \big(\frac{1}{6} + \frac{2}{9}\big) - \frac{7}{36} = ?

• p05 % \frac{7}{10} + \frac{9}{10} = ?

• p06 % \frac{8}{13} + \frac{5}{2} = ?

• p07 % \frac{8}{12} + \frac{4}{15} = ?

• p08 % \frac{2}{9} + \frac{5}{6} = ?

• p09 % \frac{7}{5} + \frac{1}{5} = ?

• p10 % \frac{2}{7} + \frac{3}{14} = ?

• p11 % \frac{5}{9} + \frac{1}{6} = ?

• p12 % \big(\frac{1}{12} + \frac{1}{3}\big) \times \frac{24}{15} = ?

• p13 % 2 - \frac{3}{4} = ?

• p14 % \big(4 + \frac{3}{4} - \frac{1}{2}\big) \times \frac{8}{6} = ?

• p15 % \frac{4}{7} + \frac{3}{4} = \frac{?}{28}

• p16 % \frac{5}{8} - \frac{3}{16} = \frac{? - ?}{16}

• p17 % \frac{3}{8} + \frac{5}{12} = \frac{? \times 3 + ? \times 5}{24}

• p18 % \frac{2}{7} + \frac{3}{5} = \frac{5 \times ? + 7 \times ?}{35}

• p19 % \frac{2}{3} + \frac{6}{9} = \frac{?}{9} = \frac{?}{?}

• p20 Least common multiple lcm(6, 8) = ?

• p21 % \frac{7}{11} \times \frac{2}{3} = ?

• p22 % \frac{2}{5} \times \frac{15}{4} = ?

• p23 % \frac{9}{7} : \frac{2}{3} = ?

Source

The data were made available by Debora de Chiusole, Andrea Brancaccio, and Luca Stefanutti.

References

Stefanutti, L., & de Chiusole, D. (2017). On the assessment of learning in competence based knowledge space theory. Journal of Mathematical Psychology, 80, 22–32. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.jmp.2017.08.003")}

Examples

data(fractarithm)

## Subset of problems used in Sefanutti and de Chiusole (2017)
R <- fractarithm$R[, c(4:8, 10:11, 15:20)]
colnames(R) <- 1:13
N.R <- as.pattern(R, freq = TRUE)

## Conjunctive skill function in Table 1
sf1 <- read.table(header = TRUE, text = "
  item  a  b  c  d  e  f  g  h
     1  1  1  1  0  1  1  0  0
     2  1  0  0  0  0  0  1  1
     3  1  1  0  1  1  0  0  0
     4  1  1  0  0  1  1  1  1
     5  1  1  0  0  1  1  0  0
     6  1  1  1  0  1  0  1  1
     7  1  1  0  0  1  1  0  0
     8  1  1  0  0  1  0  1  1
     9  0  1  0  0  1  0  0  0
    10  0  1  0  0  0  0  0  0
    11  0  0  0  0  1  0  0  0
    12  1  1  0  0  1  0  1  1
    13  0  0  0  0  0  1  0  0
")

## Delineated knowledge structure
K <- delineate(sf1)$K

blim(K, N.R)

pks documentation built on May 5, 2023, 3:08 p.m.