schoolarithm {pks}

Arithmetic Problems for Elementary and Middle School Students

Description

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

The eight subtraction problems were presented to 294 elementary school students and are described in de Chiusole and Stefanutti (2013).

Usage

data(schoolarithm)

Format

fraction17

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} = ?

subtraction13 is a data frame consisting of the following components:

School

factor; school id.

Classroom

factor; class room id.

Gender

factor; participant gender.

Age

participant age.

R

a person-by-problem indicator matrix representing the responses of 294 persons to eight problems.

The eight problems were:

• p1 73 - 58

• p2 317 - 94

• p3 784 - 693

• p4 507 - 49

• p5 253 - 178

• p6 2245 - 418

• p7 156 - 68

• p8 3642 - 753

Source

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

References

de Chiusole, D., & Stefanutti, L. (2013). Modeling skill dependence in probabilistic competence structures. Electronic Notes in Discrete Mathematics, 42, 41–48. doi:10.1016/j.endm.2013.05.144

Stefanutti, L., & de Chiusole, D. (2017). On the assessment of learning in competence based knowledge space theory. Journal of Mathematical Psychology, 80, 22–32. doi:10.1016/j.jmp.2017.08.003

Examples

data(schoolarithm)

## Fraction problems used in Sefanutti and de Chiusole (2017)
R <- fraction17[, c(4:8, 10:11, 15:20)]
colnames(R) <- 1:13
N.R <- as.pattern(R, freq = TRUE)

## Conjunctive skill function in Table 1
sf <- 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
")
K <- delineate(sf)$K  # delineated knowledge structure
blim(K, N.R)

## Subtraction problems used in de Chiusole and Stefanutti (2013)
N.R <- as.pattern(subtraction13$R, freq = TRUE)

# Skill function in Table 1
# (f) mastering tens and hundreds; (g) mastering thousands; (h1) one borrow;
# (h2) two borrows; (h3) three borrows; (i) mastering the proximity of
# borrows; (j) mastering the presence of the zero; (k) mental calculation
sf <- read.table(header = TRUE, text = "
  item  f  g h1 h2 h3  i  j  k
     1  0  0  1  0  0  0  0  0
     2  1  0  1  0  0  0  0  0
     3  1  0  1  0  0  1  0  0
     4  1  0  1  1  1  0  1  0
     4  0  0  0  0  0  0  0  1
     5  1  0  1  1  1  1  0  0
     6  1  1  1  1  0  0  0  0
     7  1  0  1  1  1  1  0  0
     8  1  1  1  1  1  0  0  0
")
K <- delineate(sf)$K
blim(K, N.R)