Responses to Geometry Problems and Knowledge Structures

Lakshminarayan (1995, 1996) presented high school geometry problems to 959 undergraduate students before and after a lesson. The problems deal with basic concepts in geometry, such as angles, lengths, circles, and polygons. Doignon and Falmagne (1999, chap. 8) refer to a subset of these data.

data(hsgeometry)

Format

Two lists, each consisting of three components:

angles

a list with components K, N.R, and changescore for five problems mostly about angles.

circles

a list with components K, N.R, and changescore for four problems mostly about circles.

K

a state-by-problem indicator matrix representing the knowledge structure in Lakshminarayan (1995, 1996).

N.R

a matrix. The row names denote response patterns, the column entries their frequencies before and after the lesson.

changescore

a 3d table. For each problem, it contains the number of students who solved or did not solve the problem at pre- and posttest.

Note

Only those 800 responses used to estimate the model parameters are reported (the held-out sample is missing).

Thanks to Kamakshi Lakshminarayan, Cord Hockemeyer, and Mike Regenwetter for their help with finding the data.

Source

Lakshminarayan, K (1996). A hybrid latent trait and latent class model of learning - Theoretical details and empirical application. Technical report No. MBS 96-07. University of Califomia, Irvine.

References

Doignon, J.-P., & Falmagne, J.-C. (1999). Knowledge spaces. Berlin: Springer.

Lakshminarayan, K. (1995). Theoretical and empirical aspects of some stochastic learning models. Doctoral dissertation. University of California, Irvine.

Examples

data(hsgeometry)
dotchart(angles$N.R[, "posttest"], pch = 4,
         main = "High school geometry problems",
         xlab = "Response frequency (pre- [o] and posttest [x])")
points(angles$N.R[, "pretest"], 1:32)
mtext("Lakshminarayan (1995)", side = 3, line = 0.5)