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Information on Bus' Learning-to-Read Data

In a study to investigate the process of learning to read seven first-grade children were tested weekly, i.e. from week 3 to 47 (except for holidays: weeks 10,19,20,29,35,36,39,43 thus 37 weeks were available) with five different tests (see Table 1 for a description). The theoretical rationale behind the tests, the details of the design, the testing procedures, and the overall quality of the data are discussed in Bus (1982), Bus and Jansen (1984), Jansen and Bus (1982,1987), and Bus and Kroonenberg (1982). Of the seven children which took the tests, one was not included in the analysis presented in Kroonenberg (1983; chap 14) as he was added to the study at a later moment, and accounted for a large part of the missing data.

Data

The data set consists 37 weeks and 5 tests and 6 pupils.

Table 1 Description of the tests and additional information

Test    Range    Description

Pupil   1-7       number of the pupil
Week Nr.3-47
Method  1-2       Reading instruction method:
                  Zo/Veilig Leren Lezen = 1; Letterstad = 2
P       1-10      regular orthographic short words
Q       1-10      regular orthographic long words
S       1-15      regular orthographic long and short words within context
R       1-15      irregular orthographic long and short words
L       1-47      letter knowledge test

A,B,C,D 0-1       versions of the tests??

Table 2 A Piece of the Data with Explanation

  Pupil Week Method  Letter     Tests
               of     Test   P  Q  S  R         A   B   C   D
         nr. Reading
=============================================================
    1     3      1     3     0  0  2  0         0   1   0   0
    2     3      1     2     0  0  1  0         0   1   0   0
    3     3      1     3     0  0  0  0         0   1   0   0
    4     3      2    11     5  1  9  6         0   0   1   0
    5     3      2     6     1  0  1  1         0   0   1   0
    6     3      2     6     1  0  1  0         0   0   1   0
    7     3      2     0     0  0  0  0         0   0   1   0

    1     4      1     4     0  0  0  0         0   1   0   0
    2     4      1     7     0  0  4  0         0   1   0   0
    3     4      1     2     0  0  4  0         0   1   0   0
    4     4      2    13     4  0  8  2         0   0   1   0
=============================================================

The two records below contain one suspicious value each. In particular, the 10 for test S in both cases. The two previous weeks, the two pupils got full marks on this test (=15), and they did again the week after. The values of 10 are therefore probably coding errors and should 15.

    4    38      2    47    10 10 10 14         1   0   1   1
    5    38      2    44    10 10 10 14         1   0   1   1

Preparing the data for analysis

Because the tests have different ranges, either 10, 15 or 47 items in the Kroonenberg analysis the data were rescaled so that all tests ranged from 0 to 1. In this way all the differences in variation was maintained in the data, while making the tests comparable. Subsequently an average learning curve was calculated by averaging over pupils and tests for each occasion. Thus a mixed additive and multiplicative model was used for the data analysing the common part of the learning curve additively (mean + main effect(weeks)) and the remainder multiplicatively with a Tucker3 model.

An advantage of the above model is that the correlations between pupils and test are no longer influenced by the average growth curve, and that the interactions between tests and pupils over time can be analysed separately.

Logistic regression model

The study by Jansen and Bus (1982, 1987) suggest that per test a logistic regression model with the same slope for all individuals is not an unreasonable model. The slopes are however different across tests. This implies that the average learning curve does not necessarily represents any one test, but it may serve as a baseline for comparisons between tests and pupils.

References

Bus, A.G. (1982). A longitudinal study in learning to read. Paper presented at the 9th Wrold Congress on Reading, July 26-30, Dublin, Ireland

Bus, A.G., and Jansen, G.G.H. (1984). Een longitudinaal onderzoek naar leren lezen in de eerste klas. [A longitudinal study in learning to read in the first form.] Pedagogische Studieën, 61, 485-495.

Bus, A.G. and Kroonenberg, P.M. (1982). Reading instruction and learning to read: A longitudinal study. Internal report, SOL-Reeks, SOL/82-08. Groningen, The Netherlands: Department of Education and Child Studies, University of Groningen.

Jansen, G.G.H. and Bus, A.G. (1982). An application of a logistic bio-assay model to achievement test data. Technical report. Groningen: Department of Education and Child Studies, University of Groningen.

Jansen, M.G. and Bus, A.G. (1987). Individual growth patterns in early reading performance. Methodika, 1, 139-154

Kroonenberg, P.M. (1983). Three-mode principal component analysis. Theory and applications. Leiden: DSWO Press.

P.M. Kroonenberg
Leiden Institute of Education and Child Studies, Leiden University
Wassenaarseweg 52, 2333 AK Leiden, The Netherlands
Tel. *-31-71-5273446/5273434 (secr.); fax *-31-71-5273945
E-mail: kroonenb at fsw.leidenuniv.nl
First version: 1-9-1998;