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In general, when fewer students are included in the dataset, the factorial scree slope is gentler. This can be seen on all three of the student-subset plots, and was also observed when analysing randomly-generated data as described in Section 3.3: in a small sample, random fluctuations seem more significant. This effect also exaggerates the disparities between the scree test and the Kaiser criterion, making it difficult to assess the correct number of clusters to use. It was often necessary to examine the clustering for different numbers of clusters and select the number that seemed to make the most sense or be the most informative. Including bonus prac questions did not appear to make much difference to the factor analysis for the top students. This could arise from the fact that very few students, even among the top 33%, attempted the bonus questions. These datasets, TMA and TMAB, both had Kaiser criteria of 12 and were plotted at 10 and 11 clusters respectively. Regardless of the number of clusters used, the data for the top students tends to form one large cluster and a number of singletons. These two datasets were plotted at a level that shows a little clustering beyond the single large cluster. The scree plot for the bottom 33% of students --- set BMAB --- is unique, in that it shows two dominating factors of almost equal magnitude. All the other plots generated from the student data show a single dominating factor. This set had Kaiser criterion of eight, and was plotted at the seven-cluster level. Dotted circles show the superclustering that would occur at the six-cluster and five-cluster levels.
Competency mapsThe competency maps are shown below. These maps have been produced from the data included in Appendix III. The points on the map have not been labelled with activity names as to do so would obscure the shape of the data; however, the point coordinates of all activities are listed here.
Set ALL
This image shows the map derived from all students' marks. Cluster 1, marked by red diamonds, contains all exam questions except for the seventh and tenth pages of multiple-choice questions, the question on digital logic, the question on linked lists, the question on generating test data, both of the sorting questions and the largest programming question; and pracs 7, 8 and 9. Cluster 2, marked by blue squares, contains the seventh and tenth pages of multiple-choice questions, the questions on digital logic and generating test data, and pracs 1--6, 10 and 11. Cluster 3 contains the exam questions on linked lists and the bubblesort algorithm, the largest exam programming question, all the prac bonus questions except those for pracs 3 and 5, and prac 12. The remaining tasks --- the exam question on selection sort and the bonus prac questions from pracs 3 and 5 --- are singletons.
Set AMAB
The competency map for the set of data derived from all students' marks, excluding bonus marks and rolling the marks from multiple-choice and short-answer questions into single marks, is shown here. The clustering for the exam questions is similar to that seen for set ALL: cluster 1 comprises all the exam questions except for the ones on digital logic, linked lists, test data, both of the sorting questions, and the largest programming question. Cluster 2 contains the exam questions on digital logic and test data, and pracs 1--4, 10 and 11. Cluster 3 contains the exam questions on linked lists and bubblesort, the largest programming question on the exam, and prac 12. Cluster 4 is a singleton, containing only the exam question on selection sort; while the remaining pracs --- 5--9 --- are all in cluster 5. Clusters 2 and 5 are closely related, and at the four-cluster level they form a single cluster. The dotted ellipse shows this superclustering.
Set TMA
This map is derived from the marks of the top third of students ranked by total mark, including prac bonus questions. It comprises a single large cluster, a smaller cluster, and a lot of singletons. In the large cluster are all exam questions except for those on linked lists, binary search, both sorting questions and the largest programming question, and all the pracs other than the bonus questions and prac 12. The secondary cluster, labelled cluster 10, comprises prac 12 and the bonus question to prac 11. All other tasks are singletons.
Set TMAB
This map was derived from the marks of the top third of students ranked by total mark, but does not include marks from prac bonus questions. It is similar to set TMA, in that it comprises a large main cluster, a smaller cluster, and many singletons. In this case the smaller cluster is cluster 1, and contains the multiple-choice and short-answer exam questions, and the exam question on debugging. The large cluster is cluster 2 and contains all the pracs except prac 12, and the exam questions on digital logic, testing and data structures, and the two smaller programming questions. All other tasks are singletons. Note that the two singletons in the top right, which are the exam questions on finding the next largest square and calculating reciprocal by reference, are not clustered together even though multidimensional scaling places them close together. This is possible because the clustering is done on the raw data, rather then the scaled points.
Set BMAB
The last competency map shows the sharpest division between prac and exam tasks. Cluster 1 contains all the exam questions apart from those on digital logic, test data and selection sort, which are singletons; it also contains prac 12. Cluster 2 contains pracs 1--5, 10 and 11; cluster 3 contains pracs 6 and 7, while cluster 4 contains pracs 8 and 9. At the five-cluster level, clusters 2, 3 and 4 combine to form a supercluster, which shown by the dotted ellipse. Note that this supercluster contains all prac tasks except prac 12. | ||||||
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