Network positions in active learning environments in physics

This study uses positional analysis to describe the student interaction networks in four research-based introductory physics curricula. Positional analysis is a technique for simplifying the structure of a network into blocks of actors whose connections are more similar to each other than to the rest of the network. This method describes social structure in a way that is comparable between networks of different sizes and densities and can show large-scale patterns such as hierarchy among positions. We detail one positional analysis method and apply it to class sections of Peer Instruction, SCALE-UP, ISLE, and Minnesota Model context-rich problems. At the level of detail shown in the blockmodels, most of the curricula are more alike than different, showing a late-term tendency to form coherent subgroups that communicate actively among themselves but have few interposition links. Initial position assignments tend to change from beginning to end of the term, but in cases where the initial assignment is stable, those students appear to become more connected to each other and to the largest network component. These trends in position structure and stability may be network signatures of active learning classes, but wider data collection is needed to investigate.

Figure 1

A sample work network, where ties mean “meets weekly with.” Positional analysis can identify layers of this example hierarchy, but structural equivalence will produce a more restrictive grouping than regular equivalence. By exact structural equivalence, only D/E (solid blue line) and F/G (dashed green line) are grouped together, with all other actors occupying single-member positions.

Figure 2

Sample of blockmodel outputs. The network (top left) can be written as an adjacency matrix showing which nodes are linked (top right). The bottom row shows the blockmodeling products: a permuted adjacency matrix (left), the matrix showing each block density (center), and a reduced network where each diagonal block is treated as a node and inter- or intrablock links are present or absent according to a density threshold.

Figure 3

(a) Network diagrams for week 1 (left column) and week 10 (right column) Peer Instruction section. Smaller circles show students who were named but did not take the survey. Nodes are colored by CONCOR partition, and indicate the same nodes in the blockmodel and reduced network below. (b) The corresponding blockmodel. Each link from the survey is a black square. The dotted lines mark the CONCOR group partitions. Colors along the sides mark which blocks of nodes belong to each partition. (c) Reduced network diagrams. Each circle represents a position from the blockmodel and stands for all of the nodes of the same color in the network diagram. Links in the reduced network plots show connections within and between positions and come from applying a density threshold to the blockmodel.

Figure 4

(a) Network diagrams, (b) blockmodels, and (c) reduced network diagrams for SCALE-UP section. Smaller circles on the network diagrams are students who did not take the survey but were named by respondents. Nodes are colored by CONCOR partition, and dotted lines on the blockmodel plots show the same partition.

Figure 5

(a) Network diagrams, (b) blockmodels, and (c) reduced network diagrams for ISLE section. Smaller circles on the network diagrams are students who did not take the survey but were named by respondents. Nodes are colored by CONCOR partition, and dotted lines on the blockmodel plots show the same partition.

Figure 6

(a) Network diagrams, (b) blockmodels, and (c) reduced network diagrams for context-rich problems section. Smaller circles on the network diagrams are students who did not take the survey but were named by respondents. Nodes are colored by CONCOR partition, and dotted lines on the blockmodel plots show the same partition.

Figure 7

Each diagram shows students’ week 1 CONCOR block assignment in the first column, and their week 10 assignment in the second column. Colors match the original block assignment to help with visually following the flow. The missing label indicates students who were not present (either as survey takers or named) in that week’s data.