Online discussion compensates for suboptimal timing of supportive information presentation in a digitally supported learning environment

This study used a sequential set-up to investigate the consecutive effects of timing of supportive information presentation (information before vs. information during the learning task clusters) in interactive digital learning materials (IDLMs) and type of collaboration (personal discussion vs. online discussion) in computer-supported collaborative learning (CSCL) on student knowledge construction. Students (N = 87) were first randomly assigned to the two information presentation conditions to work individually on a case-based assignment in IDLM. Students who received information during learning task clusters tended to show better results on knowledge construction than those who received information only before each cluster. The students within the two separate information presentation conditions were then randomly assigned to pairs to discuss the outcomes of their assignments under either the personal discussion or online discussion condition in CSCL. When supportive information had been presented before each learning task cluster, online discussion led to better results than personal discussion. When supportive information had been presented during the learning task clusters, however, the online and personal discussion conditions had no differential effect on knowledge construction. Online discussion in CSCL appeared to compensate for suboptimal timing of presentation of supportive information before the learning task clusters in IDLM

Matroid 3-connectivity and branch width

We prove that, for each nonnegative integer k and each matroid N, if M is a 3-connected matroid containing N as a minor, and the the branch width of M is sufficiently large, then there is a k-element subset X of E(M) such that one of M\X and M/X is 3-connected and contains N as a minor.Comment: 21 page

On Binary Matroid Minors and Applications to Data Storage over Small Fields

Locally repairable codes for distributed storage systems have gained a lot of interest recently, and various constructions can be found in the literature. However, most of the constructions result in either large field sizes and hence too high computational complexity for practical implementation, or in low rates translating into waste of the available storage space. In this paper we address this issue by developing theory towards code existence and design over a given field. This is done via exploiting recently established connections between linear locally repairable codes and matroids, and using matroid-theoretic characterisations of linearity over small fields. In particular, nonexistence can be shown by finding certain forbidden uniform minors within the lattice of cyclic flats. It is shown that the lattice of cyclic flats of binary matroids have additional structure that significantly restricts the possible locality properties of $\mathbb{F}_{2}$-linear storage codes. Moreover, a collection of criteria for detecting uniform minors from the lattice of cyclic flats of a given matroid is given, which is interesting in its own right.Comment: 14 pages, 2 figure