# David E. Brown

This study explores two questions: first, what conceptual resources do students use, and in what ways do they use them, to construct explanatory models? Second, what are the obstacles preventing them from constructing a useful explanatory model? Our findings indicate that students employ their conscious and unconscious knowledge in their reasoning process.(More)
• Mathematical and Computer Modelling
• 2009
Let A be a (0, 1, ∗)-matrix with main diagonal all 0’s and such that if ai,j = 1 or ∗ then aj,i = ∗ or 0. Underwhat conditions on the row sums, and or column sums, of A is it possible to change the ∗’s to 0’s or 1’s and obtain a tournament matrix (the adjacency matrix of a tournament) with a specified score sequence? We answer this question in the case of(More)
This article develops a multidimensional framework for analyzing an extended classroom interaction in an effort to understand the resources participants draw on, the alignments they form, and the meanings and context they construct. The framework is comprised of six different dynamics identified in the interaction: focal, conceptual, institutional,(More)
• Australasian J. Combinatorics
• 2012
A graph is a probe interval graph (PIG) if its vertices can be partitioned into probes and nonprobes with an interval assigned to each vertex so that vertices are adjacent if and only if their corresponding intervals intersect and at least one of the vertices is a probe. When all intervals have the same length (or equivalently, no interval contains another(More)
• Discrete Applied Mathematics
• 2009
A graph is a probe interval graph (PIG) if its vertices can be partitioned into probes and nonprobes with an interval assigned to each vertex so that vertices are adjacent if and only if their corresponding intervals overlap and at least one of them is a probe. PIGs are a generalization of interval graphs introduced by Zhang for an application concerning(More)
• Journal of Graph Theory
• 2007
A directed graph is an interval digraph if to each vertex v there corresponds an ordered pair of intervals (Sv , Tv) such that u → v if and only if Su ∩ Tv 6= ∅. A tournament is an oriented complete graph. We characterize the tournaments that are interval digraphs via the existence of a large transitive subtournament and by forbidden subtournaments. A(More)
• New directions for youth development
• 2006
The challenges facing youth who are disconnected from our nation's employment and education systems are expansive. Research has suggested that youth services and supports that are grounded in a developmental approach not only help young people avoid self-destructive behavior, but also enable them to acquire the academic and work-readiness skills and(More)