To Matrix, Network, or Hierarchy: That Is the Question

Novick, Laura R.; Hurley, Sean M.

doi:10.1006/cogp.2000.0746

Cited by 98 publications

(125 citation statements)

References 28 publications

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“…Our model helps to explain how adults discover structural forms in controlled behavioral experiments (40), and is consistent with previous demonstrations that adults can choose the most appropriate representation for a given problem (47). Our model may also help to explain how children learn about the structure of their world.…”

supporting

confidence: 85%

The discovery of structural form

Kemp

Tenenbaum

2008

Proc. Natl. Acad. Sci. U.S.A.

421

420

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Algorithms for finding structure in data have become increasingly important both as tools for scientific data analysis and as models of human learning, yet they suffer from a critical limitation. Scientists discover qualitatively new forms of structure in observed data: For instance, Linnaeus recognized the hierarchical organization of biological species, and Mendeleev recognized the periodic structure of the chemical elements. Analogous insights play a pivotal role in cognitive development: Children discover that object category labels can be organized into hierarchies, friendship networks are organized into cliques, and comparative relations (e.g., ''bigger than'' or ''better than'') respect a transitive order. Standard algorithms, however, can only learn structures of a single form that must be specified in advance: For instance, algorithms for hierarchical clustering create tree structures, whereas algorithms for dimensionality-reduction create low-dimensional spaces. Here, we present a computational model that learns structures of many different forms and that discovers which form is best for a given dataset. The model makes probabilistic inferences over a space of graph grammars representing trees, linear orders, multidimensional spaces, rings, dominance hierarchies, cliques, and other forms and successfully discovers the underlying structure of a variety of physical, biological, and social domains. Our approach brings structure learning methods closer to human abilities and may lead to a deeper computational understanding of cognitive development.cognitive development ͉ structure discovery ͉ unsupervised learning

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supporting

confidence: 85%

The discovery of structural form

Kemp

Tenenbaum

2008

Proc. Natl. Acad. Sci. U.S.A.

421

420

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“…A table allows certain reordering and classification operations to be performed and a double-8 entry structure to be applied to the data; essentially, tables cross-classify items (Marti, 2008). In a double-entry structure, the values of one variable are shared with the values of another variable, and these values are expressed in the cells that are generated during the cross-tabulation (Duval, 2003;Novick & Hurley, 2001;Piaget & Inhelder, 1967;Tversky, Kugelmass, & Winter, 1991). These features are essential to the process of building a emerge when students must organize data in tabular forms (Brizuela & Lara-Roth, 2002;Marti, 2008;Novick & Hurley, 2001;Marti, Garcia-Mila, Gabucio, & Konstantinidou, 2011).…”

Section: Tables and Their Role In Graphingmentioning

confidence: 99%

Fifth Through Eighth Grade Students’ Difficulties in Constructing Bar Graphs: Data Organization, Data Aggregation, and Integration of a Second Variable

García-Milà

Martí

Gilabert

et al. 2014

Mathematical Thinking and Learning

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Abstract:Studies that consider the displays that students create to organize data are not common in the literature. This paper compares 5th through 8th graders' difficulties with the creation of bar graphs constructed using either raw data (Study 1, n=155) or a provided table (Study 2, n=152). Data in Study 1 showed statistical differences for the type of data organization but not for grade level. Students' primary problem was choosing a format that integrated a second variable and aggregating data. In contrast, when the table was provided (Study 2), we observed that 7th-8th graders outperformed 5th-6th graders. We interpret these results in terms of older students' better data interpretation competence. We conclude that students' difficulties in bar graphing can be traced to their tabulation processes. Data organization is an essential bridging tool for understanding the essence of the data and representing them graphically, and educators should devote to it the attention it deserves. . All of your comments and all of Reviewer 5's have been addressed in the revision. Reviewer 1's comment 1 and 2 are commented in the response table but did not generate any change in the manuscript. We interpreted them as additional comments rather than "must" suggestions. Please tell us if we need to make any additional changes. All changes are highlighted in the manuscript. Powered by Editorial Manager® and ProduXion Manager® from Aries Systems CorporationThe Figures, Tables and Appendices are all the same excepte for Table 3 and Table 7 (there were small errors in the title). The paper contains 3 Appendices, 11 figures and 8 tables and its length is 35 pages long excluding cover page, letter, abstract, references, tables and figures. Aso, we have removed anonimity by adding two of our previous papers that are referred to in the manuscrit, and also, we have added the acknowledgments and proof read the text. We hope that the paper is close to publication. We again, are very grateful to the reviewers', as well as to your thorough revision of the manuscript. We hope that you will find that it is suitable for publication. With kind regards, Merce email: mgarciamila@ub.edu Cover LetterAll changes in the new manuscript are marked with the control of changes Reviewer 1 commentsAuthors' response 1. Given that the students come from multiple classrooms in multiple schools and each class is split among the two studies, it may help the readers if the authors create a graphic showing how the participant pool was created. This is just an idea but perhaps the authors could show 5 circles representing the 5 schools. Inside each school circle, a smaller circle or circles could be drawn to indicate the class or classes that came from that school. Each class circle could be labeled as a primary or secondary classroom. Each class circle could be further split with a line and the number of students that were assigned to study 1 and to study two could be labeled. I'm not sure if this is helpful but I thought I would suggest it as a way to help re...

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“…Is V dominated by PP in the first conjunct? From the diagrammatic view proposed by Novick and Hurley [15], who distinguish three categories of properties of hierarchies, the questions required the subject to consider the basic structure of the tree, as well as details about the nodes and links in the tree, and potential movement of information through the tree. The subjects were invited to take the web-based test in their own time at a quiet place.…”

Section: The Experimentsmentioning

confidence: 99%

“…As a scientific diagram, the tree diagram belongs to the category of schematic diagrams [11,15]. Schematic diagrams are abstract diagrams that provide an overview of the components and their organization of a set of raw data according to some model.…”

Section: Introductionmentioning

confidence: 99%

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Visualizing Non-subordination and Multidominance in Tree Diagrams: Testing Five Syntax Tree Variants

Smet¹,

Vries

2008

Diagrammatic Representation and Inference

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Abstract. In linguistics, it is quite common to use tree diagrams for immediate constituent analysis of sentences. Traditionally, these trees are binary and twodimensional. However, phenomena such as coordination and right node raising, have led to the view that a simple hierarchical approach of sentences is inadequate: some linguistic phenomena rather seem to involve non-subordination and multiple dependencies. The central question of the present research is this: what are workable alternative tree-like diagrams that can accommodate to this view? An experiment has been set up to test five different types of tree visualizations, including three-dimensional trees. Subjects were asked to respond to various questions concerning coordination and (non-constituent) right node raising constructions, and to mark their preference for each tree visualization. This paper will discuss the representation problems, and present the experiment and its results. It turned out that the tree most rich in information was the least usable one, whereas the tree, most close to the traditional syntax tree, but with colour enrichment, performed best.

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To Matrix, Network, or Hierarchy: That Is the Question

Cited by 98 publications

References 28 publications

The discovery of structural form

The discovery of structural form

Fifth Through Eighth Grade Students’ Difficulties in Constructing Bar Graphs: Data Organization, Data Aggregation, and Integration of a Second Variable

Visualizing Non-subordination and Multidominance in Tree Diagrams: Testing Five Syntax Tree Variants

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