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While this relationship between interaction and problem solving has been well studied in the cognitive science literatures, the visual analytics community has yet to exploit this understanding for analytical problem solving. In this paper, we hypothesize that constraints on interactions and constraints encoded in visual representations can lead to strategies of varying effectiveness during problem solving. To test our hypothesis, we conducted a user study in which participants were given different levels of interaction constraints when solving a simple mathematic game called number scrabble. Number scrabble is known to have an optimal visual problem isomorph, and the goal of this study is to learn if and how the participants could derive the isomorph and to analyze the strategies that the participants utilize in solving the problem. Our results indicate that constraints on interactions do affect problem solving, and that although the optimal visual isomorph is difficult to derive, certain interaction constraints can lead to a higher chance of deriving the isomorph.<\/jats:p>","DOI":"10.1177\/1473871611433712","type":"journal-article","created":{"date-parts":[[2012,2,21]],"date-time":"2012-02-21T20:58:30Z","timestamp":1329857910000},"page":"222-236","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":3,"title":["Toward a deeper understanding of the relationship between interaction constraints and visual isomorphs"],"prefix":"10.1177","volume":"11","author":[{"given":"Wenwen","family":"Dou","sequence":"first","affiliation":[{"name":"Department of Computer Science, University of North Carolina at Charlotte, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Caroline","family":"Ziemkiewicz","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Brown University, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lane","family":"Harrison","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of North Carolina at Charlotte, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dong Hyun","family":"Jeong","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of the District of Columbia, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"William","family":"Ribarsky","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of North Carolina at Charlotte, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaoyu","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of North Carolina at Charlotte, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Remco","family":"Chang","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Tufts University, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2012,2,20]]},"reference":[{"key":"e_1_3_3_2_2","volume-title":"EuroVis 2009 keynote address","author":"Hanrahan P","unstructured":"Hanrahan P. 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