Parsing of algebraic expressions by experienced users of mathematics

References

• Akaike , H. 1973 . “ Information theory and an extension of the maximum likelihood principle ” . In Proceedings of the second international symposium on information theory , Edited by: Petrov , B. N. and Czaki , F. 267 – 281 . Budapest, , Hungary : Akademiai Kiado .
   Google Scholar
• Arnold , A. and Guessarian , I. 1996 . Mathematics for computer science , New York : Prentice Hall .
   Google Scholar
• Baldi , P. , Chauvin , Y. , Hunkapiller , T. and McClure , M. A. 1994 . Hidden Markov models of biological primary sequence information . Proceedings of the National Academy of Sciences, USA , 91 : 1059 – 1063 .
   PubMed Web of Science ®Google Scholar
• Blackwell , A. F. , Jansen , A. R. and Marriott , K. 2000 . “ Restricted Focus Viewer: A tool for tracking visual attention ” . In Theory and application of diagrams: Lecture notes in artificial intelligence (LNAI) 1889 , Edited by: Anderson , M. , Cheng , P. and Haarslev , V. 162 – 177 . Berlin : Springer-Verlag .
   Google Scholar
• Borsley , R. 1999 . Syntactic theory: A unified approach , 2 ed. , New York : Arnold .
   Google Scholar
• Brandt , S. A. and Stark , L. W. 1997 . Spontaneous eye movements during visual imagery reflect the content of the visual scene . Journal of Cognitive Neuroscience , 9 ( 1 ) : 27 – 38 .
   PubMed Web of Science ®Google Scholar
• Cajori , F. 1928 . A history of mathematical notations (Vols. 1 and 2) , Chicago : Open Court Publishing Company .
   Google Scholar
• Durbin , R. , Eddy , S. R. , Krogh , A. and Mitchison , G. 1998 . Biological sequence analysis: Probabilisitic models of proteins and nucleic acids , Cambridge : Cambridge University Press .
   Google Scholar
• Frederici , A. and Meyer , M. 2004 . The brain knows the difference: Two types of grammatical violations . Brain Research , 1000 : 72 – 77 .
   PubMed Web of Science ®Google Scholar
• Ghosh , J. K. and Samanta , T. 2001 . Model selection—an overview . Current Science , 80 ( 9 ) : 1135 – 1144 .
   Web of Science ®Google Scholar
• Haskell , T. and MacDonald , M. 2005 . Constituent structure and linear order in language production: Evidence from subject-verb agreement . Journal of Experimental Psychology: Learning, Memory, and Cognition , 31 ( 5 ) : 891 – 904 .
   PubMed Web of Science ®Google Scholar
• Henderson , J. M. , McClure , K. K. , Pierce , S. and Schrock , G. 1997 . Object identification without foveal vision: Evidence from an artificial scotoma paradigm . Perception and Psychophysics , 59 ( 3 ) : 323 – 346 .
   PubMed Web of Science ®Google Scholar
• Jansen , A. R. (2001) . Restricted Focus Viewer (RFV) Version 2.1 User's manual and tutorial (Tech. Rep. No. 2001/87) . School of Computer Science and Software Engineering, Monash University , Victoria, , Australia .
   Google Scholar
• Jansen , A. R. , Blackwell , A. F. and Marriott , K. 2003 . A tool for tracking visual attention: The Restricted Focus Viewer . Behavior Research Methods, Instruments, and Computers , 35 ( 1 ) : 57 – 69 .
   PubMedGoogle Scholar
• Jansen , A. R. , Marriott , K. and Yelland , G. W. 2003 . Comprehension of algebraic expressions by experienced users of mathematics . Quarterly Journal of Experimental Psychology , 56A ( 1 ) : 3 – 30 .
   Google Scholar
• Johnson , N. F. 1968 . The influence of grammatical units on learning . Journal of Verbal Learning and Verbal Behaviour , 7 : 236 – 240 .
   Google Scholar
• Johnson , N. F. 1970 . “ Chunking and organization in the process of recall ” . In The psychology of learning and motivation , Edited by: Bower , G. H. Vol. 4 , 171 – 247 . New York : Academic Press .
   Google Scholar
• Just , M. A. and Carpenter , P. A. 1980 . A theory of reading: From eye fixations to comprehension . Psychological Review , 87 : 329 – 354 .
   PubMed Web of Science ®Google Scholar
• Just , M. A. and Carpenter , P. A. 1987 . The psychology of reading and language comprehension , Boston, MA : Allyn & Bacon .
   Google Scholar
• Kirshner , D. 1989 . The visual syntax of algebra . Journal for Research in Mathematics Education , 20 ( 3 ) : 274 – 287 .
   Web of Science ®Google Scholar
• Mitchell , D. C. and Green , D. W. 1978 . The effects of context and content on immediate processing in reading . Quarterly Journal of Experimental Psychology , 30 : 609 – 636 .
   Web of Science ®Google Scholar
• Osaka , N. and Oda , K. 1994 . Moving window generator for reading experiments . Behavior Research Methods, Instruments, and Computers , 26 ( 1 ) : 49 – 53 .
   Google Scholar
• Rabiner , L. R. 1989 . A tutorial on hidden Markov models and selected applications in speech recognition . Proceedings of the IEEE , 77 ( 2 ) : 257 – 285 .
   Web of Science ®Google Scholar
• Ranney , M. 1987 . The role of structural context in perception: Syntax in the recognition of algebraic expressions . Memory and Cognition , 15 ( 1 ) : 29 – 41 .
   PubMed Web of Science ®Google Scholar
• Rayner , K. 1998 . Eye movements in reading and information processing: 20 years of research . Psychological Bulletin , 124 ( 3 ) : 372 – 422 .
   PubMed Web of Science ®Google Scholar
• Rayner , K. and Pollatsek , A. 1989 . The psychology of reading , Englewood Cliffs, NJ : Prentice Hall .
   Google Scholar
• Rosbergen , E. , Wedel , M. , & Pieters , R. (1997) . Analyzing visual attention to repeated print advertising using scanpath theory (Tech. Rep. No. 97B32) . Research Institute SOM (Systems, Organizations and Management), University of Groningen, The Netherlands .
   Google Scholar
• Sakamoto , Y. , Ishiguro , M. and Kitagawa , G. 1986 . Akaike information criterion statistics , Tokyo, , Japan : KTK Scientific Publishers .
   Google Scholar
• Salvucci , D. D. (1999) . Inferring intent in eye-movement interfaces: Tracing user actions with process models . In Human factors in computing systems: CHI '99 conference proceedings (pp. 254 – 261 ). New York : ACM Press .
   Google Scholar
• Salvucci , D. D. and Anderson , J. R. 1998 . “ Tracing eye movement protocols with cognitive process models ” . In Proceedings of the twentieth annual conference of the Cognitive Science Society , Edited by: Gernsbacher , M. and Derry , S. 923 – 928 . Hillsdale, NJ : Lawrence Erlbaum Associates, Inc .
   Google Scholar
• Schwarz , G. 1978 . Estimating the dimension of a model . The Annals of Statistics , 6 ( 2 ) : 461 – 464 .
   Web of Science ®Google Scholar
• Stark , L. and Ellis , S. R. 1981 . “ Scanpaths revisited: Cognitive models direct active looking ” . In Eye movements: Cognition and visual perception , Edited by: Fisher , D. F. , Monty , R. A. and Senders , J. W. 193 – 226 . Hillsdale, NJ : Lawrence Erlbaum Associates, Inc .
   Google Scholar
• Stark , L. W. , Ezumi , K. , Nguyen , T. , Paul , R. , Tharp , G. and Yamashita , H. I. 1992 . “ Visual search in virtual environments ” . In Proceedings of the SPIE: Human Vision, Visual Processing, and Digital Display III, 1666 , Edited by: Rogowitz , B. E. 577 – 589 . Bellingham, WA : SPIE .
   Google Scholar
• Stone , M. 1974 . Cross-validatory choice and assessment of statistical predictions . Journal of the Royal Statistical Society, Series B (Methodological) , 36 ( 2 ) : 111 – 147 .
   Web of Science ®Google Scholar
• Ummelen , N. 1997 . Procedural and declarative information in software manuals: Effects on information use, task performance and knowledge , Amsterdam : Rodopi .
   Google Scholar