Automated Scoring of an Interactive Geometry Item: A Proof-of-Concept

An online interactive geometry item was developed to explore students’ abilities to create prototypical and “tilted” rectangles out of line segments. The item was administered to 1,002 students. The responses to the item were hand-coded as correct, incorrect, or incorrect with possible evidence of a misconception. A variation of the nearest neighbor algorithm was used to automatically predict one of these categories for each of the student responses. The predicted category was compared to the hand-coded category. The algorithm accurately predicted the category for 94.6% of responses.

[1]  Semire Dikli,et al.  An Overview of Automated Scoring of Essays. , 2006 .

[2]  Anat Ben-Simon,et al.  Toward More Substantively Meaningful Automated Essay Scoring , 2007 .

[3]  W. Popham Classroom Assessment: What Teachers Need to Know , 1995 .

[4]  Jinhao Wang,et al.  Automated Essay Scoring Versus Human Scoring: A Comparative Study , 2007 .

[5]  Marc M. Sebrechts,et al.  The Accuracy of Automatic Qualitative Analyses of Constructed-Response Solutions to Algebra Word Problems. GRE Board Professional Report No. 91-03P. , 1994 .

[6]  Lawrence M. Rudner,et al.  Automated Essay Scoring Using Bayes' Theorem , 2002 .

[7]  P. Black,et al.  Inside the Black Box: Raising Standards through Classroom Assessment , 2010 .

[8]  David Heckerman,et al.  Empirical Analysis of Predictive Algorithms for Collaborative Filtering , 1998, UAI.

[9]  P. Black,et al.  Assessment and Classroom Learning , 1998 .

[10]  Randy Elliot Bennett,et al.  VALIDATION AND EXTENSION OF THE MATHEMATICAL EXPRESSION RESPONSE TYPE: APPLICATIONS OF SCHEMA THEORY TO AUTOMATIC SCORING AND ITEM GENERATION IN MATHEMATICS , 1997 .

[11]  D. Schifter,et al.  A research companion to Principles and standards for school mathematics , 2003 .

[12]  Doug French,et al.  Teaching and Learning Geometry , 2004 .

[13]  Randy Elliot Bennett,et al.  Three Response Types for Broadening the Conception of Mathematical Problem Solving in Computerized Tests , 1998 .

[14]  Dit-Yan Yeung,et al.  An efficient syntactic approach to structural analysis of on-line handwritten mathematical expressions , 2000, Pattern Recognit..

[15]  Chris Sangwin,et al.  Assessing mathematics automatically using computer algebra and the internet , 2004 .

[16]  E. B. Page Project Essay Grade: PEG. , 2003 .

[17]  Salvatore Valenti,et al.  An Overview of Current Research on Automated Essay Grading , 2003, J. Inf. Technol. Educ..

[18]  T. P. Carpenter,et al.  Learning and teaching with understanding. , 1992 .

[19]  Jill Burstein,et al.  AUTOMATED ESSAY SCORING WITH E‐RATER® V.2.0 , 2004 .

[20]  L. Resnick,et al.  Mathematics and Science Learning: A New Conception , 1983, Science.

[21]  Lawrence M. Rudner,et al.  An Evaluation of the IntelliMetric[SM] Essay Scoring System. , 2006 .

[22]  William M. Carroll Geometric Knowledge of Middle School Students in a Reform‐based Mathematics Curriculum , 1998 .

[23]  Douglas A. Grouws,et al.  Handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics. , 1992 .

[24]  Douglas H. Clements,et al.  Geometry and spatial reasoning. , 1992 .

[25]  Lawrence M. Rudner,et al.  An Overview of Three Approaches to Scoring Written Essays by Computer. ERIC Digest. , 2001 .

[26]  Randy Elliot Bennett,et al.  Graphical Modeling: A New Response Type for Measuring the Qualitative Component of Mathematical Reasoning , 1999 .

[27]  Marc M. Sebrechts,et al.  Agreement between expert-system and human raters' scores on complex constructed-response quantitative items. , 1991 .

[28]  Rina Hershkowitz,et al.  Visualization in Geometry--Two Sides of the Coin. , 1989 .

[29]  J. Roschelle,et al.  Misconceptions Reconceived: A Constructivist Analysis of Knowledge in Transition , 1994 .

[30]  Michael Russell,et al.  Diagnosing students’ misconceptions in algebra: Results from an experimental pilot study , 2009, Behavior research methods.

[31]  Marc M. Sebrechts,et al.  AGREEMENT BETWEEN EXPERT-SYSTEM AND HUMAN RATERS' SCORES ON COMPLEX CONSTRUCTED-RESPONSE QUANTITATIVE ITEMS , 1991 .

[32]  E. B. Page,et al.  The Computer Moves into Essay Grading: Updating the Ancient Test. , 1995 .

[33]  Lawrence M. Rudner,et al.  An Evaluation of IntelliMetric™ Essay Scoring System , 2006 .

[34]  Dit-Yan Yeung,et al.  Mathematical expression recognition: a survey , 2000, International Journal on Document Analysis and Recognition.

[35]  Randy Elliot Bennett,et al.  Evaluating an Automatically Scorable, Open-Ended Response Type for Measuring Mathematical Reasoning in Computer-Adaptive Tests. , 1997 .

[36]  L. Resnick,et al.  Conceptual Bases of Arithmetic Errors: The Case of Decimal Fractions. , 1989 .

[37]  Martin Chodorow,et al.  Automated Essay Scoring for Nonnative English Speakers , 1999 .

[38]  Jill Burstein,et al.  Automated Essay Scoring : A Cross-disciplinary Perspective , 2003 .