Exploring the role of computer-based assessment in diagnosing children’s mathematical errors in primary education in Ireland

Concern about children’s mathematics performance in Ireland and elsewhere has prompted a range of responses from researchers, policymakers, educators and the media. While policy-level responses in Ireland include revising curricula and implementing a numeracy strategy that calls for increased tuition hours, teachers have also drawn on a wide array of resources in mediating curriculum-based mathematical knowledge, concepts and skills for the children in their classes. In the classroom context, formative assessment tools can be of particular value. This paper explores the potential role for one such tool, a computer-based assessment (CBA), in supporting the teaching and learning of mathematics at primary level. That test requires children to respond to open-format items, and the study illustrates how traditional error-analysis techniques are combined with the affordances of CBAs to enable automated scoring of responses. Discussion focuses on the positive role that digitally mediated error-analysis approaches can play in helping teachers understand better and address the challenges being faced by children in relation to mathematics in the middle grades of primary school. Suggestions for further research are highlighted.

[1]  F. G. Lankford What can a Teacher Learn About a Pupil's Thinking Through Oral Interviews?. , 1992 .

[2]  Allan L White,et al.  Active Mathematics In Classrooms: Finding Out Why Children Make Mistakes - And Then Doing Something To Help Them. , 2005 .

[3]  Neal M. Kingston,et al.  Formative Assessment: A Meta-Analysis and a Call for Research , 2011 .

[4]  Derek W. Haylock Mathematics Explained For Primary Teachers , 1995 .

[5]  Jere Confrey,et al.  Chapter 1: A Review of the Research on Student Conceptions in Mathematics, Science, and Programming , 1990 .

[6]  Sylvia Green,et al.  On-line Mathematics Assessment: The Impact of Mode on Performance and Question Answering Strategies , 2006 .

[7]  Michael Russell,et al.  Computer-based Testing and Validity: a look back into the future , 2003 .

[8]  Antonios Andreatos,et al.  Advancing Electronic Assessment , 2007, Int. J. Comput. Commun. Control.

[9]  Aihui Peng,et al.  A framework for examining mathematics teacher knowledge as used in error analysis , 2009 .

[10]  K. Brodie Learning about learner errors in professional learning communities , 2014 .

[11]  Paul Dalziel,et al.  Education and Skills , 2013 .

[12]  Milan A. Matijevic Assessment in Primary School , 2004 .

[13]  Leanne R. Ketterlin-Geller,et al.  Diagnostic Assessments in Mathematics to Support Instructional Decision Making , 2009 .

[14]  Foster E. Grossnickle Reliability of Diagnosis of Certain Types of Errors in Long Division with a One-Figure Divisor , 1935 .

[15]  Isaac I. Bejar,et al.  EDUCATIONAL DIAGNOSTIC ASSESSMENT , 1984 .

[16]  M. A. Clements Analyzing children's errors on written mathematical tasks , 1980 .

[17]  Gerry Shiel,et al.  The 2014 National Assessments of English Reading and Mathematics Volume 1: Performance Report , 2014 .

[18]  Anthony Orton,et al.  Insights Into Teaching Mathematics , 1996 .

[19]  Shudong Wang,et al.  A Meta-Analysis of Testing Mode Effects in Grade K-12 Mathematics Tests , 2007 .

[20]  Leo J. Brueckner,et al.  Reliability of Diagnosis of Error in Multiplication of Fractions , 1932 .

[21]  John Dudgeon,et al.  Children's Errors in Mathematics , 2014 .

[22]  Edward M. Levinson,et al.  A Review of the Computerized Version of the Self-Directed Search , 1990 .

[23]  Mary Pommerich,et al.  From Simulation to Application: Examinees React to Computerized Testing , 2000 .

[24]  E. Hanushek,et al.  The High Cost of Low Educational Performance: The Long-Run Economic Impact of Improving PISA Outcomes. , 2010 .

[25]  J. Confrey A Review of the Research on Student Conceptions in Mathematics, Science, and Programming , 1990 .

[26]  Graham Littler,et al.  Mathematical Misconceptions: A Guide for Primary Teachers , 2008 .

[27]  Francesco Avvisati Students, computers and learning : making the connection , 2015 .

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

[29]  R. Dottrens The primary school curriculum , 1962 .

[30]  Theodorus Johannes Hendrikus Maria Eggen,et al.  The effectiveness of methods for providing written feedback through a computer-based assessment for learning: a systematic review , 2011 .

[31]  Ivan Watson,et al.  Investigating errors of beginning mathematicians , 1980 .

[32]  Patrick McGuire,et al.  Using Online Error Analysis Items to Support Preservice Teachers' Pedagogical Content Knowledge in Mathematics. , 2013 .

[33]  Mathematics in early childhood and primary education (3-8 years): Teaching and learning , 2014 .

[34]  G. Shiel,et al.  Understanding and Applying Assessment in Education , 2017 .

[35]  Robert J. Mislevy,et al.  Automated scoring of complex tasks in computer-based testing , 2006 .

[36]  Randy Elliot Bennett,et al.  VALIDITY AND AUTOMATED SCORING: IT'S NOT ONLY THE SCORING , 1997 .

[37]  Neal M. Kingston Comparability of Computer- and Paper-Administered Multiple-Choice Tests for K–12 Populations: A Synthesis , 2008 .

[38]  Neil T. Heffernan,et al.  Addressing the assessment challenge with an online system that tutors as it assesses , 2009, User Modeling and User-Adapted Interaction.

[39]  L. Crocker,et al.  Introduction to Classical and Modern Test Theory , 1986 .

[40]  Nikki L. Murdick,et al.  Error Pattern Analysis of Elementary School-Aged Students with Limited English Proficiency , 2011 .

[41]  Randy Elliot Bennett,et al.  Validity and Automad Scoring: It's Not Only the Scoring , 1998 .

[42]  A. Su,et al.  The National Council of Teachers of Mathematics , 1932, The Mathematical Gazette.

[43]  Andrea Raiker Assessment for learning , 2007 .

[44]  Herbert P. Ginsburg,et al.  Children's Arithmetic: How They Learn It and How You Teach It , 1977 .

[45]  Christopher Chapman,et al.  School self-evaluation , 2009 .

[46]  Identifiers California,et al.  Annual Meeting of the National Council on Measurement in Education , 1998 .

[47]  Ingrid Sapire,et al.  An error analysis in the early grades mathematics - A learning opportunity? , 2014 .

[48]  Theodorus Johannes Hendrikus Maria Eggen,et al.  Comparison of the reliability of scoring methods of multiple-response items, matching items, and sequencing items , 2011 .

[49]  Bernard R. Gifford,et al.  Computer-Based Assessment in E-Learning: A Framework for Constructing "Intermediate Constraint" Questions and Tasks for Technology Platforms , 2006 .

[50]  Lieven Verschaffel,et al.  Whole number concepts and operations , 2007 .

[51]  Vic Jenkins,et al.  Getting Started with e-Assessment , 2010 .

[52]  Thomas Hoffmann,et al.  Examining the Effect of Computer-Based Passage Presentation on Reading Test Performance , 2005 .

[53]  J. Fu ICT in Education: A Critical Literature Review and Its Implications , 2013, International Journal of Finance, Insurance and Risk Management.

[54]  Laura M. Desimone,et al.  Are We Asking the Right Questions? Using Cognitive Interviews to Improve Surveys in Education Research , 2004 .