Please use this identifier to cite or link to this item: http://buratest.brunel.ac.uk/handle/2438/10973
Title: Development and evaluation of computer-aided assessment in discrete and decision mathematics
Authors: Zaczek, Kinga
Advisors: Greenhow, M
Noble, S
Keywords: E-learning;Formative feedback;Computer-aided assessment (CAA)
Issue Date: 2015
Publisher: Brunel University London
Abstract: This thesis describes the development of Computer-Aided Assessment questions for elementary discrete and decision mathematics at the school/university interface, stressing the pedagogy behind the questions’ design and the development of methodology for assessing their efficacy in improving students’ engagement and perceptions, as well as on their exams results. The questions give instant and detailed feedback and hence are valuable as diagnostic, formative or summative tools. A total of 275 questions were designed and coded for five topics, numbers, sets, logic, linear programming and graph theory, commonly taught to students of mathematics, computer science, engineering and management. Pedagogy and programming problems with authoring questions were resolved and are discussed in specific topic contexts and beyond. The delivery of robust and valid objective questions, even within the constraints of CAA, is therefore feasible. Different question types and rich feedback comprising text, equations and diagrams that allow random parameters to produce millions of realisations at run time, can give CAA an important role in teaching mathematics at this level. Questionnaires identified that CAA was generally popular with students, with the vast majority seeing CAA not only as assessment but also as a learning resource. To test the impact of CAA on students’ learning, an analysis of the exam scripts quantified its effect on class means and standard deviations. This also identified common student errors, which fed into the question design and editing processes by providing evidence-based mal-rules. Four easily-identified indicators (correctly-written remainders, conversion of binary/octal/hexadecimal numbers, use of correct set notation {…} and consistent layout of truth tables) were examined in student exam scripts to find out if the CAA helps students to improve examination answers. The CAA answer files also provided the questions’ facilities and discriminations, potentially giving teachers specific information on which to base and develop their teaching and assessment strategies. We conclude that CAA is a successful tool for the formative/summative assessment of mathematics at this level and has a positive effect on students’ learning.
Description: This thesis was submitted for the degree of Doctor of Philosophy and was awarded by Brunel University London.
URI: http://bura.brunel.ac.uk/handle/2438/10973
Appears in Collections:Dept of Mathematics Theses
Mathematical Sciences

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FulltextThesis.pdfThesis Text2.08 MBAdobe PDFView/Open
AppendixA_Readme_of_Appendices_content.docxAppendix List16.69 kBUnknownView/Open
AppendixB_CAA_ Questionnaire.docCAA Questionnaire44.5 kBMicrosoft WordView/Open
AppendixB_Questionnaire_responses.xlsxQuestionnaire Responses124.12 kBUnknownView/Open
AppendixC_Engagement.xlsxEngagement55.49 kBUnknownView/Open
AppendixC_Questions_Combined_Data.xlsQuestions Combined Data195.5 kBMicrosoft ExcelView/Open
AppendixC_Questions_Not combined data_'09.xlsxQuestions Not Combined Data '0918.35 kBUnknownView/Open
AppendixC_Questions_Not combined data_'10.xlsxQuestions Not Combined Data '1021.47 kBUnknownView/Open
AppendixC_Questions_Not combined data_'11.xlsxQuestions Not Combined Data '1123.14 kBUnknownView/Open
AppendixC_Questions_Not combined data_'12.xlsxQuestions Not Combined Data '1224.58 kBUnknownView/Open
AppendixC_Questions_Not combined data_'13.xlsQuestions Not Combined Data '13294 kBMicrosoft ExcelView/Open
AppendixD_CAA_vs_Exam_results.xlsxCAA vs Exam Results139.12 kBUnknownView/Open
AppendixD_Exams_results.xlsxExam Results54.43 kBUnknownView/Open
AppendixD_Indicators.xlsxIndicators38.01 kBUnknownView/Open
AppendixE_Graph_Theory_Adjacency_matrix_x2.qmlGraph Theory Adjacency Matrix28.62 kBUnknownView/Open
AppendixE_Graph_Theory_Degree_Degree_sequence_x8.qmlGraph Theory Degree Degree Sequence54.22 kBUnknownView/Open
AppendixE_Graph_Theory_Degree_In_and_out_degree_x5.qmlGraph Theory Degree In and Out Degree38.05 kBUnknownView/Open
AppendixE_Graph_Theory_Edge_sets_x3.qmlGraph Theory Edge Sets25.53 kBUnknownView/Open
AppendixE_Graph_Theory_Min_spanning_trees_Kruskal_x6.qmlGraph Theory Min Spanning Trees Kruskal84.73 kBUnknownView/Open
AppendixE_Graph_Theory_Min_spanning_trees_Prim_x6.qmlGraph Theory Min Spanning Trees Prim78.65 kBUnknownView/Open
AppendixE_Graph_Theory_Min_spanning_trees_x1.qmlGraph Theory Min Spanning Trees9.68 kBUnknownView/Open
AppendixE_Graph_Theory_Spanning_trees_x4.qmlGraph Theory Spanning Trees103.17 kBUnknownView/Open
AppendixE_Graph_Theory_Vertex_sets_x2.qmlGraph Theory Vertex Sets13.91 kBUnknownView/Open
AppendixE-Linear_Programming_Feasible_region_x11.qmlLinear Programming Feasible Region230.98 kBUnknownView/Open
AppendixE-Linear_Programming_Optimisation_x3.qmlLinear Programming Optimisation69.95 kBUnknownView/Open
AppendixE-Logic_Applications_x2.qmlLogic Applications33.59 kBUnknownView/Open
AppendixE-Logic_Connectives_x2.qmlLogic Connectives26.26 kBUnknownView/Open
AppendixE-Logic_Translations_x8.qmlLogic Translations128.23 kBUnknownView/Open
AppendixE-Logic_TT_2_operators_x8.qmlLogic TT 2 Operators74.88 kBUnknownView/Open
AppendixE-Logic_TT_2-3_operators_x12.qmlLogic TT 2-3 Operators122.29 kBUnknownView/Open
AppendixE-Logic_TT_2-4_operator_x24.qmlLogic TT 2-4 Operator261.35 kBUnknownView/Open
AppendixE-Logic_TT_3-5_operators_x7.qmlLogic TT 3-5 Operators82.24 kBUnknownView/Open
AppendixE-Numbers_Modular_arithmetic_x3.qmlNumbers Modular Arithmetic12.19 kBUnknownView/Open
AppendixE-Numbers_Non-decimal_ arithmetic_Binary_arithmetic_x6.qmlNumbers Non-decimal Arithmetic Binary Arithmetic31.24 kBUnknownView/Open
AppendixE-Numbers_Non-decimal_arithmetic_Hexadecimal_arithmetic_x7.qmlNumbers Non-decimal Arithmetic Hexadecimal Arithmetic34.96 kBUnknownView/Open
AppendixE-Numbers_Non-decimal_arithmetic_Number_bases_x8.qmlNumbers Non-decimal Arithmetic Number Bases39.68 kBUnknownView/Open
AppendixE-Numbers_Non-decimal_arithmetic_Octal_arithmetic_x7.qmlNumbers Non-decimal Arithmetic Octal Arithmetic34.78 kBUnknownView/Open
AppendixE-Numbers_Prime_factorisation_x5.qmlNumbers Prime Factorisation42.29 kBUnknownView/Open
AppendixE-Numbers_Scientific_notation_x9.qmlNumbers Scientific Notation82.83 kBUnknownView/Open
AppendixE-Sets_Algebra_x3.qmlSets Algebra88.96 kBUnknownView/Open
AppendixE-Sets_Cardinality_x7.qmlSets Cardinality58.68 kBUnknownView/Open
AppendixE-Sets_Cartesian_product_x3.qmlSets Cartesian Product17.9 kBUnknownView/Open
AppendixE-Sets_Complement_x13.qmlSets Complement98.75 kBUnknownView/Open
AppendixE-Sets_Counting_principle_x18.qmlSets Counting Principle96.88 kBUnknownView/Open
AppendixE-Sets_Difference_x12.qmlSets Difference98.42 kBUnknownView/Open
AppendixE-Sets_Elements_x18.qmlSets Elements122.65 kBUnknownView/Open
AppendixE-Sets_Intersection_x14.qmlSets Intersection104.07 kBUnknownView/Open
AppendixE-Sets_Partition_x4.qmlSets Partition32.34 kBUnknownView/Open
AppendixE-Sets_Power_set_x6.qmlSets Power Set41.45 kBUnknownView/Open
AppendixE-Sets_Subsets_and_set_equality_x3.qmlSets Subsets and Set Equality71.1 kBUnknownView/Open
AppendixE-Sets_Union_x13.qmlSets Union98.25 kBUnknownView/Open
AppendixE-Sets_Venn_diagrams_x2.qmlSets Venn Diagrams20.64 kBUnknownView/Open
AppendixE-Templates_brunel_general.templateTemplates Brunel General156.76 kBUnknownView/Open
AppendixE-Templates_brunel_graphtheory.templateTemplates Brunel Graph Theory31.35 kBUnknownView/Open
AppendixE-Templates_brunel_linearalg.templateTemplates Brunel Linearalg17.71 kBUnknownView/Open
AppendixE-Templates_brunel_logic.templateTemplates Brunel Logic6.95 kBUnknownView/Open
AppendixE-Templates_brunel_svg.templateTemplates Brunel SVG51.46 kBUnknownView/Open


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