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Design and implementation of multi-purpose quizzes to improve mathematics learning for transitional engineering students

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  • For students who are academically ineligible to enter a bachelor program in engineering but still want to upskill their knowledge in engineering, many universities provide an associate degree program in engineering to these students. The higher achievers from the associate degree program can transfer to a full degree program in engineering. Mathematics courses in such associate degree programs are often challenging to both the teachers and students due to various reasons. This paper presents a small part of a mathematics revitalization project on pedagogical adjustment to scaffold mathematics learning for students in an associate engineering program at Central Queensland University (CQU), a regional university in Australia, from 2018 to 2020. The design and implementation of the online multi-purpose quizzes (MPQ) to improve both the learning environment and outcomes for the engineering students from 2018 to 2020 are reported in this work. Statistically, the online MPQ empowered students to achieve their best possible outcomes by attempting the questions with time flexibility, on a confined set of topics, and with more chances of amending errors than the traditional written assessments. Hence, their performance in the online MPQ was consistently better than that in the written assignments in 2018-2020. The weaknesses of the online MPQ are also discussed.

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  • Figure 1.  Examples of MPQ for TM

    Figure 2.  Examples of online MPQ in TM

    Figure 3.  Part of the summary after completing one attempt to online MPQ in TM

    Table 1.  Weekly topics in TM prior to 2018

    Week Topic
    1 Basic algebra and operations
    2 Geometry and trigonometric functions
    3 Inequalities, functions and graphs
    4 Factoring, quadratic functions
    5 Oblique triangles and vectors
    6 Ratio, proportion, graphs of trigonometric functions
    7 Exponential and logarithmic functions
    8 Systems of linear equations, matrices and determinants
    9 The derivative
    10 Applications of derivative
    11 Integration and applications
    12 Introduction to statistics
     | Show Table
    DownLoad: CSV

    Table 2.  Assessment scheme for TM prior to 2018

    Assessment Topic Due Weight
    Written Assignment 1 Topics covered in Weeks 1-4 Week 5 25%
    Written Assignment 2 Topics covered in Weeks 5-8 Week 9 25%
    Written Assignment 3 Topics covered in Weeks 9-11 Week 12 10%
    Exanimation All topics Week 14 40%
     | Show Table
    DownLoad: CSV

    Table 3.  The new schedule of weekly topics covered in TM in 2018 and 2019

    Week Topic
    1 Basic Algebra (Ⅰ)
    2 Basic Algebra (Ⅱ) and Basic Geometry
    3 Inequalities and Sequences
    4 Functions and Graphs
    5 Polynomial Functions
    6 Exponential and Logarithmic Functions
    7 Triangles and Trigonometry
    8 Trigonometric and Hyperbolic Functions
    9 Essentials of Differentiation
    10 Applications of Differentiation
    11 Integration
    12 Applications of Integration
     | Show Table
    DownLoad: CSV

    Table 4.  New assessment scheme for TM in 2018 and 2019

    Assessment Topic Due Weight
    Online quizzes Algebra, inequalities, sequences, linear & quadratic functions covered in Weeks 1-5 Week 6 20%
    Written assignment 1 Triangles, exponential, logarithmic, trigonometric functions covered in Weeks 6-8 Week 9 20%
    Written assignment 2 Calculus covered in Weeks 9-11 Week 12 20%
    Exanimation (invigilated) All topics Week 14 40%
     | Show Table
    DownLoad: CSV

    Table 5.  Statistics of results from the first two assessments in Term 1 of 2018 and 2019

    Year Number of students OQ WA1
    Mean SD Mean SD
    2018 29 18.345 3.687 15.862 3.729
    2019 26 18.923 1.294 14.827 3.564
     | Show Table
    DownLoad: CSV

    Table 6.  The t-test results between OC and WA1 for TM in 2018 and 2019

    Year d.f. Critical t-value (α = 0.025) t-value for OQ-WA1
    2018 56 ±2.003 2.550
    2019 50 ±2.009 5.508
     | Show Table
    DownLoad: CSV

    Table 7.  Statistics of results from OQ, WA1 and WA2 for TM in Term 2 of 2020

    Number of students OQ WA1 WA2
    Mean SD Mean SD Mean SD
    21 19.476 0.981 17.047 3.232 15.690 3.376
     | Show Table
    DownLoad: CSV

    Table 8.  The t-test results between OQ and WA1 or WA2 for TM in Term 2 of 2020

    Year d.f. Critical t-value (α = 0.025) t-value for OQ-WA1 t-value for OQ-WA2
    2020 40 ±2.021 3.296 4.947
     | Show Table
    DownLoad: CSV

    Table 9.  The t-test results between OQ for TM in 2018 and OQ in 2019 and 2020

    Year d.f. Critical t-value (α = 0.025) t-value for Q-Q
    2018-2019 53 ±2.006 -0.758
    2018-2020 48 ±2.011 -1.368
     | Show Table
    DownLoad: CSV
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