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

William Guo

doi:10.3934/steme.2022015

Article Contents

2022, Volume 2, Issue 3: 245-261. Doi: 10.3934/steme.2022015 open access

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

William Guo^,

School of Engineering and Technology, Central Queensland University, North Rockhampton, QLD 4702, Australia

Email: w.guo@cqu.edu.au; Tel: +61-7-49309687
Email: w.guo@cqu.edu.au; Tel: +61-7-49309687

Received: July 2022

Accepted: July 31, 2022

Published: September 2022

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Abstract

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

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Figure 2. Examples of online MPQ in TM

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

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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

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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%

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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

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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%

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

Year	Number of students	OQ		WA1
Year	Number of students	Mean	SD	Mean	SD
2018	29	18.345	3.687	15.862	3.729
2019	26	18.923	1.294	14.827	3.564

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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

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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

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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

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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

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