Involving students in making
mathematics relevant to first year
engineering students
Birgit Loch
Swinburne University of Technology
bloch@swin.edu.au
Our observations
• First year engineering students don’t understand why they need to
learn algebra, vectors, differentiation …
• They want to be engineers, not mathematicians …
• But they are taught by mathematicians … in a mathematical way …
• And they have forgotten first year material by the time they are in
second year.
The relevance of mathematics
• Mathematicians ‘speak mathematics and not engineering’
• Students know there is a reason … but they cannot see this reason ‘until
long after the courses have ended’ (Pennell, Avitabile and White, 2005)
Australian context:
• In surveys, students agree that mathematics is relevant to their future
career. In follow-up interviews, widely varied student views (Flegg, Mallet
and Lupton, 2012)
• Higher year engineering students recognize the relevance of the
mathematics for their engineering studies to a larger extent than first
year students (Coupland, Gardner and Carmody, 2008)
What has been tried to explain the relevance
of mathematics?
• Mostly demonstrating engineering applications of mathematics learnt
(integrated engineering curriculum) (Lit review by Froyd and Ohland,
2005)
• Case studies for secondary students. Difficulty in balancing the
amount of detailed mathematical explanation and the level of realism
of the case study (Mustoe and Croft, 1999)
• A mathematics lecturer enrolled and completed an engineering
undergraduate degree at his university. Following this experience, he
changed his teaching style and started to use motivational examples
in his mathematics class, from his higher year engineering classes
(Allen and Wilson, 2013)
Engaging students as co-creators
• Horizon Report 2014 - Key Trend: Shift from Students as Consumers
to Students as Creators
• Successful project at Loughborough University in the UK, improving a
mathematics unit (Croft, Duah & Loch, 2013)
The Maths Relevance Project
• Round 1 – pilot (summer 2012/2013)
Stage: Evaluation
• Round 2 (winter 2014)
Stage: Evaluation
• Round 3 (winter 2015 … and continuing)
Stage: Data collection
Pilot project in 2012/2013 (Round 1)
• 2 academics (mathematics and civil engineering)
• Faculty funded 3 summer scholarships for third/fourth year students
• 2 engineering students (civil and mechanical), 3 animation students
• Students provided with tablet PCs, headsets, desk space, access to
academics, guidance
• Brief: “show first years how maths is relevant”
Production outcomes (Round 1)
• Students produced two animations
• One on the mathematics to construct a high-rise building
Production outcomes (Round 1)
• Students produced two animations
• One on the mathematics to construct a high-rise building
Production outcomes (Round 1)
• Students produced two animations
• One on the mathematics to construct a high-rise building
• The other on how to improve the aerodynamics of a car
Data collected
• Several interviews of project students in 2012/2013
• Focus group of first year students enrolled in Engineering
Mathematics 1 in 2013
Evaluation
1. How did the engineering students approach their brief and how did
they collaborate?
2. How did their thoughts evolve following interaction with the multimedia students and how did they collaborate with the multi-media
students?
Loch and Lamborn, 2014
1. How did the engineering students approach
their brief and how did they collaborate?
• Very close collaboration
• Identified topics they had studied in first year (common start)
• Identified their own strengths (disciplines)
• They each focused on a theme in their discipline
• Plan: lots of short animations that can be combined into one long
animation
2. How did their thoughts evolve following interaction with the
animation students and how did they collaborate with the
animation students?
• Storyboards. Animations.
“they think of it in terms as a story, which we didn’t. We just thought
we’ll produce something that’s catchy.”
• Focus moved from content to also include presentation
• One animation for each theme
• Animation students mostly worked off campus, came in when needed
Evaluation
1. How would students demonstrate the relevance of mathematics in
engineering?
2. What are first-year students’ views on the resources produced for
them?
3. Who should produce resources to demonstrate the relevance of
mathematics?
Loch and Lamborn, 2016
1.How would students demonstrate the
relevance of mathematics in engineering?
The engineers:
• “all the videos, [. . .] they were really just focusing on [. . .] academics
sitting there and just talking through things”.
• “old lecturers [. . .] give off really disengaging topics”
“A simple animation, hopefully demonstrates the relevance of maths
not in a complicated way, in a relatable method. It’s going to be
focused on different disciplines of engineering and above all going to
be fun and engaging.”
1.How would students demonstrate the
relevance of mathematics in engineering?
The animators:
“A short animation that takes you through a bit of a maths journey [. . .]
and kind of shows how mathematical concepts are used within practical
applications. So demonstrating mathematical applications.”
2. What are first-year students’ views on the
resources produced for them?
• “It makes you think ‘right okay vectors really do play a role in how and
when you design something’”
• “good” as they showed where mathematics is applied. At the same
time overwhelming because of the amount of mathematics shown.
• “too much happening in the videos”
• focus on one concept and explain it properly?
• Students wanted to be able to follow the mathematics
3. Who should produce resources to demonstrate
the relevance of mathematics?
• A combination of staff and students, but also involve a first year
student
• Staff to guide the students
• Animation students and engineering students both important
What do the students get out of this?
• Communication skills
• Civil engineer ↔ mechanical engineer
• Engineer ↔ multi media specialists
• Learning from each other
• Team work skills
• Delivering a project on time
• Quality control
• Something for their portfolios!
• The money helps
Round 2 (2014)
• 3 academics (mathematics, civil engineering and robotics)
• Winter break
• 6 scholarships funded through HEPPP (Higher Education Participation
and Partnerships Programme; Australian Government)
• 3 engineering students (biomedical and robotics/mechatronics) and 3
animation students
Production outcomes (Round 2)
4 shorter animations, covering
• Matrices (to rotate a robotic arm)
Production outcomes (Round 2)
4 shorter animations, covering
• Matrices (to rotate a robotic arm)
• Vectors (in ECGs)
Production outcomes (Round 2)
4 shorter animations, covering
• Matrices (to rotate a robotic arm)
• Vectors (in ECGs)
• Integration and Laplace Transforms (in cruise control)
Production outcomes (Round 2)
4 shorter animations, covering
•
•
•
•
Matrices (to rotate a robotic arm)
Vectors (in ECGs)
Integration and Laplace Transforms (in cruise control)
Differential equations (to calculate blood alcohol levels)
Data collected
• Several interviews of project students in 2014
• Series of surveys of first year students in 2015
• Focus groups of first year student(s) in 2015
Evaluation
1. Are the student-created resources effective in demonstrating the
relevance of otherwise abstract mathematical concepts?
2. What are the characteristics of a motivational multi-media teaching
tool?
Loch, Scott and Dunn, submitted
1. Are the student-created resources effective in demonstrating
the relevance of otherwise abstract mathematical concepts?
Survey in 2015 (Engineering Mathematics 1, 22 responses to first and last
survey)
• Videos are useful in explaining relevance of maths for future studies
(17/20) and future career (16/20)
“I had honestly never realized how matrices applied to practical work until I
saw this video. The other applications I could guess, but this was more of a
surprise to me”
• There should be videos covering all disciplines (16/21)
2. What are the characteristics of a motivational multimedia teaching tool?
• Animation they liked most:
• Designing the car (narrator humor, real life application, easily comprehendible)
• Robotic Arm (personal interest, relevant to field, well animated, explained what was
for the student a difficult concept)
• Videos best at explaining why maths taught in Eng Maths 1 is relevant to
studies: Robotic Arm and Constructing a Building
• Preference for shorter videos “less chance of zoning out”
• Preference for longer videos “more detailed explanation of the applications
of the mathematical concepts”; if of specific relevance to their degree
• Expectations of high quality resources
Evaluation (by the end of 2015)
• What aspects of the videos did the students find motivating
• Were students more motivated by videos that presented information
relevant to their discipline?
• Did the videos assist the students to see the relevance of first year
mathematics to their future studies and their careers?
• Have students’ perceptions of the relevance of mathematics changed over
the semester?
• How have students’ perceptions of the relevance of mathematics changed?
• What factors have led to changes in student perceptions of the relevance
of mathematics?
Round 3 (2015)
•
•
•
•
•
•
•
Additional focus: the relevance of physics
5 academics (mathematics, 2x astronomy, 2x physics)
Winter break
HEPP funded (Higher Education Participation Programme)
11 scholarships: 5 engineers, 3 animators, 3 film students (postgrad)
Engineers include one female student and one first year student
Production (anticipated): 3 animations and one film
The relevance of physics
• Artificial heart
• Cellphones
• Computer games
The practice exam
Data collected so far
• Interviews of project students in 2015
• Film student interview in December
Where to from here?
• Videos used to advertise Swinburne Engineering programmes (and
multi-media programme)
• Videos shown in first year units
• Need to analyse all the data we have collected, including impact on
first year students to answer research questions
• There is lots of data from interviews of project students still to be
analysed
• Analysis of the videos?
• How should we use these resources?
• Multi-media colleagues have offered students from a project unit,
without need for scholarship
Accessing the animations
• http://commons.swin.edu.au/
-> enter as guest
-> search “relevance”
• All videos carry a Creative Commons licence, BY ND NC
Acknowledgements
Teams of academics:
• Round 1: Julia Lamborn (civil engineering)
• Round 2: Julia Lamborn (civil engineering) and Michelle Dunn (robotics)
• Round 3: Virginia Kilborn (astronomy), Chris Fluke (astronomy), Brenton Hall
(physics) and Wayne Rowlands (physics)
Teams of students:
• Round 1: Josh Gallo, Daniel French, Beck Dare, Louis Bergemann and John Sipidias
• Round 2: Tiran Fernando, Michelle Bravo, Scott Fraser, Aaron Vanston, Kiersten
Casey, Marnie Edgar
• Round 3: Elizabeth Wain, Irvin Wong, Duc Phan, Thanh Vo, Suresh Kumar,
Rhiannon Bentley, Damien Rogers, David Majman, Giuseppe Pantaleo, Jose
Sanchez, Ali Bahrami
References
• Pennell S, Avitabile P, White JR. An interdisciplinary, multisemester project relating differential equations and engineering.
Portland (OR); 2005.
• Flegg J, Mallet D, Lupton M. Students’ perceptions of the relevance of mathematics in engineering. Int J Math Educ Sci
Technol. 2012;43(6):717–732.
• Coupland M, Gardner A, Carmody G. Mathematics for engineering education: what students say. In: 31st Annual
Conference of theMathematics Education Research Group of Australasia; Brisbane; 2008.
• Froyd J, Ohland M. Integrated engineering curricula. J Eng Educ. 2005:147–164.
• Mustoe L, Croft A. Motivating engineering students by using modern case studies. Int J Eng Educ. 1999;15(6):469–476.
• Allen MR,Wilson DA. Making mathematics relevant to engineering students. In: Proceedings of the 120th ASEE Annual
Conference and Exposition; 2013 June 23–26; Atlanta (GA); 2013.
• Croft, T., Duah, F. & Loch, B. (2013). ‘I’m worried about the correctness’: undergraduate students as producers of
screencasts of mathematical explanations for their peers – lecturer and student perceptions. International Journal of
Mathematical Education in Science and Technology.
• Loch & Lamborn (2014). A preliminary investigation of student collaboration to create resources that motivate the
relevance of mathematics to first year engineers. Proceedings of AAEE 2014 (Australasian Association of Engineering
Education), Wellington.
• Loch & Lamborn (2016). How to make mathematics relevant to first-year engineering students: perceptions of students on
student produced resources. International Journal of Mathematical Education in Science and Technology
• Loch, Scott and Dunn (submitted). A preliminary analysis of the effectiveness of student-produced videos on the relevance
of mathematics in engineering. ICME 2016, Hamburg.