Mathematical Modeling and Problem Solving Symposium • Weetwood Hall, Leeds • July 15th, 2013 Applications and modeling in undergraduate Materials Engineering Paul Hernandez-Martinez
BACKGROUND • Second year module on Mathematics for Materials Engineering in which many students are mathematically weak and in general, disinterested in Mathematics (neither important nor relevant). Excessively exam-oriented (“tell me how, not why”). • Developmental teaching project seeking to raise conceptual understanding (or at least some procedural flexibility).
BACKGROUND • Abundant research about mathematical modeling to motivate, engage and enthuse deep learning. The literature emphasisesauthenticity as the main motivator for learning(authentic, real, practical/useful, should have developmental consequences). Williams and Goos 2013: “We must not ignore the wider social context which also mediates change in educational technology, and which so often has provided the key obstacles to progress” • Two student interns were employed during the summer to develop authentic modeling teaching resources. One was a Materials engineering student and one was a mathematics student.
RESULTS Give your thoughts on the modelling problems Why do students feel that understanding and achieving does not go together? • Useful to see the maths in real world scenarios, relevant to the course. • Good but sometimes at loss how to start them. It would be helpful to have model solutions and feedback. • Useful but we have so much assessed work there isn't time to hand them in. • The modelling problems feel are poor, I would rather practise questions from past exams
RESULTS • There was limited success: even though some students liked the practical side of the module, most did not take the modeling activities seriously (not even with the assessed coursework) – too much emphasis on being strategic (waste of time – not used to work in groups), many other (“more important”) things in their personal and academic life. Motivation/engagement did not change – how to achieve authenticity? • Most did well in the coursework – half the groups did attempt the harder questions with some success. • In the final exam, very few showed any conceptual understanding or even procedural knowledge.
DEVELOPMENTAL WORK/WAY FORWARD • Institutional constraints have to be addressed. The department has got a bunch of resources but they are not modelling, they are sort of… you know… using the maths, is like applied maths. It was interesting and it was good to see them because you kind of know where the department is coming from, but I don’t think the department has good… I don’t think the department is focused on the maths itself because a lot of the lecturers ehmm… I think don’t feel that the maths is important except from (lecturer’s name) and a few others, I don’t think they feel that the maths is relevant.
DEVELOPMENTAL WORK/WAY FORWARD • Educational culture of performativity, not just at school but also at university – great part of pedagogical (including assessment) practices in HE, particularly in mathematics, are highly transmissionist and procedural in nature. • We should ask: is mathematics at university really useful for engineering (or STE)? What is the value of mathematics?
DEVELOPMENTAL WORK/WAY FORWARD • The work of the student interns showed that: • It is possible to establish genuine dialogue where cooperation leads to learning and personal development. • Struggle, engagement, persistence were supported by a sense of responsibility for the success of the task. I’ve never done modelling before so I was learning all the way through so I was making a lot of mistakes, I was having to go back and change things again and again. (If modelling was to be introduced in the syllabus) I think this would translate over not just to maths but to their other modules as well because they would actually think about all the other things they’re doing.
DEVELOPMENTAL WORK/WAY FORWARD • The challenge for future work is how to create a “culture of responsibility”, where spaces for genuine cooperation and learning can be opened ? What institutional changes should happen in order for this to take place? • Next semester: • A more “dialogic” pedagogy – emphasis on the responsibility of (individual and group) understanding/meaning-making through peer/lecturer interaction/explaining – a consensus rather than an imposition. • More than an emphasis on “utility” of maths, the focus is on developing work/life skills.