Queensland University of Technology

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The multi-layered challenges of teaching statistics in engineering courses : 

The multi-layered challenges of teaching statistics in engineering courses Queensland University of Technology Helen MacGillivray School of Mathematical Sciences, QUT Director, QUT Maths Access Centre Visiting Fellow, CETL, Loughborough University Carrick Senior Fellow, 2007 President-elect, IASE (International Association for Statistics Education)

Statistics: data analysis, random variables, stochastic processes, probability, statistical modelling and processes, inference, time series, reliability, multivariate, SPC, ……- everywhere in modern engineering -workplaces, applications, research : 

Statistics: data analysis, random variables, stochastic processes, probability, statistical modelling and processes, inference, time series, reliability, multivariate, SPC, ……- everywhere in modern engineering -workplaces, applications, research traffic project management communications construction hydrology mechanical tribology manufacturing avionics computer systems mining medical engineering power chemical engineering environmental engineering signal processing digital systems software engineering electronics maintenaince infomechatronics All use different aspects of statistics, often adapted, idiosyncratic or heuristically developed

Maths : 

Maths Mathematical thinking is lifeblood of engineering engineering needs the most technical maths faster than any other discipline and engineering needs the most maths generic skills faster than any other discipline Generally there is little understanding of Roles in developing generic skills Time needed & lag Long term effects from middle school Maths is like language Specific & generic skills become part of person People forget how they acquired such skills Transferability needs more than specifics required Maths fitness is like physical fitness Underpins development of field-specific skills Necessary but not sufficient for excellence in specific fields

Statistics in engineering - recent - explosive - can be idiosyncratic : 

Statistics in engineering - recent - explosive - can be idiosyncratic In engineering work & applications little coherent background can be piecemeal pertinent to particular areas techniques grown within narrow fields dominated by specific frames of reference often jargonised For engineering students full of new concepts & new ways of thinking not straight calculus/algebra but any needed must be at fingertips mathematical thinking but not deterministic

Challenges for teaching statistics into engineering : 

Challenges for teaching statistics into engineering Usually have maximum of a 1-semester unit Usually post-first year Still foundation material Lost link with school Engineering applications too difficult Balance of concepts, maths, contexts, development Coherence & motivation - not problem immersion Avoid disadvantage compared with other graduates Foundation for the specific & idiosyncratic Foundation for future development Choice of content Synthesis

Outline of structure & pedagogical approach : 

Outline of structure & pedagogical approach Statistical data investigations & analysis Can be done in 6-7 weeks Needed by all for Foundational statistical thinking & techniques Workplaces alongside other graduates Introduction to random variables & distributional modelling Including linear combinations of correlated variables & intro reliability Can be done in 3 weeks Needed for all engineering Plus Probability & risk analysis or Probability & intro stochastic processes or New (exciting) idea of intro numerical techniques in estimation

Statistical data investigations & analysis Structure, examples & learning experiences built around real data investigations from first ideas to report : 

Statistical data investigations & analysis Structure, examples & learning experiences built around real data investigations from first ideas to report Content Planning, collecting, handling, graphing, summarising, commenting on …. data Categorical data – chisq tests; principles of testing hypotheses; p-values Revision of normal; standard errors; confidence intervals and tests for 1 & 2 means, proportions, variances. Tolerance intervals ANOVA & exp’tal design (via software): interaction, multiple comparisons, checking assumptions. Unbalanced data Multiple & polynomial regression (via software): interpretation, diagnostics, re-fitting Assessment quiz-style assignments for managed learning. Side-effect of debate instead of copying own-choice group project: plan, carry out, analyse & report a data investigation (as for all engineering programs since 1995) * More on this to follow end sem exam questions as for assignments

Introductory random variables & distributional modelling focus is on learning by doing & on problem-solving : 

Introductory random variables & distributional modelling focus is on learning by doing & on problem-solving Random variables & distributions; some special distributions incl. binomial, Poisson, exponential. Identify RV, situation, distribution Correlation; linear combinations of normals. Problem-solving Introduction to reliability: MTTF, Weibull, censored data, estimating reliability, MTTF & fitting Weibull Some comments: As in data analysis, minimalist probability. Probability must be purposeful! Decline in mathematical skills of those without advanced maths from school starting to affect above e.g. in 2007 concepts for continuous distributions hampered Problem-solving skills Generic skills cannot be taught in the abstract: “generic skills are what you learn when you’re learning something else” Student comment on problem involving total demand on electrical network across regions with correlations over neighbouring regions “Great problem – no idea what to use”

Project in data analysis Planning, collecting, analysing & reporting a data investigation in context of group choice : 

Project in data analysis Planning, collecting, analysing & reporting a data investigation in context of group choice Phases of statistical data analysis (Gal & Garfield, 1998) tools and building blocks of procedures, concepts and skills synthesis of choosing, using, interpreting and discussing in whole data investigations Project is parallel activity to structured well-signposted course built around data investigations, developed through examples, many now extracted from past projects Not problem immersion: has its place but can work against coherence and linking Not case studies: have their place but can impose context on learning and can inhibit transference Group because task needs group

Evolution of free-choice group project in data analysis : 

Evolution of free-choice group project in data analysis Trialed in first year maths course in 1993 and in 1994 in engineering statistics with >400 students Initial emphasis on practical challenges of data collection/observation and exploration Key concept was that the group chose their own context, identifying what was of interest to them, what data was accessible, and how to collect it But in engineering, because the students “owned” it, they wanted to try the statistical tools as, or even before, they met them. Grew to include analysis, interpretation & reporting Principle & strategy now well-established across many courses Project enables students to consolidate, link, synthesize, understand, familiarise basics and some to go further integrates statistical thinking and tools, including computing, and communication skills

Comments on contexts : 

Comments on contexts Ownership of context does not necessarily mean context of students’ discipline Students are not yet what they are studying to be! To introduce statistical concepts within contexts in other disciplines, students MUST be comfortable in those contexts. Human curiosity Egg strengths Crash testing stubbies

Practicalities : 

Practicalities Groups formed by students website forum + staff help is provided as needed Choice of context: principle is they suggest & we respond By week 6 each group submits brief plan (by email) of the what and how of their data collection Plan for staff feedback and advice, including optimal approach for students & control of student workload. Plan NOT part of assessment Find we need to emphasize in plan identify variables and subjects & collection practicalities can describe original motivation but don’t speculate or over-hypothesize

Have learnt that we need to…… : 

Have learnt that we need to…… Counter belief in single experiment/hypothesis - “scientific method” Emphasize explore, investigate, use data Emphasize project is about CHOOSING AND USING appropriate techniques Emphasize that finding “nothing” just as important as finding “something” Emphasize identify variables, what type, & observations are per what? That is, PLAN spreadsheet/worksheet Types of variables choice of procedures Say to keep original data and order Help different cultures understand “investigation” & “analysis”

Evidence of success : 

Evidence of success “Successful” = “successful learning” choices of topics illustrate types of examples in which students want to see how statistical thinking and techniques can help increased student engagement and learning qualitative feedback from students quantitative measures e.g. exam results past students remember their projects - as do staff peer adoption - despite perception of work involved.

Student choices: nearly 2000 projects!Some titles from 2002- 2007. For pre-2002, see MacGillivray, H.L. (2002) One thousand projects MSOR Connections 2(1), 9-13 : 

Student choices: nearly 2000 projects!Some titles from 2002- 2007. For pre-2002, see MacGillivray, H.L. (2002) One thousand projects MSOR Connections 2(1), 9-13 Goodwill Bridge (a controversial pedestrian/cycle bridge completed 2002) The three minute pop song Length of corporate employee phone calls 24 hours in a service station Undie-lemma Aircraft noise levels Go go go! Internet load times Qld College of Art café sales data Exchange rates The big news about breakfast Observational study of vending machines Search engine analysis Driving behaviour and passenger trends Ceramic crush strength Accuracy of dart throws The mean journey – buses between a suburban bus station and the city Volume of MP3 players

Assessment “package” : 

Assessment “package” The projects are learning experiences, not consulting jobs Assessment requires statistical expertise, experience, concentration, reading skills, and commenting against criteria …. but use of criteria and interaction during semester can mark 3-4 an hour Because project includes judgement, choice of procedures, synthesis of operational knowledge, problem-tackling, teamwork, reporting,……. other assessment can be shorter, with formative and summative focussing on key concepts/knowledge for example, quiz-styles: fill-in-gaps, short responses

Effects on students : 

Effects on students Engagement, ownership, synthesis, learning vehicle, improved overall results Poorer students can “get somewhere” & feel more empowered Helps students missing sections due to illness, family or work problems, to catch up Better students find challenges & tend to extend by themselves (e.g. multi-factors, transformations, gen lin model) Helping groups in pracs at analysis stage They see us “play with data” & use investigative analysis. Some quotes: “You really like this stuff don’t you” “Hey look at that” “That’s magic!” They see importance & power of considering lots of variables together t-tests the bane of research in other disciplines!

Effects on teaching & course structure - lessons from student projects! : 

Effects on teaching & course structure - lessons from student projects! Types of variables key to analysis; course built on this Early introduction of concepts of testing & p-values through chisq test with categorical data – after graphs, summaries & types of data. Improvement in student comfort dramatic! Coherence & continuity. Minimalist approach to probability Explicit teaching of tolerance intervals to help avoid most common student problem with confidence intervals Use of many-variabled datasets even for simple procedures Emphasis on investigate & analyse, not on single questions

Conclusion : 

Conclusion For a teaching & learning package that is integrated, balanced, developmental, purposeful, with structured facilitation of student learning across the student diversity Need to develop sound knowledge of students’ past, present & future learning translate from engineering contexts into foundation for students identify & articulate objectives & align with assessment observe, reflect, analyse, develop provide evidence & understanding counter dogma within & without communicate, collaborate & cooperate accept time & space

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