Computer-based practicals on datasets from past student projects
Worksheets with full solutions
Fortnightly quizzes of fill-in-gaps & short response type; out Sunday, in by Friday: best 5 out of 6 contribute 10%
Workfolder containing their ongoing work on the worksheets and their marked (collected) quizzes: 3%
Whole semester group project in planning, collecting, analysing & reporting data investigation in context of group choice: 20%
In-semester test (similar to quizzes 1-4): 10%
End of semester exam (similar to quizzes 1-6, more on 5, 6): 57% *
Quizzes, test, exam: exemplars + exemplar processes Quizzes & test formative & summative; exam summative Assistance given for quizzes – most important aspect is DOING them
*For a few years also an optional essay on how statistics revolutionised science in the 20th century: 10% if improved overall result. Dropped because (i) almost never improved result (ii) attracted students who could least afford the time. Objective not worth student & staff effort
Research on numeracy/maths & statistical reasoning of cohort
Numeracy/maths on entry: highly diverse – see Wilson & MacGillivray Counting on the basics: mathematical skills amongst tertiary entrants, (2007) IJMest 38(1), 19-41
General statistical reasoning on entry: Wilson and MacGillivray, Numeracy and statistical reasoning on entering university, 7th International Conference on Teaching Statistics (2006) http://www.stat.auckland.ac.nz/~iase/publications/17/C136.pdf
Numeracy & level of maths stood out as most important predictors of general statistical reasoning
Fish question greatest discriminator between core & advanced maths preparation
A farmer wants to know how many fish are in his dam. He took out 200 fish and tagged each of them. He put the tagged fish back in the dam and let them get mixed with the others. On the second day, he took out 250 fish in a random manner, and found that 25 of them were tagged. Estimate how many fish are in the dam.
Own choice group project
Teaches & assesses data investigation & synthesis of procedure choice & interpretation
Other assessment can focus on operational knowledge & skills - tools & building blocks of procedures, concepts and procedural skills
Group because task needs a group
Guidelines & descriptors of 3 criteria with standards given (MacGillivray, Criteria, standards and assessment in statistical education, Proceedings International Statistical Institute, 55th Session, 2005)
Feedback on proposal + ongoing help; they propose – we advise
Use of past datasets in class demonstrations and practicals
Access to past projects, including assessments, and model reports
Each group receives a written assessment report with comments & marks for the 3 criteria
Each topic has preliminary experiences or exercises or discussion points (development completed 2005)
prior knowledge, foundations & seeds
perceive, unpack, analyse, extend
“Using what we already knew to learn other stuff was really good and helped us learn other stuff” A student definition of constructivism perhaps?
Formative/summative & summative components: all oriented to problem-solving
Four assignments based on class activities, examples and worksheets, with problems in authentic contexts 20% before 2006; 16% in 2006 (Assistance available. Collaboration – yes; straight copying rare)
Group project. 2 everyday processes that could be Poisson (free choice); data collected; Poisson-ness investigated by combination of tests and graphs 10%.
End of semester exam. Problem-solving based on activities, worksheets, assignments; ranging from simple to slightly complex in life-related authentic contexts. Students design & bring in own summaries (4 A4 pages) 70% before 2006; 66% in 2006
Some examples from group projects
Australian Rules (football) grand final
Time spent on phone
Pedestrian traffic in mall
Time to be served icecream
Occurrences of “Harry” per page in a Harry Potter book
Traffic on a pedestrian bridge
Distribution of leaves on tiles
Behaviour of ants
Arrivals & service at library
Distances between coffee shops
Service in “fast” supermarket checkout
Time between customers wearing high heels.
Time between changes of a baby’s nappy
New assessment component in a problem-solving environment
Problem-solving environment Gal et al (1997)
“an emotionally and cognitively supportive atmosphere where students feel safe to explore, comfortable with temporary confusion, belief in their ability and motivation to navigate stages.”
Formative assessment & assignments designed for managed optimal learning but students needed greater persuasion to learn through trying (’ave a go ….)
Some topics identified as most needful of immediate involvement of students in active problem-tackling in an environment that maximises engagement & learning
Tutorial group exercises, 2006
4 practicals structured for immediate “hands-on” learning.
Groups allocated; different groups for each practical.
No compulsion to complete exercise; credit for participation.
Assistance available as required.
Full collaborative work required, with groups ensuring that explanations were shared within the group.
Participation in each of these four special tutorials contributed 2% to the overall assessment.
Evaluation of new component
Tutors and students voted experiment success.
The tutorials were buzzing, and early departures were practically non-existent.
Student opinion was that four was the ideal number.
Other tutorials benefited significantly.
Assignments provide exemplars for exams
Data support that assignments most important in predicting exam (as desired!)
In 2005, assignments score depended on group project & PRQ score
2nd year linear algebra unit maths+others e.g. maths educ, physics, eng – approx 80-90
Mixed student cohorts with often bimodal results
Balance of theory and practice?
Some changes in continuous assessment – did they help or impede student learning?
Challenge of student engagement
Interface of first and second level courses
first level courses respond to school/tertiary interface
first year units – which are best predictors?
The examples and learning experiences in unit are motivated by higher level needs in mathematics generally & particularly computational mathematics, & by applications based on experience with industry problems.
Assessment package, 2003 & 2005
21% continuous assessment
3 Maple group assignments totalling 21%
mid-semester exam 15%
final examination 64%.
Lecturer’s observations plus feedback:
Maple group assignments too heavy for 7%
Students needed more structured help with their learning
40% continuous assessment
2 Maple group assignments totalling 24%
3 “homework” quizzes totalling 16%
final examination 60%. Similar in style, format and level to 2003
Analysis of data: assessment components
For both continuous assessment programs, a test-type component and a Maple group assignment component combined as best predictors of exam
Exam has applications but no actual Maple use, providing support of the claims in the literature, that both theory and practice contribute to overall learning and understanding in linear algebra
Reassurance that the change in the continuous assessment program is not detrimental to performance, and appears to assist in learning
Lecturer’s concerns about high marks in the 2005 continuous assessment program are reflected by only 25% of the variation in exam marks being explained
but the challenge of how to grade the continuous assessment can be tackled with confidence in the program’s facilitation of student learning across the theory and practice components of the unit
Analysis of data: 1st year predictors
1st level calculus unit and
1st level introductory linear systems and analysis unit, with the brief synopsis
linear systems and matrices; vector algebra; coordinate systems; introduction to abstract algebraic systems; complex numbers; first and second order differential equations.
Entry to 1st yr units via advanced mathematics in senior school or equivalent 1st yr unit.
Alternative prerequisites 1st yr engineering maths
Other compulsory 1st year units for maths degree are an introductory unit in computational mathematics, Statistical Data Analysis 1 & Statistical Modelling 1.
Analysis of data: 1st year predictors
Data are complex because of different pathways. But best single predictor amongst 1st yr units, of performance in 2nd yr linear algebra in 2003 & 2005* was Statistical Modelling 1.
Synthesis of techniques and problem-tackling with new contexts, theory and applications appears to be the common thread linking these unlikely partners
* Note: changes in the 1st year units since then have probably changed this
2nd year engineering maths unit all engineering programs - approx 450-520
Unit “new” in 2007 but composed of sections common across previous engineering units
Content in 2007:
Statistical data investigations & analysis (1/2 unit)
As in Statistical data analysis 1; as given in all eng programs since 1994
Introductory numerical analysis (1/4 unit)
Introduction to random variables & distributional modelling, including linear combinations of normals, goodness-of-fit & introduction to reliability (1/4 unit)
Level of unit
First year work in Science and Maths
Statistical data analysis 1
Numerical component extract from 1st yr unit
Intro rv’s & distributions extract from Statistical Modelling 1
It’s not straight calculus/algebra & any of these that are needed must be at fingertips in new contexts because of amount of material
The statistics (both parts) full of new concepts & new ways of thinking
‘tis always thus in Australian eng courses
of the philosophy of Australian eng courses (whether new, old or middling)
engineering needs the most technical maths faster than any other discipline
engineering needs the most maths generic skills faster than any other discipline
Advantages of stats being in 2nd year eng are….
they’re 2nd years in some ways & they have better maths thinking than most other disciplines
they start reflecting on their studies (I’ve been listening to & observing 2nd (or 3rd) year eng students for over 30 years)
Disadvantages of stats being 2nd or 3rd year eng are….
they think they’re 2nd years in every way
it’s stats & they’re eng students
many tend to think it’s less important than other units
Learning & assessment package focus is on learning by doing
Computer-based practicals on datasets from past student projects
Weeks 1-6 on statistical data analysis
Worksheets with full solutions
For all sections: 15 worksheets in total
Stats (¾): five quizzes of fill-in-gaps & short response type 14%
Whole semester group project in planning, collecting, analysing & reporting data investigation in context of group choice 20%
As for all eng since 1995 & as in Stat data Analysis 1
Numerical analysis (¼ ): assignment 6%
End of semester exam (based on quizzes & w’sheets): 60%
Quizzes, project & assignment formative & summative Assistance given for quizzes – most important aspect is DOING themExam summative
Assessment data: stats quizzes
Stats quizzes designed for efficient & effective learning.
Evidence of value over years & units.
Plot good – why?
Strategy introduced late ’90’s in an MBA ½ unit with highly diverse cohort with FT jobs. Then developed further in eng unit when data analysis became a ½ –unit module; strategy used to decrease time demands so as to keep the full project.
Unexpected & amazing side effect in eng unit was drastic reduction in copying. Students still worked together but argued/explained instead of copying. Similar effects observed in Statistical Data Analysis 1.
Assessment data: stats project
Project teaches & assesses synthesis of planning, thinking, understanding, choice of procedures and interpreting output.
Practicals designed to provide learning for project as well as for unit content.
Engineering projects about same standard over past decade.
Areas of choices 2007:
Most popular was transport! 21% on some type or aspect of transport.
17% observational (usually on people); 16% experimental; 12% food/drink;
8% work or study related; 5% each on computing, media, sport, surveys; 3% each on house prices/rentals & on other prices/retail
Assessment data: numerical assignment, overall
Plot indicates problems – why?
Assessment data: data quests on exam vs data quizzes, project
2007: Relationship good – a bit too much variation
2002, elect engs: excellent relationship. Less variation, partly because half size of 2007 class
Consistent over years & units; relationship & variation as it should be. Some relationship but project assesses different objectives
Assessment data: num. quests exam vs num. assign; dist’n quests exam vs dist’n quiz
These two need consideration – why?
Too much collaboration: why?
Change in engineering course inequitable backgrounds
Assignment not difficult but long & detailed
Too much other assessment because of new eng faculty rule
The students seemed to be drowning in assessment in other units weeks 8-11. In weeks 10-12 they tried, with many valiantly doing last quiz. Many were glad to be able to do project weeks 12, 13, but had difficulty engaging with new work.
Conclusions: Assessment for learning
Each item/task/component has role in integrated, balanced, developmental, purposeful learning package
Learning objectives assessment
What is of value in this item/task/component?
How do we learn & assess this objective?
Structured for facilitation & management of student learning across the cohort diversity
What balance of formative/summative does this task have?
Is this task manageable & correctly weighted for purpose?
Are the purpose & criteria of task clear within package?
Do we know enough of students’ pasts, presents & futures?
Have we clearly communicated on collaborative & individual work?
Above assist in preventing plagiarism
And explore, analyse, interrogate & interpret DATA