capturing undergraduate learning an ako aotearoa/tlri project bill barton, judy paterson, greg...

Capturing Undergraduate Learning

An Ako Aotearoa/TLRI ProjectBill Barton, Judy Paterson,Greg Oates, Caroline Yoon

The team consists of 31 people, mostly from this department, and the funding body.

We share the assumption that things can be improved. Indeed, we share an assumption of continual, rational development.

The idea behind the Project #1

Think for a moment what you would do to enhance students’

undergraduate mathematics experience.

How would you improve undergraduate learning?

How would you know that an improvement had taken place?

In this project we areturning our attentionto learning ata classlevel.

We want to understand how the way we deliver a course affects the student learning that results.


Yes, we do believe that we can significantly enhance learning in an undergraduate mathematics degree.

Sources of this belief are:(i) research knowledge1

(ii) the questioning of the dominance of traditional lecturing2

(iii) our observations of the conservative response to the changing educational environment (technology3a, student body3b, economic pressures3c).1. D Holton (Ed.) (2002) The Teaching & Learning of Mathematics at University Level. The 11 th ICMI Study. Kluwer Academic Pubs.2. A Ryan (2012) Massive Black Mirror. Times Higher Education, 4 October, 2012.3a. This Department3b. E. Anderson (2003) Changing US Demographics and American Higher Education, New Directions for Higher Education, No. 121 3c. The assumption that lecturing to larger audiences is the only way to increase student/staff ratios.


But we do not believe in change for change’s sake.

So, we want to establish a rational basis for the improvement of undergraduate teaching.That is the main idea behind the project.

We aim to develop a way to know how a course contributes to the desired learning outcomes for undergraduate mathematics.

Only if we can do this do we have a reason for changing the way we do things now.


NOTE:

We do not expect that this research will result in fundamental change to all courses, or, say, the demise of lecturing.

Rather, we expect that we will obtain evidence that different types of courses contribute to student learning in different ways, and therefore the department might decide to arrange things so that students have a range of opportunities to meet the learning expectations of lecturers and employers.


Developing a Course Learning Profile -1. Identify the broad spectrum of desired learning outcomes2. Find ways to observe these learning outcomes3. Analyse and report learning outcomes for courses as a Course

Learning Profile (CLP)

Course Innovations4. Team-based learning5. Intensive Technology6. Low lecture

Project Extensions 1. Canterbury & Victoria Mathematics & Statistics Departments2. Law, English, Psychology and Dance at Auckland

Components of the Project

Developing a Course Learning Profile -1. Identify the broad spectrum of desired

learning outcomes2. Find ways to observe these learning

outcomes3. Analyse and report learning outcomes for

courses as a Course Learning Profile (CLP)

Main Component of the Project

Our first task is to identify, and categorise, ALL the learning outcomes desired in an undergraduate mathematics course.

1. Those desired by the lecturers of the course2. Those desired by lecturers of subsequent and graduate courses3. Those desired by the university in Graduate Profiles4. Those desired by employers of mathematics graduates

For Example

5. Mathematical content6. Mathematical skills7. Mathematical processes8. Mathematical habits9. Attitudes towards mathematics10. Mathematical communication11. General thinking and learning behaviours12. ……. ????

Developing a Course Learning Profile

1. Mathematical content—examinations, assignments

2. Mathematical skills—examinations, assignments

3. Mathematical processes—observation in tutorials? specially designed tasks?

4. Mathematical habits—observations? self-report?

5. Attitudes towards mathematics—surveys

6. Mathematical communication—observations in tutorials? assignments?

7. General thinking and learning behaviours—self-report? class participation observations?

8. ……. ???? ????

Observing & Reporting Learning Outcomes


Other Components of the Project

1. Shifts responsibility towards the students.2. Provides feedback to students and lecturers.3. Uses some lecture time for students to work in teams on

tasks that apply ideas and concepts.4. Allocates students to teams as fairly as possible for the

duration of the course

This approach is used in Maths 326

See www.teambasedlearning.org/

A Team-Based Learning model of delivery:

The students do a multiple choice test on the pre-reading.They then do the same test in their team.

How?

The Readiness Assurance Process (RAP)

IF-AT scratch and win score cards

Immediate feedback for students

… the instant feedback makes sense - to learn from our mistakes and adapt to our environment this kind of testing is far more beneficial than a number out of 10 you receive a week later.

Feedback to lecturers

Feedback is most powerful when it is from the student to the teacher. When teachers are open to feedback from students, then teaching and learning can be synchronized and powerful. Feedback to teachers helps make learning visible. (Hattie 2009)

Hattie J (2009) Visible Learning; a synthesis of over 800 meta-analyses relating to achievement London; Routledge

• Business as usual for much of the course

• What to do with the lecture time we saved?

• Take a holiday?

• Students do tasks in teams – apply ideas• What sort of tasks have proved successful?

Example of a Maths 326 task – the team hands in one A4 sheet.

• A parliament with 99 seats has three parties, A, B and C. Laws can be passed by a coalition of parties with at least 50 seats.

• The largest party, C, splits into two factions. Investigate what happens to the power of the parties when party C splits into two smaller parties.

• You might ask these or other questions about the shifts in power when a party splits:

–Will the power of the two factions add to the pre-split power of Party C?–Can a dummy player gain power because of

the split?–How much shifting in power can occur?A good solution to this task will ask and answer further questions about the effects of the split of Party C.

What sorts of things do we want to take a long, hard look at?

• What sort of questions do we hear students ask as they work? Are they good questions?

• What evidence can we find of mathematical behaviour that we value – “I wish my students would……”

• I am sure they are behaving more like mathematicians but how can I convince other people that it is happening?

Course Innovations1. Team-based learning2. Intensive Technology 3. Low lecture


• We are talking about “Effective” use of technology, not indiscriminate use;

• Its here, and its use is growing rapidly – we cannot ignore it if wish to prepare our students for mathematics in a modern age;

• TSG 13: ICME-12: Teaching & Learning of Calculus - 17 presentations (12 countries); Technology was a major theme, even though two large Technology-specific TSG’s

Intensive Technology Innovation

Ponce-Campuzano & Rivera-Figuero (Delta 2011):

Value of CAS (various technologies) to reveal particular aspects, especially when considering domains of anti-derivatives, where CAS may provide inconsistencies and alternatives to by-hand solutions.

Compared the solutions provided by a variety of CAS-software (Derive 6.0, Scientific Work Place 5.5, Mathematica 8.0, Wolfram Alpha) when used to compute antiderivatives of functions.

The many examples where different CAS-technologies and by-hand computations yield different results are very interesting.

Tasks & Assessment: DefinitionsTechnology Trivial: 1999 Maths 102

Can still ask such questions in the skills tests for skills deemed necessary.

Technology Neutral: 2007 Maths 108

)( find , 13

52)( If xf

x

xxf

Technology Neutral……Thomas & Klymchuk (Delta 2011)

Sketch the graph of a function f(x) such that it is continuous on and

Does

,53 and30 xx .3,50for0)( xxxf

function?your for exist )(lim 3 xfx

Technology Active (CAS-positive)Lin & Thomas – Proceedings of Delta 2011.

Technology can help from an exploratory perspective, which will help understanding, but it will not answer the question directly.This is neither a technology neutral or technology trivial question.

2. Find the derivative of the function: 4)3sin(2ln xy

Technology Active – more examplesThomas & Klymchuk (Delta 2011)

1. If find the possible values of a. a

dxx0

2)12(

3. Find the derivative of the function:

1

1

1dx

x

Tobin & Weiss (Delta 2011): Use of CAS in differential equations in course examinations, ways of posing

questions to be CAS-active.Question 1Solve for y as a function of x

This question involves solving a first order separable differential equation which can be trivially done with just one command using CAS.

Question 1AShow that the following DE is separable and hence or otherwise solve for y as a function of x. This allows the testing of separability and still gives a chance for an answer to be found or checked by CAS, using an appropriate marking schedule.

422 xyxydx

dy

422 xyxydx

dy

“Activating” technology trivial questions

This can be quite time-consuming if you have a data-base of existing questions, and can take a while adjusting. However, it becomes easier & you gradually build up a new database.

Example: Standard definite integration problems:

Find What might we do to transform such a question?

Consider:

If Still trivial?

How about:

Often, technology-positive questions are more conceptually difficult than the standard skills-style questions we may have posed in the past;

7

2

2 )23( dxxx

7

2

7

2 )4( find,20)( dxfxdxfx

b

a

b

adxfxcdxfx )4( find,)(

The three key ideas behind this innovation are that:

(i) lectures are not the best means of imparting information or developing skills, although they are useful for overviews, “colour”, and modelling;

(ii) the best learning takes place when students are themselves engaged, both individually and together;

(iii) responsibility for content and skills learning will be handed back to students using print and web resources, but with the means for self- and lecturer-monitoring of progress.

Low Lecture Innovation

A voluntary stream (max 32 students) of MATHS 108 will be established in Semester 2, 2013, taught by the research team as extra to load.

One lecture per week. Five Engagement Sessions of 2hrs plus pre- and post-work. These substitute assignments. Tutorials, tests, exam all the same.

Significant on-line resources and monitoring systems.

Low Lecture Innovation

Timelines

Nov/Dec2012

Summer2013

Sem 12013

Sem 22013

Summer2014

Sem 1 2014

Sem 22014

Summer2015

Identifying Learning Outcomes

Observing Learning Outcomes

Analysing & Reporting Outcomes

DevelopingInnovative Courses

Teaching & Observing Courses

Investigating Learning In Undergraduate Mathematics

ILIUM

Learning in Undergraduate Mathematics and Other Subjects(or Operationalising the Spectrum)

LUMOS

CLUMSY

PLUMP

Capturing Learning in Undergraduate Mathematics Spectrum

Profiling Learning in Undergraduate Mathematics Project

MULLETMathematics Undergraduate Learning Lectures Engagement Technology

CALCIUMCApturing Learning Concepts In Undergraduate Mathematics

LearningUndergraduateMathematicsCapturingProfileLow LecturesTechnologyTeam Based LearningProjectInvestigatingResearchSpectrum

Send entries to Caroline ([email protected]) by midday 29th November

mailto:[email protected]

Thank you for your attention … … and your future assistance.

Bill, Judy, Mike, Greg, Caroline,Louise, Fiona, and Barbara

and 23 others.

capturing undergraduate learning an ako aotearoa/tlri project bill barton, judy paterson, greg...

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