Shedding light onundergraduatemathematics

Bill BartonThe University of Auckland

Research funded by Ako Aotearoa & Teaching and Learning Research Initiative (TLRI)

University of East Anglia, Mathematics Education Seminar20th May, 2013

LUMOS:

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The Output Spectrum

The first objective of LUMOS is to list and categorise all desired learning outcomes of undergraduate mathematics—at course and degree level.— Desired by whom ?— Categorised how ?

The Output Spectrum

Mathematical content

Mathematical skills

Mathematical processes

Mathematical modes

Affective outcomes

General outcomes

Observing Outputs

The second objective of LUMOS is to develop ways to observe those learning outcomes which we do not currently observe (at the course level).— Observe not measure— Practical instruments for large classes

Course Learning Profile

The third objective of LUMOS is to report on the learning outcome spectrum at course level.— We expect courses to be different from each other, not better or worse.— We visualise something like a DNA profile.

Innovative DeliveriesWe need significantly different course delivery modes so that we will know how well our observations discriminate between courses.

— Team-based learning mode

— Technology intensive

— Low lecture

Progress so far

We are in the first 6 months of a 2-year project.

We have been interviewing mathematics undergraduate lecturing staff about their desired learning outcomes.

We already have some results that appear interesting.

Content & Skills (vs) Processes & Modes

When pressed, very few of those I have interviewed will specify any particular content or skills as absolutely necessary.

They nearly all have strong views about mathematical processes or modes that they regard as essential for undergraduates.

This coincides with an earlier project.

A liking for mathematics

I expected that lecturers would be hoping that their students would continue to, or increase, their liking for mathematics.

But no, they regard “liking” as irrelevant.

Although most have affective desired outcomes: “interest in”, “respect for”, “advocacy of”, “appreciation for”.

Hmmm ?

“The Gap”

Many lecturers speak about desired behaviours when a student is faced with a problem. For example, to be able to break it down, find the tools needed, teach oneself some necessary mathematics. They also talk about the confidence to do this….

….but no-one mentions the DESIRE to do this.

Knowing when you do not know

An oft-repeated theme is ignorance.

Far from abhorring or being intolerant of ignorance, it is embraced, seen as inevitable, and appropriate ways of dealing with it are highly valued.

Critic & Conscience

Only two of twelve lecturers mentioned anything that could be construed as wanting their students to use their mathematical knowledge as a means of social responsibility.

All of which raises some interesting questions about how we may observe some of these

desired outcomes……including re-questioning about

the observations we do make.

And now……I invite you to participate.

What are your desired learning outcomes for undergraduate

mathematics ?

b.barton@auckland.ac.nz

LUMOS Web Surveyhttp://www.math.auckland.ac.nz/CULMS/