Blogging from The Tenth Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics

Prof David Wagner from The University of New Brunswick.

Previously in Swaziland

Mathematics educators: including all people who teach mathematics at any level.

What is mathematics?

Thought experiment: What is football? Translate these ideas into the question regarding mathematics:

• Football is defined by the rules? But surely it’s much more than the rules.
• You don’t know football unless you’ve been in a crowd of 10,000 with vuvuzelas!
• You don’t know football unless you play football – rules, and the culture of fans is different from the practice of it. Many rules which are not in the rule book – informal rules.
• There’s also a whole culture of marketing.
• Organisations…and so much more.

You learn things when you watch the game about how to play it.

How does this relate to mathematics? Mathematics is much more than the usual definitions, has so many facets… What we do as teachers do affects how others see mathematics.…

Blogging from The Tenth Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics

Dr Alice Hui from The University of KwaZulu-Natal.

Projective geometry as an undergraduate course: A tour of the three worlds of mathematics.

Attempt to persuade the audience to have projective geometry as an undegraduate course.

What is Projective Geometry?

Projective geometry describes objects as they appear, rather than as they are.

Two sides of a train track are parallel but look interest in the far end.

Taken from https://plus.maths.org/content/sites/plus.maths.org/files/features/projective/tracks1_small.jpg

• Advantages of having projective geometry as an undergraduate course
  • An axiomatic approach to study geometry
    • A projective plane satisfies three axioms.
    • Can allow students to study geometry using an axiomatic approach.
    • Comparison to other axiomatic formulations that may be taught in undergraduate courses:
      • We use axioms to study natural numbers, real numbers, group, ring, field, vector space, set theory. They are not geometric.
      • Euclid’s Element is not rigorous in modern sense.

Blogging from The Tenth Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics

Prof Stephan Joubert from Tshwane University of Technology.

Based on paper: On numerically solving an eigenvalue problem arising in a resonator gyroscope

Abstract of the problem:

In 1890 G.H. Bryan observed that when a vibrating structure is rotated with respect to inertial space, the vibrating pattern rotates at a rate proportional to the inertial rate of rotation. This effect, called “Bryan’s effect”, as well as the proportionality constant, called “Bryan’s factor”, have numerous navigational applications. Using a computer algebra system, we present a numerically accurate method for determining fundamental eigenvalues (and some of the overtone eigenvalues) as well as the corresponding eigenfunctions for a linear ordinary differential equation (ODE) boundary value problem (BVP) associated with a slowly rotating vibrating disc. The method provides easy and accurate calculation of Bryan’s factor, which is used to calibrate the resonator gyroscopes used for navigation in deep space missions, stratojets and submarines.…

Blogging from The Tenth Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics

Dr Maritz Snyders

Traditional tutorials. Definitions:

• A tutorial is a method of transferring knowledge and may be used as a part of the learning process.
• A period of instruction given, especially to one or two students

What is the purpose of a tutorial/practical session?

• Allow the students to apply knowledge outside of the normal situation
• Force them to do something practical

Traditional tutorials:

• Small groups, face to face (25-30 students) weekly meetings
• Students work through provided exercises
• Guidance from lecturer or assistant when stuck

Problems:

• Marking and workload intensive
• Scheduling due to variety of programmes doing same course
• Large numbers
• Available venues
• Available staff

How about Online tutorials?

Structure:

• Replacing face-to-face contact with exercises posted online
• Student completes exercises and submit assignments in their own time

Advantages:

• Fewer staff
• No scheduling problems
• Easier for large groups

Disadvantages:

• No immediate support
• Guessing
• No guarantee students actually write out detailed solutions
• Only written feedback without explanations

Can we design an online system that has all the advantages but without the disadvantages?…

Blogging from The Tenth Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics

Prof Maxine Pfannkuch from The University of Auckland.

Link to paper

The first Judy Paterson Speaker

Visualising chance in introductory probability

The problem

• Random events and chance phenomena permeate our lives and environments: volcanic eruptions, epidemics, crashes – need probabilistic reasoning to understand these.
• Current teaching approach in intro prob is mathematical – obscures nature and role of randomness in processes and the nature of chance phenomena
• Many probability misconceptions are prevalent in people’s thinking (Kahneman, 2011)
• Appear resilient to teaching – how do we get students to confront these misconceptions?
• After 30 years of research a re-think is needed

Possible solutions

• Use a modelling approach to probability
• Construct a model (Konol and Kazak)
• Explore model behavior (Pratt, 2005)
• Use dynamic visualizations to give students an opportunity to:
• Experience random behavior through simulations
• Visualize chance through creating new representation infrastructure
• gain access to previously inaccessible concepts

Study: Part 1

Interviewed seven practitioners of probability (teachers,etc.) (at least 2 hours per interview)

• What probability concepts need to be promoted?

With enormous thanks to Anita Campbell for taking these notes.

Blogging from The Tenth Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics

Prof Cristina Varsavksy from Monash University.

Placing undergraduate mathematics assessment on the national Higher Education agenda

Deborah King and Cristina Varsavsky (Cristina presented)

Context

• Changing higher education landscape
• Development of threshold learning outcomes (TLOs) in Science and Mathematics

How do we demonstrate that graduates have the outcomes we desire? That is the reason for assessment.

There was not much in literature (or last Delta conference) on assessment. This motivated their work.

Assessment in undergraduate mathematics

• High failure rates
• Students focus on answers, not on the logic followed to obtain the answers
• Shopping for marks is common (viewing scripts for marks rather than learning)

However

• Assessment practices have not changed for decades.
• 70% is closed book exams
• Little variety in other 30%
• Ticks, crosses, normalising marks is common.

With enormous thanks to Anita Campbell for taking these notes.

Blogging from The Tenth Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics

Prof Leigh Wood from Macquarie University.

Opening Real Science

Leigh Wood

Working with pre-service teachers.

$2.3 million grant (R23 million)! A large project.

Aim to link ‘real’ scientists with educators to improve the outcomes in STEM for school students.

Challenge: Values of maths and science department were about the discipline; the values of education department were about the students.

Australia has a new maths curriculum, including statistics and financial maths.

Online modules, each 4 weeks work.

• To infinity and beyond
• Statistical Literacy
• Smart budgeting
• Investing and Protecting, includes superannuation, credit, protecting through insurance

Scale is a theme used across all modules.

Design principles

Inquiry-based … (see slide)

Design requirements

On-line delivery, currently as a moodle site hosted by Macquarie University. Available for others to use.…