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

Prof João Frederico da Costa Azevedo Meyer from Universidade Estadual de Campinas

Different points of view lead to different views. Talking from the point of view of an applied mathematician – this will lead to a particular biased applied mathematician’s point of view, a utilitarian point of view, as well as an environmental scientist’s point of view.

He speaks as a customer. His students need certain skills, knowledge, etc. He is the one who needs the results of mathematical education at technical schools and university activities.

A lot of abstraction leads to unrealistic ideas: Who cares about the trigonometric functions applied to a 30 degree angle?

Fenando Pessoa: The preacher of his own truths…

Do students share our enthusiasm with what is taught in the classroom?

In fact, do WE share any enthusiasm?…

At Nelson Mandela Metropolitan University Very diverse socio-economic circumstances, mostly non-native English speakers. 23 Different languages on campus.

Why this study? There has been a large issue of poor performance and lack of engagement in mathematics.

What can we do about this?

Possible issues:

• Topics are introduced at a fast pace
• Students may not have the necessary prerequisites
• Independent learning is required

Two other issues:

Mathematics self-efficacy:

Self-efficacy is people’s judgements of their capabilities to organise and execute courses of action required to attain designated types of performance (Bandura 1986).

Mathematics self-efficacy affects performance.

This can tell us why students sometimes don’t put in the necessary effort. If a student DOES have a high level of mathematical self-efficacy they tend to work longer on problems.

There does seem to be a link between mathematics self-efficacy and gender: Higher in males (grade 10-12 and pre-service teachers – Malpass, O’Neil and Hocenar: Self‐regulation, goal orientation, self‐efficacy, worry, and high‐stakes math achievement for mathematically gifted high school students) – in another study this was not found.…

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

Dr Jyoti Jhagroo from AUT.

This is a personal reflective narrative as a student and teacher in the school/higher education contexts.

It is a hermeneutic phenomenological study with 10 immigrant students

• Considerations of cultural constructs: Languages, Beliefs and Experiences (though of course there are much more).
• Students lived experiences in their mathematics classrooms with considerations for teacher education.
• Explore some ideas of multiplications from different cultures and consider their implications for teaching and learning in a multicultural context. Take some ideas to take forward for teacher education

As a student with a personal narrative, Jyoti had been indoctrinated into the ideas of what mathematics education were about. It should be:

• Culture-free
• Factual
• Based on theorems
• Present, practice, perfect

As a teacher: a shift from a monocultural context to a multiculural context:

• Some students spoke a different language at home, potentially held different beliefs and different experiences of mathematics
• However, it seemed that the mathematics education practices and attitudes are often projected as culturally neutral ideologies.

• Prof Nouzha El Yacoubi from University Mohammed V Rabat, Morocco on The impact of mathematics on the Africa socioeconomic takeoff
• Fransonet Reyneke from University of Pretoria on First level statistics students’ performance in a large classroom environment under the magnifying glass
• Prof João Frederico da Costa Azevedo Meyer from Universidade Estadual de Campinas on Mathematical Disciplines for Undergraduate
• Prof Jeff Waldock from Sheffield Hallam University on Designing and using informal learning spaces to enhance student engagement with mathematical sciences
• Shirley Wagner-Welsh from Nelson Mandela Metropolitan University on An Investigation into the Effect of Mathematics Self-Efficacy and Mathematics Anxiety on Mathematics Performance
• Dr Jyoti Jhagroo from The Auckland University of Technology on Multicultural lecturing some challenges
• Diana Quinn from The University of South Australia on Learning from experience The realities of developing mathematics courses for an online engineering programme
• Dr Maritz Snyders from Nelson Mandela Metropolitan University on Online video-based tutorials for a first-year mathematics service course
• Prof David Wagner from University of New Brunswick on Mathematics, Culture, and the Responsibility of Mathematics educators
• Dr Alice Hui from The University of KwaZulu-Natal on Projective geometry as an undergraduate course a tour of the three worlds of mathematics
• Professor Stephan Joubert from Tshwane University of Technology on Numerical solutions for the vibrating bar eigenvalue problem: a student exercise
• Dr Maritz Snyders from Nelson Mandela Metropolitan University on Online video-based tutorials for a first-year mathematics service course
• Claire Cornock from Sheffield Hallam University on Teaching group theory using Rubik’s cubes
• Prof Maxine Pfannkuch from The University of Auckland on Visualizing chance in introductory probability
• Prof Cristina Varsavsky from Monash University on Placing undergraduate mathematics assessment on the national Higher Education agenda
• Prof Leigh Wood from Macquarie University on Opening Real Science
• Dilshara Hill from Macquarie University on Investigating how past experiences in mathematics have influenced pre-service primary teachers
• Prof Leanne Rylands from Western Sydney University on Great Expectations Expectations and attitudes of first-year mathematics students
• Karin Bothma from The University of Pretoria on Using clickers in the mathematics classroom: novelty or necessity?

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.