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

Trudie Benade

Live blogging: Note that these are notes I’ve taken live, but will edit this today into a more readable format. I want to put this up straight away though to see if I have any obvious misunderstanding.

Based on work with Dr Sonica Froneman

From 2008-2009 it was a hard time in universities for new students coming in from the new curricula.

How can we measure reasoning abilities? What do we want students to be able to do?

Mathematical reasoning is an important process through which mathematical understanding develops.

Students should be able to transfer mathematical knowledge from familiar to unfamiliar contexts (Englebrecht, Harding and Phiri, 2010)

Critical outcomes of the school curriculum:

Learners should demonstrate an ability to think logically and analytically and be able to transfer skills from familiar to unfamiliar situations.…

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

Stuart Torr Centre for Research in Engineering and Science Education.

Sasol Inzalo Foundation

Stuart is a PhD student of Tracy Craig.

Mathematics is very abstract. Students sometimes complain about this. Developing abstract reasoning is key in mathematics.

Abstraction has 2 components

1. A process involving decontextualizing and generalising
2. Abstract objects and concepts, e.g. the economy, justice, equality, numbers, functions

An abstract object is the end result of an abstract process.

Two schools about dealing with abstraction:

1)      Cognitive/empirical approach (Piaget)

1. Empirical abstraction. Recognise similarity between objects
2. Pseudo-empirical. End product like number 5
3. Reflective abstraction. Performing operations on

2)      Socio-cultural / dialectical approach (Davyov, Russian inspired by Vygotsky)

1. Recontextualisation. Making new links with objects
2. Non-linear / dialectic development. Back and forth between objects.

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

Paper by Dr Tsanwani here.

Live blogging: Note that these are notes I’ve taken live, but will edit this today into a more readable format. I want to put this up straight away though to see if I have any obvious misunderstanding. Equations will also be put into more readable format ASAP.

MASTEC Institute created in Limpopo because students have been struggling to pass.

In service training of teachers. Training the educators.

Today talking about a small part of MASTEC: Training of educators in data handling: Statistics.

Teachers are expected to have a deep understanding of mathematical content knowledge

Research indicates that those that have majored in mathematics are not exposed much in teaching methods: Not necessarily a good understanding of teaching methods with an emphasis on meaning.

Appropriate classroom discussion is affected a lot by teacher training.…

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

Dr Greg Oates -image taken from here.

Live blogging: Note that these are notes I’ve taken live, but will edit this today into a more readable format. I want to put this up straight away though to see if I have any obvious misunderstanding. Equations will also be put into more readable format ASAP.

Dedication to Judy Paterson

Discussion of the DATUM project: The Development and Analysis of the Teaching of Undergraduate Mathematics professional development discussion group.

Schoenfeld, A. H. (2010). How we think. A theory of goal-oriented decision making and its educational applications

Being videoed and then analysed is daunting. There’s often a disconnect between how we see ourselves, and how our colleagues see us.

Project at University of Auckland to video lecturers. At the beginning of the project there would be lecture notes taken by a colleague.…

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

Dr Anthony Morphett – image taken from here.

Live blogging: Note that these are notes I’ve taken live, but will edit this today into a more readable format. I want to put this up straight away though to see if I have any obvious misunderstanding. Equations will also be put into more readable format ASAP.

Dr Morphett will be talking about GeoGebra. Downloadable as a desktop or tablet application. Very fast development of applets (average 18.2 hours development time per applet – not including design). Purely html for adding to the web – makes it very easy. However, there are performance issues and it’s still somewhat immature.

Talking about work developed with Sharon Gunn and Robert Maillardet. Applets from the project can be found here.

Similar to Mathematica demonstrations from the previous post.…

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

Dr Esme Voges from Tshwane University of Technology

Live blogging: Note that these are notes I’ve taken live, but will edit this today into a more readable format. I want to put this up straight away though to see if I have any obvious misunderstanding. Equations will also be put into more readable format ASAP.

Talking about Mathematica from a lecturers point of view.

Background: Diploma and B Tech engineers students.

The students are millennials – they can figure things out for themselves.

How do you make maths applicable for engineers?

Coffee cooling problem: Using Manipulate and Animate to create an interactive graphic. Can step through, can see how the different variables change things? Taken from here:

This is an application of a differential equation.

Can explain many different concepts from a single example – what does T=0 mean?…

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

Prof Deborah King – University of Melbourne.

Live blogging: Note that these are notes I’ve taken live, but will edit this today into a more readable format. I want to put this up straight away though to see if I have any obvious misunderstanding. Equations will also be put into more readable format ASAP.

Prof King is the Coordinator of Learning and Teaching Innovation at Melbourne University

Talking about mathematics educators rather than education – interested in people – community and collaboration.

Talking about the personal perspective of an accidental teacher (Prof King as a personal story).

Background of Prof King

First in family to finish high school. Family thought she was nuts to continue in education. Definitely didn’t want to be a teacher and left uni.

Returned as a mature student in a mathematics department that valued teaching over research and started tutoring during her third year.…

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

Dr Harry Wiggins – University of Pretoria (http://www.up.ac.za/en/mathematics-and-applied-mathematics/article/1942109/mr-hz-harry-wiggins)

Live blogging: Note that these are notes I’ve taken live, but will edit this today into a more readable format. I want to put this up straight away though to see if I have any obvious misunderstanding. Equations will also be put into more readable format ASAP.

The problem:

How should we teach a mixed ability class?
Children already come to us differentiated. It just makes sense that we would differentiate our instruction in response to them (Tomlinson 1999)

We teach with an average student in mind.
Our teaching is content driven, and we don’t take our students into account.

Unfortunately (sometimes) – this leaves the academically strong students starved and bored in class.

Academically stronger students face a higher level of boredom at school than their peers.…

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

Prof Ansie Harding – University of Pretoria (http://www.up.ac.za/en/mathematics-and-applied-mathematics/article/1941897/prof-af-ansie-harding)

Live blogging: Note that these are notes I’ve taken live, but will edit this today into a more readable format. I want to put this up straight away though to see if I have any obvious misunderstanding. Equations will also be put into more readable format ASAP.

Both a privilege and a formidable task to teach hundreds of students.

Specifically, at University of Pretoria, classes of 200-500.

Questionnaire on practices, advice, engagement, humour, motivation, etc.

12 respondents, all experienced lecturers.

Why? Guidelines to someone starting out on large group lecturing.

Tried to make sense of responses to the questionnaire.

Try and find 6 skills of large group teaching, and organise them hierarchically.

1. Control and respect of the group:
   1. a large group should be controlled through authority.

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

Dr Tracy Craig – UCT (photo taken from http://uct.academia.edu/TracyCraig)

Live blogging: Note that these are notes I’ve taken live, but will edit this today into a more readable format. I want to put this up straight away though to see if I have any obvious misunderstanding. Equations will also be put into more readable format ASAP.

Research with Trevor Cloete  – UCT Centre for research in engineering and science education.

Dynamics Education research group: With mechanical engineers and the Academic Development Programme.

Current study: Vector proficiency

Originally interested in the difficulties students find with (originally dynamics) and now vectors. In particular differences in notation and terminology between mathematics and dynamics (more purely engineering).

Vectors are used throughout dynamics.

Vectors are a very divided subject:

Some students ‘get’ vectors. Other students really struggle and have to memorise the process.…