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

Dilshara Hill from Macquarie University.

Investigating how past experiences in mathematics have influenced pre-service primary teachers

Dilshara Hill, Macquarie University

Pre-service Primary Teachers

Characteristics observed:

Maths anxiety, more so than other maths students.

Aim to see if and how past experiences have influenced them, also their attitudes and past level of mathematics.

Literature

Cobb(1986) beliefs are related to social experiences, such as in classrooms.

(others)

Data collected

• Personal info
• Attitudes
• Past experiences

87% females, 71% 18 – 25 yrs old.

Maths level:

• No yr 12 maths (22%)
• Non-calculus based course (51%)
• Calculus-based course (17%)

(Typical of previous years too.)

Circle the words from 6 positive, 6 negative works, could add own

More negative (40%) than positive words (30%). 28% had both positive and negative experiences.…

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

Prof Leanne Rylands -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.

Context: 42,000 students at Western Sydney University – founded in 1989.

Background:

• A low level maths subject
• Poor mathematics background – getting worse
• Failure rate: 40-60% failure rate
• No maths prerequisites

Asked the students: Do you expect to fail? What grade do you expect to get?

All expected to pass – many expected to get very high grades

Students’ perspectives are different from the staff.

• What do students see at the start of the semester?
• Do their expectations change over the semester?

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

Karin Bothma – 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.

First time using clickers to teach mathematics.

Background: Large undegrad classes: 900 students for classes between 70 and 400.

High impact module (foundational)

Objective was successful learning.

Use clickers to promote active participation in class

Clickers are classroom communication system

Students used the clicker to respond to multiple choice questions on a screen

Class distribution of answers then displayed

To meaningfully influence student learning, clickers must be used skillfully…(Beatty, 2004)

Aim of the study:

How we do we design the questions appropriately.

Examine principles for effective use of clickers

CCS (classroom communication system) based pedagogy

Clicker questions: Designed with goals in mind:

1. Content goal-concept or concepts
2. Process goal – cognitive skill
3. Metacognitive goal-  beliefs about mathematics

Strategies:

1. Focus student attention (comparative questions)
2. Encourage cognitive processes (compare and contrast)
3. Encourage debate (set a question to highlight assumptions)
4. Provide opportunity for feedback

Questions that initiate discussion: shows a wide distribution in the answer histogram

Class discussion is essential for effective use in mathematics classroom (Kenwright, 2009)

Methodology

• TurningPoint: Voting within Powerpoint
• Clickers with multiple choice capability
• Each lecturer could set 3 questions per week
• Questionnaire on students’ experience distributed

Experience of lecturers:

• Setting multiple choice questions was not a challenge
• Intentionally designing and planning questions was difficult
• Time constraints or technical problems (sometimes questions not used)
• Practice of separate question and answer slides

Class discussion was based on how the students got the questions wrong

Misconceptions often illuminated

Metacognitive goals: Relational understanding

Experience of students: Students strongly agreed that clickers contribute to their learning, and that it improved their active participation

They found that clickers made the students aware of their own understanding.…

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.…