A tale of two tests

Leanne Rylands and Don Shearman, Western Sydney University

l.rylands@westernsydney.edu.au

Presentation at the 11th Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics in Gramado, Brazil, November 2017, “Brazil Delta 2017’

In Australia, students can come to university to study subjects requiring maths without having done maths in their last 2 years of high school! Some degrees have mathematics prerequisites but many Science degree do not have high school mathematics as a prerequisite. In 2016 at Western Sydney University, 50.5% of Australian students registered for first year mathematics and statistics did no mathematics in their last 2 years of school and 15% only studied the lowest level of mathematics at school in their last 2 years.

Conjecture: Diagnostic mathematics tests can be useful

Diagnostic tests

• Let teachers know the level of their students
• Let students know where they need to improve skills
• Predict performance
• Inform non-mathematicians and decision makers about the level of maths knowledge of students with hard data to counter accusations that you can’t teach.

Multiple representations in the study of analytic geometry: production of videos in the distance learning of mathematics

Liliane Xavier Neves

Presentation at the 11th Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics (‘Brazil Delta 2017 for short)

Qualitative research, describes students’ actions in relation to an activity of producing videos. Students were distance students studying Analytical Geometry and in Informatics applied to Maths Education.

Discuss with students using videos in maths classes and the making of the videos.

27 videos were produced by 85 students on topics from analytic geometry and calculus.

Powel, Francisco and Maher (2003), 7 stages of video production: Preview, Product description, Critical events, Transcription, Coding, Plotting, Composition of narrative.

What tools are used to analyse videos? NVivo.

Using virtual and physical learning spaces to develop a successful mathematical learning community, both for on-site and distance provision.

Belinda Huntley, UNISA, South Africa

Jeff Waldock and Andrew Middleton, Sheffield Hallam University

Presentation at the 11th Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics (‘Brazil Delta 2017 for short)

Students and staff need to feel part of community of practice.

Informal learning spaces can:

• Foster a sense of belonging
• Provide a disciplinary ‘home’
• Provide a partnership learning community
• Encourage peer support mechanisms to develop
• Have both a physical and virtual dimension
• Be co-constructed
• Engage students productively outside normal class time
• Be important in different ways

Sheffield Hallam became a university in 1992, previously a polytechnic. In 2017 received a silver teaching excellence framework so teaching is taken seriously. 31 500 students in 672 courses. 78% undergraduates, 80% full time, 60% staff in the maths department are female!…

Student enrichment in mathematics: A case study with first year university students (in IJMEST)

Harry Wiggins, Johann Engelbrecht, Ansie Harding

Presentation at the 11th Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics (‘Brazil Delta 2017 for short)

How do we teach a mixed ability class? It’s not easy. Teaching to the middle bores some and leaves others behind.

A student enrichment programme was developed at the University of Pretoria.

5 activities worked on by 22 students who were invited to join the programme. They could consult the lecturer or each other. Designed using inquiry-based learning principles. Feedback by a survey, and 4 students were interviewed.

Enthusiasm: 10% neutral, the rest said they enjoyed the project.

“I don’t see the point of you coming to study if you don’t want to challenge yourself to become better.”

Self-activity. 82% worked alone. “You don’t always rely on a lecturer, just do your own stuff…”

Depth of understanding: Student got to experience complex numbers as more than just learning the algebra.…

Creating a confident competent questioning culture

Presentation at the 11th Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics (‘Brazil Delta 2017 for short)

Anne D’Arch-Warmington and Heather Lonsdale, Curtin University, Perth, Australia.

Get students into groups and do activities from day 1, minute 1. Within 2 weeks a community is built.

Get students into groups. Choose a scribe. They must only write questions raised by the group.

Share your questions with another group.

‘Think-aloud’ – make a commentary column next to your workings for answering a question. This makes you engage with the work in different ways.

Think-Pair-Share

• Think individually about the topic. It’s okay to just say “I have no clue”
• Pair with your partner.
• Share with your partner and then the class.

POGIL: Process Oriented Guided Inquiry Learning

• Each student assigned a role
• Take turns to try different roles
• Teacher observes and guides

Reciprocal teaching

• Students summarise, generate questions, clarify, predict on a topic they are going to cover.

Nurturing mathematical creativity and curiosity in Foundation Mathematics students

Rachel Passmore, University of Auckland, New Zealand, r.passmore@auckland.ac.nz

Encourages students to see elegance in solutions. Gives challenge problems a but beyond the level of the course for fun. Solutions go on intranet and discuss which they like and dislike. That’s a different kind of creativity than what is in this talk.

Len Lye, New Zealand sculptor with kinetic pieces or the millionaire with a sculptor park, Gibbs Farm (only open 2-3 days a year).

Definitions about creativity in mathematics

• Discovery of something new to you even if it’s known to others (Sriraman, 2004)
• Differentiate between professional and student creativity (Sriraman, 2004)
• Unusual ability to generate novel and useful solutions to problems (Chamberlin and Moon, 2005)
• Non-algorithmic decision making

Activities and strategies to creativity in mathematics

• Multiple solutions spaces (Marion Small, open questions) e.g. what 2 fractions when multiplied together give a product a little less than one fraction and a lot more than the other?

Siyaphumelela Conference 2017, The Wanders Club, Johannesburg

http://www.siyaphumelela.org.za/conf/2017/#!

Carnegie Foundation Math Pathways Workshop 27 June 2017

Andre Freedman, Capital Community College, Connecticut

Bernadine Chuck Fong, Carnegie Math Pathways

Workshop goals:

• Learn about the design, goals, implementations of Carnegie Math Pathways
• Experience Pathways lessons
• Engage in design tasks to improve student success in maths and college
• Engage in conversations about professional learning to address issues and concerns that are specific to local contexts

Staff had to learn new ways to teaching maths, there had to be ‘buy in’ for it to be successful. This is a great challenge.

How to radically transform outcomes for all mathematics students?

• aim to get more student to complete maths courses and degrees
• persistence (students don’t easily give up when challenged)
• quality of learning (e.g. students can explain what a function is years after taking a maths course)
• identities of learning (students see themselves as someone who can do maths).

Modelling learning, unlearning and relearning in large classes

Claire Blackman, Department of Mathematics and Applied Mathematics, UCT

Presentation at the SANRC First Year Experience (FYE) conference, Johannesburg 24- – 26 May 2017

Context: Claire teachers first year commerce students who do not necessarily want to do maths.

Alvin Toffler quote: “The illiterate of the 21st century will not be those who cannot read and write, but those who cannot learn, unlearn, and relearn.”

Change is a way of life but adapting to change is hard and people are not very good at it. We have to learn how to learn and relearn and unlearn.

How I teach is more important than the content.

The world needs people who own and learn from their mistakes and think before responding.

Two useful models:

1. Krathwohl’s taxonomy (published by Bloom) for thinking about the individual
2. Group therapy to get students in an emotional comfortable space

Krathwohl’s taxonomy of the affective domain can help to see if students are learning

https://za.pinterest.com/source/dynamicflight.com

5. Living (Integrating values into life)
6. Organising
7. Valuing
8. Responding
9. Receiving

A group analytic framework

• Environment (psychological structure, class boundaries)
  • Students and teachers need to feel safe
• Process (how is the class run)
• Content
  • Maths
  • Tools for dealing with fear and uncertainty e.g.