## Brazil Delta Conference 2017, Leanne Rylands: A tale of two tests

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.

## Brazil Delta Conference 2017, Liliane Xavier Neves: Multiple representations in the study of analytic geometry: production of videos in the distance learning of mathematics

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.

 How clear is this post?

## Brazil Delta Conference 2017, Belinda Huntley and Jeff Waldock: Using virtual and physical learning spaces to develop a successful mathematical learning community

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!…

## Brazil Delta Conference 2017, Harry Wiggins: Student enrichment in mathematics: A case study with first year university students

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.…

## Brazil Delta Conference 2017, Anne D’Arch-Warmington: Creating a confident competent questioning culture

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.

## Brazil Delta Conference 2017, Rachel Passmore: Nurturing mathematical creativity

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?

## An oddly intuitive method to finding the distance between two skew lines in 3 space.

We begin by considering two lines. Namely, $f(t): x = 1 + 2t, y = 2 - 3t, z = 3 + 4t$ and $h(s): x = -1 + 3s, y = 3-s, z = -5 + 5s$. I now plot these two lines in 3 space in order to justify their skewness i.e. They do not intersect and are not parallel.

I now introduce a new function $D_l$ and this is defined as the distance between the two lines i.e. $|(f(t)-h(s)|$.  We now work with this equation to derive a general method for calculating the distance between two skew lines.

Before we begin, recall that $|{(a,b,c)}| = \sqrt{a^2+b^2+c^2}$

Now,

$D_l = |{(1,2,3)-(-1,3,-5)+t(2,-3,4)-s(3,-1,5)}| \\= |{(2 + 2t - 3s, -1 -3t + s, 8 + 4t -5s)}| \\= \sqrt{(2+2t-3s)^2+(-1 -3t+s)^2+(8+4t-5s)^2}\\=\sqrt{35s^2 - 58st - 94s + 29t^2 + 78t + 69}$

I now bring in some Calculus. We use the fact that minimizing a function is the same as minimizing the square of that function (does not always hold but it holds here because we are dealing with a distance function that is non-negative and monotonic). Hence, we do the following:

$(D_l)^2 = 35s^2 - 58st - 94s + 29t^2 + 78t + 69$

We now take the partial derivatives $(D_l)^2$ with respect to s and t and we set it equal to zero. This is as follows.

$\frac{\partial (D_l)^2}{\partial s} = 70s -58t -94 = 0$

$\frac{\partial (D_l)^2}{\partial t} = -58s+58t+78 = 0$

Solving the system of linear equations we arrive at $s=\frac{4}{3}$ and $t=\frac{-1}{87}$.…