# Online Professional Development Courses for High School Educators

The School of Mathematics and Statistics has developed several series of short, online professional development courses.

New Syllabus Professional Development is a series of courses focused on addressing the new parts of the new stage 6 mathematics syllabi. These are short, NESA/TQI accredited courses that can be completed within two hours. These courses are designed to introduce the mathematical concepts and help prepare teachers to facilitate the delivery of this material in the classroom.

Mathematics in the Modern World is aimed at Australian high school mathematics educators who want to enhance and strengthen their understanding of some important mathematical theories and their applications to the modern world. These six courses provide focused online lessons and activities through OpenLearning. Each course involves six hours of learning, to be undertaken over a four-week period. More information is available on our FAQ. See below for course dates and details.

Mathematical Relations is aimed at a wide range of teachers, from Primary or Intermediate level teachers and those currently teaching General Mathematics in NSW, to more Senior level teachers. There are four courses, increasing gradually in depth and complexity. Focused online lessons and activities are provided through OpenLearning. See below for course dates and details.

#### New Syllabus Professional Development

1. Conditional Probability (May 2017) Advanced MA-S2
2. Discrete Probability Distributions (July 2017) Advanced MA-S3
3. Vectors in 2D Extension 1 ME-V1 (September 2017)
4. Continuous Random Variables and the Normal Distribution Advanced MA-S5
5. Bernoulli and Binomial Distributions Extension 1 ME-S1
6. Bivariate Data Analysis Advanced MA-S4
7. Differential Equations Extension 1 ME-C3
8. Mathematical Induction Extension 2 MEX-P2
9. Projectiles and Applications of Vectors Extension 2 MEX-M1
10. The Nature of Proof Extension 2 MEX-P1
11. Vectors in 3D Extension 2 MEX-V1
12. Networks 1 Standard MS-N1
13. Networks 2 Standard MS-N3

#### Mathematics in the Modern World - Course Dates for 2017:

1. Archimedes and the Law of the Lever 6 February - 13 March
2. Curves from Apollonius to Bezier 3 April - 8 May
3. Population Growth and the Logistic Curve 5 June - 3 July
4. Primes, Modular Arithmetic and RSA Encryption 7 August - 11 September
5. Graphs, Networks and the Page Rank Algorithm (2017 dates TBA)
6. Celestial Motion and Going to the Moon (2017 dates TBA)

Click on the course name above for a course description.

Cost: All courses $90. #### Mathematical Relations - Course Dates for 2017: 1. Linear relations and the Geometry of Lines Open 6 March - FREE 2. Quadratic Relations and the Geometry of Parabolas August 3. Inverse Relations and the Geometry of Hyperbolas November 4. Power Law and Why Big Animals Live Longer February 2018 Click on the course name above for a course description. Cost: As this is our first running of the course, it will be made available at the special price of$60.

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This video introduces our suite of Professional Development courses.

### Archimedes and the Law of the Lever

This course is given by award-winning lecturer A/Prof N. J. Wildberger from the School of Mathematics and Statistics at UNSW. Click here to join the course:
https://www.openlearning.com/courses/archimedes-the-law-of-the-lever/HomePage

Topics:

Module 1: Levers and Centres of Mass

Module 2: Balancing and Expected Values

Module 3: Vectors and Barycentric Co-ordinates

Module 4: Projects and Challenges

More than 2000 years ago, Archimedes discovered a fundamental law that mathematically explains how a lever works. This insight still has wide applications in the modern world, from designing helicopters to discovering planets around distant stars. In this course teachers will strengthen their understanding of algebra, vectors, parametric equations for lines, centres of mass and planar geometry, as well as expected values (or means) of probability distributions--- all arising from Archimedes' Principle. They will also have fun with activities and small projects that they can bring to the classroom.

### Curves from Apollonius to Bezier

This course is given by award winning lecturer A/Prof N. J. Wildberger from the School of Mathematics and Statistics at UNSW. Click here to join the course:

https://www.openlearning.com/courses/curves-from-apollonius-to-bezier/HomePage

Topics:

Module 1: Classical Curves and Constructions

Module 2: Parametrics and de Casteljau Bezier Curves

Module 3: Making Curves with GeoGebra

Module 4: Bernstein polynomials and de Casteljau's Algorithm

Teachers will learn about the history of important curves such as conic sections, the lemniscate and the folium of Descartes, and learn how such curves can be viewed geometrically, algebraically and mechanically. The course explains the important modern tool of de Casteljau Bezier curves, drawing on an understanding of the previous course: Archimedes and the Law of the Lever. An introduction to the powerful classroom tool GeoGebra shows how to explicitly construct these curves, and the geometry is linked to algebra via the Binomial theorem and an interesting family of polynomials.

### Population Growth and the Logistic Curve

This course is given by award winning lecturer Daniel Mansfield from the School of Mathematics and Statistics at UNSW. Click here to join the course https://www.openlearning.com/courses/populationgrowthandthelogisticcurve.

Topics:

Module 1: Exponential Growth

Module 2: Properties of the Exponential

Module 3: The Logistic Curve

Module 4: Population Prediction with a little help from Excel

Starting with a review of compound interest, this course introduces Leonard Euler’s famous number “e” and the remarkable exponential function which describes so many aspects of growth and decay in the modern world. It reviews basic notions from calculus, gives a short introduction to spreadsheets and differential equations, and culminates with the investigation of the lovely logistic function. While applications naturally centre on the intriguing issue of what is happening to the earth’s population, we also discuss topics as diverse as radiocarbon dating to the spread of Facebook on the internet. By the end of the course, teachers will be confident in taking these concepts to the classroom, empowering your students to make their own accurate predictions in a variety of situations, bringing calculus to life..

### Primes, Modular Arithmetic and RSA Encryption

This course is given by award winning lecturer Peter Brown from the School of Mathematics and Statistics at UNSW. Click here to join the course: https://www.openlearning.com/courses/rsaencryption.

About the course: James wants to send a secret message to Q. He places the message in a box and locks it. The problem is, that he does not trust Q with the key. Only James is to have the key. How does he send the message to Q?

Sending information safely and securely on the internet (known as RSA Encryption) is a serious problem whose solution is remarkably simple and at the same time remarkably clever. The key to this is the use of Number Theory, one of the oldest and most beautiful branches of Mathematics, and the index laws. This course will present just enough basic number theory to allow us to devise a solution to the question posed above. Teachers will find in this module a range of interesting material that can be adapted to classroom use in extension lessons in the junior school.

The course will be presented by Peter Brown, Senior Lecturer in Pure Mathematics and Director of First Year Mathematics at UNSW.

The course will be run flexibly over a four week period, and consists of four Modules.

You can watch the videos, do the activities, and make comments and submissions anytime through the four week period.

### Linear Relations and the Geometry of Lines

An introduction to the algebra of linear equations and the connections with the geometry of lines in the Cartesian coordinate framework, presented via lots of practical examples from everyday life. This course will review your understanding of lines, slopes, intercepts and transformations, and how geometry and algebra meet in the Cartesian plane of Fermat and Descartes.

Applications range from slopes of pyramids to internet speeds to temperature conversions and move towards supply demand curves in economics and the important topic of regression, or best fit, from statistics. A great course for teachers wanting to improve their fundamental understanding about linear equations and gain experience with a wealth of interesting examples to bring to their classrooms.

### Quadratic Relations and the Geometry of Parabolas

Quadratic relations are definitely a step up from linear relations, and are intimately related to the beautiful geometry of the conic sections of Apollonius, in particular the parabola. In this course we review fundamental algebraic manipulations such as al Khwarizmi’s completing the square technique, how the algebraic equation of a second degree curve reflects in the position of its parabolic graph, and numerous interesting applications of quadratic equations, including the physics kinetic energy and to architectural design, such as the Harbour Bridge in Sydney.

### Inverse Relations and the Geometry of Hyperbolas

Inverse relations occur in many areas of modern life, chemistry, economics and physics. They are intimately related to the fascinating geometry of the hyperbola, and we will have a chance to show how they connect with triangulation in navigation and military problems. We look at Zipf’s law, Ohm’s law and Hooke’s law in physics, which all centre around inverse relations, and then show how the logarithmic function connects with inverse relations via the area under the graph y=1/x. This is a fascinating course which will even touch on the mysterious Benford’s law which figures in so many aspects of modern data.

### Power Law and Why Big Animals Live Longer

In this course we go beyond linear, quadratic and inverse relations to discuss power laws: a remarkable family of relations that figure prominently in economics, physics and notably biology. We start by having a look at the intriguing geometry of cubic curves, and relate to some famous number theory problems.

We look at the relation between size and metabolic rate and heart rates, consider how the number of gas stations depends on the size of a city, and even end up having a look at the remarkable claw of the Fiddler crab. There are a lot of explicit examples here that your students will be fascinated to learn about: and it is all about mathematics!

### FAQ

• What is the structure of the courses?

Each course consists of 4 modules. Each module is designed to take 1.5 hours to complete. This includes about 20 minutes to watch the video, and the remaining time for online activities.

The activities are a mix of traditional mathematical problem solving, and online interaction. For example, in Archimedes and the Law of the Lever you will use mathematical concepts to balance a lever. On the more social side of things, you will brainstorm and post pictures of levers from your daily life (and you get to see what everyone else posted).

All activities are automarked. This means you can move at your own pace through to the next module, and track your progress on the progress bar.

• So I can do the course at any time, right?

Right. Norman and Daniel will be online Monday evenings from 6-8 to answer questions, and at other times during the week, so you can do the course any time that suits you.

• What do I have to do beforehand?

Nothing. But we recommend you have a pen, paper and a cup of tea ready.

• Is there an assignment?

Yes and no. Aside from the activities, there are futher study questions at the end of each module. These are optional problems with more challenging and interesting content. You do not have to complete the further study questions to pass the course, but you might find them interesting.

• Is there discussion?

The platform we are using (openlearning) emphasises the social aspects of learning. The social nature of the activities means we'll discuss and learn together. There are opportuninties for discussion on every video and every activity. We hope you make the most of it.

• How much do I have to do to pass the course?

If you complete 50% of the activities, then you have passed the course. Your progress is tracked by a progress bar. For example, in Archimedes and the Law of the Lever there are 21 activities. Completing 21*50/100 = 10.5 activities constitutes a pass.

• What standards does this PD meet?

The Mathematics in the Modern World courses are accredited in NSW and meet the Australian Professional Standards for Teachers 2.1.2 and 2.5.2.