The next in the series of New Syllabus Professional Development Days will be on Thursday 2nd November. It was great to see so many enthusiastic teachers last time at the day in June so we're really looking forward to the next one.

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The professional development day on **Thursday 2nd November 2017** for high school mathematics teachers will cover a selection of new topics in the current draft of the proposed HSC syllabuses for HSC Standard Mathematics, HSC Mathematics and HSC Mathematics Extensions 1 and 2.

The new Standard Mathematics Stage 6 (MS) will begin with year 11 in 2018. The NSW Educations Standards Authority (NESA) has recently announced a delay in the implementation of the new Mathematics Advanced Stage 6 (MA), Mathematics Extension 1 Stage 6 (ME) and Mathematics Extension 2 Stage 6 (MEX) which are now scheduled to begin with year 11 in 2019.

The program schedule is below and includes the following sessions.

- Vectors and geometry (ME-V1)
- Vectors, lines and projectile motion (MEX-V1, ME-V1)
- Differential equations, direction fields and modelling (ME-C3)
- Networks and paths (MS-N1, MS-N2)
- Critical path analysis plus the max-flow/min-cut theorem (MS-N3)
- The max-flow/min-cut theorem (MS-N3)
- Discrete random variables including the binomial (MA-S2, MA-S3, ME-S1)
- Continuous random variables (MA-S2, MA-S5, MS-S5)
- Thinking Statistically (MS-S1, MS-S2, MS-S3, MS-S4, MS-S5; MA-S1, MA-S2, MA-S3, MA-S4, MA-S5; ME-A1, ME-S1)
- Randomised assignments

Completing all 4 sessions at the UNSW Maths Teachers PD Day will contribute 5 hours of NESA Registered PD addressing 2.2.2, 2.3.2, 2.6.2, 3.4.2 from the Australian Professional Standards for Teachers towards maintaining Proficient Teacher Accreditation in NSW. |

For further information, contact Dr Jonathan Kress (j.kress@unsw.edu.au)

#### Signing up for the day

To register for the day, please use the link below. The early bird price per participant is $50 (unti 29/9/2017) and $70 after that. Payment can be made online by credit card or by cheque.

The registration system allows multiple participants to register as a group. The participant details entered on the first page will be used for the invoice. Other participant details are collected on the following page.

#### Information for the day

A map showing the location of the Colombo Theatres where the registration desk and all presentations took place. Some transport information is also below.

**Schedule**

The registration, morning tea and lunch will be in the Colombo Building foyer. A detailed schedule is below. Morning tea and lunch will be provided.

Colombo Theatre B | Colombo Theatre C | Colombo LG02 | |

8:00am -- 8:45am | Registration | ||

8:45am -- 9:00am | Welcome (Colombo Theatre A) | ||

9:00am -- 10:15am | Networks and paths | Differential equations | Thinking statistically |

10:15am -- 10:35am | Morning Tea | ||

10:35am -- 11:50pm | Critical Path Analysis | Randomised assignments | Discrete random variables |

11:50am -- 1:05pm | Max-flow/min-cut theorem | Vectors and geometry | Discrete random variables |

1:05pm -- 1:45pm | Lunch | ||

1:45pm -- 3:00pm | Networks and paths | Vectors, lines, projectiles | Continuous random variables |

**Location**

Colombo Theatres, UNSW Kensington Campus. See the Google map below for the location or find B17 on the UNSW Campus map.

**Public Transport**

For Public Transport information, please see the UNSW Public Transport Page. Coming from Central Station it's best to take the 891 Express from Eddy Avenue and get off at the High St Gate 8 stop. The current route map is here: 891 during light rail construction.

For the latest updates on public transport diversions and road closures due to the light rail construction see the UNSWLightRail twitter feed.

**Parking**

Parking is restricted on campus and in many nearby streets. If you plan to find a park on a nearby street you should arrive early and expect a long walk. Paid parking can be found close to the Central Lecture Block on the top floor of the Botany St carpark accessed via Gate 11 on Botany St. A pay and display parking permit obtained from a parking permit machine must be displayed and costs $9 for the first 2 hours and $3.50 per hour thereafter.

You can request to join the facebook group where links to materials will be posted.

#### Workshop descriptions

The descriptions below may be updated but we don't expect major changes before the day.

**1. Vectors and geometry** (ME-V1)

Vectors provide a powerful and elegant to way to describe and solve geometric problems and are essential in physics and engineering. Vectors will be introduced as both algebraic and geometric objects and used to prove results such as "the midpoints of the sides of a quadrilateral join to form a parallelogram". The dot product will be discussed and used to find the projection of one vector onto another.

**2. Vectors, lines and projectile motion** (MEX-V1, ME-V1)

Straight lines in two or three dimensions are most naturally described using vectors. After a brief introduction to vectors, the parametric description of straight lines will be explained and projectile motion explored using displacement, velocity and acceleration vectors.

**3. Differential equations, direction fields and modelling** (ME-C3)

A direction field is a tool for understanding the behaviour of the solutions to a differential equation even when explicit forms of those solutions are not known. The latest draft of the Extension 1 syllabus introduces direction fields along with an expanded range of differential equations used for mathematical modelling in chemistry, biology and economics. In this presentation direction fields will be explained and used to explore the behaviour of important mathematical models of real world phenomena.

**4. Networks and paths** (MS-N1, MS-N2)

The rise of online social networks has put networks in a bright spotlight, not only for the general public but also for researchers across a wide range of research fields, including biology, psychology, computer science, physics and beyond. This workshop will present a useful glimpse into the study of networks. After presenting the basic definitions and properties of networks, paths, cycles, and trees, we will discuss and practice algorithms for solving practical problems on networks, such as finding shortest paths (as in Google Maps, for instance) and minimal spanning trees.

**5. Critical Path Analysis ** (MS-N3)

Critical path analysis is a tool for analysing a multistage process by modelling it as a network and finding the bottlenecks. This networks related topic from the new Stage 6 Mathematics Standard syllabus will be explained through the use of examples.

**6. The max-flow/min-cut theorem** (MS-N3)

The Max-flow/Min-cut Theorem relates the maximum through put of a network (eg water pipes, roads, the internet, etc) to the minimum cuts required to break the network. This networks related topic from the new Stage 6 Mathematics Standard syllabus will be explained through the use of examples.

**7. Discrete random variables including the binomial** (MA-S2, MA-S3, ME-S1)

In this session we will discuss random variables and the difference between continuous and discrete random variables. We concentrate on discrete random variables, giving examples including detailed discussion of the binomial distribution. We will discuss expected value and variance and the relationship between the mean of a sample and the expected value (the mean) of a random variable.

**8. Continuous random variables** (MA-S2, MA-S5, MS-S5)

In this session, we introduce the basics of continuous random variables through discrete random variables. We will generalise the concepts of the expected value (mean), variance and quantiles to continuous random variable. To illustrate the theory, we will study examples including the continuous uniform random variable, the normal random variable and the Galton machine (Normal approximation to Binomial random variables).

**9. Thinking statistically** (MS-S1, MS-S2, MS-S3, MS-S4, MS-S5; MA-S1, MA-S2, MA-S3, MA-S4, MA-S5; ME-A1, ME-S1)

Statistics and Statistical thinking are part of the new maths syllabus. This session is an introduction to what it means to be thinking statistically. We will introduce a variety of online and other resources for reviewing stats concepts and techniques, assisting with development of project based assessments and using technology. We will introduce the ( award winning) school poster competition run by the Stats Society of Australia and explain how to use this competition and the associated resources to support teaching.

**10. Randomised assignments**

Assessment in mathematics is very often in the form of a supervised test with a relatively short time limit. While this is easy to control, it is not an environment that encourages mathematical thinking and communication. Assignments are set to become a bigger feature of HSC Mathematics with the introduction of the new syllabuses. They offer the chance for students to take their time to craft good answers and explore more complex problems and can better assess skills in these areas. However, traditional assignment answers can be copied, reducing the integrity of this form of assessment. Computer generated randomised assignments can help to reduce the incidence of copying and restore confidence in their use. They can also be used to encourage student perseverance by offering options for students to verify their answers.

Some examples of randomised assignments used in first year at UNSW and high schools will be presented and their advantages and limitations discussed.