AMA Mathematics and Calculus Teachers' Day 2016

AMA Mathematics and Calculus Teachers' Day 2016

AUT City Campus, 55 Wellesley Street East, Auckland, 1010

Thursday 24 November 2016

The annual Mathematics and Calculus Teachers’ Day will be held on Thursday 24 November 2016, at the City Campus ofAUT (Auckland University of Technology) – rooms WG402, WG403, WG404, WG407, WG607, WG608 & WG609

The day is an opportunity to catch up with developments in Mathematics; to share resources and ideas; to listen to others; and to meet up with people old and new.

Registrations open on Thursday 27 October and will close on Friday 18 November.

Programme outline

8:30 – 9:00 am / Registration
9:00 – 10:00 am
/ Plenary 1 : David Pomeroy, Victoria University
10:00 - 10:30 am / Morning tea
10:30 - 11:30 am / Workshop 1 (7 separate rooms)
11:35 am - 12:35 pm / Workshop 2 (7 separate rooms)
12:35 - 1:20 pm / Lunch
1:20 - 2:20 pm / Workshop 3 (6 separate rooms)
2:20 - 3:20pm / Panel Discussion

Registration Information

Notice of late withdrawal
If, after registration, you cannot attend, you are welcome to send a replacement from your school. If you don’t have a replacement please let us know because there could be a waiting list. E-mail non-attendance to . Deadline for withdrawal and refund is 12 noon Monday 21 November 2016.

Registration Form

Before proceeding to register please ensure that you have selected the workshops you wish to attend. You willbe askedto choose, in order of preference, three workshops in each of the three sessions. We will do our best to give everyone at least 2 of their first 3 choices.

Access the registration form

Confirmation of registration

Registration will be confirmed (by email) within two days of receipt, and at the latest by late Friday afternoon 18 November 2016

Cost

AMA School Members $90 (incl. GST)
AMA Personal Members $70 (incl. GST)
Non-members $110 (incl. GST)
Pre-service Teachers $90 (incl. GST)

Payment details

Payment should be made to the Auckland Mathematical Association (GST Number 55-126-402) as soon as possible after registration is confirmed.
Details of payment methods will be included in the information sent with confirmation of registration.

Contact for queries

Tony CareySteve Buckley
Phone: 09 269 0690 ext 23409 535 2620 ext 805
Email: @macleans.school.nz

Plenary:

David Pomeroy, Victoria University –Grouping and the flourishing of mathematical ability: old debate, New (Zealand) evidence

Ability grouping (or ‘streaming’) has been a controversial topic in mathematics education for a long time, yet until recently there has been very little research on the topic in Aotearoa/New Zealand. In this talk I aim to help teachers to make well-informed professional decisions in the best interest of their students, in two ways.
1. I will review international and more recent New Zealand evidence about how different ability grouping practices can affect students’ attitudes towards and achievement in mathematics. This will be most useful for teachers making decisions about departmental or school-wide practices for allocating students into class groups.
2. I will discuss which effects of ability grouping are inevitable and which depend on particular teaching practices. There will be lessons here for how teachers can help students’ mathematical ability to flourish, whatever the approach their school takes to ability grouping.
This presentation will focus on providing a credible and coherent evidence base to support reflection and planning at both the individual and the departmental level.

Workshops:

Workshop 1(pick three in order of preference)

1ADavid Pomeroy, Victoria University - Rich Tasks: academic idealism or a way forward for mixed-ability classes?
High quality Rich Tasks are accessible and extendible, i.e. they are ‘low threshold, high ceiling’ activities. For this reason, many educators argue that they are ideally suited to classes with a wide range of mathematical abilities. This workshop will start with a short introduction to the key characteristics of high quality Rich Tasks. Most of the session will then be devoted to participating in one case study task, discussing the pros and cons of such tasks, and working through some of the challenges involved in using Rich Tasks in secondary classrooms. The session will end with an overview of some of my favourite Rich Task resources.

1BPolly Stuart,Westlake Girls - Using eLearning to make learning Maths more engaging.

There are always a wide variety of abilities and understanding in maths classes. With elearning we can cater for this in lots of ways which are engaging, open ended and target individual needs. Here are some ideas to try. Please bring your device so you can try out some of the activities!

1CPaul Cliffe, Kristin School - Teaching is not Telling

Do you believe that discovery or inquiry-based learning would be the best way to help students understand Mathematics, but find this approach difficult to implement in the classroom? How often do students say they understand but in reality they have just learned a technique or algorithm for doing something that can be forgotten just as quickly as it was “learned”. This workshop will address the conditions needed to foster an environment of student investigation and discovery that will bring meaning and foundation back into student learning. This approach can be used from Year 9 to Year 13 so come along prepared to be challenged

1DRobyn Masanga, Whangaparoa College - Enhance Learning in your Junior Maths Programme

A discussion on re-evaluating the key learning objectives of individual topics in the junior programme and tailoring the teaching, assessment methods and other initiatives to enhance students’ learning of those key objectives. I will be sharing some ideas and initiatives we have tried this year at Whangaparaoa College and highlight the successes and difficulties we had.

1E Margi Leech, Numicon NZ - Maths learning difficulties and dyscalculia

Students who struggle with maths wish every lesson could be over with very soon. They need a particular kind of support to help them understand the concepts, know how to solve problems and then have the opportunity to apply them to other spheres of maths and the curriculum. They may also have dyslexia. This workshop will give you some insights into maths learning difficulties and how to support your students.

Margi Leech is a primary teacher passionate about using structured apparatus, guided teaching practice andconversationsto help students understand and enjoy maths. She runs courses and workshops throughout NZ in primary and secondary settings. Year 9 and 10 teachers love this approach in particular, to bring their students up to NZC level in readiness for NCEA.

1FCaroline Yoon, University of Auckland - 13 ways of looking at a (calculus/discrete mathematics) problem

One’s success in mathematical problem solving is largely dependent on one’s point of view. A small shift in attention can dramatically change how one make sense of the problem, transporting one from feeling stuck and frustrated, to the aesthetic pleasure of working out a solution that seems easy and elegant in its unravelling. In this workshop, we will look at a variety of ways students look at a challenging, open-ended problem about the relationship between functions, their derivatives and antiderivatives (task 7 in the Graphical Antiderivatives booklet in the LEMMA series). We will analyse different student responses, and discuss how we might respond as teachers to encourage productive shifts in attention.

1GMarius Sandu, LynfieldCollege -iMathLync

iMathLync is a FREE web based mathematics platform which integrates diagnostic, teaching, learning and assessment, with rich mathematical content. Students can receive immediate feedback on algorithmically generated questions with numerical, graphical, or algebraic expression answers. Its functionality is only limited by the teacher's willingness to collaborate and/or move outside the classroom walls. From classroom flipping to "solve this equation" or application type of tasks, everything is possible. Thinking of embedding graphs and equations with arbitrary constants? iMathLync allows you to do that too. Drawing graphs? Of what functions? Linear - tick; Quadratic - tick; Cubic - tick; Sqrt - tick; Exponential - tick; Absolute value - tick; Hyperbolic - tick; Conic - tick; Trigonometric - tick; vectors - tick.

Last but not least, by signing up for this workshop you will get to rub shoulders with some of the great minds of Mathematics of all time, from Pythagoras to Leibnitz and even grumpy Sir Isaac.

Just sign up, bring an internet enabled device plus PEN and PAPER and we can start blending. See

Workshop 2 (pick three in order of preference)

2AAmy Shen,Howick College -Power of e

E for excellence in education, what's your perspective of e: E-learning? Empowering? Elaborate group activities? Evaluation? Enthusiasm? After a showcase of pictures in Maths classroom teaching, we will take a ‘Number Train’ to ‘e wonderland’ to discover the powerful number e associated with other mysterious numbers: π, ἰ, 1 and 0 all integrated into one formula: Euler’s Identity. We will depart from Pascal’s Triangle station where the number e will be introduced and the exponential function will be developed. Once we have inspected the properties of the exponential function, we will be guided by Pythagoras to explore π in a unit circle then De Moivre will reveal the Euler’s formula and apply his theorem into a complex number. Euclid needed the number 1 to make up his perfect number, while the Ancient Chinese used the round symbol 0 to represent the harmony between Number and Nature. Euler related them as one: eiπ + 1 = 0After arriving at our destination, we will use the number e to model nature as exponential functions in order to solve real life problems. Past Calculus Scholarship exam problems may be selected.
This presentation will cover Number patterns, Algebra, Trigonometry, Geometry and Calculus.

2BVladimir Miskovic, KingsWay School–Algebraic Visualizations

Come and experience the synergy of innovation, modern technology utilisation and beauty of algebra. Interactive Algebraic Visualizations help achieve classroom outcomes which were previously inconceivable! They equip teachers to softly and imperceptibly push forward the learning intentions for all learners. Instead of using a single frame which explains a certain learning objective, by going through a set of situations we can obtain longitudinal augmentation or we can have a cascade that expands learning outcomes in their depth (transversal enrichment). A well - paced combination generatesnew insights which help building a big picture in learning algebra and creation of meaningful links between what, how and why. COMMERCIAL

2CSara Sharples, Takapuna Grammar School -Getting students moving and talking

Why it is so important to get our students, especially our juniors, moving and talking and the type of student these activities most suit. Then a range of activities that either get students moving and/or talking with tips and hints of how to make the most of them in your courses. This will be a hands-on sessions where teachers can see why students like these activities.

2DJared Hockly, Western Spring College -Coding and Robots in Maths lessons(limited to 24-30 teachers)

This workshop is a chance to see how coding (or programming) can provide an exciting and meaning context for learning and applying mathematical ideas. We’ll have a play with some Sphero robots and do a couple of activities that relate to junior and senior level mathematics. We’ll also look at the practicalities of doing something like this in your own school.

2EJulia Novak, University of Auckland - NCEA preparation for Stage 1 Mathematics papers at UoA

Over the past five years, with curriculum changes at NCEA Level 3, the mathematical preparation of students enrolling at the UoA has become more diverse. As such there is a need to provide greater guidance to students in order to ensure they select the Stage 1 Mathematics courses that are appropriate for them. The UoA Planning and Information Office has conducted an analysis of all school leavers, with NCEA qualifications, since Semester 1, 2014 who have enrolled in Stage 1 Mathematics courses at UoA. This analysis has not only revealed the Achievement Standards that are the key indicators of success in the different Stage 1 Mathematics courses, but it has also enabled us to construct evidence based advice on the appropriate courses for students with different preparation.

The entry level Mathematics courses at UoA, Maths 102, Maths 108 and Maths 150 attract large numbers of students per year and serve as prerequisites for many degree pathways at the University. Julia will discuss the results from the analysis, including new findings and the evidence based course advice. She will also describe other transition issues that students face when they tackle tertiary level mathematics for the first time.

2FWid Al-Rahim, HoD Marist College -To cancel or not to cancel, that is the question

How many solutions does a polynomial equation have? Can we cancel out like terms in a rational expression? How about a rational equation? How will cancelling out like terms impact the domain of a function? Is it correct to cancel “holes”? In this presentation, I will be addressing the concepts above, concluding with a detailed examination of question two (e) in the 2016 MCAT and the solution offered by the NZQA marking schedule.

2GJean-Francois Maheux, University of Auckland - Playing with algorithms, an historical perspective

Calculation by hand using algorithms is often seen as a dull, mindless activity. Thus, we tend to forget how powerful these algorithms are, their importance in the history and present day of mathematics, and the special kind of mathematical experience they offer. In this workshop, I will present some elements of the history of calculation algorithms (e.g. for multiplication, division, root extraction, trigonometric evaluation, etc.), and give participants an opportunity to play with some of them. This will give us an occasion to highlight important mathematical ideas that are involved, such as surjection, convergence, recurrence, continuity, and of course our base-10 positional number system, and discuss possible classroom activities around algorithms.

Workshop 3 (pick three in order of preference)

3ARaquelTorrejon: Sancta Maria College – Flipping Calculus

Raquel has flipped her calculus course for the last three years. Students learn the concepts by watching a video at home and then spend classroom time refining their learning by questioning and investigation. The flipped classroom has made class time more pleasant for everyone.

In this workshop we share ideas and we flip a lesson of our choice. Bring your tablet or laptop!

3BSergiy Klymchuk, Auckland University of Technology - Puzzles, Paradoxes and Provocations in Maths and Calculus

This practical workshop deals with the regular use of puzzles, paradoxes and provocations as a pedagogical strategy to enhance students’ generic thinking skills. By a puzzle we mean non-standard, non-routine, unstructured question presented in an entertaining way. Typically, a puzzle appears deceptively simple. By a paradox we mean a surprising, unexpected, counter-intuitive statement that looks invalid but in fact is true. By a provocation we mean a question that looks like a routine question but in fact has a catch. It analyses the ability to pay attention to detail and use mathematical knowledge The intention of using puzzles, paradoxes and provocations in teaching and learning is to engage students' emotions, creativity and curiosity and also enhance their problem-solving skills and lateral thinking “outside the box”. Other potential benefits for students are also discussed in the talk. Many examples of puzzles, paradoxes and provocations presented in the talk can be used in the classroom.

3CWayne Atkins, HoD Pacific Advance Senior School – On Your Marks

Using Results data to understand the ethnic and decile bias in delivery of mathematics in New Zealand - Diverging Educational Outcomes. Looking at Failure Rates as an indicator of poor resource use within schools due to lack of differentiation in the classroom. How to spot it and how to improve outcomes.On Your Marks repackages the NZQA results for schools to assist with departmental reporting to BOT and to help with four-year analysis of school results data. Reports are available immediately after NZQA data release.COMMERCIAL

3DIgor’Kontorovich, University of Auckland - Definitions, conventions, notations: What can be done with them beyond memorization?

On the one hand, a student should be fluent with definitions, conventions, and notations for speaking the language of mathematics. On the other hand, their learning seems to leave a little room for a pedagogical manoeuver: what can be done with them other than taking-as-shared? In this workshop, I will present several task formats for classroom discussions that can lead to connections between seemingly unrelated ideas, new knowledge, reasoning, and mathematical fun.

3ECaroline Yoon, University of Auckland - Freedom, constraints and border crossings: multiple strategies in a modelling activity

Mathematical modelling involves shuttling back and forth between the disparate worlds of creative freedom and externally imposed constraints. The back and forth can be dizzying, but can also yield new solutions that would not have been possible in either single world. Workshop participants will be invited to work on a new mathematical modelling activity involving geometry and discrete mathematics, where freedom and constraints are visualised in geometrical ways. We will analyse multiple approaches and solutions from students and mathematicians, and discuss how to make use of the productive tensions that mathematical modelling offers.

3FMargi Leech, Numicon NZ - Supporting students in the introduction to learning algebra with visual tools

Learningalgebra brings either joy or fear to students! Toreduce the fear and anxiety, using structured apparatus and visual tools, students realise that theyhave been doing algebra for years!The abstractness andgeneralising thinking required can be helped with the use of structured apparatus. This workshop will show you how to use Cuisenaire rods, Numicon, Base 10 and geometric shapes to support children’s thinking in theintroductory stages.

Panel Discussion: 2016 MCAT & Other NCEA Issues

This is likely to be a discussion of current NCEA issues with three or four panel members chaired by Rachel Passmore (AMA President). Questions and topics for discussion will be requested from delegates in advance