The Australian Association of Mathematics Teachers

A great article from The Conversation about how maths teaching has changed …

'Why would they change maths?' How your child's maths education might be very different from yours In the past, maths teaching has focussed on procedures and right answers. Today, teachers want students to form connections between concepts and solve problems.

This week, we look at giving feedback in maths lessons with some ideas taken from the Maths in Schools podcast Strategies for Explicit Teaching - Feedback.

1) Know what feedback is and isn’t.
Feedback is not praise, rewards, criticism or punishment, but specifically information given, that is designed to help a person (the student) progress and improve in a specific task. It needs to create action or change for the improvement to occur.

2) Make the feedback specific and actionable
To be specific, feedback should let a student know what needs to be done to improve and to be actionable, it should let them know how to do it. But learning is an individualised human endeavour, so this is not a formulaic approach, instead it needs to build on empathy, trust and the connections the teacher has built with their students, to motivate them to want to improve or complete a task for themselves.

3) Make space for feedback in planning
Having clear lesson goals and success criteria including considering misconceptions, preempts likely points of feedback, which allows the teacher to consider in advance how they might need to get the students back on track. Lessons should be planned to allow time for deliberate noticing, where the teacher walks the room and collects information on how each student is progressing, creating natural opportunities for feedback.

If you are interested to learn more, check out the podcast interview with Thomas Moore https://omny.fm/shows/strategies-for-explicit-teaching/ep06-feedback and the other Maths in Schools resources on the Mathematics Hub website. https://www.mathematicshub.edu.au/understanding-maths/professional-learning/maths-in-schools-professional-learning/

Joining Allan this week on our Strength in Numbers podcast is Master Teacher, Deputy Principal and published mathematics author, Mark Hansen. Together they explore Mark’s experiences in primary schools and how he enjoys using a range of pedagogical tools to explore the four mathematical proficiencies.

They discuss the application of German psychologist Hermann Ebbinghaus’s curves of learning and forgetting, using interleaved activities to revisit previously learned concepts, examine some common misconceptions about maths learning and consider the future of maths education in our modern age: How do we bring the world into our maths classrooms?

There’s a lot to think about, so if you haven’t subscribed to our podcast yet, here’s the link to every possible streaming service: https://aamt.edu.au/teachers/event/strength-in-numbers/

To see and hear more from Mark, email him at [email protected] or find him on LinkedIn at
https://www.linkedin.com/in/markhansen1983/

Strength in Numbers - Australian Association of Mathematics Teachers Strength in Numbers is a new podcast from AAMT. Join Allan Dougan and guests as they explore the world of mathematics education.

Although non-mathematics teachers may think marking examinations and other assessments in maths is easy, it’s not always as black and white as it may seem, with multi-mark questions and answers requiring reasoning being especially tricky. This week we explore three ways to make marking assessments in maths as easy as 123…

1) Aim to award marks, not deduct them
A positive approach to marking helps students gain credit for showing what they know. It’s important to think about carried forward mistakes and how an error in an early part of a solution obviously creates the wrong final answer, but can disguise a lot of excellent and correct mathematical thinking that should be recognised. Also, if a student has made a simple mistake (such as a transposition error or using an incorrect pronumeral) but has demonstrated good understanding of a complex mathematical concept, perhaps they deserve full marks

2) Think - What is this question trying to assess?
Understanding the core skills and concept knowledge required to earn each mark in a question is essential. Often questions require multiple skills, such as converting units, finding the area of a shape and solving an associated problem and if so, each skill should be separately recognised. The easiest way to identify this is with a good marking guide prepared in advance (mentioned in last week’s post on how to write a maths exam), but if this hasn’t been provided, the marker needs to create one and ensure that they apply it consistently across all students.

3) Be flexible
This may seem to contradict the previous statement, but it’s important to recognise that there are many ways to answer maths problems and students may use strategies different to those envisaged by the exam writer. Unless a particular method is specified in the question, alternative methods should be accepted, which may necessitate making changes to marking guides and even re-marking previous papers !

This week’s special guest on our podcast almost needs no introduction. Dr. Peter Liljedahl explains to Allan why his book, Building Thinking Classrooms in Mathematics, resonates so much with teachers and the answer ‘verisimilitude’ even helps expand your vocabulary with a new word of the day.

From building a thinking primary classroom, to disrupting the system of teaching norms with cars, metronomes and beanbags, there’s something for every teacher of mathematics, to both entertain and help develop your practice. You can hear more about Peter’s forthcoming visit to Australia and if you aren’t able to see him in person, get a copy of his book, which is available from our bookstore https://mathsstore.org.au/ at the very special members’ price of $18.40, either for you or your staffroom.

Check out our website to subscribe to the podcast or search for Strength in Numbers, wherever you get your podcasts. Happy listening!
https://aamt.edu.au/teachers/event/strength-in-numbers/

This week we look at the traditional mathematics test or examination being used for formative assessment of learning. Creating a good maths exam is a skill, so we present three common sense ideas to consider when writing examinations in maths.

1) Decide what you want to assess
This may seem obvious but having a clear idea of the concepts being assessed helps guide the creation of the exam. And ensuring that the same concept is not assessed multiple times doesn’t penalise students repeatedly. Think whether you want to assess (and hence award marks for) concepts from previous terms / years. Are there going to be differentiated assessments for different students? Can students use a calculator or manipulatives, bring in notes, a ‘cheat sheet’ or use a standard reference sheet to help them? If so, the questions should reflect this.

2) Think about the time requirements and accessibility of the questions
Every school is different, but one rule of thumb for example for maths exams in years 7 to 10 is to allow one minute per mark. It’s also important that exams contain a good quantity (perhaps 75% of the marks) of familiar and standard questions that you might see in a textbook or worksheet. Multiple choice questions provide opportunities for all students to make an attempt, but have downsides too. Meanwhile, the inclusion of some more challenging problem solving or unscaffolded questions allows for greater differentiation between the higher achieving students.

3) Sit the paper and create a marking guide
Many schools have buddy systems where another teacher sits and reviews the test. If this is not possible at your school, leave the paper for a week and then sit it - it’s amazing what errors / ambiguities you can pick up after a break. And use calculators and online tools like https://www.desmos.com/ and https://www.wolframalpha.com/ to check any complex solutions. Create a marking guide or assessment rubric, especially for multi-mark questions, being clear what is needed to earn each mark, for example considering whether units, correct rounding and correct spelling are required.

We're into our second podcast in our Strength in Numbers series and this week our CEO Allan Dougan is joined by Rebecca Garrett, Head of Teaching and Learning at Trinity College, Adelaide and former President of the Mathematical Association of South Australia.

Rebecca shares stories of how she continues to learn from her fellow teachers, her passion for being involved in the wider mathematics teaching community and most revealing how she’s not that good at spear throwing.

To hear more, our website contains links to all the popular streaming services or you can search for and subscribe to Strength in Numbers, wherever you get your podcasts...

https://aamt.edu.au/teachers/event/strength-in-numbers/

The Australian Institute for Teaching and School Leadership (AITSL) have developed a draft set of Professional Standards for Middle Leaders and want to hear your thoughts.

In conjunction with Queensland Department of Education, AITSL are currently running a national validation process to get feedback on the draft standards. They want to hear the voices of Australian teachers, middle leaders and principals – and anyone else with an interest in our middle leader workforce.

The survey is quite comprehensive and takes at least 30 minutes to complete. But you need to be quick, as the survey closes on 4 August 2023.

Access the survey via AITSL's website:
https://www.aitsl.edu.au/lead-develop/teachers-who-lead/middle-leadership-standards

Professional Standards for Middle Leaders The Professional Standards for Middle Leaders will align with and complement the Australian Professional Standard for Principals and the Australian Professional Standards for Teachers.

This week we are shamelessly borrowing some ideas from Peter Liljedahl’s book, Building Thinking Classrooms in Mathematics. We’re looking at the first three of his fourteen practices, as we explore how it is Easy as 123… to build a thinking classroom.

1) Choose the right tasks
The best rich and engaging tasks don’t always map nicely into curriculum outcomes. So, Liljedahl suggests that to really get your students thinking, for a short time (he suggests a week) you need to forget the constraints of the curriculum and set truly engaging tasks for your students. Students want to think and to think deeply and are empowered to do this in non-curricular tasks, which the teacher can then build on by moving into scripted curricular tasks.

2) Form random groups
When teachers form groups for social or educational goals, their goals rarely align with those of their students, which leads to some disengagement. If instead, students work in truly and visibly random groups which frequently change, engagement, thinking and willingness to collaborate increases.

3) Get some whiteboards
In his research, Liljedahl had groups of students use vertical and horizontal whiteboards and flipcharts and traditional notebooks, evaluating a range of features including time to start the task and start writing, time on task, amount of discussion, persistence and amount of knowledge mobility. Vertical whiteboards emphatically produced the most positive results, followed by horizontal whiteboards.

If you want to learn more, we recommend that you get a copy of Liljedahl’s book, either from your local bookshop or from our online store at the very special member’s price of $18.40. https://mathsstore.org.au/product/building-thinking-classrooms-in-mathematics-grades-k-12-australian-edition/

Peter is also appearing as the guest on our new podcast Strength in Numbers in a couple of weeks, so sign up now to hear from the man himself!

Our first Strength in Numbers podcast has dropped and this week's guest joining our CEO Allan Dougan, is AAMT's very own Education Specialist Denise Halliday. Allan and Denise talk about a range of topics from current trends in maths education, how we can engage our students to a bad day in the classroom.

Follow this link to listen on our website https://aamt.edu.au/teachers/event/strength-in-numbers/ or search for and subscribe to Strength in Numbers, wherever you get your podcasts...

Welcome back to Term 3 teachers, whether it's your first day in school, or you're already into Week 2! We hope you had a great break and are refreshed and raring to go.

If you are looking for professional learning don't forget that we have our Maths300 online 1 hour PL sessions coming up on Monday and Tuesday next week. They are perfectly timed for our colleagues in Western Australia at 4pm AWST, or for those teachers elsewhere who can't make a session straight after school, that's equivalent to 5.30pm ACST or 6pm AEST.

At a cost of only $49 per teacher it's a great way to learn how to develop your pedagogy, using investigations, simulations and mathematical models in the maths classroom and to get more out of Maths300, so head to our website at https://aamt.edu.au/teachers/event/webinars/ to learn more and to register.

The importance of great teachers cannot be overstated.

These are the opening words in the Australian Government’s Quality Initial Teacher Education Review report, published at the end of last week and we can’t agree more.

The Strong Beginnings: Report makes 14 recommendations across 4 domains with a goal of aiming to improve initial teacher education to better attract, train and retain teachers. It’s well worth a read, especially for mentor teachers who supervise practicum students, or for student or prospective student teachers.

https://www.education.gov.au/quality-initial-teacher-education-review/resources/strong-beginnings-report-teacher-education-expert-panel

Strong Beginnings: Report of the Teacher Education Expert Panel - Department of Education, Australian Government Final report of the Teacher Education Expert Panel, chaired by Professor Mark Scott, AO

We're excited to announce the launch of our new podcast Strength in Numbers. The podcast features interviews with leaders in maths educational practice and research from across Australia and internationally.

Just this term, we'll be talking with expert researchers like Peter Liljedahl from Canada and Kim Beswick from UNSW, practising secondary teachers like Rebecca Garrett from SA and Denise Halliday from NSW, and primary maths specialists like Sheila Griffin from WA and Mark Hansen from Queensland.

The podcast is aimed at teachers of maths or numeracy in any school setting, or anyone with an interest in current issues in maths education. It's hosted by our CEO Allan Dougan, and even features the return of our previous CEO Will Morony. The podcast is a compact 30 minutes long and designed to fit in with busy teachers' lives - on the commute to work or while exercising - to provide a relatively light hearted but informative discussion about anything and everything around maths teaching.

So, sign up today, wherever you get your podcasts, or use the links below so that you don't miss the first episode when it drops next week!

https://tinyurl.com/AAMTpodcastspotify
https://tinyurl.com/AAMTpodcastapple
https://tinyurl.com/AAMTpodcastaudible

This NAIDOC Week, we hope that you’ve been able to develop your understanding of and appreciation for Australian First Nations Peoples’ knowledges, experiences, values and perspectives and to understand how their cultures are strong, resilient, rich and diverse.

Our goal is to allow all teachers to feel confident to begin exploring these truths in their mathematics classrooms, both to help their non-Indigenous students better appreciate First Nations Australians’ Peoples, histories and cultures and to
allow Aboriginal and Torres Strait Islander students to see themselves and their cultures reflected in the curriculum.

You can find all this week's resources on our website at: https://aamt.edu.au/teachers/resources/naidoc-week/

We appreciate the support and assistance of our colleagues at the Aboriginal and Torres Strait Islander Mathematics Alliance (ATSIMA) in contributing to these resources and invite you to explore their work at https://atsima.com/.

NAIDOC Week 2023 : For Our Elders
‘They guide our generations and pave the way for us to take the paths we can take today. Guidance, not only through generations of advocacy and activism, but in everyday life and how to place ourselves in the world.’ (National NAIDOC Committee)

Our final maths activity of NAIDOC Week is another game, this time a propeller game called Koara, which provides many opportunities to explore probability and data concepts. The resource is targeted at high school students, from Year 7 upwards.

Koara means ‘play’ in the language of the Jawi People who once inhabited Iwanyi in Western Australia. Their story highlights some of the wrongs of the past that need to be acknowledged as part of our national journey towards reconciliation.

Click here to download the complete resource:https://aamt.edu.au/wp-content/uploads/2023/07/5.-NAIDOC-Koara-game.pdf

NAIDOC Week 2023 : For Our Elders

‘We draw strength from their knowledge and experience, in everything from land management, cultural knowledge to justice and human rights. Across multiple sectors like health, education, the arts, politics and everything in between, they have set the many courses we follow.’ (National NAIDOC Committee)

Our lesson resource today explores how First Nations Australian Peoples’ knowledge of animal tracks and prints has been passed down through generations. There are rich contextual opportunities to explore mathematical measurement concepts including length, mass, position, symmetry and transformation with students from Years 1 to 5 by exploring animal tracks.

Click here to download the complete resource:
https://aamt.edu.au/wp-content/uploads/2023/07/4.-NAIDOC-Making-tracks.pdf

NAIDOC Week 2023 : For Our Elders
‘The struggles of our Elders help to move us forward today. The equality we continue to fight for is found in their fight. Their tenacity and strength has carried the survival of our people.’ (National NAIDOC Committee)

Today our maths resource explores a counting game called Segur Etug, which is targeted at Foundation Year students. This instructional game was played on Mer Island in the Torres Strait Islands, which is the home of the late trade-unionist Eddie Mabo, whose activism led to the landmark Mabo decision, which still influences and shapes Australian politics and First Nations Australians’ rights to this day.

Click here to download the complete resource:
https://aamt.edu.au/wp-content/uploads/2023/07/3.-NAIDOC-Segur-etug-game.pdf

NAIDOC Week 2023 : For Our Elders
‘It is their influence and through their learnings that we must ensure that when it comes to future decision making for our people, there is nothing about us - without us.’ (National NAIDOC Committee)

Today we feature a maths resource aimed at Year 10, which explores the concept of Indigenous Data Sovereignty, which is the right of Indigenous Peoples to control, maintain and use data that relates to them and their communities. We hope you enjoy learning more and thinking about the who, how and why of data collection and analysis through this resource, specifically in relation to First Nations Australians.

Click here to download the complete resource:https://aamt.edu.au/wp-content/uploads/2023/07/2.-NAIDOC-Indigenous-data-sovereignty.pdf

NAIDOC Week 2023 : For Our Elders

‘They are cultural knowledge holders, trailblazers, nurturers, advocates, teachers, survivors, leaders, hard workers and our loved ones.’ (National NAIDOC Committee)

During Reconciliation Week we posted about the 90+ references to understanding Aboriginal and Torres Strait Islander Peoples, histories and cultures in the new Australian Curriculum v 9.0 for Mathematics. Your response told us you want to know more, so this week, we’ve created 5 different resources in consultation with ATSIMA, the Aboriginal and Torres Strait Islander Mathematics Alliance ().

These expand on some of the curriculum elaborations and explore the cultural significance and mathematical concepts to help teachers incorporate the cross-curriculum priority into their maths teaching and learning. We hope you and your students enjoy using them in your lessons as much as we have creating them.

Today begins with a resource targeted at Year 3, exploring counting practices of the Yolŋu People of North East Arnhem Land, using base 5 to count and share turtle eggs.

Click here to download the complete resource:https://aamt.edu.au/wp-content/uploads/2023/07/1.-NAIDOC-turtle-eggs.pdf

NAIDOC Week starts today and we're excited to be joining the celebrations. This year's theme is For Our Elders. Each day we’ll choose some words from the National NAIDOC Committee’s comments about the theme:

‘Across every generation, our Elders have played, and continue to play, an important role and hold a prominent place in our communities and families.

Our loved ones who pick us up in our low moments and celebrate us in our high ones. Who cook us a feed to comfort us and pull us into line, when we need them too.

We pay our respects to the Elders we’ve lost and to those who continue fighting for us across all our Nations and we pay homage to them.

In 2023, how will you celebrate For Our Elders?’

We’ll be posting every day this NAIDOC Week to show how we can celebrate our Elders through classroom mathematics activities. Please join us!

The accompanying artwork was created by Bobbi Lockyer, a proud Ngarluma, Kariyarra, Nyulnyul & Yawuru woman born and based on Kariyarra Country in Port Hedland and NAIDOC Artist of the Year 2021.

A quick message to our Maths300 users. We're sorry to say that we are experiencing some technical difficulties with Maths300 and our team are working to fix this ASAP.