Introduction
As we know, the study of mathematics is not just limited to recalling formulas and equations, but also involves cultivating valuable problem-solving skills and critical thinking abilities that can be applied across various domains of life. The teaching of mathematics is a dynamic field that continually evolves as technology advances, researchers gain insights into how students learn and teaching strategies become more refined.
As an educator, I strive to stay up-to-date with the latest trends and innovations in the field and was honoured to have been selected as a guest on the brand new Australian Association of Mathematics Teachers (AAMT) podcast hosted by CEO Allan Dougan. In preparation for this I reflected on my own experiences and learnings as a teacher, Master Teacher, and Deputy Principal over the last two decades and have since decided to expand some of those notes into the blog post you are currently reading. I will share some thoughts and insights on what makes me passionate about mathematics education, my background as a Master Teacher, and what I have learned regarding mathematics education in schools. Please take a listen to that podcast, and subscribe to other great episodes here: https://open.spotify.com/episode/0tG4wyWw0K1gO86uACZmwz?si=HWaaVUjdT0eUy8LzbvddsQ&nd=1
What makes me passionate about mathematics education
I was never someone who was naturally good at mathematics. In high school, I struggled with the subject and it wasn’t until I fell into teaching (after working at an outside school hours care facility) that I discovered the relevance and importance of mathematics generally and also educationally. In my time as a classroom teacher I came to believe that understanding mathematics is key to understanding the world around us. Moreover, critical thinking skills, problem solving ability and financial education are essential skills that we are tested on daily.
Witnessing students make progress and experience joy in their mathematical learning is what excites me the most about mathematics education. When done well, math education can spark engaging and thought-provoking discussions that enhance students' understanding of mathematical concepts. However, I am aware that some classroom teachers prefer primarily explicit teaching which may limit this, because they may wish to have a higher degree of control of the classroom or may have anxieties about having uncomfortable discussions about mathematics curriculum (including acknowledging that math is not always ‘right’ or ‘wrong’), or being unable to answer a student’s question. The current version 8.4 Mathematics Curriculum has many Aims for the students. These include developing proficiency with mathematical concepts, fostering a positive disposition towards mathematics, and acquiring specialist mathematical knowledge and skills. Some of these aims are hard to achieve with just explicit teaching.
My Background as a Master Teacher 2015-2018
In 2015, I was fortunate to be selected as one of the first "Master Teachers" in Queensland, where I first truly understood the importance of the proficiency strands of problem-solving and reasoning (that sit alongside fluency and understanding). With additional support and training, my role as a Master Teacher included hosting meetings with year levels of teachers, classroom modelling, researching best practice and providing feedback and coaching to teachers.
I focused on mathematical warm-ups using concrete materials such as dice and cards and using authentic situations such as Dan Meyer's 3 acts to encourage positive student/teacher disposition. In addition to this I was fortunate enough to network widely within the Hervey Bay cluster and further afield with experts such as Dr Dan Meyer, Michael Ymer, Tierney Kennedy, Rob Proffitt, and Peter Carmichael. We used "Teaching Primary Mathematics" (5th edition by Booker, Bond, Sparrow, Swan, 2014) as our pedagogical ‘bible’. While most teachers are knowledgeable about what to teach, they may not always have the pedagogical skills to effectively convey mathematical concepts, particularly given the complex developmental stages that students progress through in math education. This book walked us through a lot of that. Philosophically, Dr Dan Meyer’s “Math Class Needs a Makeover” (https://www.ted.com/talks/dan_meyer_math_class_needs_a_makeover ) struck a chord with me that has resonated ever since. If you haven’t viewed this clip, I highly recommend it.
What have I learned, and how do I feel math can be taught in schools
A debate persists between proponents of explicit teaching and advocates for implicit or student-led pedagogy in mathematics education. From my experience in the classroom, I propose a balance of these with an example structured mathematics timetable to ensure each week has a combination of these approaches.
Teachers should be able to adapt to students' needs and incorporate different pedagogical approaches depending on the topic being taught as well as being aware of their own math misconceptions, and anxieties and work to change their habits to feel confident teaching the subject. Coaching and mentorship play a significant role in helping teachers learn and grow in this regard and is something I enjoy. Learning from past mistakes is also essential in helping teachers improve their teaching strategies. The use of mini whiteboards and adequate resources, both physical and human, can improve the learning experience for students. Teachers should also remember that teaching does not have to be perfect.
The 5 Practices Model (Smith, Stein et al – Orchestrating Discussions 2009) is a useful framework for teachers to facilitate mathematical discussions in classrooms. These practices involve:
anticipating student responses to challenging mathematical tasks
monitoring students' work and engagement
selecting particular students to present their mathematical work
sequencing the student responses that will be displayed in a specific order
connecting different students' responses and connecting the responses to key mathematical ideas.
My Go-To Resources
The classrooms where I work are filled with mathematical resources such as dice, playing cards, dominoes, various counting sticks and blocks. As with any tool, they are only as useful as the content and teaching which drives them. I also highly recommend the following websites which can be a great base for facilitating mathematical discussions:
Websites | Web Address | Summary |
Open Middle | Challenging Math problems worth solving | |
Esti-mysteries | Estimation mystery tasks for all year levels | |
3 Acts | 3 acts of a mathematical stories- visual/video questions to promote problem solving and reasoning | |
Estimation 180 | Estimation tasks that make mathematical reasoning accessible to students and enjoyable. | |
Would you Rather? | Asking students to choose a path and justify it with math | |
Mashup Math | Puzzles, activity books pre-algebra | |
Fraction Splat | Interactive number sense strategy that can be used | |
Solve Me Mobile | Pre-algebra visual mobiles | |
Which One Doesn’t Belong | Thought-provoking puzzles for math teachers and students alike |
The Future of Math Education
The future of math education undoubtably involves the teaching and experiences of mathematical modelling and increased communication and groupwork. I asked ChatGPT what the greatest challenge is for mathematics education and it gave some pretty decent answers:
Lack of training or experience: Many teachers may not have received adequate training on how to teach real-world problems in math or may not have much experience in doing so. This can make it difficult for them to incorporate these types of problems into their lessons effectively.
Time constraints: Teachers often have a limited amount of time to cover a wide range of material, which can make it challenging to devote enough time to teaching real-world problems. Explicit teaching can be more efficient in terms of covering material quickly.
Pressure to meet testing standards: In some cases, teachers may feel pressure to focus on teaching to the test, which can lead them to prioritize explicit teaching over real-world problem-solving.
Lack of resources: Teaching real-world problems often requires access to resources beyond what is available in the classroom, such as technology or real-world data. Teachers may not have the necessary resources to implement this type of teaching effectively.
Student readiness: Some students may struggle with real-world problems if they lack the necessary background knowledge or skills. Teachers may feel that it is easier to teach explicit math concepts that build on each other sequentially rather than introducing real-world problems that may require additional scaffolding.
On a positive note, educators today exhibit a remarkable level of dedication to facilitating learning for all students. The availability of resources and advanced diagnostic testing tools has greatly facilitated teachers in identifying areas where students may be encountering difficulties and determining their specific needs. A strong emphasis on networking and collaboration among teachers, especially in online communities, has contributed significantly to the enhancement of math education.
In classrooms, teachers are increasingly incorporating interactive and engaging activities, harnessing the power of technology to foster effective learning experiences, and offering personalized support tailored to each student's requirements. With educators constantly finding new ways to add value to math education, it's clear that the future holds infinite possibilities for our young learners.
“Teaching is a Team Sport” Mark Hansen
Endnote: (Caution: not-so-humble plug:)
I have also written two internationally published mathematical children’s books through not-for-profit US Group TBR-Books:
Math for All – Mark Hansen (2021) 
| Come on a fun-filled journey with Hope the hedgehog, Mike the macaw, Leroy the llama and Tia the turtle as their teacher Ms Penguin shows them the beauty of mathematics. Join them as she dispels their long-held myths about math and read in wonder as each student discovers their long-lost love of learning. Will they change their beliefs about math? Can they fall in love with math again and help others do the same? The answers are revealed within! | https://www.youtube.com/watch?v=tjkKzwG7erU by the Author | |
My Garden is a Square – Mark Hansen (2022) 
| My Garden is a Square: A Journey Through the Home of Numbers and Shapes. This rhyming children’s picture book enables young readers to see the patterns and structures in numbers and shapes through the magical world of Numberland; a land where numbers come to life and have their own houses and gardens! The story and pictures inspire us to find mathematics in the world around us: Number Four has 4 braids in her hair and 4 flowers in her square garden… Why? And what else can you find?The concept of Numberland was first conceived in 2004 from research into children’s mathematical development by Dr Gerhard Friedrich of Germany. | https://www.youtube.com/watch?v=5idrZO0sPrI by Education Influence |