In the last few weeks, ‘Maths Wars’ headlines have dominated the national educational conversation providing a new debate for educational leaders to weigh in on.
ACARA’s new draft curriculum advocates for inquiry approaches to mathematics where students problem solve, create, build, explore, and model during their lessons. With a significant body of evidence saying inquiry or discovery learning is less effective than teacher-led teaching, school leaders seem to be debating whether students should be taught algorithms and procedural knowledge explicitly, or given the freedom to solve authentic, real-world problems for themselves.
A heavy debate ensues when schools try to deliver one thing, one program and one standardised education for all students.
In the Seymour College Junior School, our approach to mathematics education is executed with an unwavering commitment to best practice for each learner.
John Hattie's meta-analysis of thousands of research papers outlines that high expectations from a teacher, and a teacher's belief that they can have a positive impact on a child's learning are two of the most significant factors in a child's academic improvement. There is no debate about that.
At Seymour College we believe fundamentally that:
There is no such thing as being born with a ‘maths’ brain, and no such thing as being born without one. Our students are consistently given positive messages about their potential and ability because we know that all students can achieve high levels of mathematics if they are given high level opportunities. The way that teachers create learning experiences to allow each student to reach their potential is by far the most important part of their job.
The most significant influence on learning is the feedback provided by a teacher with the intention to take the student beyond their own perceived performance ability. That is, pushing them to become better than they think they are.
If a child is struggling, they are saying one thing, “show me another way”. The support and differentiation we offer is underpinned by the latest research surrounding brain flexibility and plasticity. This research has shown the incredibly capacity of brains to grow and change in a really short space of time.
Targeted Small Learning Groups
We teach mathematics as an exciting, open, creative, and multi- dimensional subject beginning with initiating problems which provide a context for our students to dive into real and authentic mathematics. This sparks a curiosity for the topic in which they are about to cover, by providing a purpose in an engaging and fun way. The teachers are then able to identify where they need to pitch their explicit teaching to for their individual small groups, based on authentic assessment and observations.
As an introduction to Multiplication and Division, students were given the task of being an architect. They had to build ‘array’ cities, drawing a city skyline, with multiple buildings and towers, including all the windows, set in an array type pattern. Students had to write the equation at the bottom of each building, explaining how they calculated the number of windows. Students had the opportunity to record their thinking using post-it notes and pencils, or using the Show-me app, so that they could verbally explain their reasoning.
Teachers monitored how students grouped their windows and how they counted their collections. Did the students use effective strategies for multiplication and division? Did they understand the term “array”? Did the way they shaped their towers affect their ability to multiply by one- or two-digit numbers? It was also an interesting opportunity to see which students felt confident in their knowledge of their timetables. If the students encountered a need-to-know method, or required focus on algorithms or times tables, our teachers taught this to them within the context of their learning.
Therefore, our students understand how to choose and adapt different methods and to hold mathematical discussions.
Australia’s declining academic performance is old news
The Gonski review into the quality of Australian schooling highlighted declining academic performance which is “widespread and equivalent to a generation of Australian school children falling short of their full learning potential”. The report identified that Australian student outcomes have declined in reading, science, and mathematics, across every socio- economic quartile and in all school- sectors: government, Catholic and independent.
This matches the decline in Australia’s PISA (Programme for International Student Assessment) results, where students are performing two years behind their peers in the world’s best performing countries. Australian students are the equivalent of 1½ years behind top-performer Singapore's students in science; a year behind them in reading; and 2⅓ years behind them in maths.
The biggest difference in performance is in Mathematics, but why?
The indivisible link between literacy and mathematics
Comparing example questions from 2003 and 2012 PISA Mathematics papers show that students are not performing poorly because they cannot comprehend what they are reading.
Dr Misty Adoniou from the University of Canberra posits that students are performing poorly because they have poor vocabularies and cannot follow sentences that employ more complex language structures. Take a look at the examples below.
This is a Mathematics question from the 2003 PISA paper:
What is the key difference? The number of words, the vocabulary and the reading comprehension which is required for these students to unpack these mathematical questions.
Yes, results show that Australia is underperforming internationally in Mathematics, but what is getting harder isn’t mathematical concepts, it is the vocabulary, complex sentence structures and language which has changed.
Strong foundations of English and Mathematics
At Seymour College Junior School, we are not engaging in this debate. We know that strong foundations in English and Mathematics are the keystone of a quality primary education, and as a result, we begin small group learning from Reception. We proactively focus on developing the deep comprehension skills of students, and provide rich, explicit teaching based on the individual needs of our students.
Katharyn Cullen is Head of Junior School at Seymour College in South Australia