As we prepare for a new school year in a new decade, it is an apt time to reflect on the last ten years of mathematics education and consider the next ten. What, if anything, will change in our classrooms and school systems? Or will it be a case of the more things change, the more they stay the same?
Current challenges in mathematics education
Consider the current context of mathematics education in Australia and beyond. Over the past decade we have seen an apparent decline in senior secondary students’ enrolments in high level mathematics courses. We have also had continued challenges with students disengaging with mathematics and failing to see the relevance of mathematics. The last decade has also experienced a significant increase in the number of out of field teachers in secondary mathematics classrooms and we do not fully understand the potential impact of this on student learning.
According to media reporting of the 2018 Programme for International Asssessment (PISA) results, Australian students’ mathematical literacy results have declined and we are being outperformed by countries such as China, Singapore, Estonia, and others. Yet, take a closer look at the results and you will notice that there are no significant differences or trends since the last PISA testing. Nothing has really changed, but is that good enough?
Students in Australia and internationally continue to experience disengagement with mathematics as early as the primary school years. Mathematics is still viewed by many as a subject reserved for the ‘smart’ kids, and it still remains socially acceptable to openly claim to be “just not good at maths” or “not a maths person”. Despite research into student engagement identifying the elements required to address these issues, along with an abundance of fine-grained research into how students best learn specific aspects of mathematics and ways to harness the affordances of digital technologies, it appears we still face challenges. These challenges relating to student attitudes, their engagement, and a reduced desire to continue the study of mathematics beyond the compulsory years, often result in lower academic achievement. What can we, as leaders and teachers, do differently in this new decade to ensure positive change? Can we make changes that will ultimately result in an upward trend and with engaged students who value mathematics?
The tensions for teachers
Leaders and teachers experience tensions in their day to day teaching of mathematics. Should we teach to a test, or should we teach according to the specific and unique needs of our students? The levels of accountability due to high stakes testing such as NAPLAN and PISA have, in many cases, informed teaching practice due to the linking of results with school reviews. While NAPLAN was originally intended to be a diagnostic test, it has, according to Reid (2019), “moved from being a mechanism to check the pulse of one part of the education system, to being the reason that schools exist” (p.41). A further effect of standardised testing is the use of text books and other resources designed to prepare students for those tests rather than developing conceptual understanding using a broad range of pedagogies and rich tasks.
Standardisation vs. Future-focused education
In his recent publication Changing Australian Education, Reid points out that on the flip side of this educational debate is what is often referred to as ‘21st-century learning’. This future-focused approach includes strategies that appear to conflict with the standardisation approach that often results from high stakes testing. Student-centred strategies such as inquiry and project-based learning, flexible student groupings and the inclusion of general capabilities all espouse future-focused education, requiring students to be flexible, adaptable, agile and collaborative (Reid, 2019). All of these strategies are already embedded within our current mathematics curriculum, so while we may be conflicted in terms of teaching to the test or taking a more student-centred approach, we have, through our mandated curriculum, license to plan and teach in ways that are more meaningful for our students, and in time, change the landscape of mathematics education in this country.
What does this mean for mathematics for schools and classrooms?
One of the effects of a standardised approach is the ‘silo effect’ on how the mathematics curriculum is delivered in classrooms. Topics taught in isolation for the purpose of reporting and testing often result in students struggling to apply mathematics in novel situations and difficulties in making connections within and across mathematics topics. This then leads to disengaged students and a perception that mathematics is a practice that is restricted to the classroom rather than mathematics as a way of understanding and making sense of the world we live in. The following is a brief list of suggestions for leaders and teachers that may help combat the issues discussed above, and more importantly, lead to positive changes to student perceptions and performance in mathematics:
Scope and Sequence
A school’s scope and sequence document should reflect the big ideas in mathematics as well as the relationships across and within the curriculum strands. It should also be flexible to allow teachers the opportunity to spend more or less time on content in alignment with the needs of their particular students. The scope and sequence should also feature the processes of mathematics concurrently with the content. That is, the Australian Curriculum Proficiencies or the Working Mathematically strand in NSW.
Teachers should be also be given the opportunity to exercise their professional judgement. If schools subscribe to commercial programs that remove this judgement, individual student needs cannot be met. No program can replace the pedagogical relationships between a teacher and his or her students. These relationships are an essential element of teaching that directly influences student engagement and learning.
Our curriculum consists of two distinct areas: mathematical content and mathematical processes. We need to teach content via the processes. That is, we should be teaching through a problem-solving approach rather than teaching content in isolation. This reflects a ‘just in time’ approach as opposed to a ‘just in case’ approach. Teaching via problem-solving provides a context and a need to learn specific content in a way that has meaning for students. Teaching through a ‘just in case’ approach (teaching content in isolation) separates the mathematics from the numeracy and does not promote thinking and reasoning.
Using a range of resources include concrete and digital through primary and secondary schooling is also important if we are to improve students’ conceptual understanding in mathematics. Consider resources that can be used flexibly and also consider how the use of digital technology can not only enhance mathematical understanding by providing alternate and dynamic representations, it can also improve the teacher/student relationship by providing alternate avenues of communication, assessment and feedback.
Consider emphasising the ‘M’ in STEM and highlighting numeracy across the broader curriculum. While funds are still being heavily invested into STEM initiatives we must take the opportunity to ensure mathematics, which is the language of STEM, is prioritised. Opportunities for students to use mathematics in a range of contexts are critical if we want them to understand the relevance and make connections.
It takes a village
The phrase “it takes a village to raise a child” applies to mathematics education and improving future mathematics outcomes. Mathematics and numeracy is everyone’s business. Whether you are a primary teacher, a secondary teacher (of a discipline other than mathematics), a parent or carer, a politician, a celebrity, or anyone else with influence on children, we are all responsible for improving mathematics education. So let’s pause, take a deep breath, and think about what we can do differently to improve mathematics for our students as we begin this new decade.
Reid, A. (2019). Changing Australian Education. Sydney: Allen & Unwin.
I agree with most of this article, both as a parent of secondary school-aged childrenand and as a senior secondary mathematics teacher-a good read.
Thank you Dr. Attard, for your timely article.
Could it be the ‘out of field’ teachers you refer to might extend to British mathematics education authors between the 16th and 19th centuries? The reason I mention this is English language maths educators went ‘rogue’. They ignored the 7th Century Indian astronomer (Brahmagupta) who actually combined base-ten positional notation and the ‘laws of sign’ for what we call integer arithmetic, including, negative, positives and zero.
Thus, the current Australian curriculum is literally littered with logical mistakes. Mathematics is said to be the language God made the universe. However, many concepts taught in Australian schools (Grades 7 – 10) disagree with the basic laws of physics which describe our physical surroundings.
Yes, it takes a village to raise a child. Yet the best villages to have raised a child with optimal logical mathematical foundations consistent with the laws of physics were in India in the 7th Century.
Nobody in the West is solely to blame for the primary level curricula that customers (students) have been rejecting for centuries. Europeans never stood a chance of understanding India’s original (and correct) foundations of maths created by empirical astronomers. The reason is simple. India’s original and correct Integer arithmetic ‘curriculum’ was never understood in the 9th Century Arabic world.
So, with 2020 hindsight, our 2020 vision should be to overhaul our curriculum so it agrees with India’s common sense ‘lost logic’ of maths that is consistent with the laws of physics.
Yes, this comment is provocative for sure. Yet the answer to fixing maths education needs a different question. Our math garden is overrun with weeds. So, what OLD needs to be weeded and what NEW needs to be planted?
For those interested, clues can be found in my latest lecture, at the Center of Excellence in Science and Mathematics Education (CoESME), IISER Pune, INDIA.
The lecture can be watched online at http://www.j.mp/HinduMaths
The slideshow can be downloaded at http://www.j.mp/IndiasMaths
Thank you for reading this note and I wish you a happy and healthy 2020!
Jonathan J. Crabtree
Elementary Mathematics Historian
This is magnificent. You’re teaching precalculus next semester 😉