Tag Archives: curriculum

Mathematics education in Australia: New decade, new opportunities?

Post by Associate Professor Catherine Attard

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 (Attard, 2014).

Pedagogy

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.

About the author

Catherine Attard is an Associate Professor of Mathematics Education and Deputy Director of the Centre for Educational Research at Western Sydney University. Her research interests include student engagement with mathematics, mathematics pedagogy, financial literacy education and the use of digital technologies in mathematics classrooms.

Contact:                                                                                              c.attard@westernsydney.edu.au                                                                              https://engagingmaths.com

References

Attard, C. (2014). “I don’t like it, I don’t love it, but I do it and I don’t mind”: Introducing a framework for engagement with mathematics. Curriculum Perspectives, 34(3), 1-14.

Reid, A. (2019). Changing Australian Education. Sydney: Allen & Unwin.

 

 

Teaching Empathy? It’s a Process: Drama in the Primary Classroom

By Rachael Jacobs

Recently a lesson on the Stolen Generations, conducted at a Sydney school, went horribly wrong. Year 4 students were engaged in a day long ‘role-play’ in which they were told they would be removed from their families.

According to reports , a nun entered the classroom in the morning, with a letter from the Prime Minister, and told the class they would be taken away from their parents, as they weren’t being looked after properly. The exercise continued for five hours until the end of the school day when students were informed that this was a lesson on the Stolen Generations, and were asked how it made them feel.

While there was extreme concern expressed from the media and parents, Drama teachers all over watched this episode aghast, wondering how such a potentially powerful lesson had gone so wrong.

It seems an attempt was made to use the drama conventions of teacher-in-role and role play. These are two strategies found in the beautiful and transformative pedagogy of ‘Process Drama’.  Process Drama is a powerful teaching tool when used ethically, but it seems it wasn’t employed carefully in this instance. This lesson seemed much more like ‘invisible theatre’ where the participants did not know that they were in a fictional context or that the teacher was in role.

Invisible theatre is more commonly used with adults, whereas Process Drama has a pedagogy of care built in. In Process Drama, students know they are in the drama and in the fiction.  Students and the teacher move in and out of role; they don’t play themselves, rather they take on the roles of other people. At the end of a particular strategy or moment in the class, students may need to de-role (get out of role) and discuss and debrief the moments when they were in role. It’s a process students are familiar with. We see small children playing and going in and out of role all the time. When educators use drama in this way, they are protecting their students in role. Through role, we avoid the manipulation of ‘psycho-drama’ and can explore the space where the real world and the fictional world overlaps.

The teachers in the school concerned were acting with the best of intentions. They may have seen highly transformative learning experiences, such as Jane Elliot’s Blue Eyes/Brown Eyes experiment  and attempted to replicate these lessons.  It should be noted that the Blue Eyes/Brown Eyes lesson sparked outrage at the time, but is now considered a watershed moment in addressing racism in schools.

However, there are limits to Process Drama’s reach. Process Drama has been critiqued for its attempt to replicate the experiences of disadvantaged people at critical times in history. Can we really ever understand what it’s like to be part of the Stolen Generations, and is it offensive to suggest that we can replicate those experiences?  Indigenous children’s writer, Trina Saffioti, whose books were used to inspire the school’s lessons, was deeply uncomfortable with the exercise, stating that it almost cheapens the experience .

While it’s true that we can never truly understand what it was like to be a part of the Stolen Generations, the ability to see life from another’s perspective may be the most important lessons that one can ever learn.

It is abundantly clear that those facilitating these lessons were ill prepared for the nuances of this delicate teaching strategy. The transformative power of drama is still largely misunderstood in schools. New teachers can have as little as two hours training in Drama in their teacher preparation courses and this is a failure of our system . Many teachers would like to use drama to enhance empathy, challenge students’ worldviews, and to facilitate deep and critical thinking, but often don’t know where to start. If teachers make a misguided attempt, or no attempt at all, we deny our students the opportunity for them to engage with complex issues through an incredibly powerful pedagogy.

Lessons that are uncomfortable are not always bad, in fact learning itself is a dangerous act. Students cloaked in safety and shielded from discomfort will not be able to reach their potential, both as learners and active citizens. The Stolen Generations are also a dark part of Australian history which must be recognised by all members of our community if reconciliation is to occur. Students and schools are not exempt from this. Far from being too young, these students are in a prime position to discern racism, prejudice and injustice.

The school and Catholic Diocese have bravely said that these lessons will continue, albeit in another form, emphasising that the intentions were sound, but the execution was flawed. We need educators who are risk-takers, willing to tackle big issues, particularly our shameful treatment of indigenous Australians.

It would be incredibly sad if this isolated incident prevented teachers from being creative and using drama effectively in their classrooms.

 

Dr Rachael Jacobs is an Arts Education lecturer in the School of Education at Western Sydney University, Australia.

 

 

Man enough to study Physics? What do New South Wales Physics students say?

by Jessy Abraham

The proposed Stage 6 Physics curriculum for New South Wales (NSW) has been lauded as a “return to science” and has been welcomed by science-education experts who regard the current curriculum as ‘soft’ and a ‘diluted’ version of physics (Robinson & Armitage, 2017).

In her 2017 Australia Day address, Professor Michelle Simmons criticised the “feminisation” of physics in NSW (Fitzpatrick, 2017). The use of the term feminisation refers to efforts whereby curriculum developers sought to make the current physics curriculum more appealing to girls by minimising rigorous mathematical problem-solving and replacing it with a qualitative approach. The new syllabus that will commence in 2018 will move away from this qualitative emphasis and the current ‘social-context’ approach to teaching physics and bring in a greater focus on content and quantitative rigour, including mandatory equation derivations and problem solving (Crook, 2017). Stronger emphasis will be given to learning scientific principles, theories and laws.

Topics with a descriptive nature, such as historical linkages and societal implications of scientific inventions will be largely eliminated (Physics Stage 6 Syllabus, 2017). While this has been applauded by critics of the current syllabus and University-based Physics educators, concerns about equity of access have also been raised. The concern is that an increase in quantitative rigour may perhaps lead to even sharper declines in physics enrolment numbers (Crook, 2017).

How valid are the perceived beliefs that the ‘dumbing down ‘of physics content by replacing mathematical focus with the life stories of scientists, historical development and societal impacts of their inventions, will appeal more to female students? Are male students naturally better at and inclined to problem solving, experiments and mathematical applications? Such perceptions exacerbate the ubiquitous gender stereotypes regarding the ‘masculinity’ of physics.

Results of my study conducted among 247 year 11 physics students (157 males and 90 females) from the Sydney metropolitan area did not support these claims. Male and female students who were continuing physics to Year 12 held high levels of interest value, performance perceptions and instrumental value (usefulness for personal career/study plans) in relation to physics, and there were no statistically significant differences for these values between the genders. Both genders displayed similar levels of high engagement with physics, and held low levels of stereotypes on the perceived masculinity of physics.

These observations were equally valid for students who were discontinuing physics, who possessed low levels of interest, performance perceptions and engagement with physics: they also held low stereotypical gender role beliefs. No significant gender differences were found. For the four modules in the current year 11 physics curriculum, in the majority of instances there were no consistent differences in how male and female students perceived the achievement motivational factors explored in the study.

When students were asked to rate various Year 11 physics topics based on their interest value, no significant gender difference was identified. Both genders indicated higher than average levels of interest in learning laws of physics, problem solving, experiments, relating to real life situations, contributions to humanity and the abstract nature of physics. However, regarding the much criticized topics such as ‘Lives of Scientists’ and ‘Historical Contexts of Inventions’, both genders displayed a marked lack of interest. This lack of interest was equally expressed by both genders.

Likewise, both genders described physics as “interesting, challenging, yet satisfying, and something that relates to everyday life” (male student, comprehensive school). Furthermore, participants’ qualitative responses tended to reinforce traditional views on the expected nature of physics. Students reported that they expected more mathematically oriented content, and ‘crazy calculations to experiments’ (female student, selective school) when they enrolled in senior secondary physics. Nevertheless, the enacted curriculum had ‘too much language orientation’ (male student, selective school). They wanted to see ‘less literacy, more scientific content’ (male student, comprehensive school). In relation to the historical and social contexts of inventions, and descriptive topics like The Cosmic Engine (a topic on Astrophysics), the majority found these  ‘boring, dull and not useful’ (male student, Catholic school). Interestingly students gave a strong emphasis to the instrumental value of physics and tended to view the subject as a preparation course of STEM courses at university.

The results of my study support the argument that senior secondary physics students may prefer the content and quantitative analytical rigour proposed in the new curriculum and the removal of certain sections in the current curriculum. This endorses the changes prescribed in new Stage 6 Physics syllabus. However, the popular misconception that ‘dumbing-it-down- for- females’ might increase its attractiveness was not supported. Issues around whether the new syllabus may aggravate equity of access to physics will need to be examined once the implementation of the new syllabus begins.

References

Fitzpatrick, S (2017, January 24). Feminisation of science a disaster, leading quantum physicist Michelle Simmons says. Retrieved from http://www.theaustralian.com.au/higher-education/feminisation-of-science-a-disaster-leading-quantum-physicist-michelle-simmons-says/news-story/8a432da4bce81e4fb51d91da9bf7a98b

Crook, S (2017, February 22). New physics syllabus raises the bar, but how will schools clear it? Retrieved from https://theconversation.com/new-physics-syllabus-raises-the-bar-but-how-will-schools-clear-it-73370

NSW Syllabus for the Australian Curriculum. Physics Stage 6 Syllabus (2017) NSW Education Standards Authority (NESA). Retrieved from http://syllabus.nesa.nsw.edu.au/assets/physics_stage_6/physics-stage-6-syllabus-2017.pdf

Robinson, N & Armitage, R (2017, February 21). New South Wales HSC syllabus gets overhaul with more complex topic. Retrieved from http://www.abc.net.au/news/2017-02-21/nsw-hsc-syllabus-gets-radical-overhaul-year-12-teaching-changes/8288000

 

Dr Jessy Abraham is a lecturer in Primary science and technology curriculum in the School of Education at Western Sydney University, Australia.

(Un)necessary teachers’ work? Lessons from England.

by Susanne Gannon

Disembarking at Heathrow a few weeks ago, my first purchase in pounds as always was a copy of The Times to read on the train into the city. The second page headline, “CR (Creative Original): Grades on schoolwork replaced by codes” (Bennett, 2017) caught my eye. Skimming the article in my dazed jetlagged state was not ideal for a critical reading but I snapped a photo with my phone of the final paragraph:

“In 2014 the government asked teachers to tell them what created unnecessary work. Three big areas were marking, planning and data management.”

I recognise the data deluge in schooling is now overwhelming, may be driven by externally imposed system imperatives and is not always put to use to improve student learning. However, I’ve spent my professional life as a secondary English teacher, tertiary teacher educator and researcher. I could not see how “marking” and “planning” are seen as “unnecessary work” for teachers.

Planning is surely at the heart of teachers’ work. Otherwise how do we claim our status as professionals? Ideally we don’t just wing it in the classroom, nor do we follow prescriptive scripts. Systematic, responsive, syllabus-informed planning of purposeful sequences of learning and meaningful resources are what make the difference for individuals and groups of students. Well-selected and fine-grained data about student progress (not necessarily only the numerical data that is favoured by educational systems) should of course inform such planning as skilled teachers identify gaps and opportunities for extension and tailor their planning to their students’ needs and their potential.

Having high expectations and creating the conditions – through careful and ideally collaborative planning – for students to succeed and to excel are hallmarks of quality teachers. These features are characteristic of exemplary teaching in disadvantaged contexts (Lampert & Burnett, 2015; Munns, Sawyer & Cole, 2013). Careful planning need not preclude flexibility, creativity and authenticity in learning and assessment practices, but conversely may enable these qualities (Hayes, Mills & Christie, 2005; Reid, 2013). As many of these authors stress, good planning is often underpinned by a disposition of teachers to become researchers of learning within their own classrooms. Where teachers are provided some agency and capacity to gather and use data then problems are less likely to be at the low level of time consuming and potentially meaningless “data management” that is perceived as “unnecessary work” by teachers in England.

Marking is of course close to my heart as a secondary English teacher and I have spent countless hours of my life providing written feedback on student work. Whilst I have become adept at designing and using outcomes based rubrics / criteria sheets since their introduction in the mid-90s with outcomes based assessment and curriculum, I have always endeavoured to provide tailored and specific feedback to students on their texts.

This for me is “marking” as a process, and I think of it – in ideal circumstances – as sometimes like a sort of dialogue on the page between student, text and teacher, and an opening towards further dialogue. It features in formative as well as summative assessment contexts (apart from exams). Now it features in the texts in progress that are thesis chapters for my current doctoral students. In a perfect world it is diagnostic, supportive, explicit and critical in combination and students will take heed. Portfolios, peer and self-assessment processes and tools can be incorporated. As Munns et al (2013) describe, sharing assessment responsibility is an important component of the insider school. The volume and pressure of marking has always been problematic however, when short timelines for results and sheer numbers of students across multiple classes work against ideal scenarios. My research into creative writing in secondary schools (e.g. Gannon, 2014) suggests how English faculties were able to work collegially to support senior students as they developed major works in English. Marking, at best, can be rewarding, encouraging and useful for students and for teachers.

Where, then, does the aversion to marking come from for teachers in England? The article in The Times does not provide any pointers towards the government survey of 2014, but is rather an announcement of a large randomised control trial to be funded by the UK-based Education Endowment Foundation, based on a Report reviewing written feedback on student work that they commissioned and recently published (Elliot et al., 2016). The opening of the executive summary of the Report provides further detail:

[T]he 2014 Workload Challenge [UK] survey identified the frequency and extent of marking requirements as a key driver of large teaching workloads. The reform of marking policies was the highest workload-related priority for 53% of respondents. More recently, the 2016 report of the Independent Teacher Workload Review Group [UK] noted that written marking had become unnecessarily burdensome for teachers and recommended that all marking should be driven by professional judgement and ‘be meaningful, manageable and motivating’. (2016, 4)

Well, of course! What has gone wrong in England that marking is not driven by these qualities. Are there lessons for us in Australia (yet again from England) of what not to do in educational reform? Although the report acknowledges that there is very little evidence or research into written marking, they nevertheless identify some inefficient and apparently widespread practices: triple-marking, awarding grades for every piece of student work (so that the grades distract students from the feedback), too many texts required from students, marking excessive numbers of student texts, provision of low level corrections rather than requiring students to take some responsibility for corrections/ improvements, and moving on without giving students time to process and respond to feedback.

Despite the caveat in the opening section, the report is worth reading in full (though it has been criticised by local critics e.g. Didau, 2016). Secondary teachers are much more inclined to put a grade on every piece of student work, they say (2016, 9). Unsurprisingly, offering clear advice on how a student may improve their work in a particular dimension seems to be more useful than broad comments (‘Good work!’) or excessively detailed and overwhelming commentary (2016, 13). Targets or personalised and specific “success criteria” may be effective, particularly where students are involved in establishing them (2016, 20; also see Munns et al., 2013).

It is in this part of the Report that the overall logic of the newspaper article becomes apparent. Buried well down into the subsection on “Targets” is the following comment:

Writing targets that are well-matched to each student’s needs could certainly make marking more time-consuming. One strategy that may reduce the time taken to use targets would be to use codes or printed targets on labels. Research suggests that there is no difference between the effectiveness of coded or uncoded feedback, providing that pupils understand what the codes mean. However the use of generic targets may make it harder to provide precise feedback. (2016, 20).

The Times headline is therefore not quite accurate. It seems that “Grades” will not be replaced by “codes” but rather that teachers’ written comments will be replaced by codes. In another article, “Schools wanted to take part in marking without grading trial” (Ward, 2017) this is called “FLASH Marking” and is an initiative developed in house by a secondary school in northwestern England that will be rolled out to 12,500 pupils in 100 schools (EEF, 2017). The school claims that teachers will now be able to mark a class of Yr 11 exam papers in an hour. Students will receive an arrow (at, above or below expected target), and codes such as CR = “creative original ideas”, and V= “ambitious vocabulary needed.”

It seems from these news stories (and presumably EEF will put up the design protocols on their website eventually) that two different factors are being measured – one is holding back grades and the other is using codes instead of written comments. I’m curious but ambivalent, after all at university it is now mandatory to use “Grademark” software for coursework students. This enables teachers to provide generic abbreviated feedback (“codes”) but also gives us the opportunity to personalize responses, and supplement these with an extended written comment, or even an audio-recorded comment. These are highly personalised and appreciated by students.

To turn back to the English example, I wonder whether the randomized control trial design (in this case an efficacy trial that will be evaluated by Durham University) means that participating schools will not be able to improvise around the conditions of the feedback? At least, if the reduction of feedback to codes proves not to improve student results, given the need for the control (or “business as usual”) group, the damage will be limited to only half the participating schools and students. The news articles are unclear about the purpose of the study – which is described as a way to reduce teacher workload more than to improve student learning. However the EEF project description also mentions, reassuringly, that the rationale is focused on student outcomes, as “specific, actionable, skills-based feedback is more useful to students than grades” (2017). The project will follow year 10 students in senior English classes through to the end of secondary school with a report to be published in 2021. Already, I can’t wait.

References

Bennett, R. (June 17, 2017). CR (Creative original idea): grades on schoolwork replaced with codes. The Times.

Didau, D. (May 18, 2016), The Learning Spy Blog.

http://www.learningspy.co.uk/assessment/marked-decline-eefs-review-evidence-written-marking/

Education Endowment Foundation (2017). Flash Marking. https://educationendowmentfoundation.org.uk/our-work/projects/flash-marking/

Elliot, V., Baird, J., Hopfenback, T., Ingram, J., Thompson, I., Usher, N., Zantout, M, Richardson, J., & Coleman, R. (2016). A Marked Improvement? A review of the evidence on written marking. Education Endowment Foundation. https://educationendowmentfoundation.org.uk/resources/-on-marking/

Gannon, S. (2014). ‘Something mysterious that we don’t understand…the beat of the human heart, the rhythm of language’: Creative writing and imaginative response in English. In B. Doecke, G.Parr & W. Saywer (Eds), Language and creativity in contemporary English classrooms (pp. 131-140). Putney: Phoenix Education.

Hayes, D., Mills, M., & Christie, P. (2005). Teachers & schooling making a difference: productive pedagogies, assessment and performance. Allen and Unwin.

Lampert, J. & Burnett, B. (Eds) (2015) Teacher Education for High Poverty Schools. Springer.

Munns, G., Sawyer, W. & Cole, B. (Eds). (2013). Exemplary Teachers of students in poverty. Routledge

Reid, J. (2013). Why Programming matters: Aporia and teacher learning in classroom practice. English in Australia. 48(3), 40-45.

Ward, H. (June 16, 2017). Schools wanted to take part in marking without grading trial. Times Education Supplement. https://www.tes.com/news/school-news/breaking-news/schools-wanted-take-part-marking-without-grading-trial

 

Dr Susanne Gannon is an Associate Professor in the School of Education and a senior researcher in the Centre for Educational Research at Western Sydney University, Australia.