Jake Little

The release of the NSW Curriculum Review Interim Report (NESA, 2019) has stimulated discussion again about the perceived “overcrowded and cluttered” (pg. 24) curriculum. There are, however, 3 longstanding misconceptions about curriculum content in NSW:

1. the requirement to ‘teach’ every syllabus dot point,
2. the need to grade students on all syllabus outcomes,
3. that examples in syllabus documents (there to illustrate outcomes) need to be taught.

Associate Professor Catherine Attard has previously written on these misconceptions (click here).

Findings from The Mathematical Association of NSW’s (MANSW) survey of members was presented in the Interim Report and reported similar concerns (and misconceptions). Member argued that too much content led to shallow learning and very little time to explore (p. 25).

In mathematics, the knowledge-based curriculum is a structured and sequenced guide to support students develop their knowledge and skills. Teachers have the autonomy and flexibility to cover the content in ways that best suit their students. The above misconceptions by teachers and schools about the structure and intent of the curriculum has led to the perception of overcrowding. I argue that the mathematics curriculum is not overcrowded; with several ways to reduce the overwhelming burden currently felt by teachers and students. Here I present five ideas for mathematics teachers to consider in saving time throughout the teaching/learning process. Assessing (and acting on) prior knowledgeAssessing (and acting on) prior knowledge

Assessing (and acting on) prior knowledge

Well thought and targeted assessments of prior knowledge identify current student understanding and skills. They indicate a starting point for the teacher on where to begin teaching and provide an opportunity to personalize learning tasks for students. Small individual tests are common ways to assess prior knowledge, though I have also used concept mapping, short individual student ‘interviews’, groups discussions and rich tasks (more on this below).

Exam structure in secondary schools

Let’s think about the exam schedules in secondary schools- most (not all) teachers feel compelled to provide revision lessons one week out, followed by a 1-2-week exam block and then a lesson (or two) to give the exam back and to revise solutions. This can remove up to 3-4 weeks of teaching time and this is sometimes repeated twice a year in the senior years. An enormous amount of teaching time lost…

Alternative? regular formative assessment and re-thinking of school-based examinations (and exams for that matter).

Integrated curricula- reducing duplication

Duplication of content (especially in secondary schools) wastes time. Some examples include:

1. the concept of measurement is taught in mathematics, science, technology and art,
2. the concept of gradient is taught in both mathematics and geography.
3. statistical procedures are taught in both mathematics and science.

Further consideration is needed to identify common skills and understanding across disciplines. The focus on STEM in secondary schools, for example, aims to reduce this duplication of content by encouraging teachers to collaborate and discuss ideas on how to connect knowledge and skills. While significant planning time is needed, from my experience this can be a worthwhile task for secondary teachers to conduct and can stimulate interesting discussions about how each department teaches these concepts.  

Katherin Cartwright (click here) has written on ideas for making connections in mathematics.

Rich tasks

Teaching through rich tasks can provide students with valuable and engaging experiences that ‘tick off’ multiple outcomes. I use tasks from NRICH (https://nrich.maths.org/) and YouCubed (https://www.youcubed.org/. Teachers need flexibility and an open-mind in their teaching/programming as these tasks commonly cover multiple outcomes from different topics.

For example- one topic that can drag on for students (and teachers!) is fractions, decimals and percentages, if the concepts are taught in isolation from each other. This activity ‘Percentage unchanged’ (https://nrich.maths.org/515) from NRICH is a great activity that covers many outcomes in this topic that encourages multiple solution methods.

Focusing on the ‘big ideas’

Emeritus Professor Dianne Siemon (RMIT University) is well-known for her work on the ‘big ideas’ in mathematics. Number is the topics most responsible for the range of achievement in mathematics in the middle years (Siemon, Virgona & Corneille, 2001); big ideas include place value, multiplicative thinking, partitioning, proportional reasoning and generalising. Focusing on students’ development of the ‘big ideas’ can save time with many of the misconceptions and challenges students face later on in secondary school. In teaching HSC mathematics, I know that students’ understanding (or lack) of fractions can slow down teaching and learning in many (if not all) of the HSC topics.

So- what do you think? What do you see when you look at the mathematics curriculum? Over-crowding or not? A perception or reality? Or both? Please let me know your thoughts!

References

National Education Standards Authority (NESA) (2019). NSW Curriculum Review Interim Report. Retrieved 24 October 2019 https://nswcurriculumreview.nesa.nsw.edu.au/pdfs/interimreport/chapters/NSW-Curriculum-Review-Interim-Report.pdf

Siemon, D., Virgona, J. & Corneille, K. (2001). The Final Report of the Middle Years Numeracy Research Project: 5‐9. Retrieved 24 October 2019 from https://www.education.vic.gov.au/Documents/school/teachers/teachingresources/discipline/maths/mynumfreport.pdf

There is hesitation in the mathematics education community about STEM education & its’ role to play (if any some would say!) in mathematics within secondary schools. The acronym has been around since the early 2000’s, with its’ impact starting to wear off, especially in the mathematics community. Teachers feel that STEM has turned into another educational slogan, and (some) mathematics teachers feel that they have had no part to play in many school-based STEM initiatives. Mathematics teachers also have concerns that integrated STEM projects may lose mathematical integrity, may hinder the sequential approach to teaching & learning & may not cover content outcomes with rigor.

Perhaps, though, mathematics teachers need to take the risk in developing STEM integrated units of work (many schools are), uncover the possibilities for mathematics education and begin to have conversations with our students and colleagues around our current approaches.

Why bother though?

In the transition from primary to secondary school it is common for our students to find mathematics abstract and irrelevant, frequently questioning its’ usefulness and purpose. Decades of research show that levels of disengagement increase, students’ views about mathematics progressively get worse throughout these years in response to the difficulty in identifying the usefulness of the content to their lives. We cannot expect our students in these early secondary years to appreciate the beauty, complexity and power of mathematics that we see if the classroom is dominated by teaching and learning approaches that make it difficult for students to relate too. Perhaps these are keys reasons for the decline in the number of students pursuing higher levels of mathematics in the senior years.

At a time when STEM (Science, Technology, Engineering, Mathematics) seems to be the solution to every school problem, perhaps there is some merit in considering this approach to making mathematics teaching and learning more meaningful and relevant for our students. In many secondary schools, mathematics operates as an isolated discipline, distinct to other STEM disciplines, resulting in a fragmented view of mathematics in students’ minds. Several government reports and research studies are encouraging secondary mathematics teachers to make their teaching more authentic and contextualized by connecting with content in other STEM areas. For example, mathematics shares common practices such as inquiry learning and problem solving with science, and science can provide opportunities to apply mathematical concepts, can assist in the transfer of knowledge and can present real-world contexts to learn abstract concepts. Current research is indicating the benefits of a more contextualized approach to mathematics teaching and learning through STEM, improving students’ engagement, values towards and potentially achievement in mathematics.

Many of us were taught mathematics at school as an isolated discipline, dominated with a reliance on textbook questions and with little contextualization or useful application. For us, this worked- we enjoyed it, moved onto study mathematics further and now are mathematics teachers. We are, however, the small minority who enjoyed mathematics at school, unfortunately. As a mathematics community, it is challenging to consider alternative approaches to teaching and learning when we were taught through ‘traditional’ methods at school, or even through to university.

Perhaps it is time to further consider the promise of STEM education in improving student engagement, values towards and achievement in mathematics in the junior secondary years, to improve the number of students wanting to continue further mathematics study in the senior years. So I suggest the mathematics community refocuses their thoughts about the (sometimes overused!) STEM acronym & begin to re-think ‘STEM’ as a Step Towards more Engaging Mathematics.

Secondary schools are attempting to make mathematics more meaningful and relevant for their students by making connections with other STEM areas, commonly through interdisciplinary projects. A challenge for teachers is planning to authentically connect secondary mathematics outcomes in these projects, whilst maintaining academic rigor. Previous research has indicated that whilst well-intentioned projects may enhance enjoyment and enthusiasm in learning mathematics, there are concerns that mathematics can be watered down to simple calculations that review simple skills from prior knowledge learnt in primary school.

Here are 5 tips to help you overcome these challenges:

1. Start with the mathematics scope and sequence

The school I am working with planned their connected learning projects by starting with the core structure of their mathematics program- and for good reason. Mathematics is a sequential subject, so ensuring students build skills and knowledge throughout the year is important. Whilst minor changes may prove useful, there are some obvious topics that would need to be covered before others, such as Equations before Pythagoras’ Theorem. This way, content from other STEM areas can be aligned to the mathematics outcomes rather than mathematics being tacked on the side.

• Mathematics teachers as STEM leaders

A qualified mathematics teacher should be involved in all discussions around connecting content with other STEM disciplines. This is critical to ensure mathematics outcomes are covered and that other teachers are aware of what mathematics can offer the other disciplines. The Australian Council for Educational Research (Timms et al., 2018) found that in secondary schools it is rare for mathematics teachers to be leading STEM initiatives- a concern for the mathematics education community.

• Mathematics need to be taught by qualified (or training to be) mathematics teachers

This seems obvious- right? Though schools sometimes have the assumption that everyone can teach Year 7 mathematics- everyone has been to school, everyone has learnt Year 7 mathematics so how difficult can it be!? Whilst it is difficult enough for un-qualified mathematics teachers to teach mathematics, requiring them to make deep and meaningful connections with other content areas is an extremely challenging task. To maintain rigor and to ask the right leading questions, teachers in connected learning projects need to have a strong understanding of the mathematics outcomes. Potentially, team-teaching opportunities can enable other teachers to gain insight into how mathematics teachers approach particular concepts.

• Outsider observations

As part of my research I have been fortunate to observe teachers conducting these connected learning projects. An advantage of this is that I can provide feedback to teachers after watching multiple classes and share ideas from other classrooms. Having a mathematics teacher observe the connected learning projects is important to gain their perspective on how well the mathematics outcomes are being covered. From my experience, this can stimulate a useful discussion and encourage other teachers to join in with future projects.

• Use a well-researched model/framework

 Schools I am working with have found Kiray’s (2012) Balance Model useful in identifying where they are and where they want to be with their connected learning projects.

At each end of the balance is mathematics and science taught as separate disciplines (this could easily be other STEM disciplines). The Math-Centred Science-assisted integration is where few mathematics outcomes are covered in detail, whilst science is the interval discipline whose outcomes are briefly used to make relevant connections. Moving closer to Total Integration is Math-Intensive Science-Connected Integration where the mathematics outcomes dominate the program and the science outcomes are intentionally covered to make connections. Science dominates the other side of the scale. Teachers have found this model useful in planning and evaluating connected learning projects between mathematics and science.

I will presenting some practical applications from my research for mathematics teachers at the Australian Association of Mathematics Teachers Conference in Brisbane on Wednesday 10th July.

References

• Kiray, S. (2012). A new model for the integration of science and mathematics: The balance model. Energy Education Science and Technology Part B: Social and Educational Studies, 4, 1181-1196.
• Timms, M., Moyle, K., Weldon, P. & Mitchell, P. (2018). Challenges in STEM learning in Australian Schools. Victoria, Australia: Australian Council for Educational Research.

What is the problem?

It is common for students in secondary schools to find mathematics abstract and irrelevant, frequently questioning its’ usefulness- we have all been there- “but sir/miss, when are we going to use this?!” I have had colleagues try to convince me that students just need to appreciate that mathematics is useful and powerful and that it is not our job to make it useful or relevant- that mathematics “is what it is”.

In the transition from primary school, students commonly disengage (Collie et al., 2018), and their view get progressively worse as they continue through secondary school (McPhan et al., 2008). With concerns around student achievement in mathematics and the student numbers enrolling in advanced mathematics courses, it is timely to reconsider the approach to mathematics teaching and learning.

The solution

Currently, there is strong policy support (ACARA, 2016) and research recommendations (Honey et al., 2014) for mathematics teachers to make connections with other STEM disciplines to provide a relevant context to learn, apply and transfer their skills and knowledge. Science, for example, can provide opportunities to apply mathematical concepts, can assist in the transfer of learning and can present-real world contexts to learn abstract concepts. They share common practices such as inquiry learning and problem solving. As a mathematics and science teacher, I have had the opportunity to experience the overlap in content areas, to see how different departments teach the same concepts and to tinker with interdisciplinary activities and projects that have saved teaching time. Previous research has indicated that well-planned connected learning projects can enhance students’ values towards mathematics (Diedorp et al., 2014) and can improve student achievement (Judson & Sawada, 2000).

The challenges

With discipline-specific curriculum documents and assessment schedules, and that most secondary teachers are qualified to teach one discipline- this ‘solution’ is a challenging one! And let’s not hide that ultimately, after decades of research and trials with connecting learning (aka ‘integrated learning’), the discipline-specific approach to teaching in secondary schools has prevailed for mathematics. Further, some research has indicated that it is more common for connected learning interventions to impact on mathematics achievement the least (Honey et al., 2014). Perhaps, the current sequenced and structured approach to mathematics may hinder learning in connected learning experiences. More research is needed…

Why bother?

There is more promise now to curriculum change in mathematics with changes to the way knowledge is used and created, more positive findings from research being conducted with well-planned connecting learning experiences and a national urgency for more authentic practice.

I will be presenting my position paper @ the Mathematics Education Research Group of Australia (MERGA) in Perth on Wednesday 3^rd July @10 am in Room M3.

References

Australian Curriculum, Assessment and Reporting Authority (ACARA) (2016). ACARA STEM Connections Project Report. Sydney, Australia: Author.

Collie, R., Martin, A., Bobis, J., Way, J. & Anderson, J. (2018). How students switch on and switch off in mathematics: Exploring patters and predictors of (dis)engagement across middle school and high school. Educational Psychology, 1, 1-21.

Diedorp, A., Bakker, A., Maanen, J. & Eijkelhof, H. (2014). Meaningful statistics in professional practices as a bridge between mathematics and science: an evaluation of a design research project. International Journal of STEM education, 1, 1-15.

Honey, M., Pearson, G. & Schweingruber, H. (2014). STEM Integration in K-12 Education: Status, Prospects, and an Agenda for Research. Washington, DC: National Academy of Sciences.

Judson, E. & Sawada, D. (2000). Examining the effects of a reformed junior high school science class on students’ mathematics achievement. School Science & Mathematics, 100, 419-425.

McPhan, G., Morony, W., Pegg, J., Cooksey, R. & Lynch, T. (2008). Maths? Why not? Final report prepared for the Department of Education, Employment and Workplace Relations. Canberra, Australia: Author.