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NSW Secondary mathematics teachers battered by a ‘perfect storm’ May 29, 2011

Posted by Editor21C in Education Policy and Politics, Educational Leadership, Primary Education, Secondary Education.
Tags: , , ,

from Associate Professor Allan White

Here, Allan White examines nine issues he feels compromise the effective teaching and student learning of mathematics in secondary schools in New South Wales, Australia.

The Hollywood movie of the same name describes a perfect storm as a combination of dangerous conditions that together produce the worst possible event. Secondary school mathematics teachers in NSW have been suffering from such a storm. Listed below are nine dangerous conditions that have contributed to this perfect storm, and there may be others:

1. In spite of the best of goodwill and determined efforts by some primary staff, there is considerable research evidence that in general, primary teachers lack sound content knowledge and are not confident in teaching mathematics (Tobias & Itter, 2007). Negative attitudes towards mathematics may impede pre-service teachers’ ability to engage in mathematical content and pedagogical subjects designed to improve their mathematical understandings (Ebby, 1999). This has long ranging effects. For example a large Australian study into the reasons why students are not choosing to study higher-level mathematics courses reported that “curriculum and teaching strategies in the early years which engage students in investigative activities and which provide them with a sense of competence are central to increasing participation rates in mathematics” (McPhan, Moroney, Pegg, Cooksey & Lynch, 2008, p. 22),

2. There are a significant number of teachers taking secondary school mathematics classes who are not mathematics trained. Trained mathematics teachers tend to be assigned to the higher classes while the junior classes are taken by others such as PE teachers. The OECD judgement that Australia has “high standard and low equity” means that good mathematics teaching is limited to a small proportion of schools. The Assessment of the Phenomenon of Teaching Out-of-Field in WA Schools reports the overall rate of teaching out-of-field in the Perth metro region in 2008 was 16.4% for government schools, 26.9% for Catholic schools and 29.7 % for independent schools. This was mirrored in the country regions where the rate was 23.1% for government schools, 44.4% for Catholic schools and 46.1% for independent schools.

One effect of this teaching out-of-field is to hide the true extent of the shortage of trained mathematics teachers. Ponte and Chapman (2008) reported that “[while] having strong knowledge of mathematics does not guarantee that one will be an effective mathematics teacher, teachers who do not have such knowledge are likely to be limited in their ability to help students develop relational and conceptual understanding” (p. 226). Or more bluntly, “It is self-evident that teachers cannot teach what they do not know” (National Mathematics Panel Report, 2008, p. xxi).

There are some school students who do not have a trained mathematics teacher until they reach year 10. Research has highlighted the impact upon student learning that a passionate teacher can make. Again the influence of negative experiences acts as a filter to discourage capable students from studying mathematics and indeed of becoming a mathematics teacher. While non- trained mathematics teachers are often well intentioned, they do add to the load that must be carried by the trained mathematics staff.

3. The ageing teaching force has limited the positions available to new, graduate, and keen mathematics teachers. Principals are loath to implement a forced transfer of an old non-mathematics teacher who has a few years to retirement. It is much easier to assign the teacher to teach junior mathematics classes, thus closing a mathematics position. The young teachers become frustrated and take positions outside of teaching. The loss of this youth and energy has an effect on the trained mathematics staff.

4. The National Numeracy Review (DEEWR, 2008) recommended to the Council of Australian Governments that there should be 5 hours per week of learning mathematics in primary; and 4 hours per week in junior secondary. Timetabling changes in schools have seen a move to longer and fewer periods, resulting in greater gaps between classes. In the past a Year 7 student would generally take one or two periods of mathematics a day. Now, in some cases, a junior student may have a gap of a week between 120 minute mathematics classes.

5. The nature of mathematics requires both conceptual and procedural knowledge. Procedural knowledge is usually developed through drill and practice. While in the past there was arguably too great an emphasis upon drill in order to develop proficiency with procedures, the current school timetable works against this. Imagine asking an athlete to only train every third or fourth day. While conceptual knowledge is the aim, it requires a degree of procedural knowledge whereas the reverse is not necessarily true. Timetable changes detailed in point 4 have a strong effect on the development of both knowledge forms.

Meaney and Lange (2010) reported that “pre-service primary teachers identified some benefits for being tested on their mathematics content knowledge, but these were often related to having sufficient knowledge so that they did not lose face in front of a class” (p. 399). It was suggested that these students’ emphasis on performance rather than competence could exacerbate a reliance on procedural rather than conceptual understanding.

6. The teaming of Literacy and Numeracy has had deleterious effects on the latter. The literacy lobby is far more powerful and attracts the greater attention and level of resources. Literacy and Numeracy courses are usually delivered by literacy experts and in spite of their best intentions, numeracy suffers. Students are quick to pick up on the unstated message of which of the two is more important. In extreme cases literacy experts have entered territory that belongs traditionally to numeracy with their claims to Visual Literacy.

7. School career advisors are giving correct but very poor advice to senior students by telling them that the universities only require General Mathematics for entry to their courses. This advice requires the student to tackle the content of a university subject while trying to teach themselves the skills of calculus. Knowledge of calculus is required in many subjects outside those offered in university Mathematics faculties.

8. The promotion system has changed for selecting NSW school principal positions resulting in a lesser proportion of those chosen with a mathematics background. This resulted in fewer principals who deeply understood the nature of the discipline and the conditions required for good outcomes. Those principals with the mathematics background are influenced by the majority who are not. This has been most evident in changes to school timetables.

9. There is anecdotal evidence that some university students are being enticed to complete one of a vast array of Early Childhood degrees because of a lesser amount of mathematics when compared to a Primary Teaching degree. Some Early Childhood degrees are now classed as 0 – 12 years. While mathematics is included, it is often lumped with Science and Technology and taught by an untrained mathematics lecturer. Once in school these teachers are not confined to the early years and are able to teach from years K-6. Research has shown a strong direct link between teachers’ mathematical achievement and student achievement (Clotfelter, Ladd, & Vigdor, 2007). Harbison and Hanushek (1992) found a positive correlation between teacher mathematics test scores and fourth-grade tests on student achievement. The idea of pre-testing early childhood and primary teachers was one of five recommendations to the Queensland government by Professor Geoff Masters, CEO of the Australian Council of Educational Research (Masters, 2009).

Critics may target any of these conditions and, following climate change sceptics, seek contradictory evidence for one in order to reject all of the evidence. Individual schools may suffer from different combinations of these ten, but NSW secondary school mathematics teachers are being battered by the totality of this perfect storm. This perfect storm has resulted from a complex mix of forces and will require a complex mix of solutions.

The good news is that these solutions are becoming available. The Mathematical Association of NSW is a voluntary body of NSW mathematics teachers who work tirelessly to provide professional learning activities, professional advice and to encourage and support innovation and growth. In increasing numbers secondary school mathematics teachers are joining the association. The NSW Institute of Teachers has also begun to construct some of the solutions. It is hoped that secondary mathematics teachers with this support will continue to battle the storm rather than go under.

ReferencesClotfelter, C., Ladd, H., & Vigdor, J. (2007). How and why do credentials matter for student achievement (NBER, Working Paper #12828). Cambridge, MA: National Bureau of Economic Research.  Department of Education, Employment and Workplace Relations (DEEWR) (2008).  National Numeracy Review. Accessed 30 Aug 2010 from http://www.coag.gov.au/reports/index.cfm  Ebby, J.R. (1999). Learning to teach mathematics differently: The interaction between coursework and fieldwork for pre-service teachers. Journal of Mathematics Teacher Education, 3, 69-97.  Harbison, R., & Hanushek, E. (1992). Educational performance of the poor: lessons from rural northeast Brazil (pp. 81-177). Washington, DC: World Bank.  Masters, G. (2009). Australian Council of Educational Research Report to Queensland Government. Accessed 30 Aug 2010 from: http://education.qld.gov.au/mastersreview.  McPhan, G., Moroney, W., Pegg, J., Cooksey, R., & Lynch, T. (2008). Maths? Why Not? Canberra: Department of Education, Employment and Workplace Relations. 

Allan White is Associate Professor in Mathematics Education at the University of Western Sydney, Australia. He teaches in UWS’s Master of Teaching (Secondary) teacher education program, and is an internationally recognised researcher into mathematics education, teaching and learning.


1. Margaret Vickers - June 1, 2011

Hi Allan – Yes this is a very difficult climate and Mathematics teaching needs to be given a higher priority. It cannot be done by those without a strong Maths background. One thing that may not have helped the case for Maths is that many topics are not evidently ‘useful’ in everyday life so – like Latin – no one wants to do them purly for the metal excercise. However, I agree with you that consistent practice is the only way to gain fluency and skill.

Allan White - June 6, 2011

Greetings from the Southeast Asian Ministers of Education Organisation (SEAMEO) Regional Centre for Quality Improvement of Teachers and Educational Personnel (QITEP) in Mathematics

I agree that students need to see the applicability of mathematics to their lives, particularly when there has been more mathematics invented/discovered in the last 50 years than all the years before. Your mobile phone contains a ‘mathematical monster’ curve that allows you to receive signals without the use of a satelite dish or a long coat hanger. These monsters are part of fractal geometry that has revolutionised communications and Hollywood (through special effects), and has touched every person. Before fractal geometry we could only use geometry to describe the human built environment, with fractal geometry we can contain and describe the living chaotic environment. Yet this is one small aspect of the mathematics revolution that is happening globally except in NSW schools.

The trouble is that the creative group of mathematics specialist teachers have been so depleted that they have not been able to keep up. AND the amount of time devoted to mathematics has been steadily eroded which greatly limits a teacher’s abilty to explore the facinating ways mathematics has invaded our lives.

Thanks for your insight – what do others think?

Selamat sejahtera

2. Nic M - June 1, 2011

Pretty much all mathematics up to year 10 is very functional. Students will be using it regularly. I am a middle school trained maths teacher and that is my limit. I dont have the training to go above this level and would never take a job that required me to teach above year 10 as I wouldnt do my students justice. The same goes for other subjects such as physics, LOTE and chemistry in particular. I speak spanish but to teach it would require a level of correct usage that I dont have. However there are teachers teaching maths and languages that make mistakes constantly which is terrible for the students. I think that there should be subjects that teachers need to be qualified in to teach. ie they should sit the exam that they are teaching to and if they dont ace the test they cant teach the subject. ie. any subject that requires more than knowledge aquisition.

3. Allan White - June 6, 2011

Hi Nic

Having a deep knowledge of the content is important as well as the knowledge to teach it. For me though, having a passion for both the subject and the welfare of the students is crucial if the students are going to be inspired to pursue the subject.

The best way for teachers who know they have areas that need improving is to join their professional teachers association – in this case MANSW. Being part of an association of members that shares the passion is inspiring and very helpful in finding ways for students to enthusiastically engage with the subject. Every MANSW conference I attended inspired me with new ideas and approaches. I hope it will be the same for you

Best wishes

4. Hartley - June 6, 2011

There was a time when the position of Timetable Deputy provided a career pathway for maths teachers who were prepared to spend many long hours timetabling with magnets overhead projectors and other primitive technologies.
Now timetabling is so completely computerised, very little time or mathematical skill is needed. The PE teacher, who taught some maths in preparation for the time when he/she could no longer do PE, is now more likely to become the timetabler.
Of course, the timetabler is no longer worth a Deputy position and is sometimes not even a promotion position. Since promotion positions are now dependent on an ability to write an application, those who did subjects that involved writing and marking essays have a distinct advantage.
The overall result is that we can no longer depend on schools having an executive member with some sympathy toward maths like we did back in the days when there was a timetable deputy that always had some math skills.
Because those teachers who take so called “practical classes” have always succeeded in having smaller class sizes, the teachers themselves are over represented in staff meetings compared to the number of bums-on-seats in their classes. It seems to have been overlooked that the academic subjects are now much more practically orientated.
Overall this means that the lobby for a small number of long duration lessons outweighs the lobby from maths, shorthand and language teachers for more short duration lessons. Not that there are many shorthand and language teachers these days.
In short, we are now both outnumbered and powerless to do very much about curriculum issues.

5. Allan White - June 7, 2011

Dear Hartley
I remember when the timetable was always done by the mathematics staff. Yes I agree that there is a timetable problem even though many experienced mathematics teachers do break up their lessons into different activities. Nevertheless, if you are going to do the sort of mathematical thinking that is required then an 80 minute period is a joke. Splitting classes on the timetable is not difficult, but getting others to see it as an issue is the difficulty. I certainly agree that trained mathematics teachers are outnumbered but never powerless. It is up to us to make our position known because it was my experience of schools that most staff will try and accommodate the needs of different subjects.
I have always joked that I want to teach mathematics methods units to the PE pre-service students. I hope it doesn’t get to the stage where this is no longer a poor joke.

6. Carol Moule - June 7, 2011

Hi Allan
I agree with all the points in your blog except number 3 in which you give the impression that “older teachers” need to make way for younger ones. The older ones are often the only ones with enough experience to question some of the poor decisions being made in schools and of course principals will not like that! There is also a need for the newer, less experienced teachers to actually earn their stripes/learn their trade before they are “entitled” to senior classes, for my money! As the ageing group do retire an awful lot of experience is going to be lost and it will take yeasr to replace it to the level that these older ones can provide.

7. Michael Cavanagh - June 8, 2011

Hi Allan

As someone inviolved in mathematics teacher education, I have noticed that pre-service primary teachers often lack confidence in their own mathematical abilities. Many might even be characterised as maths phobic. They certainly do not relish the thought that they will soon have to teach a subject that they either profoundly dislike or deeply misundertand.

Often they tell me that their rather negative feelings about mathematics came about as a direct result of their own experiences studying mathematics at school. Some can even pinpoint the precise moment (often in the early years of primary school) when they first began to doubt that they could do mathematics.

In many respects, the issue here is principally about the nature of mathematics itself. I think that many of these pre-service teachers view mathematics as a rather meaningless activity based almost exclusively on learning rules and procedures that they do not understand and which appear to have little relevance in their everyday lives.

As a result, I have deliberately designed my mathematics education units to include numerous opportunities for pre-service teachers to work in small groups on rich tasks that directly relate to their personal experiences. Many students report that, often for the first time in their lives, these cooperative learning activities give them a greater sense of confidence in their mathematical abilities. They come to see mathematics in a quite different way and are more hopeful that they can, in fact, teach mathematics with a new found energy and enthusiasm.

I am hopeful too that the pre-service teachers I work with will become agents of change and that their renewed passion for mathematics will inspire their students to aim high in their mathematical studies.

Allan White - October 15, 2012

Dear Michael

Forgive my delay in replying. I agree with the strategies you are using and I am also hopeful that ‘a change is a coming’. I find it is often when we are considering the pedagogical issues around a content area that the pre-service teachers have an ‘ah ha’ moment where they have a new insight into the conceptual aspects which deepens their own understanding. It is often the first time that they ever understand calculus.

Best wishes

8. Paul White - June 10, 2011

The move in NSW for minimum mathematics standards for primary teachers supports your position on primary teachers knowledge, bro. In our primary course at ACU we have 4 maths units – 2 of them discipline. I know for many students these units are sources of great anxiety. You only have to look at the research into maths anxiety and suggested responses like Sue Wilson’s bibliotherapy. She has publications on the MERGA website

The number of untrained maths teachers is a concern which is much more complex than employment planning, but goes back to choices about maths in school. since 1995 participation in Year 12 higher-level mathematics courses has fallen dramatically and recent reports suggest the rate continues to fall (e.g., Forgasz, 2006). The Report points to the fact that universities have dropped Advanced Mathematics as a prerequisite for many courses and that because the curriculum in these courses is difficult, there is often a lack of appropriately qualified teachers and adequate rewards for students for taking harder subjects.

The Maths? Why Not? project (McPhan, Morony, Pegg, Cooksey & Lynch, 2008) looked at why capable students were not choosing to take higher-level mathematics in the senior years of schooling. Results found the four most important influences affecting students’ engagement with mathematics were:
• self-perception of ability;
• interest and liking of mathematics;
• previous achievement in mathematics; and
• the perceived difficulty of mathematics.
I anecdotally support the point about longer periods less often. I remember my first year of teaching in a school which had one hour periods and having a low stream year 8 class last period Friday after they had been to metalwork. I support the position subjects like maths and languages need shorter exposure on a more regular basis. I also remember being the maths teacher who did the tiemtable

The issue of students moving to early Childhood to avoid maths is, I am pleased to say, not an issue here. Our birth – 12 program has the same literacy, numeracy and science demands as the mainstream program.

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