Tags: curriculum, learning theories, mathematics education, teacher quality
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.
References: Clotfelter, 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.
The value of parents’ contributions to their young children’s mathematics understanding May 15, 2011Posted by Editor21C in Community Engagement, Early Childhood Education, Engaging Learning Environments, Primary Education.
Tags: creativity, curriculum, Education and community, mathematics education, parenting
1 comment so far
from Jana Kokkinos
In her first post, Jana Kokkinos points to the many ways in which parents of young children can help them to understand fundamental mathematical concepts through play and everyday experience.
Too often, young children’s mathematical capabilities are underestimated (Anderson, Anderson & Thauberger, 2008; Clements & Sarama, 2007; Papic, Mulligan & Bobis, 2009). Take, for example, the scenario of little David, nearly four years old (Pound, 2006). David displayed natural curiosity of mathematics during bath-time at home with his mother. He was eager to know the number of bristles on a nail brush. At this point, it may be accepted (perhaps even expected) that carrying the conversation further with such a young child would be futile. Why? There may be the assumption that further explanation may be fruitless as David will not be able to understand the complexities of grouping and counting so many bristles therefore there would be no point in discussing it. A three-year-old child will most certainly not understand large two-digit numbers?! Perhaps numbers bigger than five or ten at this stage may cause confusion and therefore inhibit further understanding?! Not so. Let’s read on and find out what happened.
David’s mother took the time to describe in detail the procedure needed to work out how many bristles the nail brush had. She talked about grouping in clusters and counting the number of bristles in each cluster: “36 lots of eight bristles” (Pound, 2006, p. 13). What do you think happened next? Over the following few days, David’s mother reported that she had observed some amazing mathematics understanding during David’s play with animals, blocks and small cars. He was grouping his toys and saying, “Oh look! I’ve got six lots of two. I’ve got three lots of three” (Pound, 2006, p. 13).
Stories like this need to be shared to exemplify the mathematical competencies of young children, and to show the importance of developing fundamental mathematical ideas through everyday experiences, conversations and general resources. Such stories also show that parents have a greater influence than they know towards developing their children’s mathematical ideas. Parents are often unaware that children explore various mathematics principles in their play (Ginsburg & Ertle, 2008). However, this does not mean that parents are unable to extend their children’s thinking about mathematics principles through play and other daily activities.
Young-Loveridge found that “children whose families give mathematics a high profile in their day-to-day lives develop a greater enthusiasm for mathematics” (as cited in Pound, 2006, p. 143). Although the frequency and quality of mathematical experiences elicited in the home environment may vary greatly (Graham, Nash & Paul, 1997), it is important for parents to understand the value of their contributions to their children’s mathematical development. Many research studies have shown a direct link between children’s development of number concepts before school and their mathematics success throughout schooling (Aubrey, Dahl & Godfrey, 2006; Mousley & Perry, 2009). This is significant information because, among many other things, it tells us that children can increase their mathematics understanding before school and parents can be proactive in their children’s mathematics achievement.
A great starting point for parents of young children is to engage in play with their children, talk/sing frequently about numbers, read books that connect with mathematical ideas, create and re-create patterns, actively encourage children to solve problems, and not for one second believe that your child is incapable. Explore, investigate, discuss and do it all over again! Children are highly capable mathematical thinkers and parents are highly capable teachers of mathematical principles.
Stay tuned to this blog for upcoming tips on encouraging mathematical thinking through everyday activities and readily available, inexpensive resources.
References: Anderson, A., Anderson, J., & Thauberger, C. (2008). Mathematics learning and teaching in the early years. In O.N. Saracho & B. Spodek. (Eds.), Contemporary perspectives on mathematics in early childhood education. (pp. 95-132). USA: Information Age Publishing. Aubrey, C., Dahl, S., & Godfrey, R. (2006). Early mathematics development and later achievement: further evidence. Mathematics Education Research Journal, 18(1), 27-46. Clements, D.H., & Sarama, J. (2007). Early childhood mathematics learning. In F.K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 461-554). Charlotte, NC: Information Age Publishing. Ginsberg, H.P., & Ertle, B. (2008). Knowing the mathematics in early childhood mathematics. In O.N. Saracho & B. Spodek. (Eds.), Contemporary perspectives on mathematics in early childhood education. (pp. 45-66). USA: Information Age Publishing. Graham, T.A., Nash, C., & Paul, K. (1997). Young children’s exposure to mathematics: The child care context. Early Childhood Education Journal, 25 (1), p. 31-38. Mousley, J., & Perry, B. (2009). Developing mathematical concepts in Australian pre-school settings: The background. In R. Hunter, B. Bicknell, & T. Burgess (Eds.), Crossing divides: Proceedings of the 32nd annual conference of the Mathematics Education Research Group of Australasia (Vol. 1). Palmerston North, NZ: MERGA. Papic, M., Mulligan, J., & Bobis, J. (2009). Developing mathematical concepts in Australian pre-school settings: Children’s mathematical thinking. In R.Hunter, B. Bicknell, & T. Burgess (Eds.), Crossing divides: Proceedings of the 32nd annual conference of the Mathematics Education Research Group of Australasia (Vol. 1). Palmerston North, NZ: MERGA. Pound, L. (2006). Supporting mathematical development in the early years. (2nd ed.). Berkshire, England: Open University Press.
Jana Kokkinos is a Lecturer in mathematics education in the School of Education at the University of Western Sydney, Australia. She specialises in the learning and teaching of mathematics in relation to children from birth to eight years of age.