of or

THELMA PERSO

Introduction • how well people apply mathematics to practical situations — a “choosing and I have recently been following with interest the using” approach; or debate about the teaching of using a • how well they draw on mathematics “ approach” or a “” when dealing with everyday situations in approach and find it quite fascinating to which mathematics is embedded — a consider these two extremes. There are some “mathematical ” approach. interesting links with the teaching and Being numerate involves aspects of each of learning of mathematics and the attainment of these. You cannot be numerate unless you numeracy. know some mathematics. You cannot be In this context I started to mull more deeply numerate unless you can apply mathematics about the teaching and learning of mathe- to practical situations or draw on mathematics matics in our schools and the contrast with when dealing with situations in which mathe- where numeracy development is compared matics is embedded. To assume that someone with the journey that literacy development has is numerate because they know some mathe- had both in Australia and overseas. I have no matics is a nonsense; knowing some doubt that we will soon be embroiled in similar mathematics is essential but not sufficient. arguments. Tests that measure mathematics understand- There currently exist proponents of ings and knowledge at best measure teaching mathematics using a focus on individual potential to be numerate. “basics” compared with a task-focussed The Australian Association of Mathematics approach. I would like to share with you some Teachers (1997, p. 15) has the following as a of my ponderings over this, particularly since description of numeracy: “To be numerate is to many might argue the task-focussed approach use mathematics effectively to meet the general may deliver better numeracy outcomes for demands of life at home, in paid work, and for students but not necessarily better mathe- participations in community and civic life.” So matics outcomes. And after all, does it matter? being numerate involves a disposition or a confidence which must exist in order for people to choose to use mathematics. Teachers play a Definitions vital role in developing numerate behaviours in children and young people. Attempts to describe numeracy have generally For the purpose of this discussion I will focussed on: define numeracy as “the disposition and • what mathematics people know — a capacity to use mathematics to function effec- “basic skills” approach; tively and fully at home and in society.”

36 amt 62 (2) 2006 Numeracy and mathematics Mathematics and numeracy in school The range of definitions for numeracy and its connection with mathematics has resulted in It is interesting to contemplate the history of a widespread misunderstanding about the teaching mathematics in school and the focus nature of numeracy. If school leaders and on mathematics and numeracy by education teachers are unclear about how mathematics systems over the last hundred years. I believe and numeracy connect they will not be able to that that word “numeracy” was first used in effectively respond to the demands that devel- the late 1950s, and this is an interesting fact oping numerate children and young people in itself. This implies that it was probably not place on them. even recognised as being a necessary outcome There are some aspects of mathematics for students prior to that. This would make that are not necessary for numeracy. I would sense. School mathematics traditionally argue that having a grasp of the field of formal focussed on calculation and it was about the Algebra, for example, is not necessary in order time of the increasing availability and access to be numerate. Likewise, there are aspects of to computational tools (albeit in the ’50s, a numerate behaviour that have little to do with slide rule) when the focus started to shift from mathematics (see Figure 1; not to scale). These computation to higher-order thinking skills, aspects are about disposition and confidence estimation and judging the appropriateness of which emanate from an attitude that says, “I answers in contexts. Advances in technology can do this”. Clearly there are some who have meant that the need for people to transfer this attitude who do not know or understand their mathematics understandings to every- aspects of mathematics, but this does not stop day life became greater: different forms of them from using what mathematics they know public transport required people to interpret even if it is not correct or appropriate in partic- more complex bus timetables; maps became ular contexts. Application of incorrect more complex, people started to deal with mathematics may eventually reduce the level greater amounts of money and cash registers of confidence and diminish the application of and adding machines meant that even over- numerate behaviours. the-counter transactions no longer focussed on pen-and-paper accounting. From this point on, the teaching and learning of mathematics in schools began to change to accommodate these new ways of operating and computing. I can remember going to school in the ’60s and it was the role of the classroom to turn me into a walking, talking calculator, since the hand- held calculator had not yet become available to the average person. Hours were spent prac- ticing computation through procedures and algorithms that made sure we all used the same methods and the teacher could find “our mistakes”. These “mistakes” unfortunately Figure 1 usually pointed to problems with memorisa- tion rather than to mathematical So, although numeracy is about the math- understandings. ematics you know it is also about having a As time went on and technology became disposition and a confidence to use it; knowing more available in the form of cheap and ubiq- some mathematics is essential but not suffi- uitous calculators, the focus on school maths cient for numeracy. However, knowing some increased from a whole-of-school and in mathematics must precede the choice to use it particular, whole-of-government perspective. or not. Increased accountability for the spending of public funds meant that the general public

amt 62 (2) 2006 37 wanted to know how well their children were underpins this however, is the understanding being prepared for further schooling and life in of numbers and mathematical “codes” and general. The focus consequently switched hence the major responsibility for developing dramatically to “numeracy” but because the students’ numeracy lies with the Mathematics links between numeracy and school mathe- Learning Area. matics were not clearly understood many put their faith in their children knowing mathe- matics as opposed to what it really meant to be Two approaches numerate and to be able to confidently use their mathematics outside of the mathematics As stated in the findings of the National classroom. This was largely because it was Inquiry into the Teaching of Literacy, although easier to “measure” mathematics knowledge the direct, explicit, systematic, teaching of than to measure the ability to transfer and phonics is a necessary condition, it is not a apply it. sufficient condition for the teaching of reading: Many teachers did not know what to do “The strengths of a whole-language approach, about the impact of increasingly available as I see it, are its insistence on a print-rich computational tools such as calculators; I had environment to stimulate a child’s desire for a teacher say to me a few years ago, “If I gave reading” (DEST, 2005, p. 12). all of my Year 3s a calculator, what mathe- Parallels can be made here with the matics would I teach them?” and so they teaching and learning of mathematics. The continued to focus on teaching their students teaching and learning of basic mathematics to be calculators instead of to use them effec- understandings and skills is essential for tively. Parental pressures to do the same have numeracy — no one would doubt it. What perpetuated and exacerbated the problem and frequently happens however, is that the hence, even now, many teachers still focus on teaching and learning of mathematics often a basic computational model of teaching becomes the teaching and learning of mathe- mathematics believing erroneously that unless matics skills in some classrooms. What is students can do the things a calculator can missing is the environment that stimulates a do, they do not understand mathematics. child’s desire for using mathematics. This in Educational systems have unintentionally turn means that confidence needed for contributed to this problem through lack of numeracy is not being generated in some the provision of quality professional learning classrooms because of the fact that the focus programs needed to inculcate the paradigm is on mathematical knowledge, procedures shifts needed by teachers. and skills with minimum attention being paid The focus instead, I believe, should be on to their application. using the technology both to enhance the I would claim that a basic skills approach learning of mathematics concepts and to take to understanding numbers is a necessary but the burden and tedium out of computation. not sufficient condition to the development of Hence teachers need to be focusing on numeracy. This is because it generally will not teaching students how to compute mentally instil in students a love of mathematics or a and how to estimate in order to understand disposition to choose to use mathematics. the numbers they expect to obtain when using Let us look at the other end of the spec- a calculator so that they can critically deter- trum: a task-centred (or application) approach mine their appropriateness. This is probably to the teaching and learning of mathematics. more about numeracy in one sense, since it For those who may not be familiar with this should be the context that largely determines approach the lesson or group of lessons the appropriateness. The degree of accuracy springs from the need to examine or inquire required by the context determines which about something such as, “How many numbers in the display need to be recorded as students bring sandwiches to school for having been obtained; which can be rounded lunch?” or “How fair are taxes?”. Students or truncated. then work together or independently to find So what we have is an increasing focus in answers and along the way are taught some school mathematics on numeracy. What mathematics that they need to use to do so.

38 amt 62 (2) 2006 They might also be taught some broader skills I believe that current “gaps” in our syllabus such as how to undertake research, how to may be a symptom of the lack of a focus on talk and write about what they are doing, how numeracy in our schools. For example, the to make choices about the strategies and current “hype” over the need for financial methods to use, and so on. literacy, some might argue, is really identifying There is widespread evidence to support the a context for critical numeracy in our success of this approach, particularly for curriculum. engaging students in the middle years. There Clearly there is still a need for both pure is still an important need to teach some math- mathematics and numeracy and that some ematics however, and many teachers would mathematical understandings must come argue it is impossible to teach all the mathe- first, but what are those understandings? Can matics deemed essential using this approach. a person be numerate without having learned Here then, is where it gets interesting. much mathematics? There are certainly Clearly the latter approach results in more people in society who are very numerate from students having some control over their a functional perspective without having learning and thus being more confident about studied much mathematics; they can for using mathematics in their lives; that is, the example read a map, read a timetable, make task-centred approach can more than likely sense of graphs and tables. They do, however, better produce numeracy outcomes than the need to have some understandings about basic skills approach which, I would argue, numbers and how they work. I would argue focusses on achievement of mathematics that a deeper level of mathematics is needed content outcomes. for critical numeracy. Describing this visually in a network diagram might result in Figure 3: Numeracy or mathematics; Numeracy and mathematics

It would appear that with the increasing need for students to stay on at school longer, our approaches to teaching mathematics in school have changed (or need to change) in emphasis from a focus on pure mathematics to a focus on mathematics as the fundamental prerequi- site for numeracy. Whereas in the past we had mathematics throughout schooling for all students and very little focus on numeracy, perhaps the context has changed to the point that the focus and emphasis now has to be on numeracy for all children throughout schooling (see Figure 2).

Figure 2 Figure 3

amt 62 (2) 2006 39 Reframing school mathematics In conclusion and numeracy The solution to the “phonics versus whole In the context of the above discussion it might language” debate over the teaching of reading be helpful to think about how mathematics/ I believe, is balance and a focus on the needs numeracy are being “done” in schools. Many of all students. teachers are now teaching mathematics from a There is similarly a need, in developing “task-centred approach” and thus attending numerate young people, to focus on the more to numeracy outcomes than mathe- teaching and learning of mathematics and matics ones. We might say that these students mathematics skills some of the time, and on are more numerate as a result. Many teachers application and tasks some of the time (not are teaching pure mathematics with a focus necessarily at discrete times). Clearly the on right and wrong answers and as a result balance needs to be flexible and dependent on students are not developing the confidence to the particular needs of any group of students be numerate. For some students confidence at any particular time. Inappropriate balance, diminishes as a result of continued incorrect that is too much mathematics and not enough answers and this frequently results in their application or too much application and not being “turned off” mathematics. enough mathematics will result in students Perhaps teachers of mathematics need to who are not numerate. rethink: are we primarily teachers of mathe- In this context, I believe that all teachers of matics or teachers of mathematics for mathematics must also explicitly see them- numeracy? This is a serious question and one selves as teachers of numeracy. A colleague of which I believe needs to be asked by the mine once said: “I’m a calculus teacher; I don’t profession. Are we able to call ourselves do student relationships.” Unfortunately, in teachers of mathematics anymore in the order to develop the dispositions needed for current cultural and social context of students to be numerate, it is extremely schooling? important for all teachers of mathematics to have strong relationships with their students and powerful pedagogies that build these in Lessons from literacy order to develop risk-taking dispositions necessary for numeracy. The days of teaching Currently, and as a result of long discussion pure mathematics are, I believe, well and truly and debate over time, as well as increasing in the past in the context of schooling. accountability through availability of data, pressure has been placed on teachers of English to become greater teachers of literacy. Reference Teachers who want to retain their identity as teachers of English have moved toward the Department of Education, Science & Training (DEST) (2005). Teaching Reading: Literature Review. Accessed 14 June 2006 teaching of English literature while for others at there has been a deliberate “blurring” of the http://www.dest.gov.au/nitl/documents/literature_review.pdf. The Australian Association of Mathematics Teachers Inc. (1997). lines between English and literacy outcomes. Numeracy = Everyone’s Business. Adelaide: Author. Some teachers of mathematics are trying to hold onto the notion of being “teachers of pure mathematics” and are still able to do that because the differences are not yet clearly understood by the general populace. This is exacerbated by the fact that our national Thelma Perso “numeracy” tests are primarily mathematics Queensland Department of Education & the Arts tests. [email protected]

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