inovasi pembelajaran matematika chapter 4.pptx

imovasi pembelajaran matematika chapter 4

1. Numeracy, practical mathematics and mathematical literacy Chapter 4 Feri Dwi Hartanto 0401513029 Dewi Apriliana 0401513046 Present by:

2. Section 2 , argued that practical mathematics should be the major focus of mathematics teaching in the compulsory school years .

3. Section 3 draws on common definitions of numeracy, in part to clarify the way the term ‘ numeracy ’ is used in this review paper, and also to elaborate three arguments. They are : that numeracy has particular meanings in the context of work, and these meanings have implications for school mathematics curriculum and pedagogy. that there is a numeracy dimension in many social situations that can productively be addressed by mathematics teachers. that numeracy perspectives can enrich the study of other curriculum subjects.

4. In this section we will discussing about: Defining numeracy Work readiness and implications for a numeracy curriculum A social perspective on numeracy Numeracy in other curriculum areas

5. Defining numeracy The term ‘numeracy’ is used in various contexts and with different meanings, such as the following: as a descriptive label for systemic mathematical assessments in subsequent reporting to schools and parents as the name of a remedial subject to describe certain emphases in the mathematics curriculum and in other disciplines

6. The Australian Government Human Capital Working Group, concerned about the readiness for work of some school leavers, commissioned the National Numeracy Review (NNR). The review panel, which included leading mathematics educators, initially used the following definition of numeracy: Numeracy is the effective use of mathematics to meet the general demands of life at school and at home, in paid work, and for participation in community and civic life. (Ministerial Council on Education, Employment, Training and Youth Affairs, 1999, p. 4) The NNR report extended that definition to argue that : … numeracy involves considerably more than the acquisition of mathematical routines and algorithms . (National Numeracy Review, 2008, p. xi)

7. This review paper prefers the more helpful clarification, which had been developed by Australian Association of Mathematics Teachers (AAMT, 1998) after extensive consultation with its members and a special purpose conference. This clarification contended that numeracy is : … a fundamental component of learning, discourse and critique across all areas of the curriculum. (Australian Association of Mathematics Teachers, 1998, p. 1 ) The AAMT affirmed that numeracy involves a disposition and willingness : … to use, in context, a combination of: underpinning mathematical concepts and skills from across the discipline (numerical, spatial, graphical, statistical and algebraic ); mathematical thinking and strategies; general thinking skills ; [and] grounded appreciation of context. (Australian Association of Mathematics Teachers, 1998, p. 1 )

8. Work readiness and implications for a numeracy curriculum Lave (1988) , observed various groups of people at work and showed that the mathematical knowledge and skills utilised, for example by shoppers and weight watchers, bore little resemblance to the mathematical routines, procedures and even formulae taught in school. In recent years, several large-scale studies of numeracy in the workplace, in the United Kingdom (Bakker, Hoyles, Kent, & Noss, 2006), and in Australia (Kanes, 2002; FitzSimons & Wedege, 2007), have confirmed Lave ’ s findings . Zevenbergen and Zevenbergen (2009) have drawn attention to ways that young people use numeracy in their school work. Zevenbergen and Zevenbergen found that young workers did not use formal school mathematics even when solving problems involving measuring or proportion and ratios, but, instead, relied on the use of intuitive methods, only some of which were workplace specific.

9. A social perspective on numeracy Consider the following sample problems, suitable for upper primary students, the first two of which are adapted from Peled (2008 ). Figure 4. 1 Julia and Tony decided to buy a lottery ticket for $5. Tony only had $1 on him so Julia paid $4. Question 1: If they got $20 back as a prize, what are some possible options for how they should share the prize? Question 2: If they won $50,000, what are some possible options for how they should share the prize ? The following example, also adapted from Peled (2008), raises similar issues . Figure 4. 2 Julia and Penny went shopping for shoes. Julia selected two pairs, one marked at $120, and the other at $80. Penny chose a pair for $100. The shop offers a discount where shoppers get three pairs for the price of two. Question: What are some possible options for how much Julia and Penny should each pay ?

10. Each of these problems requires consideration of aspects beyond an arithmetical interpretation of the situation. The problems can be adapted so they are relevant to students, illustrate an explicit social dimension of numeracy, emphasise that some n umeracy-informed decisionsare made on social criteria, and that in many situations there can be a need to explain and even justify a particular solution. Such problems can also provide insights into the way that mathematics is used to generalise such situations . Jablonka (2003), in an overview of the relationship between mathematical literacy and mathematics, argued for mathematics teachers to include a social dimension in their teaching. She suggested that numeracy perspectives can be useful in exploring cultural identity issues, and the way that particular peoples have used numeracy historically, as well as critical perspectives that are important not only for evaluating information presented in the media (an example of this is the arguments presented on each side of the global warming debates), but also for arguing particular social perspectives (for example, the extent to which Australia could manage refugees seeking resettlement)

11. Numeracy in other curriculum areas For secondary teachers, who are subject specialists, incorporating numeracy perspectives into subjects other than mathematics is something of a challenge for two reasons : First, teachers of other curriculum areas are sometimes not convinced that quantitative perspectives illuminate the issues on which they focus. Second, many teachers who are specialists in non mathematics subjects are neither confident nor skilled in approaches to working with students to model or explain the relevant numeracy.

12. Some example of other curriculum areas might benefit from incorporating numeracy perspectives

13. The geography and mathematics teachers can both benefit from collaboration on such issues. The geography teacher can learn how to better present the data which illustrates the relevant ratio comparisons, and the mathematics teacher can benefit, through listening to their colleagues’ thinking and description of their ways of dealing with data from within the discipline of geography.

14. In English literature study, the meaning and exegetical analysis of texts can be enriched by being more precise about the numeracy dimensions mentioned in the writing. For example, to truly understanding the scale of fortune that Jane Austen says that a man should amass before proposing to a woman, some comparative wealth figures from different levels of society 200 years ago, and comparative income rates from then to the present, converted to current Australian dollar values, would enhance students’ appreciation of Austen’s assertion.

15. Both history and mathematics teachers can benefit from collaboration. History teachers are best placed to comment on the significance of such comparisons, and mathematics teachers are able to inform the calculations and even suggest appropriate models that can be used. Other topics for which a numeracy perspective would enhance the learning of history is in appreciation of large numbers, such as in population comparisons, trends in population over times, and experience of visualisation of space and places.

16. In science, students in the middle and senior secondary years perform calculations related to concentrations, titrations and unit conversions. Practical work and problem solving across all the sciences require the use of a range of measurements, capacity to organise and represent data in a range of forms and to plot, interpret and extrapolate through graphs. This also requires students to estimate, solve ratio problems, use formulae flexibly in a range of situations, perform unit conversions, use and interpret rates, scientific notation and significant figures.

17. The End & Thank You