Mathematising and C - PowerPoint Presentation

Mathematising and Contextualising 2 Context, perspective and mathematics

The Term -Mathematisation What does it mean ? It is a process that happens when creating a mathematical model to solve a real life situation. There are certain cognitive competencies associated with the term. For example designing and applying strategies to solve problems, arranging, arguing, reasoning and distinguishing and also communicating .

Mathematisation Horizontal Mathematisation Mathematical process to organise and solve a real life problem. to go from real world to the world of symbols to solve the issue Vertical Mathematisation the actions and the operations done within the symbolic mathematical world in itself.to move within the symbols world through their rules and axioms. R. Grigoras (2009). Modelling in the environments without numbers - available at http:// doc.utwente.nl/64950/1/memo1875.pdf

Mathematisation

An important aspect of mathematical literacy is engagement with mathematics: using and doing mathematics in a variety of situations. It has been recognised that in dealing with issues that call for mathematical treatment, the choice of mathematical methods and representations is often dependent on the situations in which the problems are presented. (PISA -2009) For PISA, the closest situation is the student’s personal life. Next is school life, work life and leisure, followed by the local community and society as encountered in daily life. Scientific situations are furthest away. The four situation types defined and used for problems to be solved are: personal, educational/ occupational, public and scientific.

Contextualisation Creating a meaning for the learner around and in the learning activity/ ies   Fitting teaching and learning of Mathematics within the learner’s world of experiences.May be achieved by including, modifying or substituting text, context and background of the issue/problem

Contextualisation - An indigenous perspective There is a considerable body of literature that suggests that the use of meaningful and relevant contexts may be important for Aboriginal students learning mathematics. Frigo (1999) suggests that “(c)ontextualising mathematics … means finding ways of providing experiences and strategies in which students can gain meaning and develop the appropriate language that enables them to extend their skills in Western mathematics” (p.13). Although recognising that contextualising mathematics for Indigenous students is not straightforward and involves the overturning of power relations and tacitly held beliefs about Indigenous students , Matthews, Watego , Cooper and Baturo (2005) suggest that it “has the potential to change the educational environment so that Indigenous cultures and their way of knowing are valued rather than devalued and that Indigenous students have pride in their culture and believe that they can perform well in the education system” (p.519). However Brown (2008) suggests that context alone may not be enough . Further research is required that specifically targets three things: Indigenous students’ perceived value of mathematics, their conceptualisations of the usefulness of their school mathematics beyond the classroom, and the ways in which their underachievement can be improved. Insufficient research has been performed to reveal new or alternative mathematics teaching strategies that can contextualise mathematics for Indigenous students. Contextualising the mathematics curriculum would be an effective means to significantly improve both Indigenous and non-Indigenous students’understandings of mathematics. (Brown, 2008, p.93)

Contextualisation - An indigenous perspective Contextualization is not the term that has indigenous perspective only such as the terms “looking at it our way” or “bringing the community to the classroom” are used. Within academic writing, There are two main meanings in the way the term is used, namely, context as deficit and context as culture. Context as deficit is related to the well documented social and economic conditions of Indigenous Australians (e.g., Fitzgerald, 2002). Within an environment of poverty, unemployment, substance abuse, and domestic violence, young people struggle to achieve successful outcomes. Howard (1998) argues that “the contexts in which Aboriginal children live and learn may result in many Aboriginal children not achieving to their potential”. Children who live in communities with high levels of long-term unemployment may also not make the links between successful schooling and positive employment outcomes ( Howard 1997 ). This has led to some commentators arguing that the cultural, and social knowledge required to succeed in school is not present in Indigenous families; that the mismatch between home and school leads to poor educational achievement ( Frigo , 1999). However, as Frigo states: “Aboriginality is not in itself a reason to expect poor educational outcomes” (p. 6). Context as culture relates to using the home and cultural knowledge within the classroom. Gillespie (1995) argues, “Aboriginal students come to school being able to communicate and function very effectively in their communities and have an enormous amount of knowledge and skills already” (p. 145). With respect to mathematics, this form of contextualisation is “building on the mathematical knowledge that Aboriginal students utilize outside the classroom” ( Frigo , 1999, p. 14) and requires teachers “to find out what kinds of mathematics exist in the students’ communities as this forms the basis of the students’ own mathematical knowledge base”

Contextualisation - An indigenous perspective There is some research that suggest that contexts , both mathematical and pedagogical, may exclude some children. They argue that the mathematical context is often artificial, alienating, or excluding and always requires recontextualisation to draw out the mathematics, and that the pedagogical context must be made explicit to enable children to understand the purpose and make sense of themathematics.It seems that elements such as social justice, empowerment, engagement , reconciliation , self-determination, connectedness and relevance (Matthews, Howard & Perry , 2003) need to work together to ensure that learning mathematics is meaningful for Indigenous students.

The components of the mathematics domain Pisa 2009 Assessment framework

Qn.1 How important is context to the learning of mathematics ? Share any personal examples of how context helped or didn't help.

Qn.2 Are Aboriginal and Torres Strait Islander perspectives dealt with adequately in the Australian Curriculum: Mathematics?

Qn. 3 Gutstein uses social issues as a vehicle for learning mathematics, and mathematics as a vehicle for understanding the world. In which parts of the Australian Curriculum: Mathematics might this be most appropriate?

Qn.4 Can you suggest specific activities that might be appropriate at your year level?

Possible activities Think about some of the mathematical and context based activities you may design for your class e.g. sorting objects, counting objects, making patterns, constructing shapes , covering, identifying numerals and their names, cutting and pasting to represent numerals

Financial literacy

Can a 15 yr old manage money ? On average across the 13 OECD countries and economies that participated in the PISA financial literacy assessment, 10% of students can analyse complex financial products and solve non-routine financial problems, while 15% can, at best, make simple decisions about everyday spending, and recognise the purpose of everyday financial documents, such as an invoice.https://www.youtube.com/watch?v=8xe6nLVXEC0

While skills in mathematics and reading are closely related to financial literacy, high proficiency in one of these core subjects does not necessarily signal high performance in financial literacy. Students in some countries that perform well in financial literacy, such as Australia, the Czech Republic, Estonia, the Flemish Community of Belgium and New Zealand, score higher in financial literacy, on average, than their performance in mathematics and reading would predict , while students in France, Italy and Slovenia perform worse than expected in financial literacy, based on their performance in mathematics and reading. http://www.oecd.org/pisa/keyfindings/PISA-2012-results-volume-vi.pdf

Mathematical Anxiety

Mathematical Anxiety -PISA

Teacher’s role Educators should be concerned that the majority of students feels anxious about mathematics. Teachers who use formative practices, such as telling students how well they are doing in mathematics class, giving students feedback on their strengths and weaknesses in mathematics, and telling students what they need to do to become better in mathematics, help students to become less anxious.

Skills that are not used arelost it is particularly hard for countries to catch up when young people leave school with a poor set of skills. Post-compulsory education and training systems do not compensate for the country-to-country differences in performance that are observed at the age of 15. Once developed, skills must be used.

Question 1 (Data Sense) QUESTION In which month did the band No One's Darling sell more CDs than the band The Kicking Kangaroos for the first time? No Month MarchAprilMay In January, the new CDs of the bands 4U2Rock and The Kicking Kangaroos were released. In February, the CDs of the bands No One's Darling and The Metalfolkies followed. The following graph shows the sales of the bands' CDs from January to June.

Question 2 (Problem Solving) TRAFFIC Here is a map of a system of roads that links the suburbs within a city. The map shows the travel time in minutes at 7:00 am on each section of road. Julio lives in Silver, Maria lives in Lincoln and Don lives in Nobel. They want to meet in a suburb on the map. No-one wants to travel for more than 15 minutes. Where could they meet?

INVOICE Question 3 (Financial Literacy) Qn1. Why was this invoice sent to Sarah? Because Sarah needs to pay the money to Breezy Clothing. Because Breezy Clothing needs to pay the money to Sarah. Because Sarah has paid the money to Breezy Clothing. Because Breezy Clothing has paid the money to Sarah . Qn2. How much has Breezy Clothing charged for delivering the clothes?

How much money did Jane’s employer pay into her bank account on 31 July? 300 zeds 2500 zeds 2800 zeds 19 600 zeds Each month, Jane's salary is paid into her bank account. This is Jane's pay slip for July. Question 4 (Financial Literacy)