Assignment 1: Curriculum through Numeracy

The definition of numeracy means many things to many different people. One definition from PISA (2009) states that “Mathematical literacy is an individual’s capacity to identify and understand the role that mathematics plays in the world, to make well-founded judgments’ and to use and engage with mathematics in ways that meet the needs of that individual’s life as a constructive, concerned and reflective citizen” (nationalnumeracy.org.uk). To be literate in mathematics is to be numerate.

Teachers’ need to effectively choose teaching methods and help students learn, you must first know something about whom you are teaching. Your students will come from very different backgrounds and have various learning needs. Knowledge about students will enable you to refine lectures, class discussions, comments, illustrations, and activities so that they are more effective learning experiences (Commonwealth of Australia,2000).To be consistent with the above paragraph, my teaching context will be based upon senior primary. The students come from various socio-economic and cultural backgrounds, with very different academic needs and abilities.

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Some students have weekly tutors, whilst others struggle to comprehend even the basics, such as telling time. The level of comprehension from students in a year 4/5 class varies from a year 2 level up to a year 7 level. The outcome of the lessons will be for the students to learn valuable skills that they can utilize in everyday life. This should be delivered in a variety of ways to help each level of ability apply their understanding.Throughout the course of this unit it has become evident that numeracy does not just focus on mathematics but skills that are key to living a functional and successful life. The Commonwealth of Australia (2000) describes numeracy as being fundamental in equipping the students with the necessary skills and preparing them for their adult, personal, social and working lives and for life-long learning. In Activity 1.4 of Module 1, we looked at the workshop/video “Patterns and Functions: What comes next?” It was clear that student engagement was vital instrument used when discussing effective teaching and student learning. There was discussion of different ways that pattern concepts can become more real and interesting for students. Different ways that teachers can develop programs to encourage students to think about patterns and use what they know about patterns to develop critical thinking and problem solving skills were also highlighted.Image 1: Module 1.4 – Mind map of student engagement demonstrated above mentioned video.

Figure 1 demonstrates ways to capture students engagement, through a mixture of student directed learning and direct teacher instruction.In activity 1.1, the National Numeracy Report (2008), produced fifteen recommendations to help improve numeracy across the country. From these recommendations, there are three that have been selected by myself, which I

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believe identify various factors, that would affect the implementation of the total recommendations.

Recommendation 1 That all systems and schools recognize that, while mathematics can be taught in the context of mathematics lessons, the development of numeracy requires experience in the use of mathematics beyond the mathematics classroom, and hence requires an across the curriculum commitment. Both pre- and in-service teacher education should thus recognize and prepare all teachers as teachers of numeracy, acknowledging that this may in some cases be ‘subject specific numeracy’. The reports suggests that there needs to be more opportunities for mathematics to be learnt outside of math's lessons, hence developing cross curricular numeracy. NNRR (pg9) suggests that it is important to incorporate mathematics into other lessons, so that students don't just define mathematics as being the basic rules of maths (+, -, X, :-), fractions, perimeter and volume; just to name a few. It may also be teachers who do not have a Mathematics background may feel reluctant to incorporate numeracy into their lessons.The factors which could affect implementation would be finding resources/time for staff to redevelop their lesson ideas and also for other subject lessons to include numeracy, which will take away time to focus on other areas of study. Recommendation 13

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That all teachers of mathematics and numeracy be equipped to identify and understand how personal circumstances, cultural practices and the particular mathematical needs of individual students may impact upon their learning of mathematics, and to intervene as necessary, drawing on a repertoire of effective pedagogies to ensure that these learning needs are met. Factors which could affect successful implementation include lack of cultural awareness on the teachers behalf, teachers having a set structure of teaching for every student, lack of time in the classroom to be able to address individuals needs, lack of knowledge of students personal lives. All of these factors play a key role in preparing a successful and efficient classroom, therefore need to be considered. Recommendation 15That structured programs be implemented to support teachers to develop the knowledge and skills necessary to exercise effective leadership roles in numeracy and mathematics within schools.To have structured programs, schools need to be able to have the funding/time to provide for the training. They would also need to nominate a coordinator to make sure that the teachers themselves are trained in what they are teaching and that everyone is on the correct path. Structured programs may also work in one class but may need a different approach for another class. All these factors need to be taken into consideration when implementing any new program to make sure it is not just beneficial for the teachers but also the students and school as a whole. Activity 1.21. Why is numeracy a distinct area of interest?Numeracy is a distinct area o interest due to the skills arising from it that enable people to live and deal with their everyday lives. There are many daily skills that derive from numeracy such as budgeting, telling time, preparing food and/or reading maps (Commonwealth of Australia 2000). Numeracy is the foundation of which our everyday lives are based. Due to the enormous skill set that Numeracy provides, it was deemed to be a separate domain to Literacy by the late 1990's. The Australian Association of Mathematics Teachers (AAMT-) recognised that literacy and numeracy were as important as each other in learning and thus need to be individually considered. 2. How have definitions of numeracy changed over time?(What have the main changes been, and what has brought these about?)

In 1990 (Anneke, W.), in the UK defined numeracy as the ability to process, communicate and interpret numerical information in a variety of contexts.

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In 1998 AAMT stated that numeracy was "the use of mathematics effectively to meet general demands of life at home, in paid work and for the participation in community and civic life"(pg 2).

Changes in definition have been brought about to encourage more positive approaches by students in using numeracy in everyday life (Turner, 2007). “Having negative feelings about mathematics and one’s mathematical ability, implies a reluctance to use mathematics and hence a failure to be fully numerate”.

the current view places numeracy in high regard and is now seen to be used practically in everyday life with an inclusion of other skills. Skills such as listening, critical think and problem solving all contribute to the notion of "numeracy literacy" (Butcher et al, 2002).

3. In what ways is it helpful (or unhelpful) to draw a comparison between numeracy and mathematics?I believe making a comparison between numeracy and mathematics can be more unhelpful than helpful. Many people think that in order to posses 'numeracy literacy' that you need t understand advanced mathematics. That is simply not the case. For instance there are a lot of complex math's activities that get taught in school which many students will never use once they have finished such as algebra.4. Thinking about a subject area that you know well, how does (or how could) numeracy become (better) integrated within that subject area?A subject area that I know well is home economics. Numeracy can become integrated within home economics by giving students recipes where they have to measure ingredients and multiply/divide depending of quantities. For example give students a recipe that asks them to prepare a meal for 6 using a recipe that feeds four people. This type of example will prove useful in many students futures, when it come to them preparing meals for themselves or for parties.

Activity 1.8Is the What Works material telling us anything we need to be (re)considering in our 'quality' teaching and learning practices, and in our assessment and reporting practices? And are there any clear messages concerning curriculum and its relation to social capital?Please share your insights and as you're doing this, ask yourselves whether (and how) a more numerate perspective could help educators to reformulate some of these seemingly intractable issues.The 'What Works' material highlights the notion that teachers need to be aware/sensitive to the needs of their students and their backgrounds. According to Howard et al (2008), teachers need to be able to teach numeracy across the curriculum so that it can be transferred from school life into personal (real) life.

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Many students in my class are immigrants who speak English as a second language. In saying this, teachers need to be aware of the different socioeconomic backgrounds, how students think/work best and details of their personal lives, in order to deliver lessons which meet the curriculum. One point that was made is how some teachers give up due to he students not understanding particular concepts. It's not fair on the student for the teacher to give up. Maybe they ned it explained in another way or maybe they will have a flash light moment. Persistence if the key and some students just take that little bit longer. As a teacher the reward is knowing that you helped a student to learn. To grasp hold of a new concept. As the material states "success occurs where teachers believe it will and act on that belief" (What Works). My interpretation of Davis and Renert (2014) is demonstrated below (figure 2). It suggests that an important aspect of a teaching approach places numeracy content in an exciting and realistic context. This is demonstrated as a pedagogy that focusses on students working together to collaborate and explore. The image below demonstrate the link between student engagement, numeracy development and the vital role of a teacher’s numerical knowledge. Figure 2: Computer program did not let me cut and paste

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Connecting the teachings from module 1 and also making connection to teaching pedagogies, such as Davis and Renert (2014) will assist in developing lessons that focus on student engagement. This will bind numeracy in with real life situations and encourage analysis and presentation in more creative style. The lesson will be based on the framework from ACARA - ACMMG110- Compare 12- and 24-hour time systems and convert between them. Students will be learning to tell the time with the assistance of visual aids.

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Consolidation

Curriculum area - Time - compare 12hr and 24hr time

Objectives 1. Identify that there are 24hrs in a day2. Understand the difference in writing AM and PM3. Design a bus schedule using 24hr time as a game board to complete with friends. A clock will be introduced to the class that demonstrates both 12 and 24hr intervals. Teacher to explain that 1pm in 12 hour time is the same as 13:00 in 24 hour time. Students will then be asked to complete activities on IXL (interactive math's computer program), in relation to time. Their results are summarised in the program. Once students have completed the program and it is clear that they have an understanding of the concept, they can then start to design a bus schedule. The teacher will provide them with an example of what is expected. For instance, if the time is 15:00 where is Sue expected to be. Students are to then prepare a board game and share with class mates. This is reflected through the Learning by Design material, which is applied appropriately enables learners to apply teachings to real world situations. This activity does employ the use of multimodal texts and resources, by using technology the students in this modern generation are more engaged and the use of designing their own bus schedule reinforces their learning and ability to apply it to real life situations (Vygotsky).Future learning would be to further investigate (observe) lesson designs and its practicality in the real world. Explore and develop opportunities for students to discuss solutions and use critical thinking skills (National Numeracy Review 2008). A focus on balance between task based activities and pure mathematics should also be reviewed and employed in the teaching context (Perso). To further progress my learning and understanding of numeracy, I plan to continue questioning, observing and discussing with my mentors. I would like to question my mentor teachers and other staff on their thoughts of numeracy and how they think it would be best applied within the classroom/teaching context. I plan to deepen my understanding of resources to compare and connect future learning materials with those that have already been read. To have a good understanding of the curriculum and the ways that students best learn would be most beneficial in providing the best quality/ useful lessons for students as well.

REFERENCES:

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-ACARA Australian Curriculum, Assessment and Reporting Authority. The Australian curriculum: numeracy

-Annecke, W. (1990). International literacy year. Agenda, 6(8), 67-70.

-Australian Association of Mathematics Teachers (AAMT). Accessed 23/8/14

www.aamt.edu.au/

-Butcher, R., Davidson. E., Hagston, J., Ibrido, D., Lucas, J., Ridley, C., et al. (2002). The certificates in general education for adults, incorporating certificates I, II and III in general education for adults. Melbourne, Australia

-Davis, B. and Renert, M. (2014) The Math Teachers Know. New York: Routledge.

-Howard, P. et al (2008) as cited from www.aamt.edu.au/content/download/13234/.../file/apmc13-4-perry.pdf . Accessed 23/08/14

-National Numeracy, UK. Accessed 25/08/2014

http://www.nationalnumeracy.org.uk/what-is-numeracy/index.html

-National Numeracy Review Report( 2008), Commonwealth of Australia, ACT. Accessed 25/08/14.

https://www.coag.gov.au/sites/default/.../national_ numeracy _review.

-Perso, T. (2006). Issues Concerning the Teaching and Learning of Mathematics and Numeracy in Australian Schools. Australian Mathematics Teacher, 20-27

ETL 421- Module References

Module 1.4- resource- Workshop 1. Patterns and Functions: What Comes Next? Annenberg Media entitled Mathematics: What's the Big Idea?

Module 1.8- resource- R. W. Connell (1989) What Works? Curriculum politics, hegemony, and strategies of social change (Chapter 6) New York

Martelli_T_S234302_ETL421_Assignment 1

Martelli_T_S234302_ETL421_Assignment 1