Assignment 3 Folio

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Swinburne University of Technology *

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Mathematics

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Feb 20, 2024

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Chelsea Smith Student Number: 103694503 EDU10003: The World of Maths Assignment 3: Maths Resource Folio

Assignment 3: Folio Explanation of the Curriculum The Australian curriculum is a curriculum (The Australian Curriculum, Assessment and Reporting Authority [ACARA], 2018, v8.4) followed by teachers all throughout Australia through both Primary and Secondary Schools. It is a professional document which can be accessed by anyone but is aimed to be used by teachers. The document is for teachers to understand what they need to be teaching, so that students all over the Australia are taught the same content, regardless of where they come from or where they live. The Australian Curriculum progresses through the schooling years. It is comprised of three main areas which include Cross curriculum Priorities, Learning Areas and General Capabilities. The Learning Areas contain the content that is taught, which includes: English, Mathematics, Science and Social Sciences, The arts, Health and PE, Languages and Technologies. Within these learning areas are the content descriptors, which is the more specific content that is required to be taught. Cross curriculum Priorities are addressed through the Learning Areas and include Aboriginal and Torres Strait Islander Histories and Cultures, Asia and Australia’s Engagement with Asia and Sustainability. Finally, the General Capabilities are skills that are gained through the teaching of the Learning Areas. For example, literacy is a skill gained through English, and Numeracy is addressed through mathematics, although all capabilities can be gained through all learning areas. Within the Learning Area of Mathematics, the content is separated across three strands: Number and Algebra, Measurement and Geometry, and Statistics and Probability. Mathematics provides students with the skills needed to gain a concept of numeracy which is important for everyday life. The Australian Curriculum aims to create confident students of maths, with skills they can use in life beyond schooling. The Curriculum also intends that the students find enjoyment during this discipline and will successfully be able to find links of mathematics in the other disciplines. The key ideas through mathematics in the curriculum are understanding, fluency, problem-solving and reasoning; these are called proficiency strands. The Australian Curriculum intends to create an understanding of maths within students, that they will understand why and how they use mathematics. It intends to create students who are fluent with mathematics, students who can problem solve to help in solutions, and students who can use reasoning in their thinking. Numeracy is a general capability which is addressed throughout the content taught through the learning areas. The skill of numeracy is evident when students are able to use mathematics confidently throughout many aspects of their lives. It is seen when the students know when and how to use this skill in many different circumstances. Numeracy is mostly gained through the knowledge and skills used in Mathematics but is also seen in the other Learning Areas. The key ideas of numeracy include: Using measurement, estimating and calculating with whole numbers, recognising and using patterns and relationships, using fractions, decimals, percentages, ratios and rates, using special reasoning and interpreting statistical information.

Age group / Year level All templets are focused on Year 2 in Primary School and are related to the Australian Curriculum

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Template 1 Links to curriculum Year 2: Number and Algebra, Number and Place Value ACMNA028: “Group, partition and rearrange collections up to 1000 in hundreds, tens and ones to facilitate more efficient counting (The Australian Curriculum, Assessment and Reporting Authority [ACARA], 2018, v8.4) Resource ( Figure 1. Base Ten Blocks or multibase arithmetic blocks (MAB), Ebay 2021) Base Ten blocks are used to help children distinguish the different between units, tens, hundreds and thousands. MAB blocks include single cubes representing a single unit, a longer stick with 10 little cubes joined together representing tens, a square of 100 cubes joined together representing hundreds, and finally a cube with 1000 cubes joined together representing the thousands value. The MAB blocks are a visual aid where children can use them to help in maths equations and understandings. These blocks will help children break down bigger numbers to help them in understanding the number’s value. The children may be asked an open-ended question, for example, ‘Can you make me 80 with the blocks?’ Rationale This resource enhances children’s learning and engagement with understanding numbers and place value but allowing the students to endlessly create and rearrange different numbers, break them down and build them back up. A study of this resource was conducted (Fuson, K & Brairs, D) finding that many children demonstrated a higher level of meaningful multidigit subtraction and addition when using the blocks as a tool for learning. This resource could be used in conjunction with any equation to help the children create more understanding in their problem solving. The resource can help the children in breaking the number down into hundreds, tens and ones, to create more efficient counting. The Base Ten Blocks are effective in helping the children in building their numeracy skills, they provide a link between the

typical mathematical concepts and the real world (Laren 2012 - Lesh, 1979). Lesh’s translation model (1912 – Koester, 2003), states the importance between the link that manipulatives, situations, pictures, verbal symbols and written symbols have on mathematical understanding. The correlation between real life situations and Base Ten Blocks is also appreciated through a study (Koester, 2003) where the correlation is appreciated as isomorphism by Post (1977). Post (1977), believes that isomorphism is a way of transforming abstract concepts, such as the Base Ten Blocks into real life situations, thus enhancing overall numeracy skills. Cuisenaire and Gattegno (1961) suggests that “students have to have an experience with values of numbers before they learn the number names” (Laren, 2012). Some children learn better by visualising numbers, this resource is a quick and easy way to see a visual breakdown of a number. This resource is effective in allowing the children to physically visualise and feel the values. The children might and should be using mathematical thinking whilst using this resource. For example, the children might think; nine of these hundred’s blocks blocks will equal to 900, plus 10 of the ten’s blocks will equal 10000. The children can calculate whilst also visualising the size of the number. Template 2 Links to curriculum Year 2: Measurement and Geometry, Shape ACMMGO43: “Describe the features of three-dimensional objects” ( The Australian Curriculum, Assessment and Reporting Authority [ACARA], 2018, v8.4) Resource

( Figure 2. Feely Wooden Geometric Shape Box, Modern Teaching aids 2021) This resource allows children to identify and describe different three-dimensional shapes. Children can view, hold and feel the blocks to learn the different 3D shapes. These shapes can initially be used with the assistance of a teacher helping with the names. Once the children have learnt the 3D shapes, they can place them in the box. The children can put their hands inside the box so they can’t see the shape and physically feel them to identify the different aspects of the shape. This resource will help the children in learning the different features of the objects. The resource is open ended in the fact that children could decide how they use the resource, for example, they may choose to use it alone, in partners or in a group. The children might even decide to build with the shapes. Rationale This resource is effective in allowing children to be able to describe the features of a three-dimensional shape. What makes this resource effective is the ability to both see and feel the objects, which allows the brain think for itself. This resource is interesting to children as it follows a creative way of learning, the children are not just simply given an equation to do, rather a resource that they can experiment with and use creative thinking to create a deeper understanding of the shapes. Group work is a key element of modern pedagogy (Blachford,Kutnick, Baines & Galton, n.d), and can be used in conjunction to enhance this resource. Group work can encourage the children to discuss aloud their critical thinking to resolve the problem Infront of them. The children could use this resource to create a game where they explain the key features of the shape to their partner or others in the group. They could all work together to determine what the shape is based on the key features described. The children are required to expand their thinking by using guesswork and problem solving (Pound&Lee, 2011). This resource encourages the children to question what is in the box and imagine what the shape may look like in regard to what they feel to overcome the challenge they are faced with (Pound&Lee, 2011). The wooden shape box resource is an open-ended resource which can enhance children’s thinking to create a deeper overall learning (Klavir&Hershkovitz, n.d). This activity requires the children to use their problem thinking skills when feeling the object, to relate to prior experiences with the shape to determine what it is (Pound&Lee, 2011). Using prior knowledge to develop a deeper understanding of knowledge is known as constructivism (Peters, Viastfall, Slovic, Mertz, Mazzocco & Dickert, 2006). This learning takes place through this resource, creating a deeper learning for the children as they are having to recall on their previous knowledge to remember and identify the hidden shape. This resource is fun and exciting which is important in helping the children gain a positive relationship with maths. This 3D shape resource could even be used to build something, this very hands on resource is effective in helping the children to describe the features of three- dimensional shapes. Rote learning is not an efficient way of learning, it is important that children are able to learn the different features of different shapes through their own observations (Youtube, 2013), which can be made through this resource.

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Template 3 Links to curriculum Year 2: Statistics and Probability ACMSP047 “Identify practical activities and everyday events that involve chance. Describe outcomes as ‘likely’ or ‘unlikely’ and identify some events as ‘certain or ‘impossible’” (The Australian Curriculum, Assessment and Reporting Authority [ACARA], 2018, v8.4) Resource ( Figure 3. The Vile Vendor. Education Services 2016) This online game is based around understanding the concept of chance. It introduces the children to the use of outcomes such as ‘likely’, ‘unlikely’, ‘certain’ and ‘impossible’. The game asks a question regarding the chances of getting a certain flavoured drink from the vending machine. Once selecting the chance, the game will then either allow the child to move onto the next question if they answered correctly or give them another go to answer correctly. If answered incorrectly twice, the machine will then give the correct answer. Rationale Technology is such a big part of modern society and thus is important that ICT resources are included as a teaching strategy to meet the needs of contemporary education (Contemporary Education, 2020). ICT is successful for enriching an understanding of concepts for children and is essential to be used in the teaching and learning of mathematics (Ittigson & Zewe, 2003). This ICT resource enhances maths by allowing children to facilitate their own learning, they are able to read

and think on their own, with the resource giving them feedback on whether they answered correctly or not. By children being able to continue the learning on their own, they may progress quicker, and it may also encourage the children to use critical thinking before engaging with the teacher. When used in conjunction with teacher assistance, this game will be very successful for the learning of chance/probability in year 2 students. This game has relations to a real-life situation, which is important as chance and probability are a part of everyday life. This resource allows children to transfer the learnings of maths to support decisions in everyday life, “ Numeracy is the capacity, confidence and disposition to use mathematics in daily life” ( DET, 2019, p. 49). 

References Ebay. (2021). MAB Base Ten Maths Blocks Student Wooden 121 Pieces Teacher Resource Place Value. Retrieved from https://www.ebay.com.au/itm/183237188503 Contemporary Education. (2020). What is the contemporary Education Framework? Retrieved from: http://www.contemporaryeducation.com/2019/07/what-is-contemporary-education-framework.html#:~:text=Contemporary%20Education%20is%20all %20about,school%20consciously%2C%20deliberatively%20and%20intentionally 1. https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.138.6507&rep=rep1&type=pdf - (Ittigson & Zewe, 2003) Keong C, Horani S & Daniel J. (2005). A Study on the Use of ICT in Mathematics Teaching . Malaysian Online Journal of Instructional Technology . 2(3), 43-51. Retrieved from: https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.138.6507&rep=rep1&type=pdf Modern Teaching Aids (2021). Feely Wooden Geometric Shapes Box. Retrieved from: https://www.teaching.com.au/product/TH0070K Pound, L & Lee, T. (2011). Teaching Mathematics Creatively . Routledge, Learning to Teach in the Primary School Series: Taylor and Francis e- Library. Retrieved from: https://ebookcentral.proquest.com/lib/swin/reader.action?docID=667824 Klavir, R & Hershkovitz, S. (n.d.). Teaching and Evaluating ‘Open-Ended’ Problems. Research Gate. Retrieved from: https://www.researchgate.net/profile/Rama-Klavir/publication/252553956_Teaching_and_Evaluating_%27Open-Ended%27_Problems/links/ 0f317537adab23092f000000/Teaching-and-Evaluating-Open-Ended-Problems.pdf

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Blactchford P, Kutnick P, Baines E & Galton M. (n.d). Toward a Social Pedagogy of Classroom Group Work. International Journal of Education Research. Retrieved from: https://discovery.ucl.ac.uk/id/eprint/1490005/1/Blatchford2003Toward153.pdf Education Services Australia Ltd. (2016). The Vile Vendor. Scootle. Retrieved from: https://www.scootle.edu.au/ec/viewing/L118/index.html# Briars, D & Fuson, K. (1990). Using a Base-Ten Blocks Learning/Teaching Approach for First- and Second-Grade Place-Value and Multidigit Addition and Subtraction. Journal for Research in Mathematics Education, 21 (3), 180-206. Doi: 10.307/749373 Rina, K & Albert, L. (2014). The History of Base-Ten-Blocks: Why and Who Made Base-Ten-Blocks? Mediterranean Journal of Social Sciences. 5 (9). Doi: 10.5901/mjss.2014.v5n9p356 Laren, L. (2012). Mathematics teachers at the intersection of policy interventions: What practising teachers offer as challenged in teaching trigonometry. Education as Change. Doi: 10.1080/16823206.2013.947014 Koester, A. (2003). Teaching Children Mathematics. Prisms and Pyramids: Constructing Three-Dimensional Models to Build Understanding. The National Council of Teachers of Mathematics. Retrieved from: http://nimsgeometry2010.pbworks.com/f/prismsandpyramids.pdf Youtube. (2013). Constructivist Learning. Retrieved from: https://www.youtube.com/watch?v=PK2NILj3BrU&t=2s

Peters E, Viastfall D, Slovic P, Mertz C, Mazzocco K & Dickert S. (2006). Numeracy and Decision Making. Psychological Science. 17 (5). 407- 413. Retrieved from: https://cpb-us-e1.wpmucdn.com/blogs.rice.edu/dist/2/9017/files/2018/04/Joselyn-superlab-paper-2017-1a16w63.pdf Department of Education and Training [DET]. (2019). Belonging, being & becoming - The early years learning framework for Australia . Retrieved from https://docs.education.gov.au/documents/belonging-being-becoming-early-years-learning-framework-australia

Assignment 3 Folio

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