Mathematics Vs Numeracy

1. Mathematics Vs Numeracy

2. This presentation will be demonstrating my understanding of the similarities and differences between mathematics and numeracy and how these concepts can be taught to children through fun activities that will keep them engaged. Mathematics being used in the real world by relating it to interesting phenomena will also be discussed. “Strong math skills are important as we use them every day both in our professional and personal lives. Making math's fun will enable children with a solid start which will help shape a strong future” (Flanders, 2012). 

3. What is Mathematics? “Mathematics provides the foundations and processes to enable one to be numerate” (Surfing Sine Waves, 2011). “The study of the measurement, relationships, and properties of quantities and sets, using numbers and symbols. Arithmetic, algebra, geometry, and calculus are branches of mathematics(Freedictionary.com, 2013). What is Numeracy? “Numeracy involves the abilities which include interpreting, applying and communicating mathematical information in commonly encountered situations to enable full, critical and effective participation in a wide range of life roles”(Department of Education Queensland, 1994). “Numeracy is a life skill. Being numerate goes beyond simply ‘doing sums’. It means having confidence and competence to use numbers and think mathematically in everyday life” (National Numeracy, 2013). (National Numeracy, 2013)

4. Numeracy and Mathematics are clearly interrelated although they can be differentiated. Numeracy is not a synonym for mathematics (Department of Employment, Education, Training and Youth Affairs, 1997).

5. Dice Rhyme and Pattern Game • What you will need: • A 6 sided cube with an image of your choice on each side that relates to an exciting learning nursery rhyme for children. • Music of each song (Optional) • Props for each song to act song out for creativity and for more excitement(Optional) • How to play: • Once the teacher has attention from all children, the teacher rolls the die and whichever side it lands on all the children are to participate in the singing, dancing and movements to the nursery rhyme. To engage children further, the teacher may choose a child to come up and roll the die for the class which may be very special and exciting for the children. • Aim: • To engage foundation year level children through song and rhyme while developing their cognitive skills. To enhance their knowledge of the difference between numeracy and mathematical skills by regularly singing counting nursery rhymes that will further develop their memory skills, first counting skills and concepts of patterns, of which the brain will start to store the words and catchy tunes that they love to hear(Everyday Life - Global Post, 2013). The child’s Numeracy skills (beginning to associate with numbers/ counting) will be of great help in future when these skills will be needed for mathematical processing skills of which the child will become progressively numerate. Difference: Numeracy is a concrete and practical capability, whilst mathematics becomes increasingly abstract as children progress through secondary school (National Numeracy, 2013). Songs may include: Five little Monkeys http://www.youtube.com/watch?v=FG6GXdUOR_Y Five little Ducks http://www.youtube.com/watch?v=0uenvW3DrMI 1,2,3,4,5 http://www.youtube.com/watch?v=Owj7nGxMo40 This old Man http://www.youtube.com/watch?v=vFZhL92W6TE 10 little ladybugs http://www.youtube.com/watch?v=SmAkx2431JU Five little speckled frogs http://www.youtube.com/watch?v=oYX1OaiVR94

6. Learning Outcomes (Number and Algebra-Content Strand): • Establish understanding of the language and processes of counting by naming numbers in sequences, initially to and from 20, moving from  any starting point (ACMNA001) (Australian Curriculum, 2013). • Connect number names, numerals and quantities, including zero, initially up to 10 and then beyond(ACMNA002) (Australian Curriculum, 2013). • Learning Outcomes (EYLF): • 5.4 - Children begin to understand how symbols and pattern systems work(Aussie Childcare Network, 2013). • 4.2 Children develop a range of skills and processes such as problem solving, inquiry, experimentation, hypothesising, researching and investigating (Aussie Childcare Network, 2013).

7. Shape Hunt Difference: Mathematics offers absolute truths about relations among ideal objects whereas numeracy offers contingent solutions to problems about real situations (Steen, 2001). • What you will need: • Recycled egg carton • Sheets of paper • Textas to draw shapes on paper • Shapes • How to play: • Teacher asks children to bring in a recycled egg carton. Gives children a shape activity sheet of which the shapes are drawn on. The children then have to search around for that particular coloured shape and match it to its corresponding hole in the egg carton. The teacher may then ask how many of each coloured shape there are. • Aim: • To enhance foundation level and year 1 level children to learn about patterning, sequencing and matching by colour and shape in a practical way. This activity will encourage the children to develop their math skills through pattern recognition, classifying and solving problems. An understanding of numeracy (matching each shape to its corresponding hole) and mathematics (the amount of shapes and the different coloured and sorts of shapes- ‘absolute truths’) will give the children greater knowledge on how numeracy and mathematics differ. (The imagination tree, 2013)

8. Learning Outcomes (Number and Algebra, Measurement and Geometry- Content Strands): • Sort and classify familiar objects and explain the basis for these classifications. Copy, continue and create patterns with objects and drawings(ACMNA005)(Australian Curriculum, 2013). • Recognise and classify familiar two-dimensional shapes and three-dimensional objects using obvious features (ACMMG022)(Australian Curriculum, 2013). • Establish understanding of the language and processes of counting by naming numbers in sequences, initially to and from 20, moving from  any starting point (ACMNA001)(Australian Curriculum, 2013). • Learning Outcomes (EYLF): • 4.1 Children develop dispositions for learning such as curiosity, cooperation, confidence, creativity, commitment, enthusiasm, persistence, imagination and reflexivity (Aussie Childcare Network, 2013). • 4.2 Children develop a range of skills and processes such as problem solving, inquiry, experimentation, hypothesising, researching and investigating (Aussie Childcare Network, 2013). • 4.4 Children resource their own learning through connecting with people, place, technologies and natural and processed materials (Aussie Childcare Network, 2013). • 5.4 Children begin to understand how symbols and pattern systems work (Aussie Childcare Network, 2013).

9. Shopping Game • What you will need: • Price/Picture Signs • Toy Groceries • Fake Money • How to play: • Set up a play area as a shop. Teacher gives each student the same value of money, for example 10 dollars. All students are asked to go and gather some groceries that will add up to the 10 dollars given or less. All students are then to gather together and discuss what they have bought and the value of what they have purchased with their money. Older students may then be asked further instructions such as to take back items that will add up to 5 dollars. • Aim: • To develop year 1 and 2 children’s understanding of the value of money through pretend play and how both numeracy (Pricing of items, association of numbers and product to price) and mathematics (the addition and subtraction of each item to get an equivalent answer of 10 dollars) are needed in real life today (Steen, 2001). The shopping game allows further development of their knowledge of the similarities between mathematics and numeracy and to gain an understanding of the ability to use numbers and solve problems which is essential in both numeracy and mathematics (National Numeracy, 2013). • Similarity: An understanding and ability to use numbers and solve problems is essential in both numeracy and mathematics (National Numeracy, 2013). (Unknown, 2013)

10. Learning Outcomes (Number and Algebra- Content Strand): • Represent and solve simple addition and subtraction problems using a range of strategies including counting on, partitioning and rearranging parts (ACMNA015)(Australian Curriculum, 2013) • Recognise, describe and order Australian coins according to their value (ACMNA017)(Australian Curriculum, 2013). • Solve simple addition and subtraction problems using a range of efficient mental and written strategies (ACMNA030)(Australian Curriculum, 2013). • Count and order small collections of Australian coins and notes according to their value(ACMNA034)(Australian Curriculum, 2013). • Learning Outcomes (EYLF): • 4.1 Children develop dispositions for learning such as curiosity, cooperation, confidence, creativity, commitment, enthusiasm, persistence, imagination and reflexivity (Aussie Childcare Network, 2013). • 4.3 Children transfer and adapt what they have learned from one context to another (Aussie Childcare Network, 2013). • 4.4 Children resource their own learning through connecting with people, place, technologies and natural and processed materials (Aussie Childcare Network, 2013). • 5.1 Children interact verbally and non-verbally with others for a range of purposes (Aussie Childcare Network, 2013).

11. As educators what can we do? As educators we must emphasise to students, the importance of numeracy and mathematics in every day life and how we can apply it to our day-to-day living. We must encourage children to think mathematically in everyday life by talking about the ways mathematics can be used at home, at a supermarket or at the playgroundthrough fun and engaging activities (Parents-in-education.moe.gov.sg, 2013). We must be able to communicate to the children that mathematics relates to every single aspect of our lives. For example, there are natural phenomena’s everyday – like the Fibonacci sequence or bilateral symmetry. Most careers – if not all - that these children will undertake in the future will require some sort of mathematical understanding.

12. Fibonacci In Nature The Fibonacci sequence is known to be Nature's numbering system because of the Fibonacci number patterns that recurrently occur in nature. They appear everywhere in Nature, from the leaf arrangement in plants, to the pattern of the florets of a flower, the bracts of a pinecone, or the scales of a pineapple(Jwilson.coe.uga.edu, 2013). SO WHAT IS FIBONACCI? The Fibonacci Sequence is the series of numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ... The next number is found by adding up the two numbers before it.

13. Fibonacci Sequence in Pineapples The Fibonacci sequence is found in pineapple scales, which are patterned into spirals and because they are roughly hexagonal in shape. The three sets of spirals that may be observedinclude: (Unknown, 2013)

14. How can we tell that Fibonacci is displayed in pineapples? 1. Count number of spirals going left 2. Count number of spirals going right 3. Count the number of spirals going almost straight up If you choose any of these three methods to count the spirals on a pineapple you will be left with a Fibonacci number! As educators we may teach this aspect of Fibonacci by either providing students with a pineapple or allowing the children to bring in their own pineapple within the classroom environment to participate in this activity.

15. What will children achieve from this? • Children will learn through the proficiency strands: • Understanding • Fluency • Problem Solving • Reasoning • These are an integral part of mathematics content across the three content strands: Number and Algebra, Measurement and Geometry, and Statistics and Probability (Australian Curriculum, 2013).

16. Australian Curriculum Learning Outcomes: • Number and Algebra • Investigate number sequences, initially those increasing and decreasing by twos, threes, fives and ten from any starting point, then moving to other sequences. (ACMNA026) • Describe patterns with numbers and identify missing elements (ACMNA035) • Measurement and Geometry • Describe and draw two-dimensional shapes, with and without digital technologies (ACMMG042) • Year two level children may further this activity by using probability to estimate the likelihood of all pineapples displaying this aspect. They then can compare each child’s findings and graph the results. • Statistics and Probability • Identify practical activities and everyday events that involve chance. Describe outcomes as ‘likely’ or ‘unlikely’ and identify some events as ‘certain’ or ‘impossible’ (ACMSP047) • Collect, check and classify data (ACMSP049) • Create displays of data using lists, table and picture graphs and interpret them (ACMSP050)

17. Symmetry in Nature As educators we must emphasise that mathematics is important and apart of everyday life. Another way to teach children this concept is to let them learn about symmetry, which is everywhere we look in nature! This is evident when you look at plants and animals, you will find that they have symmetrical body shapes and patterns. If you divide a leaf in half, you will often find that one half has the same shape as the other half (Misterteacher.com, 2013). SO WHAT IS SYMMETRY? Symmetry is when one shape can be split down a single axis to have mirror images on each side. This means if you cut something in half both sides will be of exact size, shape and colour.

18. Symmetry in Butterflies If you were to divide a butterfly down the middle, you will find that the opposite sides of their body will look exactly the same. For example, you will find the same shape, pattern, colours and features (Antennae) on each side (Misterteacher.com, 2013). We encounter symmetry under reflection all around us — this is the familiar bilateral symmetry that characterises animals such as butterflies and numerous artifacts (Livio, 2006). Have your students produce their own symmetrical butterflies. Provide students with butterfly templates and then have students create their own patterns and colour them exactly the same on both sides so that they will be symmetrical. Students may also research pictures of butterflies from computers to look at for inspiration.

19. So what Butterfly is symmetrical ? (Unknown, 2013) (Unknown, 2013) This one? Or this one?

20. Although this butterfly looks like the same shape did you miss…… The missing Antennae ? or The different coloured wings ? (Unknown, 2013)

21. This example Is based mainly on enhancing children’s ability to use skills to associate with geometry, therefore the Australian Curriculum Learning Outcomes would include: • Measurement and Geometry • Describe and draw two-dimensional shapes, with and without digital technologies (ACMMG042) • Investigate the effect of one-step slides and flips with and without digital technologies (ACMMG045) • Identify symmetry in the environment (ACMMG066)

22. In Conclusion……. This presentation has outlined the importance of numeracy and mathematics in everyday life and how we as educators can emphasise this to children in a fun and engaging manner. The similarities and differences have been portrayed through fun activities that the children will enjoy learning from and participating in. Teaching children about Interesting phenomena in nature that we all face on a day-to-day basis will display to children the significance that we need mathematics for our future to become more and more numerate human beings.