8502: Assignment 2

Teaching Maths in Early Years: EDUC 8502

Assignment 2: Using Children’s Literature to Develop Mathematical

Understanding in K-3

Sarah Anne Dandridge20501616

Unit Coordinator: Friday, June 1Christine Howitt

2012

Sarah Dandridge 20501616

8502: Assignment 2Part A: The Book

Book: Fisher, D., & Sneed, D., & Lee, K. (2006). One Odd Day: Mount Pleasant:

Sylvan Dell Pub.(See appendix for photos)

Year level: Year three.

In accordance to the Australian Curriculum, the concept of this book looks at “identifying odd and even numbers” (ACARA, 2012)

Availability: Can buy both Hardcopies and Ebook at:

Sylvan Dell Publishing. (2012). One Odd Day. Retrieved 7 May 2012, from http://www.sylvandellpublishing.com/bookpage.php?id=Odd

Can buy hardcopies at: Amazon. (2012). One Odd Day (hardcover). Retrieved 7 May, 2012, from

http://www.amazon.com/One-Odd-Day-Doris-Fisher/dp/0976882337

Can buy eBooks at: TumbleBooks Inc (2012). One Odd Day. Retrieved 30 May, 2012, from Apple ITunes

Store

BookU.com. (2011). One Odd Day: ebook. Retrieved 30 May, 2012, from http://www.booku.com/One-Odd-Day/Doris-Fisher/ebook_453030.htm?gclid=CJ3S9LuCp7ACFVGZpAodLj2OWA

Synopses: Sarah Dandridge 20501616

8502: Assignment 2o This book looks at the idea of what life would be like if everything was an

odd number. A boy wakes up to find that he has a t-shirt with three

sleeves, his dog has five legs and his teacher has five arms. Throughout

this boys typical school day he comes across many weird and wonderful

characters that all have some kind of number concept to their appearance.

Finally at the end of the day the boy goes to sleep thinking that his very

‘odd’ day is over; only to find out he wakes up with a very ‘even’ day.

o The number concept is identifying odd and even numbers.

Analyses:

The number concept of odd and even number falls under the very general umbrella

term of number patterns. (Siemon et al., 2011) Number patterns are defined as

numbers that are arranged according to a certain rule or method. (Haylock, 2007) The

number pattern branch can be sub divided further into three main areas, these being;

arithmetic sequences, geometric sequences and special number sequences. (Haylock,

2007) Arithmetic patterning refers to a number sequence whereby the next term

originates from adding a constant to the predecessor. Geometric patterning and special

number patterning refer to the sequences in which the next term originates by

multiplying the processor with a constant and the patterns created by special numbers

respectively. (Haylock, 2007)

Within early childhood education the concept of number patterns focus largely on the

arithmetic strand of number patterns. (Willis, 2004) The concept of odd and even

numbers branch off this strand of number patterns alongside other concepts such as

skip counting, doubling, halving, dividing fractions, prime numbers and whole and

decimal number patterns. (Willis, 2004)

Number patterns are such an important concept, as they are the foundations on which

all mathematics is laid upon. Without the basic understanding of numbers and number

sense all higher mathematics will be affected. (Haylock, 2007) Mathematics also plays a

very vital role within our society. Although mathematics is an abstract concept it

emerges from the real world. (Orton, 2004) Without a sound understanding of such

fundamental concepts like number patterns our society would be dramatically

disadvantaged. According to the Australian Curriculum students from year one right

until year five should be working on building these foundational arithmetic patterns.

Sarah Dandridge 20501616

8502: Assignment 2Teaching number patterns to children will take years due to the vast expansion of this

area. Accroding to Mooney et al,. (2010) teaching of number patterns should start with

the concept of counting, with progression into the properties of numbers and then into

place value and ordering. Beyond the stage of arithmetic patterns children should

continue to look at number patterns through the other two patterning stages namely

the geometric patterning, which is focused on at the end of primary school.

The focus for the lesson plans and the teaching aid was the concept of odd and even

numbers. Odd numbers are defined as numbers that are “not divisible into two equal

parts”. (Orton, 2004, p. 33) Even numbers are defined as number that “are divisible by

two equal parts”. (Orton, 2004, p. 33) Odd and even numbers focus largely on the strand

of arithmetic patterns, with it falling under the subcategory of real numbers. Odd and

even numbers are said to be an extension of skip counting. According to Orton (2004)

teaching of this area is therefor often poorly done, as teachers assume that the children

have grasped this concept in the process of learning skip counting. According to Mooney

et al,. (2010) once the child can recognise odd and even numbers they should be

introduced to some of the properties of combining these numbers. Knowledge in this

area aids the children’s understanding of addition and subtraction of positive and

negative numbers. Odd and even numbers are specifically taught in year three and four

when the students have developed skip counting and are needed to be extended in their

knowledge.

Sarah Dandridge 20501616

8502: Assignment 2Part B: The Lesson Plans

Maths lesson 1: Odd and Even concept

Year Level/s: 3Curriculum Area:(e.g. Mathematics)

Mathematics: number concept: Odd and Even numbers

Date: 30/05/2012 Time Period: 60 Min

Specific Lesson Learning Goals (What will the students learn during this particular lesson?)

Discuss how to determine if a number is odd

Identify an odd number

Use concrete materials to determine if a number is odd

Students’ Prior Knowledge:

Know what an even number is

Can act out, draw, model to determine if a number is even

Use words/symbols to record numbers

Ability to count to beyond 100; Basic multiplication skills (up to 4 times tables).

Preparation: (classroom layout, resources, groupings)

Environment:

Mat area and group tables

Book: One Odd Day by Doris Fisher, Dani Sneed and Karen Lee

24 ‘ruler’ worksheets

Pop sticks

Teachers chair

Pens

Self:

Bring in the book

Photocopy the worksheets

Time:

5 min

10 min

Lesson Progression(Include: Introduction, Read the story Lesson Steps, Activities, Focus Questions and Conclusion)

Introduction: (Whole group on the mat)

1. Revisit and revise past concepts

What is an even number?

How do you know its an even number

o “If it has a pair” OR “If the last number is a multiple of two”

o Examples of even numbers (2 up to 20)

2. New concept

Prior knowledge.

o “What do we call the numbers that aren’t even?”

o “What does the word ‘ODD’ mean?”

“Not having a pair” OR “Something isn’t quite right” OR “Something that is left out”

Introduce concept.

o “What are odd numbers?”

o “Why are they called odd numbers?”

o Examples of odd numbers

1 to 21

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8502: Assignment 2

5 min

5 min

5 - 10 min

10 min

o This book talks about odd numbers, have a look at the pictures and the words and see how many odd numbered things you can find

o Read the story once for enjoyment

o Once for analysis

Page 2: the numbers of the clock

Page 3: numbers on wall, sock, shoe, Price tag

Page 4: shirt, ball, turtle, cage, water dispencer

Page 5: toast, dog, egg, hat, chair, table

Page 6: light, dog,

Page 7: bucket, bird, tag, shoe, shock, shirt, door, snake

Page 8: dolphins, bus, nus number, street signs, house windows, show house, letterbox

Page 9: calendar, tattoo,

Page 10: teacher (glasses, hands, feet, skirt) goat, street sign, pencil, basketball player

Page 11: flamingo number, candle, shoe, sock, castle, stars, cloud – EVEN: assassins

For even assassins count 4 on one hand, 4 on other, do they match

Page 12: fish, taxi, shoe, bed sheet, cards, bowling ball and pins, lights.

Page 13: two shoes, 4 dog feet

Odd or even?

Do on hands “do they all have partners?”

Page 14: head, door, beds

Body: (Teacher is walking around the desks monitoring)1. Concrete object work with odd numbers (children moving around in groups)

Have the children get into various odd number groups (between 1 and 10) (2 numbers)

o For each say: “Get into groups of 7”

“Do we all have a partner?”

“Is ___ odd or even number?”

Have the children get into various odd number groups (between 10 and 40) (2 numbers)

2. Easy methods to determine if a number is odd or even (desk work)

Partners are good for small numbers

If the number can divide by two and it works, not an odd number

Look at the last digit (ones column) should recognise if even OR odd or can it divide by two

3. Abstract concept – only use odd numbers (desk work)

o Make a ruler of odd numbers (see template)

Conclusion (on the mat)

Consolidation of concept

o Check rulers via partner assessing then teacher collect ruler after class

o In pairs discuss

“I know its an odd number because…”

“The easiest way to find an odd number was by……….”

o Share as a class a few ideas

Final questions and comments

Pack up

Sarah Dandridge 20501616

8502: Assignment 2

Assessment for Student Learning

What will you assess?

Discuss how to determine if a number is odd

Identify an odd number Use concrete materials to determine if

a number is odd

How will you assess? What evidence will you collect?

Q Work samples (the rulers) Anecdotal records of their understating

of odd numbers

Sarah Dandridge 20501616

8502: Assignment 2

My Odd Ruler

Instructions: See board for details:1. Cut out the rectangles 2. Stick these two rectangles together3. Write down the odd numbers starting at one and finish at 39.

Sarah Dandridge 20501616

Maths lesson 2: Odd and Even conceptYear Level/s:

3Curriculum Area:(e.g. Mathematics)

Mathematics: number concept: Odd and Even numbers

Date: 31/05/2012 Time Period: 60 minutes

Specific Lesson Learning Goals (What will the students learn during this particular lesson?)

Identify odd and even numbers

Discuss how to determine a number is odd or even

Students’ Prior Knowledge:

Know what an even number is

Know what an odd number is

Can act out, draw, model to determine if a number is even or odd

Recognise words/symbols of numbers

Ability to count to beyond 100; Basic multiplication skills (up to 4 times tables).

Preparation: (classroom layout, resources, groupings)

Environment:

Mat area and group tables

Teachers chair

Teaching aid: 4X board games (depending on class size – 6 players per board)

4 X Calculator (one per board game)

Interactive white board

Self:

Bring in the board games and calculators

Turn on IWB

8502: Assignment 2

Time:

10 min.

5 min.

10 min.

20 min.

15 min total:

5 min

Lesson Progression(Include: Introduction, Lesson Steps, Focus Questions and Conclusion)

Introduction: (Whole group on the mat)

3. Revisit and revise past concepts

What is an even number?

o Encourage/Allow all answers: record them on IWB

How do you know its an even number

o Encourage/Allow all answers: record them on IWB

What is an odd number?

o Encourage/Allow all answers: record them on IWB

How do you know its an odd number

o Encourage/Allow all answers: record them on IWB

What can we do to check that its an even/odd number

o Encourage/Allow all answers: record them on IWB

4. Skip counting (put on IWB a 100 chart)

In pairs:

o Count using only odd numbers

o Count using only even numbers

5. Introduction for teaching aid

Introduce “Odd and Even Snakes and Ladders” teaching aid

o What this game will do: it will allow you to use what you already know about odd and even numbers.

o Read instructions for the game

o Set guidelines:

What are the rules for group work?

Questions?

Body: (children back at their desks)

1. Teaching aid

Walk around and check all students understand what they are doing

Help any groups if necessary

Take anecdotal notes about the children’s Odd and Even conceptual understating’s and notes about their team work skills.

Early finishers: start designing a picture or game that uses both odd and even numbers

Conclusion: (pack up then whole group on the mat)

Pack up and tidy all the desks

Sarah Dandridge 20501616

8502: Assignment 2

5 min

5 min

Revise and revisito In pairs:

Is 41 odd or even? Why?o Share as class (3 ideas)

o In pairs: Is 42 odd or even? Why?

o Share as class (3 ideas)

o In pairs: List 2 things that you learnt about odd and even numbers

o Share as class (3 ideas)

o In pairs: How do we know that a number is odd, how do we know if a number is even

o Share as class (3 ideas)

Questions/comments

Informal Assessment of Student Outcomes

What will you assess?

Identify odd and even numbers

Discuss how to determine a number is odd or even

How will you assess? What evidence will you collect?

Anecdotal notes in regards to:

o Their understanding of odd and even numbers

o Their ability to collaborate in a group

Questions and observations

Sarah Dandridge 20501616

8502: Assignment 2Part C: The Teaching Aid

Teaching mathematics is not an easy task. There are so many negative connotations associated with it.

Most children dread mathematics because the concepts and the language used is unlike anything they

have been associated with before. Making mathematics practical, fun, collaborative and meaningful will

hopefully change the children’s attitudes towards mathematics. (Ward, 1974) A very simple technique

for achieving this is the use of teacher aids. Having a book, puppets, board game or even play dough

allows the children to attack the mathematics concept with their heads, hands and hearts. (Ward, 1974)

When teaching mathematics Pratt (2006) showed that you cannot give meaning to mathematics, rather

the children have to establish their own understandings. No matter how many times you explain

something, you cannot make a child understand, you can only provide the appropriate tools and

instructions to allow them to constitute their own meanings. Pratt (2006) explained that a child learns

the quickest if mathematics is taught through its use, rather than being taught the theory and then

having to apply it. Being able to teach mathematics through its use and application requires teaching

aids. Without aids the children would be unable to explore and develop their own meanings.

According to Piaget’s theory of cognitive development concrete objects should be used well into the

Formal Operational Stage. (Woolfolk & Margetts, 2010) Piaget shows that children require the use of

concrete objects to be able to manipulate, act, touch, see and feel things. (Marsh, 2010) Piaget has also

shown that children who lack the ability to work with concrete objects have difficulty understanding

simple mathematics. (Marsh, 2010) It is therefore essential that in early childhood education children

receive the opportunities to use concrete teaching aids.

According to Haylock (2007) teachers that have the greatest success are those able to make a lesson

purposeful to the student. In order to make a lesson purposeful Haylock (2007) suggests the use of one

of the six categories of purposeful tasks, these being; solving real problems, computer stimulation, role-

play, designing and construction, competition and games. In accordance to Haylock (2007) the use of

teaching aids such as a board game is justified on the biases that it will allow the students to find

purpose and meaning to the theory.

Haylock (2007) presented the idea that “children will learn more effectively if they think deeper”.

(Haylock, 2007, p. 151) The use of teaching aids with help children reach that deeper level of thinking.

If an activity is highly engaging and captivating, students are more likely to stay on task and stay

motivated to achieve the goal. Teaching aids also provide the child with an alternative method of

Sarah Dandridge 20501616

8502: Assignment 2learning. This will help deepen their understating and thinking, as they are more likely to want to learn

using a hands-on- approach to mathematics.

Teaching aids are very successful tools if executed properly. They are able to provide children with

hands on learning. This allows them to establish their own understandings through the use of the

teaching aids. According to Piaget developing children need to use teaching aids within the classroom,

as they provide not only the basics for understanding addition, subtraction and multiplication, but they

also allow the children to manipulate objects that are associated with the real world. Teaching aids are

also incredibly useful for helping make a lesson purposeful for the students. Finally teaching aids allow

children to think deeper. This is because the more engaged and focused on an activity child is; the more

likely they will want to apply deeper thought into the task at hand.

Sarah Dandridge 20501616

8502: Assignment 2References:

The Australian Curriculum: Maths. (2012). Retrieved 12 April 2012, from Australian Curriculum Assessment and Reporting Authority: http://www.australiancurriculum.edu.au/Mathematics/Curriculum/F-10?layout=3&y=F&y=1&y=2&y=3&y=4&y=5&y=6&y=7&y=8&y=9&y=10&y=10A&s=NA&s=MG&s=SP#level=1

Haylock, D. (2007). Key Concepts in Teaching Primary Mathematics Available from http://UWA.eblib.com.au/patron/FullRecord.aspx?p=420934

Marsh, C. (2010). Becoming a teacher: Knowledge, Skills and Issues (5th ed.). Frenchs Forest NSW: Pearson Australia

Mooney, C., Briggs, M., Fletcher, M., Hansen, A., & McCullouch, J. (2010). Primary Mathematics: Teaching Theory and Practice Available from http://UWA.eblib.com.au/patron/FullRecord.aspx?p=686476

Orton, A. (2004). Pattern in the Teaching and Learning of Mathematics Available from http://UWA.eblib.com.au/patron/FullRecord.aspx?p=436796

Pratt, N. (2006). Interactive Maths Teaching in the Primary School Available from http://UWA.eblib.com.au/patron/FullRecord.aspx?p=334432

Siemon , D., Beswick, K., Brady, K., Clark, J., Faragher, R., & Warren, E. (2011). Teaching Mathematics, Foundations to Middle Years. Victoria, Australia: Oxford University Press.

Ward, M. (1974). Maths for 10-Year-Olds. How Is It Organised? What Do Teachers Think about Maths? Mathematics in School, 3(3), 17-19.

Willis, S. (2004). First steps in mathematics : number : understand operations, calculate, reason about number patterns. Melbourne, Australia: Harcourt Education Australia.

Woolfolk, A., & Margetts, K. (2010). Educational Psychology (2 ed.). Australia Pearson Education.

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