Children's Literature in Primary Mathematics

ESM310 Assignment 1: Using Children’s Literature in Primary Mathematics

Student Name: Alanah Bresnehan

Student Number: 212210385

Campus: Burwood

PLAGIARISM AND COLLUSION Plagiarism occurs when a student passes off as the student’s own work, or copies without acknowledgement as to its authorship, the work of any other person. Collusion occurs when a student obtains the agreement of another person for a fraudulent purpose with the intent of obtaining an advantage in submitting an assignment or other work. Work submitted may be reproduced and/or communicated for the purpose of detecting plagiarism and collusion. DECLARATION I certify that the attached work is entirely my own (or where submitted to meet the requirements of an approved group assignment is the work of the group), except where material quoted or paraphrased is acknowledged in the text. I also certify that it has not been submitted for assessment in any other unit or course.

SIGNED:

Alanah Bresnehan

DATE: 24 April 2014

An assignment will not be accepted for assessment if the declaration appearing above has not been signed by the author. YOU ARE ADVISED TO RETAIN A COPY OF YOUR WORK UNTIL THE ORIGINAL HAS BEEN ASSESSED AND RETURNED TO YOU. Assessor’s Comments: Your comments and grade will be recorded on the essay itself. Please ensure your name appears at the top right hand side of each page of your essay.

Introduction

Students from an early age are exposed to narrative comprehension through the use of stories

and the elements that are composed within the pages. The stories that excite and enhance a

student’s motivation can be manipulated into other disciplinary units in the curriculum. In

particular, Mathematics, as mathematical concepts can be traditionally hard to teach to students

that have no motivation to grasp the concept. Throughout this report there will be discussion

and exploration on the use of children’s literature and to enhance engagement and conceptual

understanding in mathematics.

Discussion of Mathematical Learning through Children’s Literature Using children’s literature in order to teach mathematics can be very effective when moving through

different methods and instructions. For teachers, integration of literature in mathematics ‘provide

context or storyline that can launch or develop mathematical concepts’ (Reys et. al., 2012) The ideas

behind using elements such as objects and theories within the pages of a children’s literature allows

children to connect more closely to the teaching focuses. Inquiry-‐based and constructivist learning

‘aims to achieve…text-‐implicit open investigation,’ (Fischer, 2013) in order to see meaning in the

assigned facts in both literature and mathematics. Dewey states in ‘Experience and Education’ (1997)

that ‘education may be intelligently conducted upon the basis of experience;’ therefore a student’s

ability to take an experience such as reading book can progress to applying the proficiency to

construct their own understandings of problems and solution with help from their teacher and

peers.

In Robert Fischer’s ‘Teaching Thinking’ (2013) he highlights that ‘traditional mathematics teaching

can be regarded as kind of a Platonic activity, to do with the teaching of pre-‐existent knowledge,

procedures and algorithms.’ This suggestion highlights that the answers to mathematical questions

can only ever be right or wrong, and that there is the pre-‐eminent need for complete accuracy. The

ideas around this can be stemmed from the positivist approach of pedagogy. For positivists,

knowledge is born from factual and variable information that has been experimented by

professionals. The belief that ‘something is not “known” until it has been demonstrated repeatedly

under experimental conditions,’ (Hinchey, 2010) doesn’t leave much for teachers to construct

exploration of their own in the classroom with their students. Through integrating mathematics and

literature a teacher can juxtapose the ‘platonic’ activities that mathematics have traditionally been

viewed as. The juxtaposition allows the use of child-‐directed experiences that each child can then

relate to both personally and through the curriculum. AusVELS states that the aim for students in

Mathematics is to create ‘confident, creative users and communicators of mathematics, able to

investigate, represent and interpret situations,’ (Victorian Curriculum and Assessment Authority,

2013) this aim allows teacher to help build confidence, creativity and communication through the

use of literature.

Literature is heavily conducted through early years of schooling along with the ability to count. In

‘Helping Children Learn Mathematics’ (Reys et. al., 2012) it explains that ‘mathematics and language

skills develop hand in hand.’ This concept is being evolved and teachers are beginning to get there

students ‘do something with the information, rather than [getting] the student to repeat

information on demand.’ (Hinchey, 2010) The benefits of using a story is that it is ‘a stimulus for

thinking in the classroom… [as] a good story arouses the interest and involvement of the child.’

(Fischer, 2013) The involvement in the story can help stem into interdisciplinary subjects. The

elements of a story have different elements such as ‘objects and relationships, which unfold specific

sequences of events’ (2013) causing students to apply their own knowledge of the story into other

subjects other than literacy. Haekyung Hong researchers the uses of child-‐centred experiences of

literature in mathematics in his article ‘Effects of Mathematics learning Through Children’s literature

on Math Achievement and Dispositional Outcomes’ (1996). He states that the current views of

integrating mathematics and literature are developing in order to form child-‐directed experiences

and investigation, compared to the traditional methods, which he highlights as ‘not helping children

acquire conceptual understandings of mathematics’ (1996). In his findings he found that 85.7%

(1996) of students increased in their knowledge and also involvement when a mathematics lesson

was being conducted through the use of literature. Hong’s findings suggest that ‘stories…provide

potentially complex challenges for cognitive processing,’ (Fischer, 2013) not only in literacy but also

in Mathematics.

Through using a inquiry-‐based approach students and teachers can acquire conceptual

understandings of the mathematical concepts. Fischer (2013) explains the ‘Cycle of Learning’ when

approaching literature in a mathematics classroom. He informs that there are three stages that

teachers can help create engagement, learning focus and finally outcome through literature and

mathematics. Stage one consists of the ability to ‘Romance’ the students into developing ‘interest

and learner involvement’ (2013). This causes the students to feel connected to the book, story and

creates interest into different elements in the book. Stage two is formed through what Fischer calls

‘Precision’ which is when the teacher emphasises using the book the ‘details of what is being learnt’

(2013). This is when emphasise is on the learning focuses behind using the book in a mathematics

classroom. This stage also explains different elements of the book that students are asked to stress

throughout their mathematic work. The final stage involves ‘Generalisation’ causing the students to

explain ‘where what is learnt is applies and used’ (2013). These stages comply with the theories of

inquiry-‐based learning.

Teachers that are trying to combine literacy and mathematics concern themselves with the process

and personal understanding of the student, rather than the knowledge product. Using a

mathematical centred book is helpful in influencing appropriate mathematical concepts and

language. Marston (as cited in Bragg et al., 2013) conducted a framework for selecting texts to use in

a mathematics classroom. These frameworks include Mathematical content, Curriculum content,

integration of the mathematical content, the mathematical meaning, problem solving and reasoning,

affordance for mathematical learning, and finally the pedagogical implementation. The idea of the

book is to be able to use it throughout the classroom using different elements to cover multiple

areas of curriculum. Though these frameworks can easily be seen in simple ‘counting books’

students should be able to have the ability to investigate further into literature. Inquiry-‐based

teachers argue that it ‘is about invention, and that mathematical enquiry is a creative pursuit,’

(Fischer, 2013) which allows teachers to help students create abstract constructions through the

exploration of texts that go further than just counting. Some theorists argue that though the teacher

may encourage the use of the text, they ‘must not impose the literature on them to teach a specific

skill’ (Shih and Giorgis, 2004).

In summary, the use of literature in mathematics is a highly inquiry-‐based approach to teaching

students. It allows teachers to conduct lessons and programs that enable interdisciplinary subjects

and also frameworks that can efficiently allow students to develop better values, attitudes and

understandings to mathematics without being lectured from a teacher. As teachers move into the

inquiry-‐based learning pedagogy they construct a goal ‘to enhance and extend a students

understanding by enhancing and extending story, not by diverting attention away from the story’

(Shih and Giogis, 2004) Allowing students to use the basis of experience and communication to

better understand mathematical concepts and assign facts that relate back to mathematics and

literature.

Object by the Numbers -‐ data facts, prompts and mathematical exploration

Book details: Graeme Base, 1988, and ‘The Eleventh Hour’.

Suitable for Grade__5/6___

Brief description and rationale for the image you have selected for your poster

The image selected is one of the elephant, the main character in the picture storybook. The reason I

have chosen this image is because data facts about elephants are very easy and resourceful to come

by. The pool of facts on elephants is very large; therefore students can use the facts on the poster

and also through other factual books and Internet. The image also has a great visual representation

of an elephant and is the only character in the image allowing students to have that focus on that

animal.

Picture of front cover of book Picture of inside of book

Picture of data facts poster

List of Data Facts from poster;

Data Fact #1: An African elephant can stand up to 4 meters high.

Data Fact #2: The largest African elephant ever recorded weighed 13.5 tones.

Data Fact #3: Elephants can live up to 70 years old.

Data Fact #4: The elephant’s habitat range shrank from 3,000, 000 square miles in 1979 to 1, 000,

000 square miles in 2007.

Data Fact #5: An elephant’s family usually contains 10 elephants.

Data Fact #6: African Savannah elephants are found in 37 countries in the continent of Africa.

Selected Data Facts for further exploration

Data Fact #1: The elephant’s habitat range shrank from 3,000, 000 square miles in 1979 to 1, 000,

000 square miles in 2007.

Prompts to develop children’s mathematical thinking:

• How big do you think a square mile is compared to a square kilometre?

• How big of an area is 3,000, 000 square miles if one square miles is equal to 2.5 square kilometres?

A child’s anticipated responses to the prompts:

Prompt 1 -‐ Anticipated response:

I was on Google once with the conversion tools and was playing around with acres, miles and kilometres and

all that stuff. Anyway, I typed in one square mile as one and pressed convert. It told me that a square

kilometre was 2.59 compared to one square mile.


If we times the 2.5 with the 3 then it equals 7.5, which is 7 and a half. We can then add on the 6 zeros on the 7

which will make it 7,000,000 though we still have half. Then we divide 1, 000, 000 by 2 which equals 500, 000.

Then we add it onto the 7 million, making the answer 7, 500, 000 square kilometres.

Mathematics explored in the prompts:

The mathematics explored is the investigation between different units of measurement between

metric systems and countries. The second prompt highlights the use of multiplication, division and

problem solving in order to work out an answer.

AusVELS connection and code:

Year 5: Choose appropriate units of measurement for length, area, volume, capacity and mass (ACMMG108) -‐

Investigating alternative measures of scale to demonstrate that these vary between countries and change over time,

for example temperature measurement in Australia, Indonesia, Japan and USA

Year 5: Calculate the perimeter and area of rectangles using familiar metric units (ACMMG109)

Year 6: Multiply decimals by whole numbers and perform divisions by nonzero whole numbers where the results are

terminating decimals, with and without digital technologies (ACMNA129) -‐ Interpreting the results of calculations to

provide an answer appropriate to the context

Year 6: Connect decimal representations to the metric system (ACMMG135)

Data Fact #2: The largest African elephant ever recorded weighed 13.5 tones.


• Do you think a tonne is bigger than kilogram?

• How many kilograms does it take to make up 13.5 tonnes?



My dad works in the with big shipping crates and he told me once that 1000 kilograms is the same as one

tonne.


Therefore, the largest elephant ever recorded will be 13,000 kilograms and a half tonne. The half tonne will be

1 tonne divided into 2, which is 1000÷2, which equals 500. Which makes the answer 13,500 kilograms.


These two prompts explore students’ interpretation of Mass using kilograms and tonnes. It also uses

the use of multiplication and division with thousands and decimals.


Year 5: Choose appropriate units of measurement for length, area, volume, capacity and mass

(ACMMG108)

Year 6: Connect decimal representations to the metric system (ACMMG135) -‐ Recognizing the

equivalence of measurements such as 1.25 meters and 125 centimeters

Year 6: Convert between common metric units of length, mass and capacity (ACMMG136) -‐

Identifying and using the correct operations when converting units including millimeters,

centimeters, meters, kilometers, milligrams, grams, kilograms, tonnes, milliliters, liters,

kiloliters and megalitres -‐ recognizing the significance of the prefixes in units of measurement

Data Fact #3: Elephants can live up to 70 years old.


• What numbers can be divisible by 70?

• What happens if an elephant is aged 15, how many more 15 years does an elephant have

until they reach 70?



• One goes into seventy, 70 times.

• Two goes into seventy, 35 times.

• Five goes into seventy, 14 times.

• Seven goes into seventy, 10 times.


Well we divide seventy by fifteen. Because thirsty divided by fifteen is two, then sixty divided by fifteen is four.

Then we use long division to work out the remainder.


Both prompts highlight the exploration of division. The first prompt looks at numbers that can go

into one particular number and the other prompt asks a specific number with the answer having

remainders.


Year 5: Solve problems involving multiplication of large numbers by one or two digit numbers using efficient mental, written strategies and appropriate digital technologies (ACMNA100)

Year 5: Solve problems involving division by a one or two digit number, including those that result in a remainder (ACMNA101)

References

• Bragg, LA, Koch, J, Willis, A 2014, Once upon a time: children's literature and mathematics,

MAV 2013: Mathematics of planet earth: Proceedings of the MAV 50th Annual Conference

2013 2014, Mathematical Association of Victoria, Melbourne, VIC, pp. 13-‐22

• Dewey, J, 1997 Experience and Education, New York, Touchstone Pub.

• Fischer, R, 2013, Teaching Thinking: Philosophical Enquiry in the Classroom, London,

Bloomsbury Pub.

• Hinchey, PH, 2010, Rethinking What We Know: Positivist and Constructivist

Epistemology, Finding Freedom in the Classroom: A Practical Introduction to Critical Theory,

Peter Lang, New York, pp. 33-‐56

• Reys, RE, Lindquist, MM, Lambdin, DV, Smith, NL, Rogers, A, Falle, J, Frid, S, Bennett, S, 2012,

Helping Children Learn Mathematics, Milton, John Wiley & Sons Australia Ltd.

• Shih, JC, Giorgis, C, 2004, Building Mathematics and Literature Connection through Children’s

responses, Teaching Children Mathematics, Vol. 10 No. 6, Published by National Council of

Teacher of Mathematics,pp. 328-‐333

• Tucker, C, Boggan, M, Harper, S, 2010, Using Children’s Literature to Teach Measurement,

Reading Improvement, Vol. 47 Issue 3, pp. 154-‐161

• Victorian Curriculum and Assessmnet Authority, 2013, AusVELS: Domains – Mathematics.

Retrieved from < http://ausvels.vcaa.vic.edu.au/Mathematics/Overview/Rationale-‐and-‐

Aims>

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Children's Literature in Primary Mathematics