Course Guide Corrected

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CHILDREN LEARNING MATHEMATICS EDMA2213: Course Information. Academic Year 2009/2010, Semester 1

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The University of the West Indies

OPEN CAMPUS

CHILDREN LEARNING MATHEMATICS

EDMA2213

COURSE GUIDE

Semester 1 2011/2012

Welcome to Semester 1 of teaching and learning in EDMA2213- CHILDREN LEARNING MATHEMATICS. I am EDNALAWRENCE, your Course Coordinator.

As you know, open and constant communication is critical to success in the online learning environment. I therefore urge you to

ensure that you play your part to develop and maintain a very interactive relationship with your e-tutor.

I can be reached via the following:

Email: [email protected]: (876)912-2818/ (876)849-9751

Skype: edna.lawrence1Thank you for your commitment as your tutors and I work together to make EDMA2213 Children Learning Mathematics ameaningful learning experience.

Edna M. LawrenceEdna M. LawrenceEdna M. LawrenceEdna M. Lawrence


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August 2011

CONTENTS

PAGE

Introduction 3Course Outline 6

Course Topics 12

Course Delivery Schedule 15

Coursework Assignments and Guidelines 23

General Guidelines for Writing 26

Course Work Accountability Statement 27


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Course Code: EDMA2213

Course Title: CHILDREN LEARNING MATHEMATICS

Credits: 3

Prerequisite/s: None

Co-requisite: To be teaching mathematics at present

Academic Year: 2011/2012 (Semester 1)

Course Coordinator: Edna M. LawrenceEmail: [email protected]: (876)912-2818/ (876)849-9751

Skype: edna.lawrence1

INTRODUCTION

General Information

Some important information to keep in mind:

1. Your picture uploaded on the Learning Exchange must conform to the following a profile of just your face, a close up image

that allows you to be recognized.


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2. The Department in the Open Campus (OC) ultimately responsible for the delivery of this course is: The Undergraduate

Programmes Department. View the OC Web Site for information on your Programme: http://www.open.uwi.edu/ - the home

of the Undergraduate programme.

3. There are different avenues available to you as a student to receive support. The avenue you take is dependent on your

particular need. View the QUICK LINK in your course for Frequently Asked Questions (FAQs .)

Purpose of this Guide

This guide provides an overview of the course on which you are embarking. It gives the course outline details how the course will be

assessed and in general indicates what is required of each participant.

Course Coordinators Expectation

As individuals you will face many challenges from family, from work or from other courses while you are doing this course. I believe that your

aim is to do well. My list of expectations of you is to assist in the smooth running of the course so that you can benefit fully from what it has to

offer.

Kindly observe the following guidelines:

Become familiar with the contents of the course guide

Have access to reliable computer and internet use.

Try to enter into the moodle at least once in 24 hours to read and respond to messages relating to the course posted by the course

coordinator and tutor.

Participants commit themselves to reading the literature and be prepared to share meaningfully in the discussion forum and in all other

activities given.

Observe the time schedule given for the duration of each unit or for the set of questions posted.

Save all assignments in Word 2003 before uploading.

Write your I.D. number on all assignments.

Attach a signed Undergraduate Coursework Accountability Statement to all assignments.


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Upload all assignments in the moodle. (Do not send assignments to the email addresses of the tutor or the course coordinator. (These will

not be marked.)

As much as possible try to submit assignments before the due date and not wait on the last minute bearing in mind the technicalities that

can occur in using the technology.

Submit to your tutor and coordinator a telephone number and an email address (other than your open campus email address) by which you

can be contacted.

Participate in course orientation by completing the Meet your Classmate and E-Tutor section and ensuring that you post a photograph of

yourself.

I hope that all participants in this course will obtain more than a passing grade and that you will make every effort to incorporate that

which has been learned so that your effectiveness as a teacher can be improved and students performance can be enhanced.

General Remarks about the Course

The course, Children Learning Mathematics (EDMA2213), seeks to expose teachers of mathematics to a deeper understanding and

awareness of issues that affect the learner of mathematics and the learning of mathematics with a view to suggest ways of addressing

these issues. Participants are expected to be actively engaged in the teaching of mathematics during the period of the course as you

will need to use the classroom as a field.

The mode of delivery is online and therefore participants must observe the code of conduct that shows courtesy and respect to other

online users. You are required to use information retrieved from the internet and other sources appropriately and acknowledge the

source from which it comes. A section under General Guidelines for Writing (p. 37) will guide you how to use the work of other

people.


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COURSE OUTLINE

Course DescriptionBeing aware that teachers of mathematics need to have an understanding of the characteristics of the learner and the learningenvironment, the course provides an introduction to issues of learning in general and mathematics learning in particular.

Course Objectives

You should be able to:

1) Identify factors associated with learning and to explore the particular demands oflearning mathematics.

2) Demonstrate an understanding of the models of learning as they relate to thelearning of mathematics.

3) Use diagnostic teaching skills as a means of facilitating learning.

4) Develop and use strategies for developing childrens understanding in mathematics.

Course Units

The units to be covered in this course are as follows:

Unit Number Unit Name

Unit 1 The Learning of Mathematics

Unit 2 Models of learning

Unit 3 Enabling understanding of mathematics

Unit 4 Assessing the Occurrence of Learning


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Course Delivery

This course will be delivered over fifteen (13) weeks using online discussions, participating in activities within the course units.

The main course material will be given online within the Units of the course. Additional readings will be provided on CD.

Each participant is expected to visit the course at least once in 24 hours to make postings, interact with other peers, answer questionsposted by classmates, the e-tutor or the coordinator.

You will be provided with guidance each week on particular topics to focus on, but you must also be prepared to work through,independently, all your course material.

The course schedule will outline what the focus will be on for each week (See the Course Topics and Course Delivery Schedule (pp.

11 - 39).

Activities are given within each unit. You are expected to complete each activity and make an initial posting in the discussion section

of the related unit. After you have made your posting, you read the postings of the other peers and comment. You become engaged in

a discussion.

Also, to test your level of participation in the discussion forum, 5% will be awarded to your participation in this regard. Please see the

Course Delivery Schedule (p. 15) and note the activities and the date.

Feedback for all postings made will be posted by your e-tutor in the respective unit and/or in the e-tutors presentation section not

later than two weeks after the due date.


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ASSESSMENT

There will be five (5) course assessments as follows:

(i) Assignment #1: mini essays on Mathematics, Learning & Mathematical Understanding

(ii) Assignment #2: Essay on Theories of Learning

(iii) Assignment #3: Group Work on Communicating in the Mathematics Classroom

(iv) Assignment #4: Project on the Learner

(v) Graded discussions

The weighting for the assessments are as follows:

Assessment Item Weighting

Assignment #1 20%

Assignment #2 20%

Assignment #3: Group Work 15%

Assignment #4: Project 40%

Graded Discussions 5%

Total 100%


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READINGS

Readings are available as part of your course package. Articles have been carefully selected and the readings are supplemented by the

course materials provided in each unit.

In addition you are expected to read the following articles from the CD of readings that will be provided:

Sue-Johnston-Wilder, et.al. (1999).Learning to Teach Mathematics in the Secondary

Schools. London: Routledge

Ernest, P. Aims of Teaching Mathematics. UWIDITE material. Kingston. University

of the West Indies

Skemp, R. (1976). Relational and Instrumental Understanding, Mathematics Teaching

77: 20 6.

Selinger, M. Understanding

Watson, A. What does it mean to understand something?

Skemp, R. The formation of mathematical concepts.


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Orton, A. What cognitive demands are made in learning mathematics?

Bell, Costello & Kachmann Language

Caribbean Examinations Council Regional Workshop (1996). Diagnosis

Lappen, G. Accommodating Students Differences

Bell-Hutchinson, C. The language of Mathematics-do you speak it? Window on

Mathematics. The Daily Gleaner, August 7.

Bell-Hutchinson, C. (2001). Communicating with Symbols. Window on Mathematics.

The Daily gleaner, July 31.

Mathematics Through Problem Solving


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ADDITIONAL RESOURCES

Writing guidelines using APA 6th edition can be found at:http://owl.english.purdue.edu/owl/resource/560/01/

Important dates to keep in mind:

Important Dates

SEMESTER 1

AUGUST DECEMBER 2011

Registration (Add/Drop) August 22 September 16, 2011

Semester Begins August 28, 2011

Teaching Begins September 05, 2011

Mid-Semester Examinations October 17 through October 22, 2011

Teaching Ends December 2, 2011

Examinations Begin December 5, 2011

Examinations End December 21, 2011

Semester Ends December 21, 2011


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COURSE TOPICS

UNIT I

WEEK 1:Purposes of learning Mathematics

o What is Mathematics?o The Aims of Mathematics Educationo Useful Mathematicso Mathematics for Passing Examinations

WEEK 2:The nature, role and attainment of knowledge

o The Role of Knowledgeo The Attainment of Knowledgeo The Nature of Skillso The Role of Skillso

The Attainment of Skillso The Nature of Understandingo The Role of Understandingo The Attainment of Understandingo Teaching for Understanding

WEEK 3Major components of Mathematics Learning

o

What are Mathematics Processes?

Learning Related to Number & Spaceo Learning related to Numbero Learning related to Space

UNIT II


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WEEK 4

The Work of Learning Theoristso Theories of Development Piageto Bruners Theory of Instructiono Vygotskyo Jean Lave- Situated Cognition

WEEK 5Constructivist Theory

UNIT III

WEEK 6

Children as Individuals

Visualizing Perception and Visualization

Field Dependent & Field Independent Learners

Grasshopper and Inchworm LearnersThe Classroom Environment

The Physical Environment

The Personal Environment

The Intellectual Environment

WEEK 7o Communicating Mathematicso Communicating Conceptso Communication in the Classroomo Communicating Mathematicallyo Language in the Mathematics Classroomo Language and formation of Concepts


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o Oral Language in the Mathematics Classroom

WEEK 8o The Written Language of Mathematics

WEEK 9

o The Role of Problem Solving in Learning Mathematics

o The Nature of Problem Solvingo Problem Solving and Constructivismo Why Problem Solving?o Implications for the Role of the Teacher

UNIT IV

WEEK 10

Methods of Assessing Learning

Curriculum Changes

Assessment of Open-End Work

Written Assessment Methods

WEEK 11Diagnosis

Barriers to Understanding

WEEK 12Diagnosis

The Role of Diagnosis


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WEEK 13

Reflection

Lessons Learned

Course Evaluation

COURSE DELIVERY SCHEDULE

Semester begins August 28, 2011

Teaching begins September05, 2011

Teaching ends December 02, 2011

Semester ends December 21, 2011

WEEK

DATES

MAIN TOPIC

OBJECTIVES

Students should be able to:

ASSIGNMENT

DUE DATE

August 28-

September 4

Orientation Complete the Meet your classmates and E-tutor section

of the course. Post a close up, face only photograph of themselves.

Read through the course guide and become familiar withthe requirements of the course

Value: 1% for full

participation inorientationactivities


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WEEK

DATES

MAIN TOPIC

OBJECTIVES


ASSIGNMENT

DUE DATE

1 September 5-11 Unit 1

Topic: The Learning of

Mathematics

Subtopic #1: Purposes of

Learning Mathematics

Give their response to the question What ismathematics?

Put forward their position regarding the purposes oflearning mathematics and justify this position

Demonstrate an understanding of the various viewsconcerning the nature of mathematics and the purposes of

learning it Be aware of the various views about the nature of

mathematics and be able to put forward their own view

2 September 12-18 Unit 1

Topic: The Learning of

Mathematics

Subtopic #2: The Nature, Role &

Attainment of Knowledge, Skills &

Understanding

Describe the characteristics of knowledge, skills andunderstanding

Discuss the importance of knowledge, skills andunderstanding in the learning of mathematics

Identify some approaches that are effective in teaching forknowledge, skills and understanding

3 Sept 19-25 Unit 1 Topic: The Learning of

Mathematics

Subtopics #3: Major Components

of Mathematics Learning

Subtopic #4: Learning related to

Number & Space

Define process as it relates to the learning ofmathematics

Describe major mathematical processes

Define numeracy and describe its role in society

Identify and better understand some of the difficultiesassociated with learning related to number and space

Plan lessons to address some of the problemsexperienced by learners in number and space

Recognize the importance of models in the learning ofnumber and space


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WEEK

DATES

MAIN TOPIC

OBJECTIVES


ASSIGNMENT

DUE DATE

4 Sept. 26 Oct 2 Unit 2 Topic: Models of Learning

Subtopic #1: The Work of LearningTheorists

Summarize the key points in the mathematical learningtheories of Lave, Bruner, Vygotsky and the

development theories of Piaget

Discuss contradictions and concurrences in thesetheories

Assignment #1 due onOct. 3 at 2:30 p.m (Ja

time) & 3.30 p.m.

(EC time).

Value: 20%

5 Oct. 3 9 Subtopic#2: Constructivist Theory

List the key elements in the constructivist theory oflearning

Identify some teaching approaches that follow theprinciples of constructivism


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WEEK

DATES

MAIN TOPIC

OBJECTIVES


ASSIGNMENT

DUE DATE

6

Oct 10 16 Unit 3 Topic: Enabling

Understanding of Mathematics

Subtopic #1: Children as

Individuals

Subtopic #2: The Classroom

Environment

Explain why students need to be treated as individuals

Identify some of the differences that students bring tothe mathematics classroom

Plan lessons more effectively to meet the needs of your

individual learners

Identify the different aspects within the classroomenvironment that affect learning

Provide a classroom environment which enableslearning

7

8

Oct 17 23

Oct. 24 - 30

Subtopic #3: Communicating

Mathematics

Subtopic #4: Language in theMathematics Classroom

Improve communication between yourself and yourstudents

Facilitate beneficial communication between studentsin your classroom

Listen more and talk less

Identify words that may cause students to be confusedbecause of differences between their mathematical

meaning and their everyday meaning

Identify misuse of words in your own use ofmathematical language

Be more accurate in your use of mathematicallanguage

Write mathematical problems using clear and

Feedback for

assignment #1 to be

posted by Oct. 17.

Assignment #2 to be

uploaded by Oct. 24by 2:30 p.m. (Ja.

Time) & 3:30 p.m.

(E.C. time)

Value: 10 %)


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WEEK

DATES

MAIN TOPIC

OBJECTIVES


ASSIGNMENT

DUE DATE

unambiguous language

Understand the difficulties students encounter in theuse of mathematical language and written symbols and

notation

9

10

Oct 31 Nov 6

Nov 7 - 13

Subtopic #5: The Role of Problem

Solving in learning Mathematics

Unit 4: Assessing the Occurrence

of Learning

Subtopic #1: Methods of Assessing

Learning

Demonstrate understanding of the role of problemsolving in the learning of mathematics

Understand the role of the teacher in the problemsolving classroom

Use problem solving in your classroom

Understand a variety of ways of assessing learning

Feedback for Assg. #2

to be posted by Nov. 7


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WEEK

DATES

MAIN TOPIC

OBJECTIVES


ASSIGNMENT

DUE DATE

Assignment #3 to be

uploaded by Nov.14

by 2:30 p.m (Ja.

Time) & 3:30 p.m.

(E.C. time)

Value: 10 %)

11 Nov. 14 - 20 Subtopic #2: Diagnosis Identify factors affecting understanding

Diagnose the difficulties and misconceptions oflearners

12

13

Nov 21 - 27

Nov. 28 Dec. 4

Subtopic #2 cont.:Diagnosis

Reflection

Lessons Learned

Prepare diagnostic tests

Reflect on course and share lessons learned.

Complete evaluation

Feedback for

assignment #3 to be

given by Nov. 28

3% will be awarded for

participation in the

discussion forum


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WEEK

DATES

MAIN TOPIC

OBJECTIVES


ASSIGNMENT

DUE DATE

14 -15 Dec. 5 -18 Evaluation of Course

throughout the 13

weeks.

Assignment #4

PROJECT to be

submitted by Dec. 5 but

2:30 p.m. Ja time and3:30 p.m. E.C. time

Value: 40%

Feedback for

Assignment #4 to be

given by Dec. 19.


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WEEK

DATES

MAIN TOPIC

OBJECTIVES


ASSIGNMENT

DUE DATE

COURSEWORK ASSIGNMENTS & GRADED ACTIVITIES

You are required to upload each assignment/graded activity on or before the due date of the assignment. You are to observe the word

limit and failure to do so will attract a penalty. Late assignments may not be accepted and will also attract a penalty. You areexpected to observe the APA style in writing. Also, you must attach a signed copy of the Undergraduate Course Work Accountability

Statement to each assignment submitted.

Penalty for Late Assignment

For each day late, 10% or 1 mark (whichever is less) will be subtracted from your final mark.


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Assignment #1 (20%)

(a) In about 500 words and using relevant literature, discuss three major benefits students gain from doing and learning mathematics.

(b) In your reading you have learned about instrumental understanding and relational understanding. In your own words, give a

concise explanation of each in relation to mathematics.

(c) Given a learning task, describe three behaviours you want students to display to show that they have attained understanding?

Due Mon. 3rd October 2011 at 2:30 p.m. (Ja. time) and 3:30 p.m. (E.C. time)

Rubric for Assignment #1

Question

Criteria MarkAwarded

Maximummark

(a) Three major benefits discussedThree major benefits thoroughly discussedTwo major benefits thoroughly discussed

One major benefit thoroughly discussed

3 x 2 marks2 x 2 marks

1 x 2 marks

6

Use of LiteratureLiterature is appropriate and adequateLiterature is appropriate but not adequate

Literature is not all appropriate and inadequate

Literature used is not appropriate

3

21

0

3


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(b) Types of Understanding

Explanation of each type of understanding gives atrue pictures of what it is

2 marks

each 4

(c) (i) Three behavioursBehaviours show a true reflection of howunderstanding is manifested

Behaviours show a not so true reflection of how

understanding is manifested

Behaviours show only a slight reflection of howunderstanding is manifested

Behaviours do not show any at all a true reflection of

how understanding is manifested

3x3 marks

3 x 2 marks

3 x 1 marks

3 x 0 marks

9

Mechanics:

A few errors that do not distort the meaning of what is

written

A few errors that slightly distort the meaning of what

is written

3

2

3


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A few errors that greatly distort the meaning of what

is written

Many errors that significantly distort the meaning of

what is written

1

0

TOTAL 25


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General Guidelines for writing (APA format)

Your essay should be typed, double- spaced on standard- sized paper (8.5 x 11) with 1 margins on all sides. You should use 10 12 pt. Times New Roman font or a similar font.

Your paper should include three main sections: (i) The Cover Page that has the question, due date, your I.D. #, etc., (ii) The MainBody and, (iii) References

Your reference list should be at the end of your paper and be put on a new page. Each source that you cited in the paper must be

placed in your reference list and each entry in the reference list must be cited in the paper.

In-text citations must be properly done also the list of references at the end. For help you can visit the website:http://owl.english.purdue.edu/owl/resource/560/01/

CHILDREN LEARNING MATHEMATICS EDMA2213 C I f ti A d i Y 2009/2010 S t 1


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THE UNIVERSITY OF THE WEST INDIES

Undergraduate Coursework Accountability Statement

(To be completed by student)

ACADEMIC YEAR: __________________ SEMESTER: _______________________________

COURSE CODE: _____________________ TITLE: ____________________________________

NAME: _____________________________ ID: _______________________________________

1. I hereby certify that I am the author of the attached item of coursework and that all materials from

reference sources have been properly acknowledged.

2. I understand what plagiarism is and what penalties may be imposed on students found guilty of

plagiarism. [See UWI Examinations Regulations 97 (i)- (iv) and 103 (i) for both an explanation of

plagiarism and the penalties.]

3. I certify that this paper contains no plagiarised material.

4. I certify that this is my own work and that I did not receive any unfair assistance from others

(including unauthorized collaboration) in its preparation.

5. I certify that this paper has not previously been submitted either in its entirety or in part within the

UWI system or to any other educational institution.

6. In the case of group work, I certify that the work that is the responsibility of each member of the

group has been clearly indicated and that where no such indication has been given, I take the

CHILDREN LEARNING MATHEMATICS EDMA2213: Course Information Academic Year 2009/2010 Semester 1


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responsibility for the work as if it were the section of the paper for which I am solely responsible

and that I have not collaborated with any members of the group to breach the Universitys

regulations.

.

Signature Date

Course Guide Corrected

Documents

Transcript of Course Guide Corrected