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Textbooks and Learning Materials ProgramZambia

Grant No.: RLA-A-00-05-00073-00

Quarterly ReportJanuary 1- March 31, 2008

Submitted to:United States Agency for International Development

African Education Initiative1300 Pennsylvania Avenue, NW

Washington, DC 20523

Submitted By:Mississippi Consortium for International Development

1225 Robinson StreetJackson, MS 39203Tel: (601) 979-8648Fax: (601)9798657

BEST AVAILABLE COpy

AFRICA EDUCATION INITIATIVETextbooks and Learning Materials Program

Quarterly & Annual ReportSubmitted to Freeman Daniels, USAID TLMP CTO

Mississippi Consortium for International Development (aName ofMSI consortium ofJackson State University, Alcorn State University,

MississippiValley State University and Tougaloo College)Grant Number RLA - A-00-05-00073-00Country Zambia

Partners Ministry of Education in ZambiaUSAID/Zambia

Date SubmittedReport Covering: Jan. 1 - March 31,

2008D Annual Report Indicate Year Covered - (Due Oct 31 each year):

D Q'ly or Semi-Annual* o Oct 1-Dec 31 X Jan 1-Mar 31 Apr 1-Jun 30Reporting Period (Due Jan 31) (Due April 30) (Due July 31)

(Semi-Annual)Submitted by Vivian TaylorTitle Project DirectorContact Email I Tel. [email protected] (601) 291-8600

Section 1: Accomplishments (expected to be up to 2 pages--enter into this form)

1.1 List the Major Tasks Accomplished this PeriodUse this area to report on accomplishments during the reporting period. Indicate who, what,where. Here you may wish to talk about status of material design, field testing, evaluation,distribution, teacher training in TLM use, and overall successes. You may also wish to reporton project indicators that you have customized to measure progress. (Note that section 48 isfor capturing quantitative outputs.)

4th Grade TLMsI Grade 4 Learners Math Textbooks and the Teachers' Guide were printed.

The books are being held at the printing company, New Horizons, but will be transported andstored in the secure warehouses provided by the Zambia Education Publishing House (ZEPH)in Lusaka. From there the MOE will coordinate the book delivery process to each province,district and school. Dr. Alfred Siscaswa has been hired by the MOE to coordinate the ZEPHstorage.

Since the role of MCID will be to monitor effective distribution and use ofmaterials in schools,MCID/Zambia assigned nine Persons (staff and writers) to accompany the trucks that will carrythe books and to oversee the delivery processes in the nine provinces ofZambia.

The Permanent Secretary will ensure that the materials are on the Ministry of Educationwebsite.

MelD 2nd quarter Year 3TLMP REPORT - Zambia

CDs with 4t Grade booksMCID/Zambia received the CDs containing the 4th grade teachers and pupils manuals (4800) onFebruary 5, 2008. Some have been distributed to the Provincial Resource Centre Coordinators(PRCCs) and District Resource Centers (PRCCs) during the training of trainers workshops heldin Ndola and Lusaka, as well as to different offices of MOE. However, the bulk will bepackaged and distributed with the books around July.

5th Grade TLMsThe typesetting of 5th Grade Learner's Textbook and Teacher's Guide was done in USA, andthe final product was sent to Zambia. Final corrections and formatting were made by the teamin Zambia.

The letter of approval from the Chief Curriculunl Specialist for Grade 5 materials was receivedon January 28, 2008. (See the Appendix 1.)

Also, the evaluation team met on January 19-20,2008 to evaluate bids for Grade 5 materials.After evaluating all the bids, the team recommended New Horizon and the contract was signed.(See Appendix 2.). (New Horizon was also awarded the bid for the 4th grade TLMs.)

Development of Supporting Posters for Grade 4 and Grade 5 MathematicsGrade 4 and Grade 5 charts/posters were fully developed and approved by the Chief CurriculumSpecialist (see signed letter in the Appendix 3). Copies of these posters were submitted toMCID's main office and were delivered to Mr. Rick Henning at USAID Mission and to thePermanent Secretary on March 27, 2008 for approval. (See attached copies of posters in theAppendix 4).

An ISBN has been allocated which will be included with the final printing of the posters.

In February 2008, an Invitation for Quotation was developed and sent out for printing theposters. Two responses were received by the February 15 deadline -- Pro Print Limited andProgib Printers Limited. Associated Printers Limited, Digiprint Limited and Printech Limiteddecline to compete. It is recommended that the contract for printing, supply, and delivery of98,600 Grades 4 and 5 mathematics posters be awarded to Pro Print Limited.

Training of Trainers WorkshopsTwo workshops for training of trainers were held in Ndola, February 25-27 Agenda is attaced inthe Appendix 5), and in Lusaka, March 3-5, 2008 (Agenda is in the Appendix 6.) A total of166 participants were trained broken down as follows:

Venue Female Male TotalNdola Workshop 36 58 94Lusaka Workshop 22 50 72Totals 58 108 166

20f9


The purpose of these workshops was to orientate Provincial Resource Centre Coordinators,District Resource Centre Coordinators, Zonal In-Service Coordinators and College Lecturers onusing the Grade 5 pupils' mathematics textbook and the Teacher's Guide. Trained participantswill provide further training to Grade 5 mathematics teachers in their provinces and districts.

Persons facilitating the training were Ms. Martha M Lukanga, (MCID), Mr. Dominic Nyambe,Mr. Musheke Kakuwa, Mr. Makumba F. Kaite, Mr. Raphael Banda, Mrs. Mercy M. Zulu, Mr.Lazarous Mutale, and Mr. Crispin Mapulanga from MCID/Zambia; Mrs. Rhoda M. Mtande,from MOE; and Mr. Muhau Tabakamulamu, Lecturer, Department of Math and ScienceEducation, and Mr. Musheke Kakuwa, Head of Advisory Unit for Colleges of Education,University of Zambia (UNZA).

The two facilitators from the University of Zambia, Mr. M. Tabakamulamu and Mr. M.Kakuwa, made presentations on "Using Children's Mathematical Thinking in TeachingMathematics" and "Approaches in Teaching Mathematics in Prinlary Schools," respectively.Copy of these presentations is attached in the Appendix 7.

TravelDr. Vivian Taylor traveled to Zambia, January 19-25, 2008. The highlights are bulleted below:

• Chief Curriculum Specialist, Ms Mutinta Mweerrlbe, at the Curriculum DevelopmentCentre - poster set, distribution, teacher training workshops

• Permanent Secretary at the Ministry of Education - The PS will work to identify a replacemeant scholarship candidate; she committed to do a written plan for distribution of Grade4 materials which will entail all Provincial Officers (POs) reporting to the MOE to pickup TLMPs and traveling back (along with transport for TLMs) to their respectiveprovinces to assume responsibility/accountability for distribution

• University of Zambia's Mr. Muhav Tabakamulamu, Lecturer, and Mr. Bentry Nkhata,Deans II/Lecturer, Department of Mathematics and Science - the University expressedits continued interest in TLMP and exploring research collaboration, teacher and studentexchanges, and writing of future TLMs in the event of new funding

• Mr. Rick Henning, USAID Education Officer - The main issues discussed weredistribution of Grade 4 materials and teacher training. Regarding the distribution ofGrade 4 materials, Mr. Henning indicated that Joe Kitts had informed him thatapproximately $200,000 may be provided to the mission in support ofTLMPdistribution. He stated that the PS had requested to use the money to purchase two trucksto inlprove their fleet, but neither he nor Mr. Kitts thought that purchasing a truck was inthe "spirit" in which the money was proposed, therefore, her request would be denied.Mr. Henning informed Dr. Taylor that the Coca-Cola Company may be willing tocollaborate to assist with distribution. He plans to meet with them for negotiation. (Hedid contact MCID after the visit to state deal fell through.) Regarding the TeacherTraining, Mr. Henning indicated that Ms. Beatrice has concerns about the nature andcontent of the teacher training, and that he had concerns relative to the use of theTraining of the Trainers Model (TOT). Dr. Taylor explained that the nature and contentof the training is determined by the MOE's Curriculum Development Specialists and theCDC Chief who sits at the table during the planning as well as attends and helps to

30f9


facilitate training sessions. Also, she shared her discussions with the PS regardinginvolving the Teachers Colleges more in both pre-service as well as in-service training.Regarding the TOT Model, Mr. Henning expressed no confidence in the teachers' abilityto train each other. He was informed that the PS is hoping to be able to factor teachertraining in the MOE's 2008 budget.

• Site visits to schools in Lusaka and Livingstone to meet with teachers, administrators andstudents. Dr. Taylor also accompanied the Mt Calvary Baptist Church Mission Groupfrom Jackson, Mississippi, on their visit to Jacaranda Basic School. (The learners are onthe covers of Grade 4 and Grade 5 are fron1 this school.) Mount Calvary adoptedJacaranda Basic School and Rev. John Cameron presented the Head teacher with a checkand supplies in support of the Textbooks and Learning Materials Program (TLMP) inZambia and as a way of building relationships. Later, Dr. Taylor and the Mission Groupalso visited Palm Grove Basic School in Livingstone where the Mission Group againdonated money and supplies.

• Dr. Taylor also met Zambia MCID staff for extensive discussions.

Appendix 8 contain pictures took during Dr. Taylor's visit to those schools.

USAID Africa Regional Education Workshop 2008At his request, MCID met with Dr Alfonso F de Guzaman with the Science ApplicationsInternational Corporation on March 1i h

. MCID met with him for the majority of the day tobriefhim on MCID's project from beginning to date in order to prepare him for the Conference.

A group of four team members are preparing for the Workshop. They were Vivian Taylor,MCID Project Director, Ally Mack, MCID Executive Director, Martha Lukanga, MCID InCountry Coordinator, and Mutinta Mweembe, MoE Zambia Curriculum Specialists.

Information Sharing Related to the ProgramMOE/PS plans to place information relative to the progran1 on the MOE website and anewsletter updating program activities is in progress.

1.2 List the Major Tasks Anticipated for the Next Period

Use this area to report on plans for the upcoming reporting period. Indicate who, what, where.You may wish to talk about status of material design, field testing, evaluation, distribution,teacher training in TLM use, and overall successes.Attendance at the USAID Africa Regional Education Workshop Global Education Conferencein Ethiopia April 12-19 by the Project Director, In-Country Coordinator and MoE partner.Printing of Grade 5 TLMs including books and CDs.Contracting and printing of Poster Sets for Grade 4 and 5.Finalize plans for the Handover in June - July 2008.1.3 Problems and Challenges Encountered or AnticipatedDescribe challenges that you have Describe solutions that you have implemented or planfaced during implementation. to implement to address the challenges you face.

40f9


Section 2: Institutional Capacity Building (expected to be 1page--enter into this form)

2.1 MSllnstitutional Capacity Building Activity this Period

List institutional capacity building activities for increased skills. (Example areas are: textbookdesign, management of printing bids and contracts, financial management.) Also note how theincreased capacity has proved beneficial with applications.

2.2 Partner Institutional Capacity Building Activity this Period

List similar -capacity building activities with others, including direct partners, MOE, printers, andothers you may have worked with. Also note how new skills have been applied.

2.3 List Any Lessons Learned from Institutional Capacity Building Activities

2.4 Sustainability: List Developments/Activities

Discuss efforts designed to sustain the host country's ability to produce textbooks after theTLMP has ended. For example, apart from a transfer of skills above, explain how newpublic/private partnerships could be sustained after the project ends.

Section 3: Partnerships (expected to be 1 page--enter into this form)

3.1 New Partnerships Formed

Briefly describe the nature of the partnership and include partner(s)' name, address, telephone,email, and contact person.Efforts to fonnulate Public, Private Partnerships (PPP) are in progress; a list ofbusinesses hasbeen generated for partnership consideration; correspondences have been sent out; and anorientation meeting has been facilitated involving some of the business representatives. TheMoE Pennanent Secretary had stated her intent to lead this effort since MCID presented theconcept to her in November 2006. However, MCID has continued to support her within itscapacity as much as possible. At this time, the PS plans to fonnalize the PPP when thehandover of the books take place upon completion of the printing of Grade 5 materials.3.2 Describe type of partnership (Le. public, private, NGOs, educational, institutional,committee or other) and any in-kind or financial contributions of the partner<s}.

3.3 Verification

How can the partnership information be verified?

Contact info (if applicable)

Name/title/company

Email & telephone

50f9


SECTION 4A: PUBLICATION & UTILIZATION - Publications List

o Check if no change since last quarter (do not complete form)

Key for Publication Status: D= Design Completed, F=Field Tested, P=Printed, D=Distribution in Process or CompletedKey for Types of Material: T=Textbooks, SW=Student Workbooks, SRB=Supplementary Reading Books, TM=Teacher Manuals, and O=Other*Indicate whether or not a report was produced followinQ an evaluation or an assessment of a TLM(s). Indicate number of evaluations or assessments.

cizE(I)

.:t:::

TLM Title GradeLevel

Subject(5): Language

z(I)>:c_<cC>~- (I)::::t:-(I)

0:::

z... >:(1)"tJ CC ca(I) >C)~

(I)

0:::

(I).c0"tJ-(I)=t:I:-.5(I) ...ac.....taf-

m~-~ta (I)

-~(1)(1)·m.c~

~-

o-:E.!!!.-IOfo (I).c >CJ·-m (I)~CJ

o e=t:I:

o-:E-1f-'Q.~::J0c..o';ca

0:::

1

2

3

Enjoy BasicMathematics: 4th

Grade MathManual

Enjoy BasicMathematics 4th

Grade TeacherGuide


Grade Math CDs-Pupil andTeacher's guide

4

4

4

Math

Math

Math

English

English

English

T

TM

o

Y

Y

Y

Y

Y

Y

P -- in thePrinter's

251,000 Warehouse

P -- in thePrinter's

5,000 Warehouse

p-deliveredin January

4,900 2008

4,619;72teacherresourcecenters44,619;72teacherresourcecenters

4619;72teacherresourcecenters

1

1(Teacher)* 1 perschoolandteacherresourcecenter

Yes

Yes

Yes

60f9


ozEG):!::


Subject(s):

Language

:s-1-... ~~~

o G)G) mc.~

~-I-

z(/)>:c_-c~co> >- G)J:-G)

0::

z.. >:G)_

"cC coG) >C)~

G)

0::

G).c0"-G)

=1:1:-.5G) ..C)o....~

m::s--~co G)

-~(/)G)·m.c~~0..

m-G)o >0·-.cG)~(,)(,)-1me ...""'"00_=1:1:

~-1....0.""'" ::s00...2 0ni0::

Poster Set forEnjoy BasiclMathematics 4th

4 Grade

Enjoy BasiclMathematics 5th

Grade Math5 lManual

Enjoy BasicMathematics 5th

Grade Teacher6 Guide


Grade Math CDs~Pupil and

7 ~eacher's ~ide*

4

5

5

5

Math

Math

Math

Math

English

English

English

English

a

T

TM

o

Y

Y

Y

Y

Y

Y

Y

Y

47,800 D

D, T, F(printingset for May

251,000 . 2008)

D,l,F(printingset for May

5,000 2008)

n-waitingon finalformattedcopy from

4,800 printer

4619;72teacherresourcecenters4619;72teacherresourcecenters4619;72teacherresourcecenters


* 1 perschoolandteacherresourcecenter No

1 Yes

1(Teacher) Yes* 1perschoolandteacherresourcecenter yes

70f9


cizECI)~


Subject(s):

Language

z(1)>=c_- C~ ca> >- CI)::I:-(I)

0::

z->=(1)"tJCC ta(I) >C).!~

(I).c0"tJ- (I)=tt:--.:CI) C)c..-{J.

o~_>0'1ca CI)-.lll::(I) CI)·0.c~~c..

o- CI)o >0.-.cCl):!E(')(')...J0! ...."'-00_=tt:

:!E...J_.....0."'-~0c...2 01a0::

C "tJo CI).- ~1a0.!~Q.Q.

caCl)E> 0:: 0!fJ 0

Poster Set forEnjoy BasicMathematics 5th

8 Grade 5 Math English 0 Y Y 47,800 0

TOTAL NUMBER OF TLMs TO BE PRINTED 308,700 4th grade and 308,600 5th grade TLMs - TOTAL 617,300

Comments (indicate item #):

8of9


* 1 perschoolandteacherresourcecenter No


SECTION 4B: PUBLICATION & UTILIZATION - Outputs

D Check if no change since last quarter (do not complete form)

*Printing Costs per TLMs = The printing amount divided by the # of materials.

Indicator Qtr 1 Qtr2 Qtr3 Qtr4 Annual ReportBefore 9/1/07

(9/1-12/31 07) (1/1-3/31,08) (4/1-6/30, 08) (7/1-9/30,08)Cumulative

Total# of TLM prototypesproduced (item drafted,

2 2 6approved, but yet to beprinted)

251,000 pupil

# of TLMs Printed ~ 4900 CDsbooks5000 teacherbook~

100 CDs to# of TLMs Distributed ~ ~ Resource

Centers

# of Teachers Trained 278 166

$.90 (ninety$1.55 pupilPrinting Costs Per TLM* ~ US cents per

CD)$3.50 teacher

90f9

APPENDICES

APPENDIXl

Letter from the Ministry of EducationApproving Printing the Grade 5th Materials

2

All communications should be addrct>scd to:the PcrmanfJnt SecretaI)' to the Ministry ofEdUCCJtionIl0f 10 any individual by name.

J"elephOII6: 2508551251315/251283251298125131812512912513061251319

REPUBLIC OF ZAMBIA

In reply please quote:

No.:, , ..

MINISTRY OF EDUCATION

14th February, 2008.

Mr. Nathan beAssisProgramme ManagerUSAr[>LUSAKA

'RE: SUSMrSSl:ON OF THE FINAL CAMERA ~AbY GRADE5t£ARNER'S TEXTBOOK AND TEACHER'S GUIbE

P.O. BOX 50093LUSAKA

I acknowledge receipt of your letter dated 18th ..January, 2008 .in which yousubmitt.edthe Final Camera Ready Grade 5 Learner's Textbooks andTeacher's Guide.

r would like to thank you for the support you are giving the Ministry.

The· Ministry fully supports the programme and approves that you go ahe~d

and finalise.

Lillk;n E.L.Ka~u·(Mrs)Permanent SecretaryMINISTRy· OF EbUCATI:ON

Ibbc·

3

APPENDIX 2

Bid Grade 5th Materials Evaluation Report

4

Bid Evaluation Reportand

Recollllllendation for Award of Contract

Name oiProject: MISSISSIPPI CONSORTIUM"fOR INTERNATIONALDEVELOPMENT

Contract Name: TENDER FOR THE PRINTING, SUPPLY ANDDELIVERY OF PUPILS' TEXT BOOKS AND TEACHERS'GUIDES FOR GRADE FIVE (5) IN ZAMBIA

Identification Number: TLMP/G5/2007

Date of Submission: 19th DECEMBER 2007

. 6

1.0 BACKGROUND

1.1 The Mississippi Consortium for International Development{MCID) under anagreement with the United States Agency for International Development (USAID)for the '~Text Book and Learning Materials Program" invited 'Sealed bids fromeligible bidders for the Printing, Supply and Delivery of Pupils Textbooks andTeachers Guides for Grade Five (5) Mathematics for use in Zambia.

1.2 An open tender was floated in November for a period ofthree.(3) weeks using theNational Competitive Bidding {NCB) process; the advertisement [nost appeared inThe Post Newspaper on 28th November 2007.

1.3 Of the 32 prospective bidders who collected the bidding documents foursubmitted their bids when the tender closed on 19th December at 14:30 hrs. Theread out prices were as per Table 1

2.0 EVALUATION TEAM

2.1 The Evaluation Team comprised the following:

2.1.1 John Bo'sco Makumba, Consultant -Chairman2.1.2 Geoffrey Mulenga, Senior Education Standards OffICer - Ministry of Education.2.1.3 Lazarous Mutale, Curriculum Development Specialist - Ministry of Education2.1.4 Ferdinand Sambulo, Senior Purchasing and Supplies Officer - Ministry of

Education2.1.5 Saidi'Sakala, Acting Purchasing and Supplies Officer - Ministry if Education2.1.6 Noria Mwenda, MCID Secretariat

3.0 EVALUATION PROCEDURE

3.1 The following procedure was applied:

(a) Preliminary Examination

Under Preliminary evaluation, Members checked for the following:

Verification

Whether the bid was properly signed and if the bid was from a Joint Venture, a signed JointVenture Agreement was expected to be 'Submitted together with the bid.

Eligibility

Eligibility was restricted to Zambian Companies with printing facilities in.zambia; el~giblebidderswere however free to partner with each other to enhance capacity.

Bid"Security

The amount was expected to be not less than two (2%) per cent. The validity of the Bid Securitywas expected to be thirty (30) days after the expiry of the Bid Validity Period. If the bid security

7

was in the form ofa Bank Guarantee, it was expected to be from a Commercial Bank andconsistent with the sample form provided in the bidding documents.

Completeness of Bid

Bidders were expected to quote for the entire quantity of each item and hundred pereent (100%) ofthe number of items to be treated a'S complete andgavlW'ally checked whether the offer containedmaterial qualifICations.

Bidders"found responsive on these preliminary checks pioooeded to the next stage of the evaluationproooss.

(b) Substantial Responsiveness

Members checked as to whether the bidder met the Tochnical and Commercialr-equirements of the Bidding documents.

(i) Technical Evaluation

Bidders were expected to ,either meet or exceed &e'Specilications provided by the Purchaser to

,be considered responsive including documentary evidenve.

(ii) Commercial Evaluation

Members checked for the following:Pri-cePayment terms as outlined in the bidding documents,Delivery period a'S outlined in the bidding documents.

(c) Detailed Evaluation

This covered.<fetailed prioo'Comparisons ofbids taking into account anyunconditional discounts, exchange rates etc

(d) Post qualification

,Whether the Bidder provided-evidence for the following information:

I.A minimum of three years in operationprior to the date ofbid submission with animportant part of its business being the manufacturing ofprinted and bound,educationalmaterials.

2. Successfully completed a minimum of two contracts similar in size and 'SCope

3. Financial capability: audited fmancial aecountsror at least two {2) complete fiscal years,'demonstrating the 'Soundness of its fmancial position and that it had the fmancial resow;cesto perform the proposed contract.4. The annual production required was expected to be atkast 2.5 times the value of thecontract during the last three years. It musthave had available the following facilities andthe appropriate skilled staff to operate them;

8

i) Cameraii) Plate making.iii) sheet-fed or web-fed offset printing machinery capable of printing

in one 'Colour or multiple colours, depending on the contractrequirements.

(iv) Finishing and binding(v) Packing(vi)Delivery(vii)Warehousing and distribution

Additionally,a list of major plant and equipment with the detail'S specified in the bidding documents.a list of its staffshowing theirskills and their years of experieRCe.

S.·Must have provided samples or dummies of the books underconsideration.

9

Table 1. Bid Prices {as Read Out)

Bidder Identification Read-out Bid price(S)lName City/Stat Country Curren Amount(s) or % Comments

eor ~y(ies)

Province_Ia) /b) (c) (d) Ie) If)

'Bidder 1: Mission Press Ndola Zambia ZMK 2,989,200,000.00 VAT inclusive

Eidder2: New Horizon Lusaka Zambia U'S$ 517,'552.25 VAT inclusivePrinting Pl:e8SBidder 3: Times Ndola Zambia ZMK 2,82~;69S;OOO.OO VAT inclusivePrintpak (Z) LtdBidder 4: InsakaPress Lusaka Zambia US$ 209,920.00 VAT ExclusivePublishers Co. Ltd

Mississippi Consortium for International Development

R~f:TLMPlG5/2007

411> February 2008Shawley HemaidanThe Managing DirectorNew Horizon Printing PressPlot No .Lus/9815/4 Kame RoadLusaka zambia

Dear Mr Hemaidan,

RE: Tender for the Printing 'Sopply and Delivery of Pupils Textbooks and TeachersGuides for Grade Five (5) in zambia

NOTIFICATION OF AWARDReference is madeto your offer dated 20U. December, 2007 on the above captioned Tender.I wish tonotHy that you have been awarded a contract for the Printing, Supply and Delivery of2S1,OOOPupils'Text Books and 5000 Teachers' Guides for.grade 5 in,,Zatribia at a total cost ofUnitedStates DollarS four 'hundr~ and forty thousand, four hundr.oo and seventy only (US$ 440,470.00) asfollows:

No. Itent Desedption1 Pupils' Text BOoks

Total

Quantity25].000

5,000256,000

AmountU8$431.720.00USS.8.75O.00

Delivery P~riod

I2-15Weeks12-15 Weeks12 - 15 Weeks '.

You shal1berequii'ed tofurnish aPerfonnance security often00%) percent ofthetotahonttaetvaluewitbintifteen (l5)daysofreceiptoftbis Notifkation Letter.Kind.yack:now]~receiptand contents ofthis notifieationofaward letter•

.?!k::~- .Pl*ot~PItl) ~,Cc: AJI)·¥8c:k.MClQJaCl,<sOJtMS. USA

MutintaMweemb¢•. Ch:i~fCurciculum.Specia1istCDCProgtainMllnager~ MelD Longll.crcsLUSAKA

APPENDIX 3

Letter from Zambia Ministry of EducationApproving the grade 4th and 5th Posters

12

No.: "" .

RSPOSUc OF ~AM6IA

MINISTRY OF EDUCATfO·N-EDUCATiONAL SERVlCt:-S CENTRE

CURRlCULUMOE¥ELOPMENT CENTREPO. BOX 50002

HAILE SElASSIE AVENUELUSAKA

29 February 2008

The Progrannne ManagerTeKtbooks and Learning Materials Prosrarome (TLMP)MeID ZambiaLUSAKA

RE; Grade 4( andS Tea.ching Posters

We would like to again thank the Mississippi ConstJrtium 'fer International Developmentfor the ptOduetion ofOradc 4- and S tcac:hingpostcl' whichprolide 4 summary ofthepupils·~ devel<>ped undertbeproje.ct.

Given· that the books bave beettappt()vedfor use in the zambian school and are in linewith the approved currie. we would therefore. allow for the pmductionoftbe poswrsas supplem,cntary materials since ~'azeb4S'¢d on already 8ppl'O''ed textbooks.

In this regard. as CurrieulmnDevelopro:entCentre we would allow fortlle production ofthe posterS as being p&."'t oftile approved textbooks for Grade 4 and. S.

¥OQIS f.atthfully.

MntintaMweembeCb.iefCumculum SpecialistCumoulumDevelopment Centt~

Co PermatlentS.e¢retaryMinisttyofBdueationDirectorof'Stan(1anls. Minlstr,yqfS4Ucation

2

APPENDI4

Grade 4th and 5th Posters

14

T:EXT'BOOKS ANDL'EARNING'MATERIALS PRpGRAMME

MATHEMAT'ICS CHARTS FORGRADE 4 LEARNE'RS

I· .

ItI

II

II

II

II!III

I

III

IIII

,. S

.~~; ...

~.\ " .- ..

emb,:~~"

·mem~

95·

E

Cat is a memb~·.'· of animClls

Cat E {anima· ·is read a

E is read as "i.;9!'is read as "is· ..

.·M.".. '. :IE··;';~····M····::·,.·.····.···.·'·B·;·········.E·:·R·········S..·",·~·.·H·'-·.······.:·.i,.,.: .•.'· . O'.. ·F····'\ ..' ".,\;«' ':" : ".', .';..' .'::-. < ;:" '.\ •. '.'

o' .' •••. . • _.. ...... .

J.

,N.

@ Copyright reserved<if: USAID .\IiI\,-~..,.I--- ~ Grade 4

. II

( .

.. ·IQUALSETS~ .

......

{b, c,d, f, g} ={d,·g,b,C, f}

:{ 2, 4, 6, 8,10, 12} ={ 10, 6, 2,12, 8, 4 }

.Equal sets have the same membersand the ·sa.me number of m·e:mbers

@ Copyright reserved Grade 4

One h.undred ten

Five hundred tenOne hundred fifty

. c:::- .

One hundred forty

One hundred

One hundred thirty

One hundred twenty

Five hundred twe:nty

Ninety -

Fifty

Sixty

ThirtyForty

'SeventyEighty

5060708090

150

110

140

100

120130

520

.30·40

. 510

,.,.:. . '. .' ..U. Sixf.,.. . 530 .Five hundred thirty

fl1 .lev-',,· 540 Five .hundred forty

[t8EI.,..." 550 Five hundred fiftyr19 Nin.teen .. 560 .Five hundred sixty~~ . ".' -:- ' ..'~ : =

~20 Twenty 1 000 One thousand!~~·1.. :-

@ Copyright reserved Grade 4

" ."~. "

_3~ is represented on the abacus.

8 3 5 6

. In exp'anded form 8 356 is

.8 t;h:ousands + 3 hundreds + 5 tens + 60118s

8000+300+50+6

@ Copyright reserved •(!v.'-:"~ USAID liII~/ ---- ZfIl4 Grade 4

, ~)·23820 + 34 148 in expanded form is

'20,01010 + 3000- +8,00 +'2;0 +0300:00' + 4000 + 100 + Ala +8

SO 00:0 +7 '0·00 +900+,6;0 + 8;;:

87 881 - 73 622 in expanded form is

80000 + 7 000, + 800 + '8iO + 1- 70 000 - 3 000 --60:0 - 2'0.. 2

2 cannot be subtracted from 1. We get one ten\ ' from 80. Add the'ten to 1 to get 11. 'Subtract 2 from

11 and the, result f~ 9.

80000 + 7 000 + 800 +7'0 + 11-70 000 - 3 000 .. 600 .. 20 -2

10000 + 4 000 + 200 + 50 + 9 = 14 259

@ Copyright reserved • {!tJ USAID YIII ~..:;.r-- ZflI\l Grade 4

6 X4= 4+ 4+4 + 4 .. ·4 + 46X4=24

i; .

! .. 6X

: ,.iI ,ii

i'"·i

:.MultlpIJcatlo,nby 10

!, .

!;;

f

1 X 10 = 1010 X 10 = 100

100 X 10 = 1 0001 000 X 10 = 10 000

,,, ., .,

:' Any number multiplied by zero is zero,,

.... Theprodu;ct ofcl'ny num·be;' by 10 is thatnumber with ze,ro written at the end.

© Copyright reserved Grade 4

MULTIPLICATION TAIILI

3 6, 7·8 9

2 46 1012 1416 18 2.0

3 6 9 12 151821 2427 30

4 8 1216202428 3236 40

5 10 1520 253035 40 45 50

6 12 18 24 30 36 4248 54 60

7 14 21 28 35 42 49 56 63 70

8 16 24 3240 48 56 64 72 80

9 18 2736 45 5463 72 81 90

10 20 30 4050 60 70 80 90 100.

11 22 33 44 55 66778899 110

12 24 36 48 60128496 108 120 !


ZAMBIAN MONEY

K20

K 5110

K1000a

K50

K1000

K20000

KS·OO:O

K50·000

K100

":'.",

: ..

1n5n10n20nSOn


I]1

I'II·. I

.), I

JI,I

II

412

26

18

, '.. '

1,4,

1'8·';·,'..

,..... , ..:~ .

8.. . ...

13

';-- ~ c"""- "1'''

,;.2

··.QUALPRACTIONS

. -, '"

14

18;

1 2 4The shaded parfsabove show -2 - -4 - -8

-.." ...- .........._~--...- ........' .,~

.~. '

.,i


. . ~ : .' ".. . . .

...........

24

14

II .Iii

i!I!; :i .,i

,,i .

2-6

+

36

2 ·3 5-+--. _.6 ··.6-6

--56


...-

; ,i.

. i

;I ~

14

2,6

..........................

1·6

12-6 - 6-36

-36

34

3.2 1- -4 - 4 ~ 4


"','. "'\ ....

, ..,: -', ;,'"

.4.: '.,~

.- ". ~ ,"

',.

.. ....,. \_",

,<,.' ,.! •.......

'.i- .

,r

"';.:

. ..,."'.:. .~ .

! c

A ={C:OWi,

B :;:c {ca:t,

© Copyright reserved • ,<tit"; USAID\''!"'!:'''---

Grade 5

,,i'

L7 ones1..,---,.;-- 4 tens

'--------.-- 3 hundreds'-------- 6 thousands

5 ten thousands

's'··6···· 3"4·7···"..···• .'~. • '~. .' Yo .:

......

':"'~.:.'.'.'.' .. ' -".'.'.: ; ..-::...... -:-.,' '., .'.. : '.. ,", ,,".. ,,: . . ." - '. : .- "'-'" .' '" .~:;., '. ., . .

{" .. ' , .,-'>",. .: "" , .....• --, '.. " _."

This means

'7 ones or 7 X 1'~4 te,ns or 4 X 10.3hund.reds or3 X 100, thousa:nds or 6 X 1 000," Te,n fhous·onds or 5 X 10 000

740

3006 000 ~

50000

. . ~

© Copyright reserved GradeS

, .

AD" O"IT"'I'O"N; AND e'U'B"T'RA'··"'T····I·O·N• __~": " ", ,'.;-:~ . :.....: : : ,. : .~ .". _" ,',." .., ..... J.. <.~ .'. _" _. :' ,": ":'

USING A NUMBER LINE

Addltion .

5 + 3is shown on the number line as... - - - - -- - -~ III

01234567.8960 + 30 is shown on the number line as

_________ -...... LZ ~

o 10 20 30 40 50 60 70 80 90'

Subtraction

Show 400 - 250 on the number line

-----------------~I· I I I II I I I~-"""

o 50 100 150 200 250 300 350 400 450

700 - 400 can be shown on the number line as

~----------~ .. _---DIl!II-- ... --_~I I I I I I I I I ......o 100 200 300 400 500 600 700 800 900

. ;


LO'NG DIVISION "

"Divlsor

'\.. .. ..136 4 . Quotient

2 8 [3 8 1 0 4 - Dividend. -28 ! . ..

1 0 1- 84

170-1 6 8

2 • -- Rerr10inder

~813 810 is the same as 3 810 + 28 or

,: 381028


!

!.

:'~"O 000.00

K35000.00

MPLE

t'

>'

r·

~"

© Copyright reserved ~ USAID GradeS

C('Fy

;.'~

Measuring tape

Ruler

Thermometer

Clock

....~.. -' ..,.... "

Scale

Some Measuring Instruments~.I·,,....

~

~;

© Copyright reserved !(~~U$AID\f'?'..;1--- GradeS

". -- ~~7:···

, "'J/

CONVERSIONS

<1;lImtlfim~tr1!B~lQEnlfimetre:fi~;i~~~l~i"."'"..:.J; ,'. JD 'rY!l:eJ'B';'~ lrtdo;metr:e

, I


The length of a rectangle is 12 em and thebreadfh is 8 em.

8cm

or P =2 X (12 + 8)=2 x (2;0)=40cm

12.cm

12cm

8cm·

P = (12 + 8) X 2= (2,0) ,x 2= 40cm

\i

./


TYPES OF FRACTIONS

4 ..4----- .4----

7 ••----

Num:ra~~,Division lineDenominator

'.

,GradeS:'iii-, USAID"'~.I __--•

Proper Fractions4yis a proper fraction. Numerator iss,mOllerthan the denominator.

©Copyright reserved

MEASUREMENTSConversions

, "

, ' .

le;"'gthandd'i~sta,n~Q'e . .; ... , .

1 kilogram =1 o~oo gram,s1 tonne =1000 kilo,grams '

, .~..

, '.

~ ~:,'c

. ~~.

. ,

:. . >. 1centimetre=10millimetres

; ·,:~.:r)~~'.'.:.••.,:.•.••,,'.:~•• ·'" 1 metre:c·100 oentimetrt)$, ~. 1 kilometre =1 OOOmetre·s ."

I'I '

, C,a,pacity

1 litre =1000 millilltres :'

©Copyright reserved 'GradeS

----- Decimalparf------- Decimal point

···DECIMAI.S

~------------- Whole num'ber

. . .

'1 834.05 is a decimal number ..

'~r.'.

1~.'::.lit.,((., .

, A decimal number :has a w;hoJe .~ . . . - .

: ~.: .. numberl a decimal point and the.' decimal part.

©Copyright reserved GradeS

TriangleSquare

------

Circle

I

Rectangle

I}--

I

• .1 •..........._........ ...._....... ._...,-.._ ..._~ ......._...... . .._·.'._"'"""-_...."'-...._~~.. ·.__~_.._·.L_L_..... ~.~ .. _,.."....."...__,..._"'-_~..-_ ... . _

Solid Shapes

Flat shape~

~..

©Copyright reserved • ,t!i;1USAID ~....W,,/-- _ GradeS

·,rt:

~.

..;.:-=--: ......

II','

NETSNet

- --I

1 1 1I I II I

........

- -, I

1 1 11 1 11 1 II 1 I

·1 1 --- 1

Tetrah~dral

Cuboid

.-' .

S· 'q''u,'rt'rc~ P'urrtr.'nid:'. '..... W.I··:~: .,. U-I--I'-.Il~-'

, ....

,.!

©Copyright reserved • GradeS

r"'-, ,-1 .... ~.

·H· PICTURE GRAPHS" \) I: .'. :.'., ., .'. . ..... . .. '. . .•• '. . .'.! j' Picfuregraph of:drinks that learners drank ot .'l:~ school in a Week

, .;

From the graph

Tea

I ". "

I· ,I ' ...--.....IIB1iIIllaI..........~iIIIiIIIIiIlI-............... ....~.....- ...

I ~. . DrinksNiJrnber pfb~.arner5 .j ~~ ....

I ~' ~

1\ Maheu

I ' .....---.........------.........-------.......I ;.. MilkI ~)

! : ...---.....- ....-.--............--...---....--4f i,t .

j"" Water!~,.! .

; '\

a) 4 boys and 2g'i:rls dJCl.n'kmaheub) 5 boys.an.d $ 'girlsdrtJn'k milkc) 4 girls and 4.bqys drank waterd) 6 boys andS girls drank tea

©Copyright reserved • GradeS

N:umb,er ,ofohUdren.' ' '.-,"', , •• " • ..". >, -.. "••

P'I"C""T"'>·U·····R·'E" O''RA'P'M'"8'".. .. . . ~,' . . '.. . .'. .,':" ' '. .:.. ...,'

Mango

a) 5 chiJdrenate mangob) 6 children ate masukuc) 3 boys Qtebananasd) 5 girls cdeoranges-

.Drinks

'. (i)(Q~(i)

lA, Masuku ••..... W~Wff .I', - ft!~ ....--.....-~'!/IIII!!f-'~---------------.........--IiltBanana · ft(,':·' W";:·'·; ft:.:~.·.:li~~l~f

!'I~.·: ,.....-------I~-.,--- ........--~- ......, .; ~.

:~ ,Oranget .; -----.....-----..............._-----..!if From the grap~

i~,

I~·~~ .

!i ~r

'(~;' Plcturegra'~h of fruits thateachchUd ate athome

,j

©Copyright reserved 'GradeS

Grade 5

a

Nighf04 OOhJ6

(~., USAID Mill..~..:;~~;.., --- -

1 minute =60 seconds1 hour :: 60 m:inutes

1 day =24 hours1 week:; 7 days1 year =1 year

•

Reading and Wrifi'ngTime

'2'." H:'0"'·'/U';R'·:...••. ··C·,··;·L··Q.r.····C·········K····... ~'. ,: ~ ~' ~·,d·_.'. _ ". ..'. >. :

OCopyright reserved

i. ;.'~.''i];'

.~.: ':"

APPENDIX 5

Agendas for the Training of Trainers Workshop

Savoy Hotel, NdolaFebruary, 25 - 27, 2008·

15

,/~4'

~7~~~~ USAID1\~li\£I~J.""\<;..\1f/l\~fh.!W11 FROMTHEAMERICAN PEOPLE~

Textbooks and Learnin.g Materials Programme (fLMP)

Training of Trainers WorkshopSavoy Hotel, Ndola

February, ,25 - 27,2008

Description:The purpose of this workshop is to orientate Provincial Resource Centre Coordinators, DistrictResource Centre Coordinators, Zonal In-Service Coordinators and College L-ecturers on using theGrade 5 pupils' mathematics textbook and the Teacher's Guide who will in turn provide furthertraining to Grade 5 mathematics teachers in their provinces.

Dav 1 Monday.. 25 FebruaryOpening Session, Dominic Nyambe, Presiding

08:00 hrs

09:00hrs

09:30 hrs

10:00 hrs

10:15 hrs

10:45 hrs

11:15hrs

11:45 hrs

12:15 hrs

12:45 hrs

13:15 hrs14:15 hrs

Registration, Opening Prayer

Welcome Remarks and Introductions, Ms Martha M Lukanga, Program CoordinatorOverview ofActivities and Objectives, Dominic NyambeGround rules/Expectations, Dominic Nyambe

Framework under which the book had been written/general summary of the book - thisincludes HIV/AIDs, gender Dominic Nyambe

Tea Break

Strategies/methods of teaching: Chapter 1 - Sets and Chapter 2 - Number NotationFacilitator: Makumha F. Kaite

Strategies/methods of teaching: Chapter 3 - Addition and Chapter 4 - SubtractionFacilitator: Raphael Banda

Strategies/methods ofteaching: Chapter 5 -Multiplication, Facilitator: Mercy M Zulu

Strategies/methods of teaching: Chapter 6 -Division,Facilitator: Lazarous Mutale

Strategies/methods of teaching: Chapter 7 - ArithmeticFacilitator: Crispin Mapulanga

Strategies/methods ofteaching: Chapter 8 - Number PatternsFacilitator: Rhoda M Mtande

LunchDiscussion and comments on Chapters 1 - 8

5

14:30 hrs

15:00 hrs

15:30 hrs

15:45 hrs

16:15 hrs

17:00-hrs

17:15 hrs

Strategies/methods of teaching: Chapter 9 - Fractions,Facilitator: Rhoda M Mtande

Strategies/methods of teaching: Chapter 10 -Decimal NumbersFacilitator: Lazarous Mutale

Afternoon Tea

Strategies/methods of teaching: Chapter 11 - Factors, Facilitator: Mercy M Zulu

"Strategies/methods of teaching: Chapter 12 - lJeasurementsFacilitator: Crispin Mapulanga

Discussion and comments on Chapters 9 - 12

Closing Prayer

END OF DAY 1

Dav 2 Tuesdav, 26 FebruarvRhoda M. Mtande (Presiding)

os:OO hrs08:05 hrs

08:30 hrs

09:00 hrs

09:30 hrs

10:00 hrs

10:30 hrs

10:45 hrs

12:45 hrs

13:30 hrs

14:30 hrs

15:00 hrs15:15 hrs

Opening PrayerRe-cap on previous day's work

"Strategies/methods ofteaching: Chapter 13 - Shapes, Facilitator: Lazarous Mutale

Strategies/methods of teaching: Chapter 14 - Graphs,Facilitator: Makumba F. Kaite

Discussion and comments on Chapters 13 - 14

Assessment in Mathematics, Facilitator: Dominic Nyambe

Tea Break

Approaches in Teaching Primary MathematicsFacilitator: Mr Musheke Kakuwa (Head ofAdvisory Unitfor Colleges ofEducation,University oJZambia (UNZA)

Participants break into groups for group work., Facilitator: Mr Kakuwa

Lunch

Group work presentations, Facilitator: Group Representatives

Afternoon TeaUsing Child Mathematics Thinking in Teaching Mathematics

6

16:15 hrs

17:00 hrs

Facilitator: Mr Muhau Tabakamulamu (Lecturer under Dept. ofMaths and ScienceEducation, University ofZambia (UNZA)

.Participants break into groups for group work, Facilitator: Mr Tabakamulamu

Closing Prayer

END OF DAY 2

Dav 3 WednesdavJ 27 FebruaryMakumba F. Kaite, Pr-esiding

08:00 hrs0'8:30 hrs

10:00 hrs

10:15 hrs

13:00 hrs

14:00 hrs

15:00 hrs

15:15 hrs

16:30 hrs

17:15 hrs

. Prayer and recap on the previous day's work:~Group work presentations, Facilitator: Group Repre~entatives

Tea Break

Group Work Presentations, Facilitator: Group Representatives

Lunch

Participants break into their respective ProvinceslDistricts and prepare written reportson in-service training conducted/or not conducted for ·grade 4 mathematics materialsand to plan for in-service training for grade 5

Afternoon Tea

.Provincial Resource Centre Coordinator to report on the in-servi'Ce training for grade 4materials and plans for in-service training for grade 5 materials

Evaluation ofWorkshop, Facilitator: Martha M Lukanga

Closing Remarks and Prayer

END OF WORKSHOP

7

APPENDIX 6

Agenda for the Training of Trainers Workshop

Andrews Motel, LusakaMarch, 03 - 05, 2008

19

MS1ATes--t..~~ -----~~~

1~71J£m!1 \~\ USAID(*( ~ n~~# FROI'1THEAI'1ERICAN PEOPLE

Textbooks and Learning Materials Program (TLMP)

Training of Trainers Workshop

Andrews Motel, LusakaMarch, 03 - 05,2008

Description:The purpose of this workshop is to orientate Provincial Resource Centre Coordinators, DistrictResource Centre Coordinators, Zonal In-Service Coordinators and College Lecturers on using theGrade 5 pupil's' mathematics textbook and the Teacher's Guide who will in tum provide furthertraining to Grade 5 mathematics teachers in their provinces.

Dav 1 Monday! 03 March

Opening Session - Dominic Nyambe, Presiding08:00 hrs Registration! Opening Prayer09:00 hrs Welcome Remarks and Introductions- Ms Martha M Lukanga, Programme Coordinator

Overview ofActivities and Objectives - Dominic NyambeGround rules/Expectations - Dominic Nyambe

09:30 hrs

10:00 hrs

10:15 hrs

11:15hrs

11:45 hrs

12:30 hrs

14:00 hrs

14:30 hrs

15:00 hrs

15:15 hrs

Framework under which the book had been written/general summary of the book - thisincludes HIV/AIDs, gender - Dominic Nyambe

Tea Break

Approaches in Teaching Primary Mathematics, Facilitator: Mr Musheke Kakuwa (HeadofAdvisory Unit for Colleges ofEducation, University ofZambia (UNZA)

Participants break into groups for group work, Facilitator: Mr Kakuwa

Group work presentations

Lunch

Strategies/methods of teaching: Chapter 1 - Sets and Chapter 2 - Number NotationFacilitator: Makumba F. Kaite

Strategies/methods of teaching: Chapter 3 - Addition and Chapter 4 - SubtractionFacilitator: Raphael Banda

Strategies/methods ofteaching: Chapter 5 -Multiplication, Facilitator: Mercy M. Zulu

Afternoon Tea

9

15:30 hrs

16:00 hrs

1t>:30 hrs

17:00 hrs

Strategies/methods ofteaching: Chapter 6 -Division, Facilitator: Lazarous Mutale

Strategies/methods of teaching: Chapter 7 - ArithmeticFacilitator: Crispin Mapulanga

Strategies/methods of teaching: Chapter 8 - Number PatternsFacilitator: Rhoda M Mtande

Closing prayer

END OF DAY 1

Dav 2 Tuesday. 04 MarchLazarous Mutale (Presiding)

08:00 hrs08:05 hrs

08:45 hrs

09:15 hrs

Opening PrayerRe-cap on previous day'-s work

Strategies/methods ofteaching: Chapter 9 - Fractions, Facilitator: Rhoda M Mtande

Strategies/methods ofteaching: Chapter 10 - Decimal NumbersFacilitator: Lazarous Mutale

Strategies/methods of teaching: Chapter 11 - FactorsFacilitator: Mercy M Zulu

09:45 hrs Strategies/methods of teaching: Chapter 12 - MeasurementsFacilitator: Crispin Mapulanga

10:15 hrs

10:30 hrs

Tea Break

Chapter 12 - Measurenlents -continued, Facilitator: Crispin Mapulanga

11 :00 hrs Strategies/methods ofteaching: Chapter 13 - ShapesFacilitator: Lazarous Mutale

11:30 hrs

12:00 hrs

13:00 hrs

14:00 hrs

14:30 hrs

Strategies/methods of teaching: Chapter 14 - GraphsFacilitator: Makumba F. Kaite

Using Children Mathematics Thinking in Teaching Basic MathematicsFacilitator: Mr Muhau Tabakamulamu (Lecturer under Dept. ofMaths and &ienceEducation, University ofZambia (UNZA)

Lunch

Participants break into groups for group work, Facilitator: Mr Tabakamulamu

Group work presentations

10

15:00 hrs

15:15 hrs

16:30 hrs

Afternoon Tea

Assessment in Mathematics, Facilitator: Dominic Nyambe

Closing Prayer

END OF DAY 2

Day 3 Wednesday. 05 MarchRaphael Banda, Presiding

08:00 hrs08:15 hrs

PrayerRecap on the previous day's work

08:30 hrs Using Children's Mathemati.cal Thinking in teaching Basic School Mathematics.Facilitator: M Tabakamulamu (UNZA)

09:10 hrs

09:40 hrs

10:00 hrs

10:30 hrs

11:00 hr

11:30hrs

12:00 hrs

12:30 hrs

Participants break into groups

Tea Break

Group Reports

Assessment in Mathematics

Participants break into their respective Provinces/Districts and prepare written reportson in-service training conducted/or not conducted for grade 4 mathematics materialsand to plan for in-service training for .grade 5

Plenary

Evaluation ofWorkshop, Facilitator: Lazarous Mutale

Closing Remarks and Prayer

11

APPENDIX 7

Paper Presented at a Training Workshop by the professors from theDepartment of Mathenlatics and Science Education

School of Education, University of Zambia

Ndola: 25 - 27 February 2008 andLusaka: 3 - 5 March 2008

23

USING CHILDREN'S MATHEMATICAL THINKING IN TEACHiNG PRIMARYMATHEMATICS

Paper Presented at a Training Workshop for Provincial and DistrictResource Centre Co-ordinators.

Ndola: 25 -27 February 2008Lusaka: 3 - 5 March 2008

Prepared byM Tabakamulamu

Department ofMathematics and Science EducationSchool ofEducationUniversity ofZambia

13

1. INTRODUCTION

What do we mean by using children' s mathematical thinking in teaching mathematics? We simply

mean taking into account what children already know in mathematics and incorporating it into our

planning and presentation of lessons. Now, I know that many teachers will say, '<But that is exactly

what we do on a daily basis as we plan our lessons!"

Well, what I am going to talk about is not quite the -same thing. For example, do you know that

children have their own, often untau.ght, ways of performing simple arithmetic tasks involving

addition, subtraction, and nlultiplication? In fact, research has shown that even before they begin

formal schooling young children already know a great deal of mathematics (see e.g. Carpenter et aI,

1999; Ginsburg and Baron, 1993; Hughes, 1986). As these authors show,

• By the time they begin primary education children have learned to use their countingskills to solve simple word problems, involving addition, subtraction, multiplication anddivision.

• This ability to solve simple arithmetic problems is a result of children's early encounterswith a variety of situations involving quantities.

• Generally educators have not recognised how much children understand about basicnumber ideas. Consequently, mathematics instruction particularly in the early primarygrades does not capitalise on children's rich store of informal mathematical knowledgeand is, therefore, disconnected from the ways in which children think about and solveproblems in daily life.

But how do young children come to learn so much mathematics at such an early age? According to

Ginsburg and Baron (1993), regardless of where children live on planet earth they will inevitably come

into contact with situations that provide opportunities to engage in mathematical thinking. Indeed, as

these authors point out,

In what culture, however impoverished, does the child lack things to count? In whatculture cannot one add to what one had before? Mathematical events andphenomenon appear to be universal in the physical [and social] world....Childrenhear adults counting. They see adults using numbers in shopping. They see numberson telephones..•and [on] houses. And [if they live in the cities] they may evenencounter 'educational' television programs in which characters count andoccasionally calculate (p. 5).

2. WHY USE CHILDREN'S MATHEMATICAL THINKING IN OUR LESSONPLANNING AND CLASSROOM TEACHING?

14

The answer to this question should already be apparent from what we have said

above. Nevertheless, to help us understand fully why this is necessary we need

to consider briefly how mathematics is usually taught in many primary school

classrooms in Zambia. Below is a description of a 'formula' one primary

school teacher I interviewed not a long time ago -said she used in teaching

mathematics:

You solve one or two questions; then you write some morequestions on the chalkboard for the children to do.

Thus according to this teacher 'once you have gone through one or two worked

examples and have given children some work to do, you can consider your

teaching task done for the day. Now, this may not look too bad since it is what

many ofus do. But listen to what else the same teacher said later in the

interview:

Researcher:

Teacher:

Researcher:

Teacher:

Researcher:

Teacher:

Researcher:

Teacher:

Researcher:

Imagine that during a mathematics lesson you teach children to adopt aparticular calculation procedure, and emphasise this by using it in workedexamples. What would you do if one of the children in the class uses adifferent procedure but works out things correctly?

If it is correct I would just mark it correct. Then I would ask the child touse the taught method, the one I used in worked examples.

OK.

I would also ask: "How did you arrive at this result?"

If the child explained the logic behind her method and you can see that itactually works, would you allow her to continue using it during lessons?

I would discourage her.

Even though you can see it works?

Yes.

What if when she uses your method she gets the answer wrong but whenshe uses her own she gets it right?

15

Teacher: [Laughs].

What do we learn from the above interview extract? At least two things about the classroom behaviour

of the teacher in question, namely;

• A lack of tolerance for children's own mathematical understandings; and,• The belief that children come to school to learn only from the teacher.

This is not an isolated ·case. For example, after attending a workshop whose aim was to acquaint

teachers with research findings concerning children's pre-school mathemati'Cal knowledge, another

teacher (from a different school) admitted:

I always believed that [young] children came into school empty especially in terms ofmathematics, and I was the one to tell them what to do.

Do the above examples describe your own classroom behaviour when teaching mathematics? If they

do, you need to make some adjustments in your thinking. This is what we look at next.

3. HOW CAN WE USE CHILDREN'S MATHEMATICAL THINKING IN PRIMARYMATHEMATICS?

How, then; can we use children's mathematical thinking in teaching primary

mathematics? Specifically, how can we incorporate children's mathematical

thinking into our teaching ofmathematics, when using the new Grade 5

textbook? In the preface of the new Grade 5 mathematics textbook{see either

the Teacher's Guide or the Learner's book) we find the following statement:

The aim of this book is to make mathematics a 'living subject' where the backgroundof mathematics that learners have becomes the bench mark upon which learningbegins.

Now, I should have told you earlier that my presentation actually hinges on this statement. But what

does the above statement mean? Let me illustrate. Baroody. and Standifer (1993) tell the story of the

mathematical behaviour of a young girl in Grade 1, which story I have changed slightly below to make

it easier for us to understand it.

A teacher asked a little girl on her first day at school the question: What is. 3 + 2? Thegirl could not answer the question and in fact appeared not to know what to do. Theteacher then rephrased the question: If your mother gave you three sweets, and your

16

father gave you two more, how many s\\'eets altogether? The girl immediatelyraised three fingers on one hand; two more on the other hand, counted all, and saidfive.

Why did the girl fail to answer the first question and yet find the "second so easy? In other words, what

was missing in the first question that the teacher supplied in the -second? The answer seems to be the

link between what the child already new and what the teacher was asking her to do. If the teacher had

not rephrased the question, he or she could have concluded that the child was unable to answer the

question. This perhaps explains why, according to Ginsburg and Haron (1993), a six year old when

asked what she was doing in mathematics at school responded that she knew how to do two plus two

but needed to learn" how to do the mathematics. It would "'Seem that while the child understood

something about what it means to do two plus two,she was not acquainted with the specific procedures

and ways ofworking that the teacher insisted she should adopt.

Clearly, then, we need to make a connection between what children know and what we teach them.

We need to find out not only what children learned in previous grades, but also how they think about

the mathematics we are teaching them.

4. CLASSROOM DISCUSSION AND CHILDREN'S

MATHEMATICAL THINKING

Research has shown that one way teachers can make sure that children's own mathematical

understandings are listened to; is to allow a certain level of classroom discussion during mathematics

lessons (i.e. discussion among learners; and between the teacher and the learners). Classroom"

discussion achieves a number of things: It allows children to think more carefully about the answers

they give to questions in mathematics (since they will be required to justify their reasoning); it makes it

possible for other learners in the classroom to know the reasons why certain anBwers may be

acceptable or not acceptable; and also gives the teacher the opportunity to adopt and improve

children's informal solution strategies that appear to work, so that the whole class can have access to

them.

Some of you will probably say, "How can one eXPect children with limited linguistic ability to engage

in classroom discussion?" A few years ago it was indeed difficulty, if not impossible, for many

Zambian primary school children to engage in meaningful discussion during mathematics lessons,

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because they were required 'to talk' mathematics in the English language all the time. They had to

cope·with two tasks· at the same time: to make sense of the mathematics they wer-e learning and, at the

same time, to think about how to -express mathematical ideas in an unfamiliar language.

But things have now changed. I am sure you are· all acquainted with the new language policy in

education. It says: initial literacy and numeracy in Grade 1 should be taught in a familiar language;

and that teachers should then gradually initiate children into the use of English as the medium of

instruction in all content subjects by Grade 4. I used to think that this new language policy meant that

by Grade 4 no Zambian language would be used in teaching mathematics for example. I was wrong,

for on page 23 of The Basic School Curriculum Framework, a document published by the Ministry of

Education in 2000, we find the following statement:

Apart from initial literacy, the medium of instruction shall continue to be English.However, at all levels and in all subjects teachers are encouraged, whenevernecessary and relevant, to use a familiar language for explanations, clarifications,questions and answers. Likewise, pupils are at liberty to use the language in whichthey are able to express themselves confidently and competently, even when themedium of instruction is English.

This means that even at Grade 5 level teachers can encourage children to talk about mathematics in a

language they understand best although, of course, one would hope that eventually children willieam

the official language of instruction and use it in these exchanges.

5. MANAGING PRODUCTIVE CLASSROOM DISCUSSION

How can teachers manage classroom discussion so that it achieves the goals we stated above? Success

in managing classroom discussion seems to require two main things: knowing how to 'press' children

to engage in discussion about the mathematics they are learning; and having a good knowledge of the

mathematics one is teaching, so that one can capitalise on children's contributions during the

discussion (see e.g. Yackel, 2002; White, 2003).

In 'pressing' children to talk about their mathematics teachers can ask questions such as:

• Tell me why you think....

• That looks interesting. Can you explain it to me?

• Which do you think is the better method among these? Why?

• How many of you got the same result? Can I see your hands? Yes, Mambo, -can you explain

what you did?

Finally, we can 'Summarise the teacher's role in managing classroom discussion as follows:

• Valuing children's ideas (i.e. showing them that their ideas are valued).

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• Exploring children's answers.

• Incorporating children's background knowledge in what the class is doing.

• Encouraging children to engage in 'classroom discussion.

6. CONCLUSION

If we want to help children to learn mathematics we should not be the same people who make it

difficult for them to do that, by placing unnecessary barriers in their way. Let us learn what the

children already know in mathematics and use it to plan and present meaningfulmathemati'Cs lessons.

REFERENCES

Baroody, A; J. and Standifer, D. J. (1993). Addition and Subtraction in thePrimary Grades. InR. J~ Jensen .(Ed.). Research Ideas for the Classroom: Early ChildhoodMathematics (pp. 72 - 102). New York: Simon and Schuster Macmillan.

Carpenter, T. P., Fennema, E., Franke, M. L, Levi, L. and Empson, -So (1999).Children's Mathematics: Cognitively Guided Instruction. Portsmouth, NH: Heinemann.

Hughes, M. (1"886). Children and Number. Oxford: Blackwell.

Ginsburg, H. P. and Baron, J. (1993). Cognition: Young Children'sConstruction of Mathematics. In R. J. Jensen,. (Ed.). Research Ideas for the Classroom: EarlyChildhood Mathematics (pp. 3- 21). New York: 'Simon and Schuster Macmillan.

Ministry ofEducation. (2000). The Basic School Curriculum Framework. Lusaka:Curriculum Development Centre.

Ministry of Education/Curriculum Development Centre. (2008). Enjoy BasicMathematics 5: Teacher's Guide (Draft). Lusaka: MOE/CDC.

White, D. Y. (2003). Promoting Productive Mathematical Classroom Discoursewith Diverse Students. Journal ofMathematical Behavior, Vol. 22, pp. 37 -53.

Yackel, E. (2002). What We Can Learn from Analysing the Teacher's Role inCollective Argumentation. Journal ofMathematical Behavior, Vol. 21, pp. 423 - 440.

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APPENDIX 8

Pictures from Dr. Taylor visit to ZambiaJanuary 2008

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Dr. Taylor and the Mission Group (Mount Calvary Baptist Church)during their visit to Jacaranda Basic School

Dr. Vivian Taylor meeting the students from Palm Grove Basic School in Livingstone

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textbooks and learning materials program zambiapdf.usaid.gov/pdf_docs/pdacl897.pdf · education,...

Documents