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DOCUMENT- RESUMEED 242 552TITLE-INSTITUTIONPUB DATENOTESE 044 352Adult Basic Education Mathematics CurriculumGuide.British Columbia Dept. of Education, Victoria.83141p.; For Science Curriculum Guide see SE 044358.PUB TYPEGuides - Classroom Use - Guides (For Teachers) (052)EDRS PRICEDESCRIPTORSMF01/PC06 Plus Postage.*Adult BaSic Education; Curriculum Guides;*Matfiematics Curriculum; *Mathematics Education;Mathematics 1nStruction; Resource Materials;*Teaching MethodsBritish ColumbiaIDENTIFIERSABSTRACTThis curriculum guide from British Columbia isdivided into five parts. Part 1, on using the guide, first explainsthe place of the guide in the provincial curriculum development andarticulation processes. Four purposes are definwd; the scope of thecurr-iculum is outlined; and an overview of curriculum aim, learnergoals, and topics is given. in part 2, the curriculum design ispresented, beginning with a background survey of the current stateand future needs in adult basic education (ABE) Mathematics.Guidelines for specific program and course planning are included,with representative course designs. Part 3, (Learning Tasks andResources) coritains a.systematic array of mathematics topics,including descriptioas of typical learning tasks keyed to a limitedselection of resolurce texts. Part 4, (approaches to Teaching andLearning) presents a variety of ideas for instructors to consider inplanning ABE mathematics instruction, including brief sections onprinciples and methods of adult learning, math anxiety, problemsolvino, computers, and issues in evaluation. Part 5 contains a listof selected instructional resources and professional references,along with a list of publishers' addresses. The final pagesconstitute a response form for users to comment on thiS draftcurriculum. ****************************Reproductions supplied by EDRS are the best that can be made*from -the original ******************************.
IML DEPARTMENT OF EDUCATIONNATIONAL INSTITUTE OF EDUCATION)UCATIONALRESOORCES INFORMATIONCENTER (ERIC)This document hai Peen reprOduced asreceived from the person or organization;originating itMinor changes have been made to improvereproduction quality'e Points of view or opinions stated in this doolFment do not necessarily represent official NIEposition or porkyAA-A-"PERMISSION TO REPRODUC ESHISHAS EEN GRANTED AVTO THE EDUCATIONALRESOURCESINFORMATION CENTER (ERIC)."
ADULT BASIC EDUCATIONMATHEMATICSCURRICULUM-GUIDEPROVINCE OF BRITISH COLUMBIAMINISTRY OF EDUCATION1983
ACKNOWLEDGMENTSThe Ministry of Education acknowledges the work of thefollowing people who have contributed to the production ofthis guide:Curriculum DeveloperJohn Evans, Camosun CollegeCurriculum WritersJack Crane, Camosun CollegeLarry Platz, Okanagan CollegeDavid Harrison, Fraser Valley College(Ministry of Education Consultant)Project. Advisory CommitteeSheldon Harvey; Ministry of Education (Chair)Pal Aggarwal; Pacific Vocational. InstituteBarbara- Bowmar, Okanagan CollegeJoan Connors, College of New CaledoniaTom Davis, Fraser Valley CollegeWarren Little; University of VictoriaChuck Nelson; School District #36; SurreyPatricia Nelson, Malaspina CollegeGordon Pawelchak, Vancouver Community CollegeRiChard Warrington, Ministry of EducationReview PanelJack Chernoff, Cariboo CollegeGordon Danskin, Douglas College,Jack McLaren, Fraser Valley CollegeMary O'Neill, School District #43, CoquitlamLarry Stone, Malaspina CollegeMary Telford, Northern Lights CollegeKae Williams,' Northwest Community CollegeTypistSher6 Estes, Ministry of EducationSpecial thanks are also extended to members of the AdultBasic Education Associatton of British Columbia, for manyvaluable suggestions; and to Camosun College for co-operationin administering the project.
CONTENTSPageAcknowledgmentsThe Plan of This BookPart 1iiUSING THE CURRICULUM GUIDECurriculum Guides and Program ArticulationPurposes of the GuideScope of the CurriculumOverview of Curriculum Aim, Learner Goals, and TopicsPart 2CURRICULUM DESIGNABE Mathematics:,Current State and Future seedsDesign of Programs and CoursesRepresentative Course DesignsPart 3LEARNING TASKS AND RESOURCESMathematics for Personal UsePersonal Math FundamentalsPersonal Math ApplicationsMathematics for CareersCareer Math FundamentalsCareer Math ApplicationsMathematics for 'TransferTransfer Math 1FundamentalsTransfer Math ApplicationsPart 4353643565764838492APPROACHES' TO TEACHING AND LEARNINGPrinciples,of Adult Learningmath AnxietyProblem Solving in MathematicsTh,e Computer -- A Teaching ToolEvaluation of Student ProgressPart 5131923105108110114123SELECTED RESOURCESInstructional ResourcesProfessional ReferencesPublishers' Addresses129132137Response Form139iii
THE PLAN OF THIS BOOKThis curriculum guide is divided into five distinct partsfor ease of use ?ne, r2Ference.Part t Using the L:orr;culum Guide first explains theplace of thein the provincial curriculum developmentand axticuliti-v processes.Four purposes of-the guide arethen defined.NeAZ, the scope of the curriculum is outlined,followed by the overview of curriculum aim', learner goals,and.tapics.Part 2Curriculum Design begins with the backgroundsurvey of- the ciArrent state and future needs in ABEMathematics, which guided the overall design of thiscurriculum.The following section provides instructors andprogrammers with guidelines for specific program and courseplanning, and includes representative course designs.Part 3 Learning Tasks and Resources is the 'workingsection' of the book.It'contains a systematic array ofmathematics topics, including description of typical learningtasks keyed into a limited selection of resource texts.Part 4 Approaches to Teaching and Learning presents avariety of ideas for instructors to consider in planning ABE,mathematics instruction.This part includes brief sectionson principles and methods of adult learning, math anxiety,problem solving, computers, and issues in evaluation.Part 5 Selected Resources contains a- list of selectedinstructional resources and professional references, alongwith a list of publishers' addresses.The final pages of f-the book constitute the 'response form',which users are requested to return to the Ministry withtheir comments on this draft curriculum.
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CURRICULUM GUIDES AND PROGRAM ARTICULATIONThis document is one of a series of adult basic educationcurriculum guides issued by the Continuing Education Divisionof the Ministry of Education.The guides cover the areas ofEnglish and Communications, MathematicS, and Science, fromthe end of basic literacy through secondary school completion'or equivalent.It is intended that a wide variety of courses includingABE 3, ABE 4, college preparation, and secondary schoolcourses for adults will be developed or revised within theframework of the curriculum guides.For this purpose, eachguide contains a section on course design, including samplesof a range Of representative courses.Specific coursecontent or textbooks are not, howeyer, prescribed by theseguides.Over the past two years, several groups hayl:: suggested to theMinistry that an articulation of ABE curriculum andcertification should be accomplished.Specifically, in theSpring of 1983, the project advisory committees for both theScience and Mathematics curriculum guides recommended that"the Ministry should initiate a process to &ddress provincialarticulation concerns Of the ABE curriculum in Science,English and Communicationsand Mathematics. ".Consequently, during the year 1983/84, the Ministry ofEducation plans to initiate a consultative articulationprocess fOr adult basic education programs. Expectedoutcomes of this process are as follows:
- rationalization of program and course titles; establishment of certification-criteria;consensus on appropriate balance of subjects within aprogram.The articulation process will involve consultation with abroadly based committee drawn from institutions involved inthe delivery of adult basic edu6ation. The three ABEcurriculum guides produced to date will be an important partIt is expectedof the 'working papers' of the committee.that this activity will, among other benefits, improvetransferability of ABE students between institutions.Meanwhile, this guide is being distributed as a 'RespomseThis step in the curriculum development processDraft'.provides further opportunity for practitioneri to examine,-discuss, and comment on this major area of adult learning.Written comments-and suggestions should be sent:, either onthe sheet at the end of this book, or separately, t:Co-ordinator, AdultoBasic EducationContinuing Education DivisionPost-Secondary DepartmentMinistry of- EducationParliament Buildingsby March 31, 1984.Victoria, B.C. ,V8V 2M4It is the hope of the Ministry o:" Education that instructors,administrators, and representative groups will take thisopportunity to provide the 'response from the field' thatwill improve the effectiVeness and use of this document.Ron FarisExecutive DirectorContinuing Education Division
PURPOSES Of THE GUIDEBeyond the global purpose of encouraging high - qualitylearning opportunities for adults in ABE mathematics courses;this guide has four specific purposes.a.,The,firstis to define the place of mathematics in adultbasic education by a statement of aim and goals-.The second purpose is to present an array o f Learning topics,with sample tasks and resowroes for instruction. Instructorsand course designers can select from this array when planningspecific courses or units, making local adaptaticin.Sasappropriate to student goals,'Instructor preferences, andlocal resources.The third purpose is to pravide a flexib le stru c ture forcourse design, which can accomodate:-* various effective approaches to mathematicsinstruction for adults;* selection and adaptation of curriculum so that it isappropriate to adult interest and need;* various de-livery modes including-on-campusinstruction; outreach classes or distance learning;* direct group instruction or self-paced learning;* adaptation to a wide range. of texts and otherresources that may change from time to time;* other constraints of time, space, and resources.Tne fourth purpose of the guide is to provide administratorsand instructors with a planning framework that Op assistthem to:* co-ordinate courses within an institution;* articulate course outcomes among institutions acrossthe province;assets and certify levels of student achievement;* define, curriculum development needs.
SCOPE OF.THE CURRICULUMThis curriculum is intended for adult learners who have gonebeyond the minimum competency level best described as'numeracy'.A minimum facility with the basic operations ofthe base 10 number system is assumed.The upper limit of thecurriculum range may generally be taken as secondary schoolcompletion or equivalent.-Current titles of courses within this range include ABE/BTSDlevels 2, 3, and 4, College Foundations or College .Preparatory Mathematics, Mathematics Improvement, andMathematics 10, Algebra 11 ,and Algebra 12, Business andConsumer Mathematics 11, Industrial and Trade Mathematics 11in the adult secondary school program.Furtherrationalizatesin of Curriculum in these, courses will befacilitated by ABE articulation efforts now underway (seepage 1);.The primary approach; of "this guide, however, is to definecurriculum for a wide client le of adult learners who wantimpr'Ove their competence in athematici.a.Grade 4vel equimalents and conventional course titles have/therefore been put -aside for the :purpose of this-guide.Jnstead; the topics and learning tasks emerge from a general:aim and three broad goals :established for the ABE mathematicscurriculum, i.e.; mathematics for-personal use; for careerneeds, and for transfer to further edu,cation.f1.1
OVERVIEW OF CURRICULUM' AIM, LEARNER aDALS, AND TOPICSThe curriculum aim; learner goals and topics were establishedby the curriculum development team on the basis-of:5*a survey of the, current state and future needs in ABEMathematics (summarized in Part 2 of,this guide);*direction from,a field-based, provincial advisorycommittee;cons.ultation With a field review panel of ABE mathematicsinstructors;current trends in mathematics education.The-topics' are first categorized according to learner goal,Personal, Career or Transfer.They are then subdividedintd sets of Fundamental and Application topics.,Le a r r i ng tasks and resources are outlined for each topiC andare prc.esented in detail in-Part 3 of the guide41.u
The relationship of the aim, goals, topics, tasks, andresources is shown by this diagram.THE CURRICULUM AIMis achieved by providing for adults to attainLEARNER GOALSthat may be broadly categorized asTransferPersonalCareerGoalsGoalsGoalsThe curriculum is divided intocorresponding sets ofTOPICSthat in turn are classed asCareer,TransferPersonaland divided into two levelsFundamentals and ApplicationsThus there are six sets of topics fromwhich to build a mathematics course"Personal MathFundamentalsCareer MathFundamentalsTransfer:-MathPersonal 'MathCareer Math.ApplicationsTransfer -MathApplicationsFundamentalsApplicationsFor each set of topics, the curriculum guide identifiesLEARNING TASKS and RESOURCES-613
CURRICULUM AIMThe aim is to enable adult learners to acquire themathematical knowledge, skills, and strategies needed toattain personal or career goals and/or transfer to furthereducation.LEARNER GOALSPersonal: Acquire the competence in mathematics requiredfor personal use in the societal roles of family member,consumer, community member, and citizen.Career: Acquire the competence in mathematics requiredfor career use in the societal roles related to work.Transfer: Acquire the competence in mathematics requiredfor transfer to further educational study in thesocietalrole of lifelong learner.
sonal Math FundamentalsWhole NumbersDecimalsFraction-sMetric MeasurementPercentagesTables, Graphs and ChartsCalculatorsPersonal Math ApplicationsBank AccountsBudgetCash TransactionsConsumer CreditHousingTravelTransportationHome RenovationInsurancePay ChequesIncome TaxProperty TaxUtilities
(CF)CFI:CF2:CF3OF4CF5:CF6:CE7:( CA12:CA13:CA14:CA15:CA16:CA17:CA18:CA19:Career Math FundamentalsWhole NumbersDecimalsFractionsMetric Measurement.FormulaeRatio and ProportionPercentagesCareer Math ApplicationsNumerical DataGeometry - Ltnes and AnglesGeometry - Circles and PolygonsPlane Figures - Basic MeasuresSolid Figures - Basic MeasuresPythagorean TheoremRight Triangle TrigonometryGeometric ConstructionProfit and LossSimple and Compound InterestDiscount and CommissionPayrollStatisticsPlane Figures -. Linear and Area MeasurementSolid Figures - Surface Area and VolumeTrigonometryAdvanced ConstructionsAdvanced Interest and DiscountCompound Interest and Annuities9. 16
(TF)TF1:TF2:TF3:TF4:TF5:TF6:TF7:(TF)'Transfer Math FundamentalsProperties of the Number SystemRational Numbers and ExponentsPolynomialsLinear EquationsCartesian GraphingSystems of EquationsQuadratic SentencesTransfer Math ApplicationsPolynomials and Rational ExpressionsRadical ExpressionsQuadratic SentencesSystems of EquationsTrigonometry - BasicsImaginary and Complex NumbersConicsExponential and Logarithmic FunctionsPolynomial Functions and Graphing Techniques,TA10: 5equences, Series and Binomial Theorem-TAU: Trigonometry - AdvancedTAl:TA2:TA3:TA4:TAS:TA6:TA7:TA8:TA9:
ABE MATHEMATICS: CURRENT STATE AND FUTURE-NEEDSInstitutions throughout British Columbia offer instruction in.Mathematics in a variety of forms and at a:number of levels:Mathematics represents a major component of most Adult BasicEducation programs from Level I through Level 4,. collegepreparatory, and adult secondary completion;Courses-areoffered at central campuses.i at isolated satellites; andthrough distance learning. They are often vailable both dayand; night, zind for both full-time or part-time learners.Instruction may be by conventional classroom lecture/demonstration methods, by individualized tutoring andlear-ning laboratories, by a self-paced, modular. method, orbythese and other methods in combination.While a review of current course offerings in ABE mathematicsrevealed this diVersity, it also discovered a need fordefinition and clarification' of the:common ground in thecurriculum.A recurrent theme voiced by practitioners wasthe need for'a clearly defined, proNince wide curriculum thatwould provide guidance in discussions and decisions aboutcourse content, standards, certification, transfer of studentcredit, and general program articulation and co-ordinition.In its investigations into the current state and future needsin ABE:mathematics, the development team were able to draw onthe, -experience and advice of three groups of practitioners.A broadly based advisory committee included representativesfrom colleges, school districts, and both the post-secondaryand schools departments of the- Ministry of Education; theadvisory committee provided project guidelines and reviewedmajor drafts.A field review panel, from seven colleges and13
a large school district program provided specific feedback oncurriculum content; especially regarding the arrays of(The membership of theselearning tasks and resources.groups is.shown in the Acknowledgments section of thisAlso valuable were the suggestions of 15guide).participants in an instructor's workshop held in co-operationwith the Adult Basic Education Association of BritishColumbia in March, 1983.Common to these discussions were several faMiliar curricularquestions.*What should be the aim of ABE mathematics instruction?*What use is mathematics to the adult learner?*What topics should be included in an adult mathematicscurriculum?*What is the-most useful way to array these topics in acurriculum guide?Summarized belothe curriculaare the broad answers to these questions, asvelopment team interpreted them in thecourse of their -work.What should-he the aim of ABE mathematics instruction?Abroad statement of aim can help set the overall directionWhile it is a generalof a curriculum revision effort.statement; this aim is built around.six, key words:the
knowledge, skills, and strategies that constitute thediscipline. of mathematics, and the personal, career; andtransfer goals of the learners. ThuS, the aim of thecurriculum is as follows:"to enable adult learners to acquire the mathematicalknowledge, skills, and strategies needed to attainpersonal 9r career goals and/or transfer to furthereducation ".What aspmathematics to the adult learner?The value of any new learning (or refreshing the memory ofpast learning and experience) in an adult education contextis capable of almost infinite, and very individual,variation.A group of 30 adult learners could readily attestto well over 30 different uses that mathematics might havefor them.Yet a curriculum developer seeks to categorizethese actual or: potential uses in some way to guidecurriculum design.If the design and content direttlyreflect adult learning needs, then the resulting curriculumwill likely display the characteristics of adult interest,relevance, practicality, challenge, and flexibility.The approach taken in several current provincial curriculumdevelopment projects (including the ABE English andCommunications Curriculum Guide, the ABE Science CurriculumGnidP,- and the (ESL) English for Work guide once again provedto be a useful organizer.The approach is outlined in aworking paper on curriculum development in ABE (B.C. Ministryof Education, 1983), Which analyzes adult learning needs inthe context of six societal roles.
These are the roles defined for the purpose of curriCuumdevelopment and design.7--Family MemberConsumerCommunity MemberCitizenWorkerLearnerIn each
The Ministry of Education acknowledges the work of the following people who have contributed to the production of this guide: . Okanagan College Joan Connors, College of New Caledonia Tom Davis, Fraser Valley College . computers, and issues in evaluation.
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