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ABSTRACT

DOCUMENT RESUME

SE 064 225

Mapping Math & Science Outcomes to IT Curriculum: Tools &Frameworks. Building a Foundation for Tomorrow.NorthWest Center for Emerging Technologies, Bellevue, WA.National Science Foundation, Arlington, VA.2000-00-0098p.

DUE-9813446NorthWest Center for Emerging Technologies, 3000 LanderholmCircle SE, N258, Bellevue, WA 98007-6484; phone:425-564-4215; FAX: 425-564-6193; web: www.nwcet.org.Reports Research (143)MF01/PC04 Plus Postage.*Curriculum Development; Elementary Secondary Education;Higher Education; *Information Technology; *MathematicsEducation; *Science Education; Surveys

During the research phase for the Millennium Edition of"Building a Foundation for Tomorrow: Skill Standards for InformationTechnology", data was gathered from a wide range of information technology(IT) professionals on the math and science skills required or recommended forIT students. A survey was conducted to identify which specific areas of mathand science are most beneficial to IT professionals, and as result should beincluded in IT education and training programs. This document presents thesurvey results identifying which math and science skills are important to ITtraining and education. Specific math and science concepts and tools arecorrelated to the IT career cluster areas to which they most often apply andare presented in tables. An outline of the Northwest Center for EmergingTechnologies (NWCET) IT Core Curriculum program outcomes is offered. A maprepresenting the relationships between critical math and science skills andlearner program outcomes from the NWCET IT Core Curriculum is also included.This document supports the review, evaluation, and integration of math andscience skills in IT education and training programs. (ASK)

Reproductions supplied by EDRS are the best that can be madefrom the original document.

S-,Tools & Frameworks

MAPPING

MATH & SCIENCE

OUTCOMES TO

IT CURRICULUM

2

SC

PERMISSION TO REPRODUCE ANDDISSEMINATE THIS MATERIAL HAS

BEEf,11 GRANTED BY

TO THE EDUCATIONAL RESOURCESINFORMATION' ENTER (ERIC)

U.S. DEPARTMENT OF EDUCATIONOffice of Educational Research and Improvement

EDUCATIONAL RESOURCES INFORMATIONCENTER (ERIC)

cument has been reproduced asreceived from the person or organizationoriginating it.

Minor changes have been made toimprove reproduction quality.

Points of view or opinions stated in thisdocument do not necessarily representofficial OERI position or policy.

NVVCETNORTHWEST CENTER far EMERGING TECHNOLOGIES

Funded in part by a grant from the

National Science Foundation.

Grant No. DUE9813446.

Opinions expressed herein are those of the

authors and do not reflect those of the

National Science Foundation.

.Ni COMph

For information on NWCET Compliance Review,

please contact NWCET.

For more information, contact:

NorthWest Center for Emerging Technologies

3000 Landerholm Circle SE, N258

Bellevue, WA 98007-6484

Web: www.nwcaorg

Email: [email protected]

Phone: (425) 564-4215

Fax: (425) 564-6193

Copyright ©1999, 2000

The NorthWest Center for Emerging Technologies (NWCET)

through Bellevue Community College (BCC). All rights reserved.

Permission to Photocopy and QuoteGeneral permission is granted to educators to photocopy limited material from preparedcurriculum for non-commercial instructional or scholarly use. Permission must be soughtfrom BCC in order to charge for photocopies, to quote material in advertising, or to reprintsubstantial portions of the document in other publications. Credit should always be given tothe source of the photocopies or quotes by citing a complete reference.

To Order Additional Copies or for more information onNWCET Curriculum Products, visit our website at:

www. nwcet. orgor call us at:

(425) 564-4215

Mapping Math and ScienceOutcomes to IT Curriculum

4

TABLE OF CONTENTS

OVERVIEW 1

APPENDIX A: Overall Math and Science Survey Summary 5

APPENDIX B:Specific Math Concepts and Tools Most Often Cited as 10Supporting IT Skill ClustersSpecific Science Concepts and Tools Most Often Cited 11as Supporting IT Skill Clusters

APPENDIX C: IT Core Curriculum Program Outcomes 13

APPENDIX D: Relationships Between Critical Math and 19Science Skills and IT Core Curriculum

5

Overview

BackgroundDuring the research phase for the Millennium Edition of Building a Foundation forTomorrow: Skill Standards for Information Technology, data was gathered from a wide rangeof information technology (IT) professionals on the math and science skills required orrecommended for IT students. Not surprisingly, the level of specific math and science skillsvaried directly with the level of educational attainment sought.

While experts have varying opinions on the exact scope and proportion of specific math andscience content, there is a high level of agreement on what outcomes are desired. In otherwords, there is significant consensus that everyone desires the benefits of the thought,reasoning, observational and analytical processes that math and science courses can instill.

A survey was conducted to identify which specific areas of math and science are mostbeneficial to IT professionals and as a result should be included in IT education and trainingprograms. The math and science skills that were identified based on the survey results asimportant to IT education were mapped specified in the outcomes of the NWCET IT CoreCurriculum. See the NWCET Information Technology Core Curriculum document for adetailed list of outcomes and competencies. This map shows excellent overlap between theIT Core curriculum outcomes and the math and science skills. This demonstrates that aprogram design based on the NWCET IT Core Curriculum supports the attainment of criticalmath and science skills.

The methods by which students acquire math and science skills vary from well-developed,discrete courses, all the way to "embedded" content-supporting technical instruction.Preliminary analysis suggests that development of an information technology-specific mathand science core course may ensure that required concepts and skills are, in fact, taught andaccurately assessed. In some cases however, it may not be practical to offer a discrete mathand science course. An effective option is to identify specific elements of math and sciencethat support topic areas and to embed these elements in their related courses, so long as theyare appropriately assessed. The NWCET IT Core Curriculum provides a venue to infusemath and science concepts into an IT training program.

This report presents:The survey results identifying which math and science skills are important to an ITtraining program (Appendix A);Tables relating specific math and science concepts and tools to the career cluster areas(see Building a Foundation for Tomorrow: Skill Standards for Information Technology)to which they most often apply (Appendix B);

p- An outline of the NWCET IT Core Curriculum Program Outcomes (Appendix C);A map representing the relationships between critical math and science skills and theNWCET IT Core Curriculum outcomes (Appendix D).

6

©NorthWest Center for Emerging Technologies 1999, 2000 1

Overview

The information presented in this report can be used in the following ways:: To justify the inclusion of math and science skills and concepts in IT curriculum;: To identify which math and science skills and concepts are most relevant to specific IT

training programs;: To document which math and science skills are taught to and demonstrated by students

completing a program based on the NWCET IT Core Curriculum design.

For further information on integrating math and science skills and concepts into IT educationand training programs, please refer to the following NWCET documents: Science Skills forTechnical Support Module and Math and Science for Media Technology Module.

Math and Science SurveyThe purpose of this survey was to identify areas of math and science that strongly support ITprograms. The survey questions focused on math and science processes (such as "analyticaland logical thinking"), as well as math and science content (such as "arithmetic concepts andtools").

Survey DesignIndustry professionals (across the 8 IT career clusters described in Building a Foundation forTomorrow: Skill Standards for Information Technology) were surveyed to fmd out abouttheir work-related usage of math and science tools and concepts. An electronic survey,designed using specific learning outcomes identified in the NWCET IT Core Curriculum,was sent to a directed sample of in-depth interview and focus group participants. Surveyedprofessionals were asked to indicate how often they used the specific math or science conceptor skill (competency areas) in their job, using this scale:

0 Almost never; 1 Seldom; 2 Sometimes/Occasionally; 3 Often; 4 Frequently/AlmostDaily

Responses were generated for each of the following 7 math and science categories (coveringa total of 61 competency areas):,. Analytical and Logical Thinking (6 competency areas)

: Conceptualization, Pattern Recognition and Modeling (8 competency areas),. Data Gathering, Organization and Analysis (5 competency areas)Hypothesis Development and Experiment Design (3 competency areas)

: Problem Solving (3 competency areas): Arithmetic Concepts and Tools (20 competency areas)

Science Concepts and Tools (16 competency areas)

The results summarized and presented in Appendix A reflect data received.

7

2 ©NorthWest Center for Emerging Technologies 1999, 2000

Overview

Survey ResultsThere is substantial agreement that industry values the ability to conceptualize, to gather andorganize data, to recognize consistency and think analytically, to solve problems andtroubleshoot, and to make judgments based on quantitative relationships (such as cost-benefitanalysis). Even though specific areas of math and science content were reported as beingused "often" or "frequently" in certain IT career clusters, in general content was rated lowerthan process skills.

A summary of the survey responses (averaged over all survey respondents for math andscience skills/concepts) is presented in Appendix A. The following areas of math andscience were rated particularly high:

Analytical and Logical ThinkingData Gathering, Organization and AnalysisProblem Solving

The survey results were also analyzed to identify math and science concepts and tools mostoften cited as supporting specific IT skill clusters. This information is presented in AppendixB. The tables show that all IT skill clusters are supported by a wide range of math conceptsand tools, while only half of the clusters strongly rely on the use of specific science conceptsand tools.

The NWCET will conduct further studies to determine what core math and science conceptspertain to the information technology industry at large, and what specific math and scienceelements are recommended for community college students who intend to transfer touniversity or for working professionals seeking graduate level education.

Mapping to IT Core Curriculum Program OutcomesIn 1999, the NWCET published its Information Technology Core Curriculum. Thiscurriculum was derived from the IT Skill Standards and includes a detailed list of learneroutcomes and competencies for an IT core program. After the math and science surveyresults were analyzed, an assessment of the correlation between the math and science skillsdeemed important by industry and the IT core outcomes was conducted. The purpose of thisstudy was to evaluate the effectiveness of the IT Core Curriculum in covering these math andscience skills.

The IT Core Curriculum outcomes are listed in Appendix C. These outcomes are organizedin the following categories:

Project and Process Flow SkillsCoordination and Communication SkillsBusiness Environment SkillsAnalytical Skills and Problem SolvingCore Computer Software and Hardware Skills

0 8©NorthWest Center for Emerging Technologies 1999, 2000 3

Overview

The math and science skills that rated important (2.75 or higher on the survey scale) aremapped to the IT Core Curriculum outcomes, and included in Appendix D. Shaded areasrepresent areas of strong correlation.

The IT core outcomes that showed the highest level of correspondence with math and scienceskills are in the following skill areas:

Project and Process Flow SkillsResearchAnalysis and SynthesisProposal WritingPlanning and OrganizationDesign and DevelopmentUser Testing and Validation

Coordination and Communication SkillsCustomer RelationsTask ManagementProject Management

Analytical Skills and Problem Solving' Problem Solving

Analytical and Logical ThinkingData Gathering, Analysis and OrganizationHypothesis Development and Design of ExperimentationEstimation and Cost/13enefit AnalysisStatistical Analysis

Core Computer Software and Hardware SkillsWindows EnvironmentHardware Installation and ConfigurationSoftware Installation and ConfigurationNetwork TechnologiesSpreadsheet ApplicationsPrinciples of Programming

9


APPENDIX A:Overall Math and Science Survey Summary

10'


Overall Math and Science Survey Summary

How Often Do IT Professionals Use These Math & Science Tools and Concepts?

Analytical and Logical Thinking: Using logic as a reasoning and critical evaluation tool in problem solving and decision

making;Recognizing and correcting logical flaws in analyses and arguments.

Reason using relationships among propositions in terms of implication and contradiction 3.22Recognize consistency and inconsistency; recognize and resolve ambiguous statements 3.52Identify testable implications of hypotheses, to make logical connections betweendiffering hypotheses 2.83Simplify the analysis of complex situations by recognizing internal components andstructures 3.26Classify problems 3.35Sustain a consistent approach in complex, multi-step solutions 3.39

Conceptualization, Pattern Recognition and Modelingi Recognizing and building on approximate parallels between superficially different

situations;> Applying and manipulating abstract representations;=. Developing and applying abstract models of concrete situations.

Apply appropriate abstract concepts to concrete situations 2.74Distinguish between fundamental and incidental features of a concrete situation 2.91Recognize patterns from discrete instances 3.17Generalize from specific instances to general features, formulas, etc. 2.78Apply appropriate general models to specific instances 2.70Create algebraic, geometrical or graphical models representing data relationships 1.52Use models productively as tools for generating and refining hypotheses and forpredicting results 1.87Make critical judgments concerning the universality or limits of generalizations 2.39

Data Gathering, Organization and Analysisi Developing a valid empirical basis for decision making;`)=. Applying logical and statistical tools to reach a valid conclusion from available data;

Identifying and estimating uncertainties in a conclusion based on empirical data.

Identify and characterize needed data and to judge (in)sufficiency for task 2.91Observe, organize and record data 2.70Recognize unexpected evidence 3.35Judge the reasonableness of results 3.43Evaluate and analyze data leading to conclusions and decisions 3.09

iY



Hypothesis Development and Experiment DesignFraming an hypothesis as a troubleshooting tool or as an aid for understanding a concretesituation;

> Planning an experimental or observational test of hypotheses.

Construct a hypothesis from which an experiment could be designed 1.74Specify the data that would support or contradict a hypothesis 2.04Design an experiment or observation to test a hypothesis, validate results, understandcontrol factors 2.35

Problem Solving: Identifying essential features of a complex phenomenon;: Approaching unfamiliar problems in an efficient and systematic manner, appropriately

applying past experience and knowledge;i Extending past experience with creative and innovative approaches.

Approach problems in a systematic way, to look for patterns, to recognize elements thatare consistent or inconsistent with past experience 3.48Break problems down into smaller components, to restructure them, to adapt familiarapproaches, to develop new approaches 3.74Brainstorm to challenge assumptions, to frame and answer "What if .." questions, tosuspend judgment pending appropriate tests 3.43

Arithmetic Concepts and Tools> Correctly computing and interpreting ratios and percentages;

Correctly using scientific notation, exponents and logarithms;Using and converting among decimal, binary and hexadecimal representations inappropriate contexts.

MeasurementExpress, manipulate and calculate using measured quantities in appropriate units 2.17Critically evaluate conclusions based on measured quantities 1.83Algebraic Concepts and ToolsGenerate formula or equation from verbal or pictorial description of a concrete situation 1.35Translate formula or equation into verbal or pictorial description of a concrete situation 1.35Apply proper algebraic techniques in solving mathematical problems 1.57Use algebraic representations as a tool for qualitative reasoning (e.g., rates and ratios,distinguishing between direct and inverse relationships, etc.) 1.87ComputationAccurately perform mathematical operations, using appropriate software (e.g.,spreadsheets) 2.35Estimation and Cost/Benefit AnalysisApply estimation techniques in business situations 2.57Apply statistical techniques to analyze variables 1.83

12

©North West Center for Emerging Technologies 1999, 2000 7


Geometric Concepts and ToolsDevelop and interpret geometrical data (e.g., spatial layouts) 1.17Apply basic geometrical principles in the analysis of graphs 1.26GraphingProduce and interpret graphs 1.91Interpret and analyze graphs 2.43Relational AlgebraApply basic operations in the design of database queries 1 1.91Statistical AnalysisApply basic probability theory 1.26Identify statistical data distributions 1.35Produce statistical descriptions from data 1.17Apply hypothesis testing techniques to a data set 1.04Trigonometric Concepts and ToolsApply basic trigonometric tools in concrete contexts (e.g., spatial measurements) 0.39Apply basic trigonometric tools in abstract models (e.g., phase relations in AC circuits) 0.39

Science Concepts and Tools: Correctly using scientific concepts and tools.

Animation RealismApply physics principles in the accurate representation of motion I 0.26Basic Electricity and MagnetismApply fundamental concepts and tools of DC circuit analysis 0.35Apply fundamental concepts and tools of AC circuit analysis 0.35Apply basic magnetism principles in the technology of magnetic data storage 0.39Data TransmissionApply basic principles of optical and RF signal transmission 0.65Identify, distinguish and evaluate among (both analog and digital) encoding techniques 0.57Identify and analyze sources of interference 0.78Integrated CircuitsApply basic concepts of semiconductor device operation 0.30Analyze basic IC logic circuits 0.26Apply troubleshooting techniques for IC devices 0.26Optics and VisionApply principles of additive and subtractive color combination 0.74Apply understanding of human visual perception to computer graphic design 1.30Apply geometric principles to 2-D representation of 3-D objects 0.91Apply optical principles in the use of cameras and other imaging systems 0.57SoundApply analog and digital encoding techniques 0.57Evaluate bandwidth and frequency response requirements in audio processing 0.74

13

8 ©North West Center for Emerging Technologies 1999, 2000

APPENDIX B:

Specific Math Concepts and Tools Most Often Cited asSupporting IT Skill Clusters

Specific Science Concepts and Tools Most Often Cited asSupporting IT Skill Clusters

14


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APPENDIX C:IT Core Curriculum Program Outcomes

19


IT Core Curriculum Program Outcomes(Excerpted from the NWCET Information Technology Core Curriculum.)

Project and Process Flow SkillsResearch

Identify and use traditional and non-traditional sources of informationApply effectively and choose appropriately from a variety of research methods and toolsAnalyze, organize and present research material

Analysis and SynthesisGather data to identify project requirements, and to interpret and evaluate therequirementsIdentify constraints, generate alternatives, consider risks and evaluate optionsDefine the scope of work to meet project requirements and constraints, and develop aproject outline

Proposal WritingExplain the necessary elements of a proposal and their respective purposeDevelop a proposal that meets the client's requirements and effectively presents thephases of the project

Planning and OrganizationDevelop a project plan that is realistic and that effectively serves the project goalsOrganize the different phases of the project in an efficient manner

Design and DevelopmentApply the design and development process from beginning to endEvaluate and assess the effectiveness of the design and development process

User Testing and Validation'I= Develop and implement an effective testing and user validation program that supports all

phases of the development process

Technical and Project DocumentationSelect and use technical documentation formats meeting the intended purpose and theguidelines of the organizationDevelop effective and accurate technical documentation appropriate to various audiencesand purposes

Quality AssuranceExplain and apply quality assurance processes as they relate to the development processDiscuss quality issues in a technology organization

20

14 ©North West Center for Emerging Technologies 1999, 2000

IT Core Curriculum Program Outcomes

Coordination and Communication SkillsOral and Written CommunicationF' Select and evaluate appropriate communication strategies and styles for a specific

purposeDevelop effective written communication, and develop and deliver effective oralpresentationsEffectively adapt communication strategies and styles to specific audiences

Customer RelationsEffectively listen and ask critical questions to identify customer issues and concernsResolve customer issues and concerns in a timely and appropriate manner

TeamworkWork collaboratively in a team settingWork and communicate effectively with people of different backgrounds and expertise ina group environmentRecognize expertise and learn from others

Task ManagementOrganize multiple tasks in the most effective way, and allocate time and energyaccording to task complexity and priorityEvaluate task outcomes and continuously improve organization process

Project ManagementExplain the basic terminology, principles and techniques of project managementSelect, implement and evaluate appropriate project management techniques and toolsEffectively adapt project management techniques to specific situations

Business Environment SkillsBusiness Organization and Environment

Present and discuss contemporary business principles, practices and organizationPresent and discuss how computer systems impact the operation and management ofbusiness and society

Computer Trends in Business and SocietyDiscuss the issues affecting the selection of a computer system for a specific environmentPresent current computer technology and systems trendsDiscuss the impact of information technology on society and the workplace

Principles of AccountingExplain and apply basic accounting principlesExplain how computer applications support the financial workings of a businessorganization

21

CAorthWest Center for Emerging Technologies 1999, 2000 15


Professionalism> Demonstrate successful work environment-related attitudes and skills

Establish and maintain professional relationships

Professional Development> Identify and close gaps between one's knowledge and skills, and those required by the

situation> Identify sources of learning/training most appropriate for the topic and context, and for

one's personal learning style> Formulate and implement a personal development plan

Analytical Skills and Problem SolvingProblem Solving. Select, implement and evaluate appropriate problem solving techniques and tools> Effectively adapt problem solving techniques to specific situations

Analytical and Logical Thinking> Apply analytical and logical thinking to gathering and analyzing information, designing

and testing solutions to problems, and formulating plans

Conceptualization> Visualize and articulate complex problems and concepts

Data Gathering, Analysis and Organization> Gather, analyze and organize data using a logical and systematic process

Pattern Recognition and Modeling> Recognize patterns in complex sets of data and develop practical models

Hypothesis Development and Design of Experimentation> Develop hypotheses and design test experiments

Estimation and Cost/Benefit Analysis> Develop estimates and projections, to conduct cost/benefit analysis on specific

alternatives

Statistical AnalysisApply statistical methods to analyze and resolve business and technical problems

Core Computer Software and Hardware SkillsWindows Environment

Perform basic operations and troubleshoot basic problems in a Windows environmentCustomize the operating system environmentRun multiple applications at the same time, and import and export data betweenapplications

22



Hardware Installation and ConfigurationName individual parts that make up a stand-alone PC computer system, and describe therelationships between componentsInstall and configure hardware in a PC computer systemPerform basics of PC hardware troubleshooting and maintenance

Software Installation and ConfigurationInstall software programs and perform basic configuration operationsExplain software and hardware compatibility issuesTroubleshoot basic configuration problems

Network TechnologiesPresent the characteristics of overall design and components of a LAN and WAN systemPerform basic setup and configuration of network hardware and software

E-mailExplain basic e-mail system components and organization

'0= Use e-mail effectively and appropriately

InternetUse the Internet as a research tool in an efficient mannerCreate and maintain Web pages

Word ProcessingUse basic word processing features, such as document formatting, editing and usingtablesCreate simple word processing documents such as letters, memos and basic reportsCreate compound documents, such as newsletters, with graphics and objects frommultiple software applications

Spreadsheet ApplicationsDesign, create, modify and troubleshoot spreadsheetsCreate graphs and chartsApply spreadsheet principles to real-life situations and to solve business problems

Presentation SoftwareUse the components of presentation software creatively and effectivelyDemonstrate proficiency in using presentation software functions

Database ApplicationsDefine and use the basic terminology of relational databasesUse the tools and skills needed to create and utilize databases

Principles of ProgrammingPresent basic programming principles and explain programming structuresDesign, code, build, test and troubleshoot basic custom applications

( 23©NorthWest Center for Emerging Technologies 1999, 2000 17

APPENDIX D:Relationships Between Critical Math and Science Skills

and IT Core Curriculum

24


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umen

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2827

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Wes

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ter

for

Em

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olog

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1999

, 200

021

Rel

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ps B

etw

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ills

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Proj

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ills

Proc

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lls

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1999

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0

3132

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Rel

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nshi

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etw

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Mat

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Rel

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Em

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1999

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3536

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Rel

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nshi

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etw

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Cri

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Mat

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Em

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1999

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Rel

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Rel

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1999

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4344

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Rel

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nshi

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etw

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ftw

are

and

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dwar

e Sk

ills

Ana

lytic

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hink

ing

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son

usin

gre

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nshi

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mon

gpr

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and

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ogni

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ake

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tify

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onne

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nsbe

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47

©N

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Wes

t Cen

ter

for

Em

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ng T

echn

olog

ies

1999

, 200

0

48

31

Rel

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nshi

ps B

etw

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Cri

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Mat

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kills

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ecog

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lem

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emen

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49 32 ©

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Rel

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ning

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51

©N

orth

Wes

t Cen

ter

for

Em

ergi

ng T

echn

olog

ies

1999

, 200

0

52

33

Rel

atio

nshi

ps B

etw

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Cri

tical

Mat

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d Sc

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tal a

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s, to

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pas

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53

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Rel

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Cri

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man

ner

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ter

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Em

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ng T

echn

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1999

, 200

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Rel

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ps B

etw

een

Cri

tical

Mat

h an

d Sc

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ills

and

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rdin

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ills

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atte

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lem

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ving

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ific

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eral

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mw

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llabo

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team

set

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mm

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Org

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gy a

ccor

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to ta

skco

mpl

exity

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luat

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inuo

usly

impr

ove

orga

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ess

Proj

ect M

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in b

asic

pri

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term

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chni

ques

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emen

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lect

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plem

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ppro

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ent

tech

niqu

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ols

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ectiv

ely

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ject

man

agem

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s to

spec

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onm

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S

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lem

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ving

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een

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tuat

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ogni

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ttern

s fr

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scre

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stan

ces

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spec

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inst

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sto

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eral

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ture

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rmul

as, e

tc.

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roac

h pr

oble

ms

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syst

emat

ic w

ay, t

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r pa

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s, to

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pas

tex

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ak p

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mal

ler

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pone

nts,

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ctur

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em, t

oad

apt f

amili

arap

proa

ches

, to

deve

lop

new

appr

oach

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to c

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mpt

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, to

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sts

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ines

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rgan

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ion

and

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iron

men

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esen

t and

dis

cuss

cont

empo

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bus

ines

spr

inci

ples

, pra

ctic

es a

ndor

gani

zatio

nPr

esen

t and

dis

cuss

how

com

pute

r sy

stem

s im

pact

the

oper

atio

n an

dm

anag

emen

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busi

ness

and

soci

ety

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pute

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rend

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iscu

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e is

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affe

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e se

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com

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asp

ecif

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yste

ms

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dsD

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e im

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info

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s 19

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Rel

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nshi

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etw

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Cri

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Mat

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ills

and

IT C

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Cur

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Bus

ines

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onm

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s

Con

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lem

Sol

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eral

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ture

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rmul

as, e

tc.

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ay, t

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, to

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oach

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inst

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to c

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, to

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f ...

"qu

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ns, t

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spen

dju

dgm

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endi

ngap

prop

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sts

Prof

essi

onal

ism

Dem

onst

rate

suc

cess

ful

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k en

viro

nmen

t-re

late

dat

titud

es a

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kills

Est

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aint

ain

prof

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tify

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psbe

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ills,

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thos

ere

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e si

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aini

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d fo

r on

e's

pers

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rmul

ate

and

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emen

ta

pers

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elop

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an

61

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Rel

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ps B

etw

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Mat

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Cur

ricu

lum

.....

Ana

lytic

al S

kills

and

Prob

lem

Solv

ing

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cept

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atio

n, P

atte

rn R

ecog

nitio

n an

dM

odel

ing

Prob

lem

Sol

ving

,

Dis

tingu

ish

betw

een

fund

amen

tal a

ndin

cide

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ures

of

aco

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tesi

tuat

ion

Rec

ogni

zepa

ttern

s fr

omdi

scre

tein

stan

ces

Gen

eral

ize

from

spec

ific

inst

ance

sto

gen

eral

fea

ture

s,fo

rmul

as, e

tc.

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roac

h pr

oble

ms

in a

syst

emat

ic w

ay, t

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r pa

ttern

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gniz

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emen

ts th

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nsis

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nsis

tent

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tex

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ak p

robl

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to s

mal

ler

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pone

nts,

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ctur

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em, t

oad

apt f

amili

arap

proa

ches

, to

deve

lop

new

appr

oach

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inst

orm

to c

halle

nge

assu

mpt

ions

, to

fram

ean

d an

swer

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f ...

"qu

estio

ns, t

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spen

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dgm

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prop

riat

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sts

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lem

Sol

ving

Sele

ct, i

mpl

emen

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eval

uate

app

ropr

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prob

lem

sol

ving

tech

niqu

es a

nd to

ols

Eff

ectiv

ely

adap

t pro

blem

solv

ing

tech

niqu

es to

spec

ific

situ

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nsA

naly

tical

and

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ical

Thi

nkin

App

ly a

naly

tical

and

logi

cal t

hink

ing

toga

ther

ing

and

anal

yzin

gin

form

atio

n, d

esig

ning

and

test

ing

solu

tions

topr

oble

ms,

and

for

mul

atin

gpl

ans

Con

cept

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and

artic

ulat

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mpl

ex p

robl

ems

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conc

epts

Dat

a G

athe

ring

, Ana

lysi

s an

d O

rgan

izat

ion

Gat

her,

ana

lyze

and

orga

nize

dat

a us

ing

alo

gica

l and

sys

tem

atic

proc

ess

63

©N

orth

Wes

t Cen

ter

for

Em

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ng T

echn

olog

ies

1999

, 200

0

64

39

Rel

atio

nshi

ps B

etw

een

Cri

tical

Mat

h an

d Sc

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and

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ore

Cur

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al S

kills

and

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lem

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tal a

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sto

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eral

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ture

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rmul

as, e

tc.

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roac

h pr

oble

ms

in a

syst

emat

ic w

ay, t

o lo

okfo

r pa

ttern

s, to

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gniz

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nsis

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tex

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ak p

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to s

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, to

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new

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oach

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inst

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to c

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assu

mpt

ions

, to

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ean

d an

swer

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"qu

estio

ns, t

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prop

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nitio

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odel

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atte

rns

inco

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deve

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Des

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exp

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t/Ben

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it an

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nsp

ecif

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66

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xpor

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abe

twee

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be th

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67

©N

orth

Wes

t Cen

ter

for

Em

ergi

ng T

echn

olog

ies

1999

, 200

0

68

41

Rel

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ps B

etw

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Cri

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Mat

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8079

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Nov 17 00 11:56a NWCET 425 562-6193

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