..DOCUMENT RASH 131 865- JC 760 420 TITLE- Training Program for Teachers of Technical Mathematics in Two-Year Cutricnla. INSTITUTION Queensborough Community Coll., Bayside, N Y. SPONS AGENCY New York State Education Dept., Albany. D v.of Occupational Education Instruction. PUB DATE Jul 76 GRANT VEA-78-2-132 NOTE 180p. EDRS PRICE MP-$0.83 HC-S10.03 Plus Postage. DESCRIPTORS *College Mathematics; Community Colleges; Curriculum Development; Engineering Technology; *Junior Colleges Mathematics Curriculum; *Mathematics Instruction; *Physics Instruction; Practical ,Mathematics Technical Education; *Technical Mathematics Technology ABSTRACT -This handbook 1 is designed'to.aS ist teachers of techhical'mathematics in:developing practically-oriented-curricula -for their students. The upderlying.assumption is that, while technology students are nOt a breed apartr their: needs-and orientation are_to the concrete, rather than the abstract. It describes the:nature, scope,and dontett,of curricula.. in Electrical, TeChnClogy,liedhanical Technology4 Design DraftingTechnology, and: Technical Physics', ..with-particularreterence to:the mathematical skills which are_important for the students,both.incollege.andot -tle job. SaMple mathematical problemsr-derivationSeand.theories tei be stressed it..each of_these.durricula-are presented, as- ate additional materials from the physics an4 mathematics. areas. A frame ok-reference-is.provided through diScussiotS ofthe\careers,for.which-. technology students-are heing- trained'. There.iS alsO &section deioted to the development of reading and studY.skills and:to general. claSSroom_Aatagement. (Author/DC),'- *************************** ******* ****** ** **************** Documents acquired.by ERIC include many info mal unpublished * materials not available. from other sources. ERIC makeseiery effart *ito obtain the best copy,available. Nevertheless, items of marginal * reproducibility are often'encountered and this affects the gUality of the microfiche and hardcopy reproductions ERIC makes available via the ERIC Document Reproduction Service (EDRS). EDES is not responsible for the\guality of the original document. Reproductions supplied by EDRS are the best that can be made from the original. ******************************************************************** U.S DEPARTMENT OF HEALTH, EDUCATION E WELFARE NATIONAL IN1TITUTE OF EDUCATION THIS DOCUMENT HAS BEEN REPRO- DUCED EXACTLY AS RECEIVED FROM THE PERSON OR ORGANIZATION ORIGIN- ATINO IT POINTS OF VIEW OR OPINIONS STATED DO NOT NECESSARILY REPRE- SENT OFFICIAL NATIONAL INSTITUTE OF EDUCATION POSITrON OR POLICY 'Tr ining PTO tain. for.Teachcrs Of echria MathetnaVet in.Twalfeaid Curricula INeefisbOratigirCfomMunity -College- THE CITY UNIVERSITY OF NEW YORK BAYSIDE1 NEW YORK. TRAINING PROGRAM FOR TEACHERS OF TECHNICAL MATHEMATICS IN TWO-YEAR CURRICULA A HANDBOOK PREPARED EOR TIlE _VFORMATIONOF. PARTICIPANTS IN THE SEMINAR PROGRAM HELD AT QUEENSBOROUGH COMIIUNITY COLLEGE OE THE CITY UNIVERsrry OF NEW YORK fUNE 7 - 18. 1976 Partially Pinch York Statc Editcatian Depart? I/EA Grant No. 76-2-132 Published by -enshorough Community College Bayside, New York - WIN 1976 Contents Page Introduction ..1 Development of the Technology Curriculum 2 ..7 Electrical Technology . .. .. .... .. .. .. Introduction to Electrical Technology . ... ... .....10 Electrical Circuit Analysis . 16 Electronics 33 ..36 Transient Circuit Analysis .... ... .. .. Development ofLaplace Transformation. Mechanical and Design Drafting Technologies 61 . .5621 Mechanical Technology ..... .... ..62 Design Drafting Technology . .. ... .... .. ...... Mathematics for Mechanical Technology and DesignDrafting Technology .63 Applied Mechanics_ 64 ..79 Strength of Materials. ... Fluid Mechanics 87 Thermodynamics . ...... .97 Machine DFsign 103 Introduction to Numerical Con rol 106 Design Drafting 112 Statics and Strength of Mate als 3 Surveying and Layout 119 Technical Drawing 121 MechanIsms 124 istrative Uses of Mathemazics Not Covered inOther Areas 128 Technical Physics 156 . 6 Probliems in Proportionality. ... ..... ... .11558 Graphs Trigonometry and Angles . 159 Units, Constants, and Conversions 163 Learning Strategies Study Skills 166 Preface This handbook was written and compiled by the staff of the Training Program for Teachers of Technical Mathematics in Two-Year Curricula held at Queensborough Community College Bayside, New York in June 1976, as pai-t of the materials for the participants' use. .The entire program was partially funded by a grant from the New York State Department of Education (Vocational Education Division) for the pe.iod July 1975-June-- 1976,- We wish to acknowledge the work of Professor Joseph B. Aidab, electrical techriology, Professor Anthony Behr, mathematics, Professor Juliana Corn (program coordinator), mathetnaties, and ProfesSor Sheldon I. KATI, mechanical technology; and of the consultants, Mr. Amos Ben-Hut, student personnel services, Dr. Elie Lowy, physics, and Professor BarbariPennipede, basic educational skills. We also wish to thank Ms. Carol Zim, program secretary, for her diligence in deciphering the incomprehensible symbols of mathematics and science so that' the manuscript could be typed. Thanks also go to Ms. Katherine Rangos, Director of College Publications, for her unfailing optimism, ingenuity and competence in producing this book under trying conditions. Mr. Joseph Felician, manager.of printing services, and his fine staff have our gratitude. iii .introduction This handbook is compiled, not as a definitive guide to success in 'teaching technical stu- dents, but as a series of questions and suggestions, which, combined with the experiences and insights of the reader, will point the way to improved teaching, both in content and teaching methodology. Suggestions as to course content and usable applications can at hest consist of a large body of material containing more information than can be absorbed into-any particular course, th reby leaving each user theoption Of selecting those topics that apply to specific prograinsj The underlying assumption is that, while technology students are not a breed apart, thkir needs and orientation are to the concrete, ratherthan the abstract. While there are differ rices_between technology students andother students, the authors believe that in today's multi-media world, many techniques of impartinginformation must be developed; i.e., the classical "go home and read the book" days aregnhe forever. in order to help the reader build a viable teaching plan based upon these assumptions, the authors have attempted to provide a frame of reference by discussing the careers for which technology students are being trained. The nature, scope, and content of the tech- nical- curricula will be examined, with particular reference to the mathematical skills which are important for the students, both in college and on the job. The staff of the training pro. gram have compiled a list of concrete applications of mathematicS to technology, some drawn from actual textbooks currently in use in technical courses. Additional materials from the physics and mathematics areas are ineluded. A section is devoted to the develop- ment of reading and study skills, as well as gene,ml classroom management techniques. Development of the Teehnolowy Curriculum In the period from 1950 to 1960, engineering colleges shifted from a practical (laboratory- oriented) currieulum to a science (theory-oriented) one. Thus the engineers graduated from these programs gravitazed to industrial positions demanding a research and, developrrient background. This la: a void in the engineering and scientific spectrum in the more practical area. The scientist and the engineer were at one end of this spectrum, and the craftsman was at the other end. There existed, then, a need for practical technical personnel in the area between these two ends. not surprising that the demands of industry engendered the advent of a new type of / program for the academic training of these hewly required technical personnel. The prolif- eratiOn of associate degree prograrns in engineeringJechnOlogy starting in 1960 was the inevitable result. The`kinds of institutions offering educational programs in engineering technology va They belong primarily in one of the following classifications: (a) Monotechnical institutesSingle purpose institutions offering, engineer ng tech- nology. (b) Polytechnical InstitutionsInstitutes with a variety of progras related to business, health, or public service as Well as to engineering. ) Comprehensive Community CollegesCommunity and/or junior colleges which include in their offerings various occupational-technical prograrns as well as "university parallel" or "transfer- programs. (d) UniversitiesSenior institutions which include associate degree programs in engineer- ing technology as part of their offerings. Engineering technology iS Concerned primarily with the application of established scientific and engineering knowledge and methods. Normally, engineering technology is not concerned with the development of new\principles and methods. Technical skills such as drafting, in one instance, are characteristic of engineering technology. The associate degree graduate of an engineering technology program is called an engineering technician. The graduate of a baccalaureate program in engineering technol/./ ogy is known as an engineering technologiSt..The engineering technologist has acadeinic training which lies between that for:the engineering technician at d the