DOCUMENT RESUME ED 212 804 CE 031 198 UTHOR Newton, Lawrence R. T LE Shop Math for the Metal Trades. Combination Welder Apprentice, Machinist Helper, Precision Metal Finisher, Sheet Metal Worker Apprentice. 2. Report on Metal Trades Industry Certified, Single-Concept, Mathematical Learning Projects to Eliminate Student Math ear, INSTITUTION Weber Coll., Ogden, Utah. SPONS AGENCY Department of Education, Washington, D.C.; Utah State Office of Education, Salt Lake City. Adult Education Unit. PUB DATE Jul 81 NOTE 415p..1 AVAILABLE FROM Utah State Office of Education, Adult Education Unit, 250 East SOO South, Salt Lake City, UT 84111 (Report: $20.00 each; Machinist Helper and Precision Metal Finisher Handouts: $20.00 each). EDRS PRICE MF01/PC17 Plus Postage. DESCRIPTORS Course Content; Job Skills; Learning Activities; Learning Modules; Machinists; *Mathematical Applications; *Mathematics Anxiety; Mathematics Curriculum; *Mathematics Instruction; *MetalVerking; Postsecondary Education; Pretests Posttests; Sheet Metal Work; Shop Curriculum; Skilled Occupations; *Student Projects; *Technical Education; Two Year Colleges; Vocational Education; Welding IDENTIFIERS ^ Utah ABSTRACT This project (1) identifies basic and functional mathematics skills (shop mathematics skills). (2) provides pretests on these functional mathematics skills, and (3) provides student learning projects (project sheets) that prepare metal trades students to read, understand, and apply mathematics and measuring skills that meet entry-level job requirements as defined by the metal trades industry for the following occupations: combination welder apprentice, machinist helper, precision metal finisher, and she-qt metal worker apprentice. Each project sheet contains three elements: (1) identification of information, training conditions, training plan, and training goal; (2) review of basic mathematies principles; and (3) shop problems. The project sheets are included in the overall training outline, called the Student Training Record, for each of the occupations listed above.,Each Record lists the milestones (major training subjects) and projects (learning activities) the student is to accomplish. Along with teaching the mathematics skills needed for the four occupations, the guide is also intended to reduce the students' mathematics anxiety. Input for the project was obtained from metal trades employers, instructors, and students throughout Northern Utah. (Author/KC) S SHOP MATH FOR THE METAL TRADES (.0 GO Combination Welder Apprentice Machinist Helper Precision Metal Finisher Sheet Metal Worker Apprentice ('J uJ A REPORT ON Metal Trades Industry Certified, Single-Concept, Mathematical Learning Projects to Eliminate Student Math Fears by Lawrence R. Newton Curriculum Development Coordinator Weber State College Skills Center Weber State College Skills Center 1100 Washington Blvd. Ogden, Utah U.S. DEPARTMENT OF EDUCATION NATIONAL INSTITUTE OF EDUCATION "PERMISSION TO REPRODUCE THIS EDUCATIONAL RESOURCES INFORMATION July 1981 MATERIAL HAS BEEN GRANTED BY CENTER IERICI Tho document has been reproduced as .1/1 reclyed from the person or organtzepon ongmarg rt Minot changes have been made to .mproye reproduchon quaky Pants of view or optmons stated m the; docu TO THE EDUCATIONAL RESOURCES anent doom nktsanly represantothcalNIE INFORMATION CENTER (ERIC)." posrhon of poky FUNDING INFORMATION Project Title: Shop Math for the Metal Trades: Combination Welder Appren- Machinist tice, Helper, Precision Metal 'Finisher, Sheet Metal Worker Apprentice Contract Number: Educational Act Under Which Funds were Administered: Section 310 of Adult Eucation Act (Public Law 93-380) Source of Contract: Utah State Office of Education Adult Education Unit 250 East 500 South Salt Lake City, Utah 84111 Project Officer: C. Brent Wallis, Director Weber State College Skills Center 1100 Washington Blvd. Ogden, Utah 84404 Project Director: Michael J. Bouwhuis, Special Projects Coordinator Weber State College Skills Center Prc,ject Coordi nator: Lawrence R. Newton, Curriculum Development Coordinator Weber State College Skills Center Disclaimer: The activity which is the subject of this report was supported whole in or in part by the U.S. Office of Education and the Utah State Office of Education. However, the opinions expressed herein do not necessarily reflect the position or policy of the United States of Office Education or the Utah State Office of Education, and no official endorsement by these offices should be inferred. Discrimination Prohibited: The program assures that "Na person in the United States shall, on the gmunds of race, color, sex, handicap, age or national origin, be excluded from participation be in, denied the benefits of, or be subjected to discrimination under any program or activity receiving Federal financial assistance." Amount of Contract: .$15,000 o 3 i PROJECT PERSONNEL Lawrence R. Newton, Project Coordinator, is Curriculum Development Coordinator at Weber State College Skills Center, Ogden, Utah. He has worked as a Video Train- ing Specialist with Lockheed Missiles and Space Co., Sunnyvale, California, writ- ing producing video training programs and written materials for Polaris, and Posiedon and Trident missile systems. He has also worked in commercial radio and television as announcer, engineer, production technician, and editor. Mr. Newton received his B.A. from Humboldt State University, Arcata, California, and his M.A. in Education from San Jose State University, San Jose, California. Jack Cline, Project Math Consultant, is a Curriculum Writer and Mathematics In- structor at Weber State College Skills Center, Ogden, Utah. He has taught math at the secondary and post-secondary levels and has tutored extensively in the technical and engineering fields. Mr. Cline is a retired Air Force Colonel with thirty-five years service. His most recent assignments included duties as Division Chief of Engineering Services at Hill A.F.B., Utah and Division Chief of Engineer- ing and Maintenance at the Pentagon, Washington, D.C. He is the author of numerous, technical documents on various Aerospace Weapon Systems. He received his B.S. at Oregon State College, Corvallis, Oregon; an M.S. degree in Aerospace Engineering the University of Colorado, at Boulder; and an M.S. degree in Applied Mathe- matics at Sacramento State College, Sacramento, California. Barbara A. Smith, Project Writer; is a Curriculum Writer at Weber State College Skills Center, Ogden, Utah. She has taught in several elementary schools and has helped teach in-service classes in Ethnic Heritage and Colorado History. She is the author of trip guide, field a Historic Denver for Kids, University of Denver, 1978. She wrote some of the activities for Teaching About Energy: 33 Activities, University of Denver, 1979. She also wrote test items for a national social studies assessment for the National Assessment of Educational Progress of the Education Commission of the States, 1979. Ms. Smith received her B.A. and M.A. degrees at the University of Northern Colorado at Greeley. Alice Taylor, Project Illustrator, is a Curriculum Writer, Graphic Artist and Photographer for Weber State College Skills Center, Ogden, Utah. She was Display Artist for Marshall, Field, Chicago; Sears Roebuck; and the Utah State Fair Assoc- iation. She has been an illustrator for Meridian Publishing Co., Carlsen Printing, and Permaloy Corporation. She has taught at Weber State College, Eccles Art Center, and Ogden Headstart Program, Ogden, Utah. Ms. Taylor received a B.F.A. from the Art Institute of Chicago, University of Chicago. She has taken additional seminar work art at Alfred University, N.Y.; the University of Wisconsin; and Univeristy of Utah. Luana Richardson, Project Layout Typist, is Curriculum Secretary at Wilber State College Skills Center, Ogden, Utah., Ms. Richardson has worked extensively as an administrative secretary, stenographer and typist. ii ABSTRACT This Project (1) identifies basic and functional math skills (shop math skills), provides pre-tests on the above functional (2) math skills, (3) provides and student learning projects (Project Sheets) which prepare metal trades students to read, understand and apply mathematics and measuring skills that meet entry level job requirements as defined by the metal trades industry for the fol.:owing occupations: Combination Welder Apprentice D.O.T. 819.284-008 Machinist Helper D.O.T. 600.280-026 Precision Metal Finisher .D.O.T. 705.484-010 Sheet Metal Worker Apprentice D.O.T. 804.281-010 Input for this project was obtained from metal trades employers, instructors, and students throughout Northern Utah Front (Wasatch North). Each student project provides review a needed (1) of mathematical principles, and (2) selected simulated on-the-job word problems for students to solve (Shop Problems). Copies of this report, as well as pre-tests and student handouts for each occupa- tion, may be obtained from: Utah State Office of Education Adult Education Unit 250 East 500 South Salt Lake City, UT 84111 Cost of report: $20.00 Cost of Student Handouts: Combination Welder Apprentice: $18.00 Machinist Helper: $20.00 Precision Metal Finisher: $20.00 Sheet Metal Worker Apprentice: $18.00 iii TABLE OF CONTENTS Section Title Page Funding Information Project Personnel ii Abstract iii Table of Contents iv INTRODUCTION 1 1-1 2 CHAPTER 1: Shop Math Student Training Records 2-1 Shop Math for Machinists 2-2 Shop Math for Precision Metal Finishers 2-3 Shop Math for Sheet Metal Workers 2-4 Shop Math for Welders 2-5 3 CHAPTER 2: Shop Math for Machinist Helper Pre-Test and Student Learning Projects 3-1 1. Math Pre-Tests 3-2 Shop Math for Metal Trades: Pre-Test, Part 1 3-2 Shop Math for Metal Trades: Pre-Test, Part 1 (Computerized) 3-10 Shop Math for Metal Trades: Pre-Test, Part 2 3-22 Shop Math for Metal Trades: Pre-Test, Part 2 (Computerized) 3-29 Shop Math for Metal Trades: Pre-Test, Part 3 3-37 Shop Math for Metal Trades: Pre-Test, Part 3 (Computerized) 3-46 Shop Math for Metal Trades:-Pre-Test, Part 4 3-60 Shop Math for Metal Trades: Pre-Test, Part 4 (Computerized) 3-67 2. Math for Measuring Instruments 3-74 Project 1: Addition and Subtraction of Fractions 3-74 Project 2: Multiplication and Division of Fractions 3-82 Project 3: Addition and Subtraction of Decimals 3-94 Project 4: Multiplication and Division of Decimals 3-106 Project 5: Fraction-Decimal Conversions 3-117 Project 6: Review of Measurement Numbers 3-127 Project 7: Working With Metrics 3-137 3. Specialized Math Skills 3-149 Project 1: Shop Algebra: Part 1 3-149 Project 2: Shop Algebra: Part 2 3-170 Project 3: Shop Algebra: Part 3 3-206 Project 4: Shop Geometry: Part 1 3-238 Handout: Formulas for Plane Geometric Figures 3-273 Project 5: Shop Geometry: Part 2 3-275 Handout: Formulas for Solid Geometric Figures 3-312 Project 6: Introduction to Trigonometry 3-314 Project 7: Shop Trigonometry: Part 1 3-334 Project 8: Shop Trigonometry: Part 2 3-364 4 CHAPTER 3: Conclusions and Recommendations 4-1 APPENDIX A 5 5-1 Machinist Helper Student Training Record.. 5-2 Precision Metal Finisher.Student Training Record 5-8 Sheet Metal Worker Apprentice Student Training Record 5-13 Combination Welder Apprentice Student Training Record 5-16 This project was accomplished between January 5 and June 30, 1981. This report contains the training outline, called Student Training Record, for each of the occupations listed above. The training outlines titled "Shop Math for Combination Welder Apprentice", Shop Math for Machinist Helper", "Shop Math for Precision Metal Finisher", and "Shop Math for Sheet Metal Worker Apprentice" identify the basic functional math skills needed for each occupation. Each Student Training Record lists the Milestones (major training subjects) and Projects (learning activities) the student is to accomplish. This report also contains the individualized, single-concept, student learning projects, called Project Sheets, pre-tests and handouts for Shop Math for Mach- inist Helper. Each Project Sheet contains three elements: 1. Front Page--Listed here are the following instructions and information: A. Heading: Listed at the top of the page is the Cluster, Occupation, Module, Milestone and Project to properly identify where the project is contained within the specific Student Training Record. B. Training Conditions: Listed here are the equipment, tools, etc. needed to successfully perform and complete the Training Project. C. Training Plan: First, an explanation of WHAT will be done and WHY it must learned are given be (i.e., the purpose and objective of the project). Second, a step-by-step procedure of HOW to do the project is given. D. Training Goal: This entry identifies exactly how well the student is expected to do in solving the Shop Problems at the end of the Project Sheet. 2. Review of Basic Math Principles--The first part of the text of each Pro- ject Sheet contains a brief review of the basic math principles, along with example problems, to help the student see the application of the math principles. This review, as well as the example problems, are de- signed to help the student successfully complete the Shop Problems at the end of each Project Sheet. 3. Shop Problems--At the end of each Project Sheet are a series of eight to fifteen typical shop problems the student will incurr on the job. These problems are descriptive shop problems which challenge the student all as if he or she were an employee with the Shop Problems as an assigiAlent. Project Sheets shop math for each of for the other three occupations listed differ above slight wording changes only in of example problems as well as different Shop Problems for students to solve. The pre-test is a criterion referenced assessment instrument designed to deter- mine student's out the level knowledge for his/her metal of math of trade occupation. Both a comprehensive version of the pre-test (fill-in the blanks) and multiple- choice version suitable for computer scoring are provided in this report. INTRODUCTION Research has shown that most math students do not see the relationship of numbers, letters, hypotheses or theorems and how they arc or may be used in their daily living at home or on the job. In the Spring/Summer 1980 issue of Science Education News, published by the American Association for the Advancement of Science, Robert Davis, associate director of the Computer-Based Educational Research Laboratory at the University of Illinois said, Most students believer mathematics doesn't make They think it's any sense. a dumb game that really doesn't work." Davis goes on to say that most students she has observed don't see any connection be- tween the mathematics symbols they manipulate on paper and anything else. At Weber State College Center* we Skills found similar math application a barrier in training students for entry level jobs in the metal trades. Students had difficulty in applying their classroom math skills toward the solution of practical shop problems associated with the metal of math trades. One level proficiency is the ability to solve groups of similarly written problems that require little or no ingenuity. This is the level that students normally reach during high school math. Our vocational students need a higher level--the level beyond the math application barrier. Students in the metal trades, and perhaps other in trades well, as must have the ability to select and apply the appropriate math skills required to solve the job For example, at hand. a machinist must know whether a particular problem can best be solved by using the techniques of Geometry or Trigonometry. Cnce the selection has been made, the machinist must also have the ability to apply appropriate math skills that will result in a meaningful solution. This project provides the vocational student a means of eliminating the math application barrier. In this project, we set out to achieve two goals: 1. Identify basic and functional math skills which prepare metal trades students to read, understand, and apply mathematics and measuring skills that effectively meet entry level job requirements as defined by metal trades industry for: Combination Welder Apprentice D.O.T. 819.284-008 Machinist Helper D.O.T. 600.280-026 Precision Metal Finisher D.O.T. 705.484-010 Sheet Metal Worker Apprentice D.O.T. 804.281-010 2. Develop individualized, self-paced, single concept, student learning projects which prepare students to read, understand, and apply basic and functional mathematir, and measuring skills for entry required level jobs in the four oc- dations listed above. *Weber State College Skills Center is a vocational training facility operated by Weber State College. The purpose of Skills Center is to increase the employ- ability of the individual--through a partnership with employers. tn addition to developing specific job skills, students learn other things that lead to success the work environment--things like in a good attitude, the ability to communicate, and the importance of dependability and. punctuality. Skills Center is open to all applicants 16 and over who will benefit from the training and be an employable age when their training program is complete. summaries of geometric on the Student Training Record are The handouts listed . area and volume formulas introduced in the Project Sheets. employed at Weber State College Skills A complete list of the Training Modes Center appears in Table A. written for metal trades vocational All student materials for this project were learning materials is fifth to training students. The reading level for student eighth grade. as copies of materials developed for well Permanent copies of this report as and Sheet Metal Worker Combination Welder Apprentice, Precision Metal Finisher are on file and available from: Utah State Office of Education Adult Education Unit 250 East 500 South Salt Lake City, Utah 84111 four metal the complete Student Training Records for each of the of Copies A. trades occupations cited in this report, appear in Appendix .111.111.11 1.44 WSC SKILLS CENTER LEARNING 110DES t III If IFFII77.1.11 I 1.1").#0, 7 1,,-.10.1, '.441 ..011111, .4 .MONSTRATION I AUDIO- VISUAL :ode Training Mode Code Training Mode Code Training Mode PS Project Sheet: Individulized LT Lecture: Lecture-style present- MP Motion Picture: 16mm sound motion self-paced, single concept, ation. May involve one student, picture film. graded reading student a small group, or the entire handout. class. ST Slide-Tape: 35min slides in carousel with audio cassette. DC Discussion: Group discussion led by Instructor. FT Filmstrip -Tflpe: Filmstrip with TX !ext.: Reading assignment in a audio cassette. textbook or s' op manual. DM Demonstration: Demonstration of an activityInstructor demonstrates to student(s), CT Cartridge: Visual and audio pre- or student(s) demonstrate sentation in one self-contained proficiency to Instructor unit. and/or other class members. 11andout: Written materials 110 other than Project Sheets. VC Video: 3/4 inch U-matic cartridge May be given to the stu- RP Role Plat: Group of students or 1/2 inch EIAJ reel-to-reel video dent to keep. role play and discuss YA an on- tape. the-job situation. TP Transparancies: Overhead trans- TR Field Trip: Students visit an parancies. off-Center facility. 0./ Quiz: Written evaluation QZ ofessential points within AT Audio Tape: Cassette tape. a Module or Milestone. RV Review: Verbal evaluation of essential points within a Module or Milestone. CI Computer Assisted Instruction: Computer terminal. / /0 Aim/ /,/iwiteighe /Pa" ( Table