By John C. Peterson
The role and nature of mathematics needed for advanced technology programs was the subject of two CRAFTY workshops in October 2000 and a National Conference in May 2002. The workshops were conducted as part of the project ’Technical Mathematics for Tomorrow: Recommendations and Exemplary Programs,â? awarded to the American Mathematical Association of Two-Year Colleges (AMATYC) by the National Science Foundation. Project directors, in addition to the author, are Mary Ann Hovis (James A. Rhodes State College, Lima, Ohio) and Robert Kimball (Wake Technical Community College, Raleigh, North Carolina).
Los Angeles Pierce College, Woodland Hills, California and J. Sargeant Reynolds Community College, Richmond, Virginia, served as host sites for the CRAFTY workshops. Participants were not mathematicians but people selected for their experiences in education or industry and their ability to provide suggestions on the mathematics needed by people preparing to work in the areas of Information Technology, Biotechnology and Environmental Science, Manufacturing and Mechanical Engineering Technology, and Electronics, Telecommunications, and Semiconductors. Participants addressed the mathematical content students must master during the first two years in order to complete their AAS program, enter the job market, advance up the career ladder, and continue their education.
The National Conference was held May 2002 in Las Vegas. The 83 participants included mathematics educators, technical personnel from business and industry, and technical faculty from two-year colleges. The non-mathematics educators were from the technical fields mentioned above and had attended one of the CRAFTY conferences sponsored by the project.
In most cases, with the exception of elementary statistics, the mathematical needs of these technicians did not extend beyond the content contained in most precalculus courses. In fact, the Biotechnology and Environmental Science report states:
’There is little need for mathematics past algebra when people enter the workplace. Some trigonometry is needed, but probably not advanced trigonometry....
’While everyone in the group agrees that a lot of advanced mathematics (such as calculus and trigonometry) is not needed in our fields, we also agree that everyone should know more mathematics than is required in their everyday job. However, this probably does not include such mathematics as calculus.â?
So, rather than advanced mathematics, it was felt that technicians must be able to think critically, solve problems, and function with linear and non-linear thought processes. The focus must be on reasoning skills and creative problem solving rather than specific content.
The Electronics, Telecommunications, and Semiconductors group reminded us that ’Technicians are basically troubleshooters or repair persons. Some work in the field repairing items such as copy machines while others work on a test bench. Some technicians work for a manufacturing company and repair assembly equipment. The best job as a technician is working in an engineering lab. Some technicians are the highest trained technical people in the company... Technicians have had to locate and replace discreet parts in the past, but the troubleshooting of the future is at board level and requires more system troubleshooting.â?
In order to perform this troubleshooting function, technicians must be able to solve problems and communicate solutions. Mathematics faculty can help develop these skills by providing practical examples, using open-ended non-trivial problems that require the use of teamwork, and encourage the use of appropriate technology?including spreadsheets. One way that will help instructors relate the mathematics to the technical subject areas is for the material to be team taught with faculty from technical areas.
As if to emphasize the above statement, the Information Technology (IT) group stated that ’It can be difficult to identify specific math content required as job skills for individual IT positions; in fact, many IT technicians have jobs that require few quantifiable math skills. Therefore, academic mathematics preparation for students pursuing IT careers may not require advanced math but should include a solid foundation of fundamental content, with an accompanying strong emphasis on the analytical mental training that understanding mathematical concepts demands.â?
The Manufacturing and Mechanical Engineering Technology group emphasized this further by stating that ’the student must be computer literate in a modern manufacturing setting and needs to be exposed to both mathematics software and simulation which would be used in both design and process planning and statistical process control applications in business. Again all technicians should be able to use standard business software as well as the Internet for communication and presentation skills.â?
However, it was the pedagogy that was the biggest concern to these groups. Perhaps the Manufacturing and Mechanical Engineering Technology group said it best when they stated, ’Our technical community college faculty felt that major changes were required in the ways in which mathematics is taught in college today. Curriculum needs to be presented in a modular just-in-time format to suit the specific technical content area being taught. The mathematics problems need to be more connected to the real world and must be relevant to the technical field being studied. Experiment with different classroom approaches to provide real world experiences for the students.... Both the students and faculty should have the opportunity for internships and capstone projects with industry.â?
While all four groups came up with extensive lists of the mathematical requirements for students in their technical areas, the recommendations boiled down to the following:
Some topics should be emphasized: statistics, geometry, basic skills (arithmetic and algebra), estimation, and measurement conversions
Topics should be de-emphasized if technology provides alternatives
Modeling is vital
The mathematical content is not as important as the pedagogy. In response to the question ’What instructional methods might mathematics instructors use to develop or reinforce non-mathematical skills or understandings in your discipline or company?â? one group listed the following:
Report writing and presentation skills (Communication)
Just-In-Time TeachingÃ¹teach the mathematics concept and application as it is required in the content areas.
Work together with technology colleagues to identify expectations, try different approaches, adjust the delivery, etc., to focus on the desired outcomes.
Teach that there may be a range of answers versus a single answer.
Use student teams on problem solving applications. Use of team problem solving techniques should begin as early as possible as the skill develops over time.
Have students present how they solved a problem.
Mathematics faculty should serve on technology advisory committees.
John C. Peterson teaches at Chattanooga State Technical Community College. This article is based on work supported by the National Science Foundation under DUE grant no. 0003065. Any opinions, findings, and conclusions or recommendations expressed in this article are those of the author and do not necessarily reflect the views of the National Science Foundation.