Introductions of Presenters Michael Hacker, PI, michael.hacker@hofstra.edu, CoDirector, Center for STEM Research, Hofstra University, NY Bernie Gorman, Co-PI, bernard.gorman@ncc.edu Research Lead, Hofstra University, New York Paul Horwitz, Co-PI, phorwitz@concord.org Senior Scientist, The Concord Consortium, MA Jay Martin, jemartin@waketech.edu, Wake Tech, NC PI, Connecting Industry to Math Instruction (CIMI) Gerhard Salinger, Co-PI, evgersal@gmail.com Retired NSF Program Officer, New Mexico
Marilyn Barger Director, FLATE
Rosemary Brester, CEO, Hobart Machining
David Cassell, Deloitte Research Associate
Sol Garfunkel, Exec. Dir. COMAP
Bernard Gorman, Research Lead/Co-PI Hofstra Univ.
Paul Horwitz, Co-PI, Concord Consortium
Jay Martin, Wake Tech
NEEDED MATH PROJECT MANAGEMENT TEAM Michael Hacker, PI Hofstra University Center for STEM Research
Lois Miceli, Hofstra Center for STEM Research
Deborah Hecht, CUNY External Evaluator
Rod Null, Co-PI, Rhodes CC
Gerhard Salinger, Co-PI Former NSF Program Officer
Gordon Snyder, Holyoke CC
Session Agenda • Overview of NM • Survey Results • Scenario Purposes and Framework • Relating NM to the CIMI Project and Scenario Example • Collaborative Working Groups • Questions and Discussion
Project Intent • To improve alignment of the mathematics taught in two-year technical college programs with the mathematics manufacturing technicians need and use in the workplace. • To develop a list of mathematical skills and competencies that technicians need in the manufacturing workplace. • To set in motion a mechanism for the development of authentic scenarios illustrating what technicians do in industry. These can be useful in discussions between industrialists and technical educators.
Survey Research Approach To develop survey items, research included: • Industry site visits • Reviewing manufacturing skill sets, competency models, CC course syllabi • Certification exams relating to manufacturing • Discussions with technical and math educators • Reviewing technical mathematics textbooks
Manufacturing Sectors Biomanufacturing (biological product manufacturing, pharmaceuticals) Chemical manufacturing (organic & inorganic chemical manufacturing) Digital/electronic technology manufacturing (PC hardware,
electronic computers, test instruments)
Food manufacturing (flavorings, frozen foods, dehydrated foods) Materials fabrication and machining (machine shops, plastic
products, sheet metal work)
Micro and nano Technology (semiconductors and chips) Raw material production (alumina refining, iron and steel mills, glass
manufacturing, petroleum refineries)
Other advanced manufacturing (e.g., auto and aircraft manufacturing, mechatronics)
The Needed Math Survey 2023 Bernard S. Gorman, PhD David Cassell, PhD
Purpose
We developed, conducted, and analyzed a survey to assess the use of math skills and the perceived amounts of preparation needed to perform these skills by three groups: Manufacturing Technicians (n=107), Applied Mathematics Instructors (n=56), and Technical Subject Educators (n=150). Forty items were generated by the NM team.
Developing Survey Items A validation panel of people from technical education and industry reviewed the items. Our evaluator requested that we ask to do “thinkalouds” with a few of those to be surveyed. We pilot-tested survey items. We sent the final survey to about 9000 technicians and faculty from D&B lists. We received 313 “clean” responses.
Usage Items For example, for an item referring to assessing measurement tolerance (Q5) , the Usage item had this format: Q5: How often do you do work that requires accuracy to a specified tolerance? It had these choices: • 1= Never/hardly ever • 2 = One or twice yearly • 3 =Monthly • 4 = Once a week • 5 = Almost Every Day
Preparation Items The corresponding Preparation item had this format: Q5A. How well-prepared were you to do work that requires accuracy to a specified tolerance? It had these choices: • 1= Not at all • 2 = Slightly • 3 = Moderately well • 4 = Very Well • 5 = Extremely Well
Grouping Items into Facets • On the basis of judgments by the research team, the items were then grouped into seven facets: Algebra, Arithmetic, Geometry, Measurement, Modeling, Use of Technology, and Statistics. • The fit of the items to the facets was assessed by confirmatory factor analysis using the R package, lavaan (Rosseel, 2012). The hypothesized models for the 40 usage items and 40 the preparation items provided good to adequate fit to the data.
Confirmatory Factor Analysis Item Fit • The usage measurement model indicated adequate fit (CFI = .93, TLI = .93, RMSEA = .08, SRMR = .09) • The preparation measurement model indicated good fit to the data (CFI = .99, TLI = .99, RMSEA = .04, SRMR = .07).
Factor Scores Composite factor (facet) scores were computed as the mean scores across items within each hypothesized factor. Scores were computed separately for use and preparation items.
Examples of the Measurement Factor
Data Analyses In order to detect differences among the means of the three role groups, analysis of variance (ANOVA) and pairwise post-hoc Games-Howell tests were conducted with factor scores as the dependent variables and roles as the independent variable.
Means, ANOVA, and Post-hoc Tests for the Top 10 Usage Items
Factors and Mean Ratings of Needed Math Subgroups Factor
Item
Use Prep Use Arithmetic Prep Use Geometry Prep Use Measurement Prep Use Modeling Prep Use Statistics Prep Use Technology Prep Algebra
Technical Math Technician Post-Hoc Tests Educator (1) Educator (2) (3) 2.96 3.22 3.04 ns 2.67 2.93 2.72 ns 3.26 3.81 3.55 (2>1), (2>3) 2.89 3.05 2.85 ns 3.43 3.87 3.35 (2>1), (2>3) 2.82 2.75 2.63 ns 4.49 4.55 4.31 (3<2), (3<1) 3.13 2.92 2.79 (3<1) 3.26 3.63 3.23 ns 2.46 2.30 2.42 ns 3.69 3.89 3.49 (3<2) 2.75 2.61 2.55 ns 3.40 3.86 3.05 (2>1), (2>3), (1>3) 2.69 2.45 2.41 (3<1)
Differences As can be seen, there are some significant differences between the means of the three roles on usage and preparation. For half of the factors, technicians differ from one or both of the educator groups.
Correlations of Usage and Preparation Factors We investigated whether there were relationships among ratings of the use of mathematics tasks and the amount of perceived preparation rated by members of the three roles.
Correlations of Usage and Preparation Factors (cont.) That is, if a task is performed frequently, are technicians well-prepared to perform the task? Conversely, if technicians rarely perform a task, are they less-prepared to perform it? In order to assess these questions, Pearson productmoment order correlation coefficients among the seven usage factor scores and their corresponding preparation factors scores were computed.
Correlations between Use and Corresponding Preparation Factors by Roles
About the Correlations As can be seen, although there were statistically significantly correlations, the correlations among use and preparation were generally low to moderate for all three roles. This was especially so among the Technicians. Therefore, frequent use of mathematics skills is not a guarantee of preparation for these skills.
Tentative Findings It is clear that technicians, mathematics educators, and technical educators differ on their judgments of the usage and preparations needed for mathematics skills. Of these differences, the most important ones are between technicians and Instructors Assessments of usage and preparation are not strongly correlated. This is especially true for technicians.
Further Analyses What are the demographic differences among the three roles? What are the differences among subgroups of technicians? For example, in biomanufacturing and materials fabrication and machining?
Scenarios Purpose: To provide realistic, contextualized examples of the use of math in the manufacturing workplace • To answer the question: “When am I going to use this?” • Math ≠ arithmetic! • Most low-level manipulations are, or easily can be, “baked into” process technology • What mathematical concepts do technicians need to work successfully with such “smart” technology? • A model for adapting to changes in industry
Scenario Framework 1. Problem Statement A succinct statement describing a workplace situation that would be encountered by a manufacturing technician. This would normally be supplied by an Advisory Board member from industry. Example: A technician needs to determine that the photoresist is of uniform thickness across the wafer, to determine that the layers fall within specified tolerances and recognize patterns in data to anticipate production problems. Specific Scenarios: Inhaler, Vaccine development , Chip manufacture
Scenario Framework, Continued 2. Scenario Description and Specific Example ▪ A description of the context within which the technician is working, and a short explanation of the processes involved. ▪ This models the discussion between industry representatives and technical educators to understand the problem. ▪ General issues and constraints ▪ Develop a specific example
Scenario Framework, Continued 3. Issues to be Addressed ▪ Issues might flag common misconceptions, attractive but erroneous approaches that might lead to mistakes being made, and issues to which particular attention should be paid. ▪ Additional questions that would stimulate discussion, clarify ways in which the problem might be approached, explain conclusions, and interpret data.
Scenario Framework, Continued
4. Mathematics ▪ The mathematical competencies technicians need and use to solve the presented problem.
CIMI and Needed Math
Were the Industry Findings Similar?
CIMI Industry Facts • 20 STEM Industry Partners over 3-year grant • Industries fields were: • Biopharmaceutical • Civil Engineering • Manufacturing • Surveying • Architectural • And a few others… • High school and community college math teachers visited industry. • We provided the math topics in NC MATH4 to Industry and asked, “What do you do on the job that applies these topics?”
CIMI Findings Compared to NM Survey Troubleshooting with Data / Interpreting Graphs
CIMI Findings Compared to NM Survey Ratios and Rates
CIMI Findings Compared to NM Survey Conversions
Use stormwater runoff to size pipes for draining water off roads.
CIMI Findings Compared to NM Survey Tolerances – Inhaler Production
Net Fill Weight 6.9 6.8 6.7
Fill Weight (g)
6.6 6.5 6.4 6.3 6.2 6.1 6 5.9 5.8 1
100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400
Sample Inhaler Series2
Series3
Series4
Needed Math Scenario Format - Tolerances Sample Needed Math Project Scenario Award # 2100062
PROBLEM STATEMENT A technician needs to take samples, make measurements, determine if manufactured metered-dose inhalers fall within specified tolerances, and recognize patterns in data to anticipate production problems.
Needed Math Scenario Format - Tolerances SCENARIO DESCRIPTION‒SPECIFIC EXAMPLE Manufacturing metered-dose inhalers requires assembly of several parts including the canister that contains the medication, and the pump valve that dispenses it. Production processes crimp the valve onto the canister, pull a vacuum on it, and inject the precise amount of medication. Whether production is in R&D or in the mass production phase, in-process checks (product sampling) must be done to ensure that parameters are within acceptable tolerances. Pulling samples at regular intervals and measuring parameters will ensure quality products. Most manufacturing companies follow a GMP (Good Manufacturing Practice) model to ensure that products meet high standards.
Figure 2. Parameters and Tolerances
Needed Math Scenario Format - Tolerances ISSUES TO BE ADDRESSED When manufacturing inhalers, machinery will occasionally produce some that are either not crimped together properly and could dispense incorrectly, or the amount of medicine injected into the canister could be too little or too much in volume. Technicians pull sample canisters off the manufacturing line and take measurements to determine if the canisters are being manufactured according to design. Each measurement must be within a specified tolerance (range). Technicians need to determine when a measurement is out of the given tolerance range. Also, technicians need to recognize patterns that exist in the data being recorded on the measurements to predict when the measurements will probably go out of tolerance.
WHERE DOES MATHEMATICS COME IN? Tolerances, creating and reading line graphs (MS Excel), mean and standard deviation, sampling to determine any trends. These could be added: Questions for teachers to address, potential solutions to questions and issues raised Teacher resources and notes; pedagogical hints Additional supporting materials that could come from educators or industrialists
CIMI Website – 35 complete Lessons • Launch Video • Desmos Launch • Student Activity Sheet • Teacher Notes • Excel Files / Data where appropriate • For Solutions – email jemartin@waketech.edu
Collaborative Working Groups
PURPOSES • Conduits to industry • Dissemination agents • Provide sustainability • To develop ideas for scenarios and perhaps to develop the four parts of one or two. • To see whether using a scenario deepens the discussion of the mathematical competencies needed.
Types of Collaborative Working Groups LOCAL OR REGIONAL • Central Virginia Community College, VA • Ohlone College, CA • Support Center for Microsystems Education, NM • Washington State Governor’s Aerospace and Advanced Manufacturing Pipeline Commission MANUFACTURING, GENERALLY • Under consideration: Two statewide CWGs might be established—one in Ohio and one in Massachusetts.
How You Can Help Would you be willing to host a Collaborative Working Group? Would you be willing to help us develop scenarios? Contact us: NeededMath@gmail.com