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Paper ID #38341
P-12 Engineering Performance Matrices: Where Did They Come From and
How
Can They Be Used? (Research to Practice)
Dr. Greg J. Strimel, Purdue University at West Lafayette (PPI)
Greg J. Strimel, Ph.D., is an associate professor of Technology Leadership and Innovation and the program
leader for the Design & Innovation Minor at Purdue University. Dr. Strimel conducts research on design
pedagogy, cognition, and assessment as well as P-12 engineering teacher preparation.
Mrs. Amy Evans Sabarre,
Dr. Tanner J. Huffman, The College of New Jersey
Tanner Huffman is an associate professor in the Department of Integrative STEM Education, and director
of the center for excellence in STEM education in the School of Engineering at The College of New Jersey
(TCNJ).
©American Society for Engineering Education, 2023
P-12 Engineering Performance Matrices
Where did They Come from and How can They be Used?
(Research to Practice)
Introduction
To help remove barriers to engineering career pathways, foster a sense of belonging in the field,
develop important skills for student success in any career they may choose, and ultimately create
a transformed engineering workforce that can better serve the whole of society, it can be critical
to act early in the educational experiences provided for our nation’s youth. While initiatives to
engage children in engineering learning experiences over the last couple decades have been
encouraging and millions of students participate in formalized P-12 engineering-related courses,
there has been uncertainty as to how engineering should be intentionally taught across schools in
a coherent manner. To help fill this void, the Framework for P-12 Engineering Learning was
published in 2020 by the American Society for Engineering Education. This framework is
positioned to offer a unifying vision and guidance for informing state and local decisions to
enhance the purposefulness, coherency, and equity of engineering teaching and learning. While
the framework supplies the potential “endpoints” for each component of engineering literacy
(i.e., habits of mind, practices, and knowledge) and details what students could learn by the end
of secondary school, it does not specify a potential blueprint of how the engineering concepts
and sub-concepts may be related and build upon each other to arrive at these endpoints.
Accordingly, following the review of literature and the collection of insights from a variety of
engineering education stakeholders, including teachers, professors, and industry representatives,
an Engineering Performance Matrix (EPM) conceptual model was created to provide an
instructional/assessment blueprint for engineering programs/initiatives. In addition, an EPM for
each engineering concept found within the framework was drafted to help teachers scaffold
learning to their students’ needs and progress teaching toward a targeted performance goal. This
paper will highlight the research and development work that was enacted to draft the EPMs and
discuss how they can be used for developing engineering lessons and activities as well as
aligning/scoping P-12 engineering programs.
Where Did They Come From? The Research & Development Process
The Framework for P-12 Engineering Learning states that engineering literacy is three
dimensional and involves engineering habits of mind, practices, and knowledge (See Figure 1).
The framework also describes that engineering literacy should be developed for students across
the span of their P-12 education experience, scaffolding from more explicitly developing
Engineering Habits of Mind in the early grades and moving toward more explicitly developing
Engineering Knowledge at the higher grades—all while developing competence in Engineering
Practice (see Figure 2).
Literacy Dimensions
Main Components
Engineering Habits of Mind
Optimism
Persistence
Conscientiousness
Systems Thinking
Creativity
Collaboration
Engineering Practices
Engineering Design
Material Processing
Quantitative Analysis
Professionalism
Engineering Knowledge
Domains
Engineering Sciences
Engineering Mathematics
Engineering Technical
Applications
Figure 1. Dimensions of Engineering Literacy.
Engineering
Habits of Mind
Engineering
Practices
Engineering
Knowledge
Primary School
(Grades preK-2)
Elementary School
Grades 3-5
Middle School
Grades 6-8
High School
Grades 9-12
Figure 2. Scaffolding toward Engineering Literacy across the three dimensions of engineering
learning (The darker shading indicating a more explicit emphasis of instruction with the lighter
shading indicating more implicit instruction).
In addition, the framework provides a taxonomy of engineering concepts and sub-concepts
related to the three dimensions of engineering literacy (see Appendix A) as well as a list of
performance expectations for students to strive for by the end of secondary school. The
taxonomy of engineering concepts and sub-concepts found within the framework were
established through a modified Delphi study approach. The Delphi study method is a mixed
methods approach to build a consensus of opinions related to a specific topic across a group of
specialists through multiple rounds of questioning (Helmer & Rescher, 1959). This can typically
involve one qualitative round of questioning followed by two or more rounds of more
quantitative questions to assess agreement among the specialists with the responses to the
previous questions. In this case, the modified Delphi approach included three rounds of questions
in survey format and one final round in a face-to-face focus group setting. Through this
questioning, the specialists, which included representatives from the engineering, engineering
education, technology and engineering education, and teacher education communities, were
asked to identify, rate, and then verify core concepts and the corresponding sub-concepts deemed
important for inclusion in a framework for engineering learning at the pre-college level. More
specifically, the four rounds consisted of concept discovery, concept prioritization, concept
rating, and then concept verification/refinement. Lastly, a synthesis of relevant literature at the
time (i.e., Carr, Bennett, & Strobel, 2012; Custer & Erekson, 2008; Merrill, et al., 2009; National
Academy of Engineering, 2009; 2010; Sneider & Rosen, 2009) as well as the National
Academies’ Taxonomy of Engineering, the Fundamentals of Engineering Exams (National
Council of Examiners for Engineering & Surveying, 2017), a first-year engineering program
review (Strimel et al., 2018), the Accreditation Board for Engineering and Technology (ABET)
standards, and the International Technology and Engineering Educators Association’s
Engineering Endorsement Responsibility Matrix were used to inform the prioritization and
refinement of the concept taxonomy.
While this research resulted in a “menu” of concepts to be included in a framework in which to
build instruction around, it did not specify how the concepts and sub-concepts build upon each
other to support engineering learning across educational experiences. That said, during the
framework development process, EPMs were also developed, tested, and refined through a
design-based research approach. This approach, which included three multi-day symposia,
brought together engineering learning specialists and stakeholders to articulate how the
engineering concepts and sub-concepts are related and how they can be connected to support a
student’s progression toward engineering literacy performance expectations.
An EPM is a conceptual model (adapted from Strimel et al., 2020) that demonstrates ways in
which the concepts identified in the Framework for P-12 Engineering Learning can be used to
guide engineering instruction and serve as an assessment blueprint for the development of
engineering literacy. EPMs are then intended to provide teachers with a sharper understanding of
how concepts and sub-concepts may be related in order to influence more equitable, timely, and
specific feedback through purposeful instructional practices. The hope is that the EPMs help
teachers think through the engineering concepts to inform their instruction from day-to-day or
week-to-week. Accordingly, the EPM template in Figure 3 was developed based on relevant
literature (Corcoran, Mosher, & Rogat, 2009; Duncan & Hmelo Silver, 2009; Lehrer &
Schauble, 2015; Magana, 2017) and then, following the consultation with over 200 P-12
engineering education stakeholders from 32 states at the multi-day symposia, an EPM for each of
the concepts in the engineering taxonomy (see Appendix A) were created. More specifically, the
development of these EPMs involved iterative cycles of research, design, and experimentation
over the process of three years. These cycles included a) establishing an instructional blueprint
for sequencing the learning of these engineering concepts, b) coordinating focus groups for
validation of these blueprints, c) designing sample socially-relevant/culturally-situated learning
activities, and c) establishing pilot sites for testing and refining this work within K-12
classrooms. As a result of this work, 60 EPMs that cover the concepts related to engineering
habits of mind, engineering practices, and engineering knowledge have been created. Figure 3
provides an example of one of these EPMs for the concept of Problem Framing which is core to
the practice of engineering design. Figure 3 also provides an explanation of each component of
the sample EPM. All 60 of the EPMs can be accessed for free at
https://www.p12engineering.org/epm. While these EPMs can indicate how to scaffold learning
across different depths of student understanding from basic to advanced, it is important to note
that learning experiences should be shaped according to the individualities of students and their
communities. That said, the remaining sections of this paper will further describe how the EPMs
can be used to plan instructional materials and develop/align P-12 engineering programs/courses.
Figure 3. Engineering Performance Matrix Example and Explanation.
Developing Engineering Lessons/Activities using the EPMs
The Framework for P-12 Engineering Learning (2020) included a lesson planning model to
assist in the preparation of engineering instruction. The lesson planning model was based upon
the 5-E lesson model created by Bybee (2002) and later adapted for engineering learning by
Grubbs and Strimel (2016). The lesson planning model has three main components which are the
lesson content elements, the lesson contextual elements, and then the step-by-step 5-E lesson
plan. First, the lesson content elements include 1) the lesson overview and purpose, 2) the
targeted engineering concepts and the related STEM standards for the lesson, 3) the learning
objectives, 4) the enduring understandings for the lesson which are the key knowledge points
that can transcend the lesson itself, and 5) the driving questions that can help direct students in
their information gathering efforts in an attempt develop solutions to the overarching issue or
challenge at the center of the lesson. The lesson contextual elements include 1) the socially
and/or locally relevant issue/challenge/problem at the center of the lesson, 2) the cultural
connection between the lesson and the students as well as the local community, 3) the
connections between the lesson content and the related careers, and 4) pre-requisite knowledge
and skills that will enable students to be successful within the learning experience. Then, the 5-E
plan includes the following sections for guiding the structure of the specific lesson activities:
• Engage: This section of the lesson should set the context for what the students will be
learning in the lesson as well as captures their interests in the topic by making learning
relevant to their lives and community
• Explore: This section of the lesson should allow students to build upon their prior
knowledge while developing new understandings related to the topic through student-
centered explorations.
• Explain: This section of the lesson should summarize new and prior knowledge while
addressing any misconceptions the students may hold.
• Engineer: This section of the lesson should require students to apply their knowledge
and practices to identify a problem and then design/make/evaluate/refine a viable
solution.
• Evaluate: This section of the lesson should allow a student to evaluate their own learning
and skill development in a manner that supports them in taking the necessary steps to
master the lesson content and concepts.
The EPMs are then positioned as a tool to aid in the process of developing engineering
curriculum and instruction using this lesson planning model. Figures 4 through 9 will illustrate
how the EPMs can help establish the lesson content elements. The example EPM for the core
concept of computational thinking for the engineering practice of quantitative analysis is
presented on the rights side of each figure with the lesson planning model on the left of each
figure.
Figure 4. The EPM can be used to establish the lesson purpose and overview.
Figure 5. The Core Concept from the EPM can be used as the Engineering Content for the lesson.
Figure 6. The Sub-Concepts of the EPM can also be used as the Engineering Concepts for the lesson and also help to determine any
other relevant STEM standards to address in the lesson.
Figure 7. The "I Can" statements for each sub-concept of the EPM can be used to determine the appropriate learning objectives based
on the class's prior knowledge.
Figure 8. The overview of the EPM can be used as the enduring understanding for the lesson as it describes the concept and its
relationship to engineering literacy as well as engineering-related careers.
Figure 9. The Performance Goal can be posed as a "how can I" question to help direct a student’s own learning throughout the
engineering lesson.
Scoping and Aligning P-12 Engineering Programs Using the EPMs
The increasing interest for engineering programming in schools around the country provides a
unique opportunity for using the habits of mind, practices, and knowledge identified in the
Framework for P-12 Engineering Learning along with the EPMs to review existing curriculum
and determine areas of strengths and areas of opportunity for striving toward engineering literacy
for all students. This was the focus taken by one city public school system in the mid-Atlantic
region. This section will highlight this example to show how the research related to the
framework and the EPMs can be put into practice. The approach provided can be one way that
teachers and district leaders scope and strengthen existing, or new, engineering or STEM
curriculum
First, the school team conducted an initial review of the engineering literacy/content organization
and the guiding principles for engineering programs found in the Framework for P-12
Engineering Learning as well as the 60 EPMs. The team, consisting of a group of teachers
(engineering, biology, chemistry, and computer science) and the STEM instructional specialist,
then decided to pursue five main objectives as they used the framework and EPMs over the
course of the school year to scope and align their STEM programming. These objectives
included:
1. Analyzing the current curriculum to identify where the concepts related to the
engineering habits, practices, and knowledge are explicitly taught and assessed.
2. Determining additional areas of opportunity to address the missing engineering concepts.
3. Creating more intentional areas for integrating engineering concepts within biology and
chemistry courses.
4. Creating vertical maps for engineering units and projects to ensure the engineering
concepts are addressed over time.
5. Developing instructional materials during common teacher planning times using the
EPMs to address all of the core concepts for engineering learning.
In order to analyze their current curriculum and to identify where concepts related to the three
dimensions of the framework were currently being implemented with fidelity, the team focused
first on the engineering practices. In analyzing each unit of instruction, the teachers used the
EPMs and were able to identify the level at which each sub-concept was being addressed. At this
step the group also horizontally aligned the career and technical education standards for the state
to each of the engineering practices to ensure that state standards were aligned and met. It was
clear in doing this step that the framework provided a clearer picture of what the enduring
understandings and key knowledge points were as it relates to engineering practices. The next
step within the process focused on the engineering knowledge dimension. The EPMs in this
dimension enabled the team to create a map of where their current curriculum embedded the
science, mathematics, or technical concepts within the knowledge dimension. These first two
steps of the process took multiple days. While the process of creating individual lessons
continued throughout the school year, after the initial analysis was complete, obvious areas of
strengths within the STEM programming were illuminated. Subsequently, the process also
pointed to key knowledge areas and engineering concepts that were areas of opportunity for
enhancing the current curriculum. Once the initial review was complete and the team had
identified missing or underdeveloped engineering concepts areas, they were able to embed many
of the sub-concepts naturally into the school system’s curriculum. The team found that this
process enabled many pre-requisite knowledge connections to be built into the curriculum and
corresponding lessons. One of the highlights of the process happened within this phase of the
project as natural conversations and discussions arose and many innovative ideas and additions
were articulated related to the current units. An unintended consequence of using the framework
and its taxonomy is that it provided an opportunity for the school team to discuss their
understandings and provide support to one another in their background knowledge. The
framework also helped to highlight where there were needs for professional learning and
understanding of the teachers. The framework and the EPMs provided an innocuous way to then
discuss what professional development was needed to enhance instruction.
The philosophy of this school system is one of STEM integration. Therefore, having biology,
chemistry and computer science teachers a part of the unpacking and analysis of the framework
was instrumental to fostering increased intentional integration across subjects. Most importantly,
through the process described above, the science teachers were able to see their standards and
subject matter within the engineering knowledge dimension. This was extremely helpful to
making increased engineering connections in areas like chemistry where integration between the
subjects had been a challenge. The knowledge dimension was helpful in providing the other
STEM teachers an opportunity to see how their coursework connected to engineering. In
addition, by having them hear and participate in the unpacking and auditing of the engineering
practices within the engineering coursework they were able to find ways to embed these skills
within their instruction and make the integration more of a two-way endeavor.
In the school system involved there has been a high investment in STEM education across K-12.
So, in order to better prepare students for future success, the framework was used to create
vertical maps at each grade-level for engineering units to ensure the engineering concepts are
addressed over time. For example, Figure 10 provides a sample of the mapping of engineering
habits of mind and the content related to the practices of engineering design and quantitative
analysis. In this example, looking at elementary instructional units, each unit name is notated at
the top, while in the far-left column each of the engineering habits are listed. Since each core
concept also has sub-concepts, the numbers beside each core concept correspond to the specific
sub-concept in the EPMs. The elementary school team noted where a unit supported a habit or
practice with an x and, if the unit intentionally taught a sub-concept, then the number of that sub-
concept was listed.
Unit 1:
Force to
the Rescue
Unit 2:
Bubbles
Bubbles
Unit 3:
Teddy Bear
Playground
Unit 4:
Wiggling
Worms
Unit 5:
Build a
Beak
Unit 6:
Kinetic
Cars
Unit 7:
Keep it
Cool
Engineering Habits of Mind
Optimism
x
x
x
Persistence
x
x
x
x
Collaboration
x
x
x
x
x
Creativity
x
x
x
x
x
Conscientiousness
x
Systems Thinking
x
x
x
x
x
x
Engineering Practices
Engineering Design
Problem Framing 1,2,3
1,2
1,2
1,2
1,2
Project Management 1,2,3,4
1
Information Gathering 1,2,3
1,2
1,2
1
1,2,3
1, 2
1,2
1,2
Ideation 1,2,3
1,2
1
1,2
1
1,2
1,2
Prototyping 1,2,3,4
1,2
1,2
1,2,3
2,
1,2,3
1,2
1,2,3
Decision-Making 1,2,3,4,5
2,5
1,2,5
1,5
1,5
1,2
1,2
Design Methods 1,2,3,4,5
4
4
2,5
Engineering Graphics 1,2,3,4
3
Design Communication
1,2,3,4
1,2,3
x
Quantitative Analysis
Computational Thinking
1,2,3
1
Computational Tools 1,2,3
1
Data Collection, Analysis, &
Communication 1,2,3,4,5
2,4
1,2,3,4
System Analytics 1,2,3,4
4
Figure 10. Engineering content alignment for STEM units provided across grades K-5.
As seen in Figure 10, in elementary the school team determined that the focus of engineering
learning is centered on the engineering habits of mind as well as the core content related to the
engineering practice of engineering design. However, at the elementary level, the team saw that
the engineering knowledge dimension could be connected to each engineering challenge as it
relates to the standards of learning for science, mathematics, or technology for the state.
At the middle school level, the engineering vertical alignment tool (see Figure 11) assisted in
creating opportunities for discussion about the engineering practices that were not included in the
current curriculum and how to embed these into instruction moving forward. In many cases,
these were small changes to the curriculum while in others it stimulated the development of new
lessons. At each instructional level, the engineering vertical alignment tool can provide a starting
point for discussions of what each engineering practice means and hopefully helps to further the
development of teacher capacity toward achieving engineering literacy for students. In some
cases, as the school team used this tool with a STEM unit, they began to see that the unit may not
be as strong as originally perceived and may need to be retired in order to better serve the
students and promote deeper engagement with engineering learning. In the example section of
the middle school vertical alignment tool provided in Figure 11, the cold frame engineering
design project is highlighted. The middle school teachers took a similar approach to using the
tool for the unit scoping and alignment as the elementary teachers did. However, since middle
school is able to incorporate more of the EPMs, the teachers listed the sub-concept numbers at
the top and delineated separately the sub-concepts for each core concept that were used. For
example, the core concept of problem framing has three sub-concepts. In this unit the teachers
specifically incorporated: identifying design parameters (1), problem statement development (2)
and considering alternatives (3). Since this unit is based on life science standards of learning and
the group of teachers were trying to track and be intentional about mathematics concepts, one
can see how they have adjusted the tool to include mathematics practices as part of their
knowledge dimension. As with the integration of the knowledge dimension at the elementary
level, at the middle school level the science standards of learning as well as the career and
technical education competencies become an additional part of the integration of science,
mathematics and technical knowledge used in the engineering-focused instruction.
UNIT: Cold frame
Sub-Concepts
Dimension & Core Concepts
1
2
3
4
5
6
7
Engineering Habits of Minds
Optimism
x
Persistence
x
Collaboration
x
Creativity
x
Conscientiousness
x
Systems Thinking
x
Engineering Practices
Engineering Design
Problem Framing
1
2
3
Information Gathering
1
2
3
Ideation
1
2
3
Prototyping
2
4
Decision-Making
2
3
4
5
Project Management
1
2
Design Methods
3
4
Design Communication
Engineering Graphics
3
Material Processing
Measurement & Precision
1
2
Manufacturing
Fabrication
1
2
3
4
5
Material Classification
Joining
1
Casting/Molding/Forming
Separating/Machining
1
2
Conditioning/Finishing
Safety
1
2
3
Quantitative Analysis
Computational Thinking
Computational Tools
3
Data Collection, Analysis, & Communication
1
2
3
4
System Analytics
1
2
Modeling & Simulation
Professionalism
Professional Ethics
Workplace Behavior/Operations
Honoring Intellectual Property
Technological Impacts
1
7
Role of Society in Technological Development
2
Engineering-Related Careers
Engineering Knowledge Domains
Mathematical Knowledge
Computation Basics
Y
Supports Algebraic Thinking
Y
Precision & Accuracy
Mathematical Thinking
Y
Number Sense
Significant Digits
Scientific Notation
Ratios
Data Analysis
Y
Figure 11. Engineering Vertical Alignment Tool for a Middle School STEM Unit.
Lastly, at the high school level, the teachers were able to align across all three dimensions of
engineering literacy described in the engineering framework. The rigor and concepts of the
knowledge dimension that were developed for high school coursework found in the EPMs can be
applied at the intended high school level. As appeared evident in both elementary and middle
school, the use of the framework and EPMs seemed to foster valuable discussions between
STEM educators that resulted in enhanced collaboration across subjects and adjustments to the
engineering-related curriculum.
Conclusion
The Framework for P-12 Engineering learning and the connected EPMs can be more than a
conceptual model. They appear to be a useful tool for supporting coherence and structure in
regard to engineering learning. When put into practice, they seemed to provide a common
language and understanding around the engineering habits of mind, practices, and knowledge
that could help guide teachers, district leaders, and other stakeholders in making informed
decisions when developing STEM educational programming. It is the hope that the framework
and EPMs, along with the examples of their use presented in this paper, can help to guide
instruction and prepare schools/teachers to move toward meaningful and relevant engineering
learning. For example, a guide for using the EPMs is provided to help in the development of
engineering lessons/activities that includes defining the desired engineering concepts,
establishing learning objectives, crafting enduring understandings for the students, and posing
driving questions for the instructional activities—all within meaningful contexts for learning.
Also, an example is provided for aligning, scoping, and enhancing engineering or STEM
programming/curriculum to help strive for achieving engineering literacy for all students
throughout their K-12 experience.
References
Advancing Excellence in P-12 Engineering Education & American Society of Engineering
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Appendix A
Taxonomy of Content for Engineering Practices
Practice
Core Concepts
Sub-Concepts
Engineering
Design
Problem Framing
Identifying Design Parameters
Considering Alternatives
Problem Statement Development
Information Gathering
Research & Investigation
Information Quality Assessment
Data Collection & Organization
Methods
Ideation
Spatial Visualization
Convergent Thinking
Divergent Thinking
Prototyping
Testing & Modification
Manufacturing Processes
Computer Aided Design &
Material Selection
Manufacturing
Decision Making
Evidence/Data-Driven Decisions
Application of STEM Principles
Using Decision Making Tools
Balancing Tradeoffs
Group Decision Making
Project Management
Initiating & Planning
Risk, Quality, Teams, & Procurement
Product Life Cycle Management
Scope, Time, & Cost
Management
Design Methods
Iterative Cycles
User Centered Design
Troubleshooting
Systems Design
Reverse Engineering
Design Communication
Engineering Graphics
Dimensioning & Tolerances
3D Parametric Modeling
2D Computer Aided Design
Technical Writing
Material
Processing
Measurement and Precision
Measurement
Units & Significant Figures
Accurate Layout & Precision
Measurement Instrumentation
Manufacturing
Design for Manufacture
Subtractive Manufacturing
Additive Manufacturing
·
Fabrication
Tool Selection
Product Assembly
Equipment & Machines
Hand Tools
Quality & Reliability
Material Classification
Metals & Alloys
Polymers
Ceramics
Composites
Joining
Fastening
Adhesion
Welding
Soldering
Brazing
Casting/Molding/Forming
Forging
Rolling
Extruding
Separating/Machining
Drilling
Cutting
Turning
Grinding
Milling
Reaming
Conditioning/Finishing
Grinding
Burnishing
Polishing
Safety
Laboratory Guidelines
Attire & Equipment
Machine Safety
Quantitative
Analysis
Computational Thinking
Algorithm Forming
Software Design, Implementation, &
Testing
Programming Languages
Computational Tools
Spreadsheet Tools
Computational Environment
System Design Tools
Data Collection, Analysis,
and Communication
Data Collection Techniques
Estimation
Data-Driven Decision Making
Data Visualization
Reporting Data
System Analytics
Inputs & Outputs
Optimization
Feedback Loops
System Optimization
Modeling and Simulation
Scaled Physical Models
Mathematical Models
Computational Simulations
Design Validation through
Calculations
Failure Analysis & Destructive
Testing
Professionalism
Professional Ethics
Morals, Values, & the Ethics
Continuum
Legal and Ethical Considerations
Engineering Code of Ethics
Workplace
Behavior/Operations
Public Health, Safety, & Welfare
Workplace Culture
Agreements & Contracts
Public Policy & Regulation
Ethical Business Operations
Professional Liability
Responsible Conduct of
Research
Honoring Intellectual
Property
Patents, Copyright, & Licensure
Intellectual Property Terminology &
Laws
Referencing Sources & Plagiarism
Impacts of Technology
Environmental Impacts
Global Impacts
Economic Impacts
Individual Impacts
Cultural Impacts
Political Impacts
Social Impacts
Role of Society in
Technological Development
Societal Needs & Desires
Design for Sustainability
Appropriate Technology Applications
Inclusion & Accessibility
Cultural Influences
Scaling of Technology
Public Participation in Decision
Making
Engineering-Related
Careers
Professional Licensing
Engineering Entrepreneurship
Professional/Trade Organizations
Recognition of Engineering-Related
Careers
Engineering-Related Career
Pathways &
Disciplines
Taxonomy of Content for Engineering Knowledge
Domain
Auxiliary Concept
Sub-Concepts
Engineering
Sciences
Statics
Resultants of force systems
Equilibrium of rigid bodies
Frames & Trusses
Area moments of inertia
Equivalent force systems
Centroid of area
Dynamics
Kinematics (e.g., particles and rigid bodies)
Mass moments of inertia
Impulse momentum (e.g.,
particles & rigid bodies)
Force acceleration (e.g., particles &
rigid bodies)
Work, energy, & power (e.g.,
particles & rigid bodies)
Mechanics of
Materials
Stress Types & Transformations
Material Characteristics, Properties, &
Composition (e.g. Heat Treating)
Material Equations
Phase Diagrams
Young’s Modulus
Stress-Strain Analysis
Material Deformations
Mohr's circle
Fluid Mechanics
Fluid Properties
Pumps, Turbines, & Compressors
Fluid Statics & Motion
(Bernoulli’s equation)
Lift, Drag, & Fluid Resistance
Pneumatics & Hydraulics
Circuit Theory
Series & Parallel Circuits
Ohm’s Laws
Wave forms
Signals
Resistance, Capacitance, &
Inductance
Kirchhoff’s Laws
Current, Voltage, Charge,
Energy, Power, & Work
Thermodynamics
Thermodynamic Properties, Laws, & Processes
Power Cycles & Efficiency
Gas Properties
Heat Exchangers
Equilibrium
Mass Transfer &
Separation
Molecular Diffusions
Separation Systems
Humidification & Drying
Continuous Contact Methods
Convective Mass Transfer
Equilibrium State Methods
Chemical
Reactions &
Catalysts
Reaction Rate, Rate Constant, & Order
Chemical Equilibrium
Fuels
Conversion, Yield, & Selectivity
Engineering
Technical
Applications
Electrical Power
Motors & Generators
AC & DC
Voltage Regulation
Transmission & Distribution
Electro-magnetics
Electrical Materials
Magnetism
Electronics
Instrumentation
Components
Closed & Open loop & Feedback
(systems – system response)
Integrated Circuits
Digital Electronics (e.g. gates &
logic)
Computer
Architecture
Computer Hardware
Computer Software
Interfacing
Processors & Microprocessors
Memory
Communication
Technologies
Digital Communications
Photonics
Networks
Telecommunications
Chemical
Applications
Applications of Inorganic Chemistry
Applications of Organic Chemistry
Material Types &
Compatibilities
Membrane Science
Corrosion
Chemical, Electrical,
Mechanical, & Physical
Properties
Mechanical Design
Machine Elements (e.g. springs, pressure
vessels, beams, piping, cams & gears)
Manufacturing Processes
Machine Control
Process Design
Process Controls & Systems
Recycle & Bypass Processes
Process Flow, Piping, &
Instrumentation Diagrams
Industrial Chemical Operations
Structural
Analysis
Physical Properties of Building Materials
Deflection
Deformations
Implementation of Design Codes
Column & Beam Analysis
Hydrologic
Systems
Hydrology
Water Distribution & Collection Systems
Open Channel
Closed Conduits (Pressurized)
Pumping Stations
Watershed Analysis
Laboratory & Field Tests
Transportation
Infrastructure
Street, Highway, & Intersection Design
Traffic Designs
Pavement Design
Transportation Planning &
Control (safety, capacity, flow)
Geotechnics
Laboratory & Field tests
Erosion Control
Bearing Capacity
Drainage Systems
Foundations & Retaining Walls
Geological Properties &
Classifications
Slope Stability
Soil Characteristics
Environmental
Considerations
Ground & Surface Water Quality
Environmental Impact
Regulations & Tests
Wastewater Management
Engineering
Mathematics
Engineering
Algebra
Recognizing, Selecting, & Applying Appropriate
Algebraic Concepts & Practices
Curve Fitting
Linear Algebra
Manipulation of Algebraic
Equations
2D & 3D Coordinate Systems
Engineering
Geometry
Recognizing, Selecting, & Applying Appropriate
Geometric Concepts & Practices
Manipulation of Geometric
Equations
Application of Trigonometry
Vector Analysis
Engineering
Statistics and
Probability
Recognizing, Selecting, & Applying Appropriate
Probability & Statistical Concepts & Practices
Probability
Regression
Applications of Basic Statistics
(normal distributions, percentiles)
Inferential Statistics & Tests of
Significance (e.g., t-tests,
statistical tolerance)
Engineering
Calculus
Derivatives
· Differential Equations
Integrals
Vectors
