MathScience Innovation Center's Curriculum

Integration of Engineering Concepts Into the Science, Mathematics, and Technology CurriculumKevin Kokal speaks to an engaged audience.
Curriculum Strands with Associated Objectives and Concepts developed by MathScience Innovation Center in July, 2011.

Major Curriculum Strands

1.0 Nature of STEM. The scope and characteristics of science, technology, engineering, and mathematics differ.

2.0 Design and Build. Engineers follow a specific but open ended process to create new products and processes.

3.0 The Engineered World. The wide range of engineering disciplines and engineered products can be shown to have significant impact on society over time.

4.0 Civil Engineering. This is a major area of engineering and deals with the design, construction and maintenance of the physical and natural built environment, including works such as bridges, roads, canals, dams, and buildings.



1.0 Nature of STEM. The scope and characteristics of science, technology, engineering, and mathematics differ.



Major concepts

1.21 Distinguish among science, technology, engineering and mathematics.

1.211 Science expands understanding of the natural world.

1.212 Technology includes anything human-made that is designed to solve a problem or fulfill a need. Technologies assist humans to accomplish tasks easier, faster, more efficiently and/or with more complexity.

1.213 Engineering creates products and process that meet the needs of society.

 1.214 Mathematics explores the abstract science of number, quantity, and space.

1.22 Distinguish between the processes used by scientists, and engineers, and mathematicians to achieve their goals.

1.221 Scientists research questions about the natural world through the process of inquiry, commonly known as “the scientific method”.
a) Identify a question
b) Research prior experimentation
c) Develop potential hypotheses
d) Select a hypothesis to investigate
e) Design an experiment to test the hypothesis
f) Conduct the experiment and collect data
g) Analyze data to determine if hypothesis is supported
h) State a conclusion
i) Make recommendations for future investigations

1.222 Engineers explore practical questions and solutions through the “Design and Build” process.
a) Identify need or problem
b) Research the need
c) Develop possible solution(s)
d) Select the best possible solution
e) Construct a prototype
f) Test and evaluate the prototype
g) Communicate the solution
h) Redesign

1.223 Mathematicians formulate conjectures through the process of inquiry, using the “problem solving process.”
a)Understand the problem
b)Plan your strategy
c) Implement your strategy
d) Look back and reflect 

1.23 Describe interactions among science, technology, engineering, and mathematics.

1.231 Engineered products and technologies enable science and mathematics to advance, e.g. microscopes, telescopes, satellites, computer hardware and software.

1.232 Scientific and mathematical advances provide engineers with the fundamental concepts to develop new products and processes, e.g. nuclear power, electrification, light and fiber optics, and video compression.

1.233 Engineering applications occur throughout the traditional scientific fields of earth, biology, chemistry, physics, mathematics, and computer science.

1.234 Engineers use math and science to design and build a product (object, process, system) to meet a need or solve a problem that can change over time.

1.235 The scientific and mathematical application of scale can impact the function of technologies created by engineers.


2.0  Design and Build. Engineers follow a specific but open ended process to create new products and processes.



Major Concepts

2.21 Construct and test an object using a specific set of plans.

2.211 Construction involves reading and interpreting written materials and diagrams within a plan.

2.212 Multiple diagrams may be needed to communicate how the object looks in 2-D and 3-D.

2.213 Appropriate materials and tools are needed to construct an object.

2.214 Testing is required to determine if an object works; this testing often includes data collection and analysis.

2.215 Testing may result in initial failure or reveal modifications needed to improve the object.

2.216 Findings can be communicated through oral, written materials, or multimedia.

2.22 Given a set of potential materials, design, build and test an object to meet a specific need.

2.221 Constraints exist on the engineering process, e.g. materials, time, finances, knowledge base, etc.

2.222 Engineering involves developing an optimal solution to the need within the constraints.

2.223 Research and brainstorming prior to deciding upon a solution generally result in a better product.

2.224 Plans containing appropriate written materials and/or working diagrams are necessary for good prototype design.

2.225 Quantitative test data are preferred when testing a prototype.

2.226 Within constraints, use of data to inform modifications will generally improve the product.

2.227 In reporting findings, engineers generally follow the steps used in the engineering process (see 1.222).

2.23 Identify a practical problem and use the “design and build process” to create a product or process.

2.231 Engineering design requires creative thinking and consideration of a variety of issues to solve practical problems. Engineers can simulate nature to solve a human problem.


2.232 Design development includes consideration of the impact of potential solutions on different groups and society at-large.


2.233 Planning a prototype includes development of working drawings, diagrams and plans.

2.234 Design features such as size, shape, weight, function, and costs limitations affect the construction of a given prototype.

2.235 Appropriate tools, materials and machines are needed to construct a prototype of a given engineering design.

2.236 Prototypes are tested and data collected to determine effectiveness and inform recommendations for re-design.

2.237 Solutions are recommended via oral, written, and multimedia presentations; these generally follow the sequence of the “design & build” process.

2.24 Compare the processes of “scientific and mathematical inquiry” and “design and build” and how individual(s) may use elements of both in an endeavor.

2.241 Both processes involve background research and brainstorming before selecting a hypothesis, conjecture or “best solution”.

2.242 Descriptions of materials and methods used are part of both inquiry and prototype design.

2.243 Data are collected to determine the validity of a hypothesis or conjecture and the effectiveness of a prototype.

2.244 Findings are communicated to peers using standard reporting procedures developed by the discipline.

2.245 Continued improvement through further experimentation, problem-solving, or redesign is the key to advances in science, mathematics, and engineering.

2.246 Teams of scientists, engineers and mathematicians work together in complex systems development, e.g. space exploration.


3.0 The Engineered World. The wide range of engineering disciplines and engineered products can be shown to have significant impact on society over time.



Major concepts

3.31 Identify and describe advances in engineering that profoundly impacted the 20th century.

3.311 Major advancements in the 20th century include safe water, agricultural mechanization, refrigeration and air-conditioning, automobile and airplane, electrification and electronics, telephone, radio and television, and computers.

3.312 Advances have sometimes impacted the environment in unintended or unexpected ways (both positively and negatively).

3.32 Identify major fields of engineering and their focus.

3.321 The major fields of engineering are organized into the areas of aerospace, chemical, civil, electrical and electronic, environmental, and mechanical engineering.

Aerospace Engineering is the design of aircraft, spacecraft, and related topics. Chemical Engineering is the conversion of raw materials into usable commodities. Civil Engineering is the design and construction of public and private works, such as infrastructure, bridges, and buildings. Electrical Engineering is the design of electrical systems, such as transformers as well as electronic goods. Mechanical Engineering is the design of physical or mechanical systems, such as engines, powertrains, and vibration isolation equipment.

3.33 Describe how one prepares to become an engineer

3.331 Coursework in in math and science at the middle and high school levels, with a focus on problem-solving, is important in preparation for the study of engineering.

3.34 Describe career opportunities in engineering.

3.341 There is a very wide range of career opportunities in many engineering fields, as science and math skills can be applied to many fields. Opportunities exist in such diverse areas as biomedical engineering, molecular engineering, environmental engineering, nano-engineering, and info-engineering.


3.35 Identify and describe scientific advances that will profoundly impact engineering in the early part of the 21st Century.

3.351 The rapid advancement of technology is having a strong impact upon the development of many new fields of engineering, such as computer engineering, software engineering, nanotechnology, molecular engineering, and mechatronics.

3.36 Identify and describe engineering needs whose solutions would profoundly impact the 21st Century.

3.361 Major engineering needs for the 21st Century center around the development of an overall sustainable infrastructure, which includes safe drinking water, sufficient food, secure transportation, reliable communications, and efficient sources of energy.


4.0 Civil Engineering. This is a major type of engineering that deals with the design, construction and maintenance of the physical and natural built environment, including works such as bridges, roads, canals, dams, and buildings.



Major concepts

4.41 Identify major types of engineers involved in civil engineering

4.411 Structural, Mechanical, Electrical, Site, Geotechnical, Environmental, and Construction engineers all are involved in creating the built environment of civil engineering.

4.42 Describe energy transformations that occur in civil engineering projects.

4.421 Many forms of potential and kinetic energy are used to power systems developed by engineers.

4.422 Electrical systems generate, transfer, and distribute electricity. Components of a circuit include the energy source, conductor, load, and switch/controllers. Ohm's Law describes the relationship among resistance, voltage, and current.

4.423 Thermal systems involve the transfer of energy through conduction, convection and radiation. Thermal systems impact the external environment.

4.424 Fluid systems are made of liquids (hydraulic) or gases (pneumatic) and allow force to be transferred from one location to another. Open and closed fluid systems have components such as valves, controlling devices, and metering devices.

4.43 Identify and explain scientific and engineering principles used in construction engineering.

4.431 Construction engineering involves building structures for shelter and recreation, transportation, manufacturing, and communication.

4.432 Major parts of a structure include the foundation, floor, wall, and roofing systems.

4.433 Properties of materials critical to structural engineering include density, tensile strength, conductivity, elasticity and plasticity.

4.434 The forces of tension, compression, torsion, bending and shear affect the performance of structures.

4.435 The three major types of bridges (arch, beam and suspension) have different characteristics and appropriate uses.

4.44 Identify and explain scientific and ecosystems, abiotic and biotic factors.

4.441 Environmental engineers use principles of ecosystems, abiotic and biotic factors, and human influences in the design and construction of elements of the built environment.

4.442 Environmental engineers incorporate the principle of sustainable development to minimize the impact of energy, materials, and water use on an area.

4.443 Geotechnical, environmental, structural, and civil engineering principles are all important considerations in connecting the built environment with the natural environment.

4.444 Civil environmental engineers are concerned with designing structures that control air quality, water quality, hazardous waste, storm water, erosion and sediment, and preservation of wetlands.

4.45 Describe the different mathematics skills needed for Engineering

4.451 Engineers use skills of estimation, multiplication, division, addition, and subtraction on a daily basis.

4.452 Engineers use principles of proportions to develop scale drawings and models that include whole numbers, fractions, decimals, and percent’s.

4.453 Engineers use ratios, mean, median, mode, and range to analyze sets of data.

4.454 Engineers display data using tables and graphs that include raw data, frequency distributions, line plots, stem-and-leaf plots, box-and-whisker plots, and scatter grams.

4.455 Engineers employ simple linear equations and other proportions, formulas, and functions to solve problems.


References: The concepts presented in this document are adaptations of concepts and objectives from these sources:

  • American Association for the Advancement of Science. (2001). Atlas of Science Literacy, Project 2061. Washington, DC: American Association for the Advancement of Science.
  • American Society for Engineering Education Corporate Member Council. (2008). K-12 STEM Guidelines for All Americans. American Society for Engineering Education, The Corporate Member Council. American Society for Engineering Education. Retrieved from
  • International Technology Education and Engineering Association. (2007). Standards for Technology Literacy3rd Edition, Technology for All Americans Project. Reston: International Technology Education and Engineering Association. Retrieved from
  • Massachusetts Department of Education. (2006). Massachusetts Science and Technology Engineering Curriculum Framework. Maiden: Massachusetts Department of Education. Retrieved from
  • The Virginia Department of Education. (2010). The Standards & SOL-based Instructional Resources. Retrieved February 2011, from Virginia Department of Education:
  • Barlow, Ed. 2007. 21st Century Literacies Audit. Creating the Future, Inc.
    Batterson, Jim. September, 2007. Some Results Regarding 21st Century Content Standards in Physics, Chemistry, and Engineering as Developed by Three Panels of Practicing Scientists and Engineers. Special presentation to the General Assembly of the Commonwealth of Virginia.
  • National Science Education Standards. 1996. National Academy of Sciences., National Academy Press, Washington, DC.
    Those Amazing Engineers. 2005. 2nd Edition. American Council of Engineering Companies. Trilogy Publications, LLC. Englewood Cliffs, New Jersey.