mathematics at work

mathematics
at work
Civil Engineering

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Mathematics in Civil Engineering Technology
Civil engineering technicians are a key element in
in public works to grow our economy and secure our
the planning, construction and maintenance of the
infrastructure, skilled civil engineering technicians will
structures and facilities that make up the United States’
remain in high demand for years to come.
infrastructure. The nearly 600,000 bridges, 4 million miles
of roads, thousands of water treatment and distribution
Core Mathematics Knowledge
plants, and scores of high-rise buildings throughout the
in Today’s Civil Engineering
United States are made possible by precise applications of
Technology Jobs
mathematics and physics. To ensure our buildings, roads
Developed by secondary, postsecondary, business,
and bridges remain safe and sound for decades to come,
industry and government leaders, the national Career
civil engineering technicians must have an educational
Cluster Pathway Plans of Study for Design/Pre-Construction
background that helps them remain on the cutting edge
and Science, Technology, Engineering and Mathematics
of emerging technologies, as well as use mathematics to
recommend a set of rigorous mathematics courses for
problem solve in a wide variety of job settings.
students to take at both the secondary and postsecondary
levels in traditional or vocational settings to pursue a
Available Civil Engineering
career track in civil engineering technology. These Plans
Technology Jobs
of Study show in detail how the foundation provided
Within the civil engineering industry, there are a variety
by courses such as Algebra I, Geometry, Algebra II,
of entry-level jobs that pay well and provide opportunities
Trigonometry and Calculus equips high school graduates
for advancement — jobs for high school graduates
with the mathematical knowledge and skil s needed for
with postsecondary training or education but less than
success on the job. High school students considering civil
a four-year college degree. Individuals pursuing this
engineering technology need to understand the advanced
career pathway have many opportunities to work for
mathematical and technological skil s required in the field
federal, state or local governments; join any branch of the
to meet the demands of this high-growth industry. For
armed forces; or enter the private sector. With a growing
more information on the Career Clusters Initiative, see
commitment from our federal government to reinvest
www.careerclusters.org/resources/web/pos.cfm.
Percentage of total jobs by
Jobs
Median yearly
education/training (ages 25–44)*
Number of total jobs
salary
High school
Some college
2006
2016
% change
Civil engineering technicians
$40,600
27%
54%
90,700
99,900
10%
Architectural and civil drafters
$42,000
13%
62%
115,500
122,500
6%
Surveying and mapping
technicians
$32,300
42%
51%
75,600
90,200
19%
*Remaining percentage of workers in occupation have a bachelor’s degree or higher
Source: Bureau of Labor Statistics, U.S. Department of Labor, Occupational Outlook Handbook, 2008–09 Edition.

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Ensuring College and Career Readiness:
The American Diploma Project
In 2001, Achieve and several partner organizations
To help pinpoint the academic knowledge and skills
launched the American Diploma Project (ADP) to
required for future employment, ADP commissioned
identify a common core of English and mathematics
leading economists to examine labor market projections
academic knowledge and skills, sometimes referred to
for the most promising occupations — those that pay
as “benchmarks,” that American high school graduates
enough to support a family and provide real potential
need for success in college and the workforce. These
for career advancement. ADP then surveyed officials
ADP benchmarks, released in the 2004 report Ready or
from 22 industries, ranging from manufacturing to
Not? Creating a High School Diploma That Counts, are
financial services, about the most useful skills for
the result of two years of intensive research conducted
their employees to bring to the job.
in colleges and universities as well as workplaces across
the country.
ADP also worked closely with two- and four-year post-
secondary faculty from five partner states to determine
The real-world expectations identified by ADP are signi-
the prerequisite English and mathematics knowledge and
ficantly more rigorous than many current high school
skills required to succeed in entry-level, credit-bearing
graduation standards — which helps explain why many
higher education courses. These conversations revealed
high school graduates arrive at college or the workplace
an unprecedented convergence of the knowledge and
with major gaps in their English or mathematics
skills employers and postsecondary faculty say are
preparation.
needed for new employees and freshmen beginning
credit-bearing coursework to be successful.
“Mathematics at Work” Series
Following up on the work of ADP, Achieve has produced a series of “Mathematics at Work” brochures to
examine how higher-level mathematics is used in today’s workplaces. The brochures present case studies
drawn from leading industries nationwide to illustrate the advanced mathematics knowledge and skills
embedded in jobs that offer opportunities for advancement and are accessible to high school graduates.
The series underscores the value of a rigorous high school curriculum in mathematics. All high school
graduates — regardless of whether they enroll in college, join the workforce or enter the military —
benefit from acquiring a comprehensive knowledge base and skill set in mathematics.
To view or download the ADP benchmarks, go to www.achieve.org/ADPbenchmarks. To view or download
a PDF of additional “Mathematics at Work” brochures, go to www.achieve.org/mathatwork.

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Mathematics engineers safety

Career Preparation for Civil Engineering Technicians
The vast majority of the 100,000 civil engineering
Included within these criteria are learning outcomes for
technicians employed in the United States — including
students — what ABET believes are the minimum units
the nearly 10,000 workers who will be hired in the next 10
of knowledge and skills that every graduate from an
years — will receive associate degrees from community
accredited associate degree program in civil engineering
colleges, technical schools or other comparable
technology should possess. Among the expectations for
postsecondary institutions. These two-year programs in
graduates are:
civil engineering technology require applicants to have
a range of skills and knowledge in math and science.
n Conducting standardized field and laboratory testing
High school graduates entering these programs need
on civil engineering materials (properties of materials,
strong foundations in subjects like algebra, geometry,
volumes of geometric shapes, physical forces and
physics and chemistry to succeed in commonly required
stresses, measurement, statistics)
postsecondary courses such as Precalculus/Trigonometry,
n Using modern surveying methods for land
Drafting and Design, Topographic Surveying, Soil
measurement and/or construction layout (right-
Mechanics, and Strength of Materials.
triangle trigonometry; geometric figures; powers
and square roots; unit conversions for lengths,
If and when technology fails us in the
areas and volumes)
field — batteries run out unexpectedly,
“
n Determining forces and stresses in elementary
the satel ite signal is lost or desert heat
structural systems (functions, vectors and matrices;
waves distort survey data col ection —
chart interpretations; units and unit conversion)
we must rely on our math and science
n Estimating material quantities for technical projects
skil s to get our job done safely and
and performing cost estimates (proportions, reading
complete the mission.
and interpreting charts, equations with multiple
variables, interest computations)
Sgt. 1st Class Paul D. Welborn
”
Technical Engineer, Instructor/Instructional
In addition to possessing a range of mathematical skills,
Program Developer, U.S. Army
today’s civil engineering technicians must be able to com-
It is no surprise that the wide variety of associate degree
municate via written, oral, graphical and electronic media.
programs in civil engineering technology share a com-
They must be able to clearly communicate technical
mon core of expectations and learning objectives. ABET,
concepts not only to their co-workers, but also to clients
Inc., is the leading accreditor for college and university
or customers who may not have technical backgrounds.
programs in applied sciences, computing, engineering
Teamwork skills also are critical because the civil engi-
and engineering technology. ABET — composed of almost
neering field relies heavily on team-based approaches to
30 professional and technical organizations representing
the analysis of complex problems and the design of solu-
disciplines in applied science, computing, engineering and
tions to those problems. ABET standards for engineering
engineering technology — has developed rigorous criteria
technicians stress the importance of creativity, analysis
for the accreditation of engineering technology programs.
and the ability to function effectively on teams.

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Mathematics engineers safety

Bridging the Divide: The Mathematics of Infrastructure
The infrastructure of the United States — in particular the
Before building a new road, for example, civil engineering
4 million-plus miles of road and nearly 600,000 bridges
technicians are on the front line of the initial survey, using
— is widely acknowledged to be in dire need of structural
cutting-edge equipment to map the topography, which is
and functional improvement to ensure safety. Thousands
the horizontal and vertical shape of the land. They must
of new roads, bridges and water supply systems also are
calculate multiple discrete distances from one curve in
currently under construction or being planned and must
the landscape to the next to determine the final vertical
be built to last. Civil engineering technicians will play an
and horizontal lengths and widths of the entire roadway,
increasingly critical role in shoring up America’s current
which requires a firm understanding of measurements,
infrastructure and in building the next generation of
geometry and trigonometric functions of angles. Once
roads, bridges and other public infrastructure.
the technicians compute the individual alignments, they
can place the road’s center line, shoulders and ditches
Surveying the Land
accurately and, ultimately, design the entire highway.
Measurement, Geometry and
Evaluating the water runoff and testing the soil at
Trigonometric Functions
a site are two other vital tasks. If a proposed locale
No bridge, road or structure can be constructed on a site
includes a creek, the civil engineering technicians must
before a team of engineers, engineering technicians and
determine the area and volume of the channel — which
surveyors examines the land and maps features such as
is commonly trapezoidal in shape — and estimate
elevations, utilities and waterways. Understanding how
how much water is present during its peak season. The
these elements interact is critical to determining a
technicians also test the soil composition to calculate
safe and sound location for any new develop-
saturation levels, how much weight the soil can support
ment and requires strong mathemati-
and the rate of erosion. Precise calculations are crucial
cal competence on the part of
to determine the placement of the road and how thick
the surveying team.
the concrete must be to prevent flooding, erosion and
structural weaknesses.

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Mathematics engineers safety
Civil Engineering Technicians in the Military:
Opportunities across the Armed Forces
In addition to the civilians employed as civil engineering
Civil engineering technicians in the military — in job titles
technicians, thousands of officers and enlisted members
such as technical engineer (Army), engineer assistant
within the armed forces work on infrastructure projects.
(Marine Corps) and engineering aide (Navy) — receive
While the Army Corps of Engineers may be the most
training upon enrolling in the services and typically
well-known organization that provides vital engineering
learn many of the required skills on the job but often are
and design management, individuals can hone their civil
expected to have completed algebra, geometry and even
engineering skills across all branches of the military.
trigonometry in high school. These positions provide a
Civil engineering technicians in the armed forces use
clear pathway to advancement because many of these
their knowledge and skills in a variety of ways such as
technicians go on to manage projects and train incoming
building temporary roads and bridges in combat areas,
engineer assistants and equivalent officers. Those who
constructing military bases at home and abroad,
leave the armed forces with civil engineering technology
and managing permanent civilian projects like
training are sought after widely by private firms due to
hydroelectric dams.
their technical and leadership skills.
For more information, see www.todaysmilitary.com/careers.
Ensuring the Soundness
concrete), requiring civil engineering technicians to
of Bridges and Roads
calculate the strength and durability of various materials
both in the aggregate and individually to ensure that no
Physical and Materials Properties,
element of the bridge will be a weak link. The type and
Proportions and Force
ratio of materials involved in designing a bridge depends
Once the routing for the proposed road has been estab-
on a number of factors including its length and width, the
lished, a civil engineering technician’s job has just begun.
amount of weight it needs to sustain, and the tolerance of
Technicians are responsible for another vital task prior to
each material — not to mention the project’s budget.
construction: testing the strength (or load-bearing capac-
ity) of the roadway materials. For example, technicians
Calculating the weight a bridge must sustain involves
calculate the strength of concrete in pounds-force per
taking into account not only the weight of the bridge
square inch by mixing a sample, pouring it into a cylindri-
materials, but also the weights of the vehicles that will
cal mold, curing it and applying pressure until the concrete
be traveling on the road, their rates of speed and how
breaks. Calculating the amount of compression the con-
many are expected to be on the bridge at any given time.
crete can handle before it literally cracks requires a strong
To help with these calculations, technicians often use
understanding of the physics of tension and compression.
trend data and the results of computer-based models
Proportions play a role as well because different concrete
that predict traffic patterns. Throughout the surveying and
mixtures — based on the ratio of water, gravel and sand
engineering processes, the civil engineering technicians
— inevitably will have different load-bearing capacities.
rely on their proficiency with computer-aided design and
geographic information systems (GIS) to design the plans
Bridges, however, can be made of multiple materials,
and share information with other project team members.
such as reinforced concrete (steel re-bars encased in

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Mathematics + Teamwork = Success
Keeping the nation’s infrastructure safe and sound
While these technicians may be responsible for testing
takes a lot of hard work from a number of highly skil ed
the tension and compression limits of the construction
individuals. Civil engineering technicians constantly are
materials used, they also are tasked with ordering
engaged as critical members of teams of engineers,
the right amount. The volume of concrete needed to
technicians, surveyors and equipment operators that
complete a project, for example, is related directly to the
plan, design and develop infrastructure that supplies
calculations the civil engineering technician performs
safe drinking water, protects the environment, and
when determining the concrete’s strength, the soil’s
provides transportation systems that make it possible
properties and the potential water runoff. Not only must
for Americans to get to work safely and on time. At
the civil engineering technicians ensure the accuracy of
every stage of an infrastructure project, strong math
their initial calculations, but they also must work with
and teamwork skil s are instrumental to success.
third-party vendors to keep the project on budget.
When civil engineers and civil engineering technicians
Research gathered by ADP shows that collaboration and
work together to develop a design plan for a road, they
communication skills are important factors for success
upload the design parameters, like the road thickness
both in the workplace and in the college classroom. In
and location of the safety railing, onto a memory card
the planning, design and construction of infrastructure
that links the design to the GIS. Modern construction
projects, civil engineering technicians must apply their
equipment uses GIS data to read those memory cards,
mathematical knowledge continually as contributing
guiding the bulldozer or road grader where to go and
members of a larger team. The breadth of knowledge
providing information about what to do. Civil engineering
and skills that civil engineering technicians need to be
technicians must review and check the calculations
successful in the civilian and military sectors is reflected
constantly and, working with equipment operators,
in the mathematics that students must take in associate
make midcourse adjustments to ensure the road under
degree courses of study or equivalent training programs.
construction reflects the actual design. Without an
Students interested in pursuing the crucial and exciting
understanding of trigonometric geometry on the part of
civil engineering technician career pathway must
civil engineering technicians, neither the design nor its
graduate high school with college- and career-ready
implementation would succeed.
expectations, particularly in mathematics.
Civil engineering technicians must compute mathematical y to solve numerical
problems, they must visualize mathematical y, and they must think mathematical y
“to respond quickly and understand the consequences when errors occur or when
circumstances change. The ability to visualize and think mathematical y can be
far more valuable than the ability to only write formulas and ‘crunch’ numbers.
Technicians must be able to recognize when the results from computations,
measurements or tests just don’t look right.
Dr. David E. Hornbeck, P.E.
Professor Emeritus of Civil Engineering Technology
” Southern Polytechnic State University

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About Achieve
Achieve, Inc., created by the nation’s governors and business leaders, is a bipartisan, non-profit organization that
helps states raise academic standards, improve assessments and strengthen accountability to prepare all young
people for postsecondary education, careers and citizenship.
About the American Diploma Project (ADP) Network
In 2005, Achieve launched the ADP Network — a col aboration of states working together to improve their academic
standards and provide all students with a high school education that meets the needs of today’s workplaces and
universities. The ADP Network members — responsible for educating nearly 85 percent of all our nation’s public
high school students — are committed to taking four college and career readiness action steps:
1. Align high school standards with the demands of college and careers.
2. Require all students to complete a college- and career-ready curriculum to earn a high school diploma.
tions
3. Build college- and career-ready measures into statewide high school assessment systems.
4. Hold high schools and postsecondary institutions accountable for student success.
The world has changed, and high schools must change with it. The ADP Network is leading the charge in
ensuring that all high school students graduate with a degree that works.
KSA-Plus Communica
Visit our Web site for more information about the ADP Network and the ADP benchmarks (www.achieve.org/
ADPbenchmarks) and to view additional “Mathematics at Work” brochures (www.achieve.org/mathatwork).
Copyright © January 2009 Achieve, Inc. All rights reserved.
Achieve, Inc. n 1775 Eye Street NW, Suite 410 n Washington, DC 20006 n www.achieve.org
Editorial assistance and design:

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