technology and engineeringTEACHER - Unionville High School ...

VOLUME 72 ISSUE 5
technology and
engineering TEACHER
February 2013
COLUMBUS
CONFERENCE
EXHIBITORS
stem
BRINGING
STEM TO LIFE
urban
education
INTEGRATIVE
STEM ED AT
VIRGINIA TECH

BRINGING STEM TO LIFE
BRINGING
Our high school students have been warned repeatedly that they must prepare
stemTO LIFE
BY MIKE BERKEIHISER AND DORI RAY
Have you been looking for quality STEM activities for your technology and engineering
program? Would you like to expose a wider variety of students to your curriculum? Do
you strive to involve your Technology and Engineering Education Department in inter-
disciplinary activities with other academic subject areas?
The interdisciplinary approach that STEM projects inspire in
both teachers and students “brings to light a larger picture that
been shown to increase undergraduate persistence in STEM”
(diverseeducation.com).
Our high school students have been warned
repeatedly that they must prepare themselves
exist. These warnings have resulted in an
increased emphasis on cooperative problem
solving, innovative solution writing, and technological
skill acquisition across the curricula of
secondary schools. By pairing mathematics and
technology classes together in unique ways,
jobs may demand (Figure 1).
At Unionville High School in Kennett Square,
PA, calculus teacher Dori Ray requires her
advanced placement calculus students to build
three-dimensional solids of known cross-section
out of layers of hand-cut foam. The process
is very similar to the process technology and
engineering teachers have used for years to make 3-D models
from sheet goods using laser cutters, vinyl sign cutters, CNC
routers, and manual processes. Each slice of a thin material is
the result is a functional 3-D model (Figure 2).
Figure 1: Engineering CAD and AP Calculus students draw a parabola using AutoCAD.
February 2013 technology and engineering teacher 21

BRINGING STEM TO LIFE
Figure 2:
This year, Ms. Ray’s students completed their models by hand
using graphing calculators, spreadsheets, scissors, and glue.
They converted coordinate units to centimeters, determined
functions, and painstakingly cut each shape to build their mod-
technology and engineering teacher at UHS. The two teachers
then created a new and exciting stage of the project in which the
calculus students could communicate their sophisticated scaling,
slicing, and cutting needs to Mr. Berkeihiser’s engineering CAD
drafting students who would expand the task to one involving
AutoCAD and a laser cutter (Figure 3). Calculus students and
Figure 3:
22 technology and engineering teacher February 2013
engineering CAD students were paired into teams so they could
better use each student’s unique background and skills. A few
of Mr. Berkeihiser’s current and past engineering CAD students
were also in Ms. Ray’s calculus class and proved tremendously
valuable in translating the task between calculus terminology
and CAD terminology and back to calculus terms when it came
time to evaluate the volumes of the resulting models.
interrupted by a few absences which, fortuitously, provided Ms.
Ray with an additional learning opportunity. Because some
calculus students were absent, there were extra engineering
CAD students without partners, and Ms. Ray, knowing that a
solid model of a known cross section produces different looking
solids depending on the axes of the slices’ orientations, wondered
if the extra students could be added to the existing groups
to complete a second model with slices featuring these alternate
orientations. No sooner had the question been posed than the
engineering CAD students jumped at the chance to undertake
horizontally and vertically sliced models, are many times more
valuable as teaching tools in AP Calculus because they provide
powerful visual aids in explaining an abstract mathematical
concept.
to use as the base region for the solid. Calculus students were
advised to pay close attention
at this step to accommodate
the 3mm thickness of the
masonite they would be using
to build their models since their
40-50 slices. Students were
then allowed to pick the shape
of the cross-sectional slice
of their solid. Their choices
included an equilateral triangle,
a semicircle, an isosceles right
triangle, and a rectangle. They
then named the formula that is
used to calculate the area of
that shape.
At this point, calculus students
communicated the size and
shape of the ellipse that they

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60.0000 64.9923 69.3974 73.3212 76.8375 80.0000 82.8493 85.4166 87.7268 89.7998 91.6515 93.2952 94.7418 96.0000 96.5386 97.9796 98.7117 98.9945 99.6550 99.9200 100.0000
Figure 4: Sample student drawing. Figure 5: Laser cut triangle pieces ready for assembly.
the CAD students for their stage of the project. Since AutoCAD
were forced to carefully use their language arts skills to assure
that they were communicating clearly with each other.
Once base areas were conveyed, the calculus students sat back
and watched in amazement as the engineering students generated
the ellipse on the screen, deftly sliced it into 40 pieces, and
began measuring key dimensions of those slices with the simple
click of a button. After these measurements were labeled on the
AutoCAD diagram, the engineering students quickly generated
another drawing that held all
of the individual slices that
would make up the threedimensional
solids (Figure 4).
After having completed all of
these tasks by hand during
AP calculus students raved
about the capabilities of the
computers as well as their
engineering partners who
did the work so quickly. One
student said, “Using the design
students’ experience with the
equipment and software, we
were able to quickly and easily
assemble an accurately sliced
model.” It was wonderful to see
engineering students tutoring
calculus students so that they
too could try using the technol-
sent to the laser-cutter so that all pieces would be cut out (Figure
5) and ready for assembly at our next meeting. Engineering
students even developed another component in their diagrams
of the individual slices that included a tiny groove in each slice
that would allow students to line pieces up easily once they were
ready to assemble and glue their models (Figure 6).
The activities described above allowed the AP calculus students
to be exposed to engineering applications of a classic calculus
problem. Engineering CAD students were able to get a glimpse
Figure 6: Students assembling a model using their groove in the bottom of the shape for alignment.
February 2013 technology and engineering teacher 23

BRINGING STEM TO LIFE
of the mathematics at work behind the scenes of their software
environment. Perhaps most importantly, both the students and
the teachers were able to communicate and problem-solve in an
These models will be useful instructional aids in our Academic
and AP level calculus classrooms when students investigate the
volumes of solids of known cross-sections. More importantly,
however, we are keeping the STEM ideals alive for our learners.
design students greatly changed my experience of building the
model by allowing us to utilize technology to create a more sophisticated,
intricate product. I now have a clearer understanding
of the relationship between engineering and calculus after
working with the design students.”
ties
that are spurring unprecedented cuts for education. After
completing this unique project, Ms. Ray and Mr. Berkeihiser and
their students can continue to complement each others’ curricular
knowledge and experiences in ways that provide cuttingedge,
cross-curricular academic experiences without adding
24 technology and engineering teacher February 2013
REFERENCE
Figure 7:
AP Calculus student
works with an Engineering
CAD student.
Cox, Matthews, and Associates, Inc. (2012). President Obama’s
2012 commitment to STEM. Diverse: Issues In Higher
Education. Retrieved from http://diverseeducation.com/blogpost/333/president-obama-s-2012-commitment-to-stem.
html
Mike Berkeihiser is a technology and engineering
teacher at Unionville-Chadds Ford
School District in Kennett Square, PA. He can
be reached via email at mberkeihiser@ucfsd.
org.
Dori Ray is a calculus teacher at Unionville-
Chadds Ford School District in Kennett
Square, PA.