Good Connections: Connecting Technical Drawing and Mathematics Concepts by David A. Janosz, Jr. - June 2002
Technical Drawing and Computer Aided Drafting and Design (CADD) require knowledge of mathematical concepts in order to achieve student success.
In terms of CADD instruction, it would be very helpful for the CADD teacher to understand and be able to explain appropriate mathematical concepts using the same terminology as their colleagues who teach mathematics. Consistency of this sort will also be helpful to students as the attempt to master both technical drawing techniques as well as geometric, algebraic, and trigonometric concepts.
Another benefit of making this connection is that students will be able to apply mathematical concepts to practical design situations. Not only will they be able to apply these concepts; they also will be applying them in a visual context. This is sure to help those learners who have difficulty grasping mathematical concepts without a visual/spatial element.
Below listed are some common concepts between these subject areas. The connections between these concepts are explained in further detail below.
The Cartesian Coordinate System
The coordinate system used in CADD is the same system used to demonstrate several mathematical concepts. Students could engage in any number of operations to display knowledge of CADD and mathematics at the same time. Mathematics concepts that may be explored include plotting slope/intercept problems and plotting points and fitting lines to the points.
Scale and Proportion
The concept of scale is very important to an architect, engineer, or draftsperson since many of the CADD drawings they produce will be drawn and/or plotted to a smaller or larger scale. Students must be able to regularly apply this concept as they read dimensions from a plotted drawing.
Measurement (Linear)
Students drawing dimensioned orthographic objects must become aware of several options for units of measurement. Students may draw using base units, millimeters, or feet and inches. Students become expert at reading the divisions of an inch and also converting fractions to decimals as is required in base units drawing. For example, if a student is drawing an object in base decimal units, they must be able to convert the fraction 3/8 to .375 and so on.
Measurement (Angular)
From the beginning stages of the CADD course in which students draw isometric objects, students become aware of angular measurement. Students must realize early in the course that two-dimensional shapes are drawn both by hand and by computer upon a 360-degree plane. During the more advanced levels of CADD, students may also begin to utilize more precise forms of measuring angles. They may use degrees, minutes, and seconds to measure angles for a site plan drawing that would be used in architecture.
Triangle Geometry
The 30-60-90 triangle is used quite often during the initial stages of the CADD course as students use it to measure angles in their hand drawn sketches. The Pythagorean Theorem and sine, cosine, and tangent rules may also be applied and easily proven as the students work in CADD. As an example of a connecting activity, students could draw a right triangle on the CADD screen, then use formulas to calculate the angles. They could then use the software to verify their calculations.
Geometric Shapes
A CADD system makes it easy for students to draw complex geometric shapes. A student may draw a triangle, rectangle, or rhombus on screen and verify its area using the software. As another example, students may draw an octagon to other multi-sided object on screen and verify its inner or outer angles.
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