Table 1 (Continued)Comparison of Professional Competencies Required for Engineers **and** **Technology** TeachersCompetencyContentKnowledgePedagogicalKnowledgeApplication ofKnowledge **and**SkillsEngineersABET Criteria For AccreditingEngineering **Technology**Programs (**2008**)An appropriate mastery of the knowledge,techniques, skills, **and** modern tools oftheir disciplines.Content Proficiency. Engineeringprograms require proficiency in statics,strength of materials, thermodynamics,fluid mechanics, **and** electric circuits.Mathematics **and** Science. Programsrequire proficiency in mathematics throughdifferential equations, probability **and**statistics, calculus-based physics, **and**general chemistry.Engineering topics. One-**and**-one-halfyears of engineering topics consistingof engineering sciences **and** engineeringdesign appropriate to the field of study.Design. Students must engage in a majordesign experience based on the knowledge**and** skills acquired in earlier course work**and** incorporating appropriate engineeringst**and**ards **and** multiple realistic constraints.An ability to use the techniques, skills, **and**modern engineering tools necessary forengineering practice.**Technology** TeachersNCATE/ITEA/CTTE ProgramSt**and**ardsPrograms for the Preparation of**Technology** Education Teachers (2003)Develop an underst**and**ing of the Designed World.Subjects. Areas of study in the DesignedWorld include medical, agricultural **and**related biotechnologies, energy **and** power,information **and** communication, transportation,manufacturing, **and** construction technologies.An ability to analyze, select, use, **and** effectivelyimprove technologies in Designed-Worldcontexts.Design, implement, **and** evaluate curricula basedupon St**and**ards for Technological Literacy.Underst**and** students as learners, **and** howcommonality **and** diversity affect learning.Use a variety of effective teaching practices thatenhance **and** extend the learning of technology.Design, create, **and** manage learning environmentsthat promote technological literacy.Follow safe practices **and** procedures in the use oftools **and** equipment.Develop abilities for a technological world.30 • The **Technology** Teacher • **No**vember **2008**

When it comes down to it, isn’t the level of rigor (suchas with mathematics; i.e., calculus) one of the keycomponents that separates the teaching of technologyfrom the teaching of engineering due to the differences inthe level of reasoning that takes place?You’re exactly right about the mathematics. **Technology**teachers don’t take very much mathematics or science asundergraduates. But there is a real opportunity for ourteachers to make a real contribution to core disciplinaryknowledge, particularly in mathematics.Because mathematics is often taught in an algorithmic way,students question its value; **and** it’s true that some of themathematics that is required of students, particularly atthe middle level, is not easily related to grade-appropriatecontexts in other subjects. Some math, however, that isdifficult for students **and** occurs frequently on st**and**ardizedassessments can indeed be contextualized within atechnology education program. And it doesn’t rise to thelevel of calculus. It’s algebra **and** geometry **and** numbersense; ratio **and** proportion **and** scale. It’s a matter of ourteachers first knowing what math kids are responsiblefor, **and** second, knowing how to teach it. I’ll give youan example. A math assessment item that kids have realdifficulty with is this one:“Solve multistep equations by combining like terms, usingthe distributive property, or moving variables to one side ofthe equation.”**No**te: The distributive property is an algebraic propertythat is used when you multiply terms within parenthesesby a term outside the parentheses. As an example, 4(5 +6) = 20 + 24 = 44 (the 4 is distributed across the terms inthe parentheses). This math concept appears frequently onst**and**ardized tests.OK, say the kids are designing an emergency shelter forvictims of an air crash on a snowy mountain top wherea cargo plane was carrying materials to be delivered to ahome center distribution facility, **and** these materials arenow strewn around the mountain. Makes for a pretty gooddesign problem if the kids are the four- or five-personcrew that survives **and** they have to build a shelter that willsustain them until a rescue team (that they radioed for help)is able to reach them. If the shelter must be heated by bodytemperature **and** an external heat source when the outsidetemperature is say, 25 o Fahrenheit, we have a heat-flowproblem that can be modeled by a simple algebraic equation.Once the kids propose a design, they have to determine iftheir proposed shelter would provide an inside temperaturethat allows the inhabitants to be comfortable, or if theywill need to make changes to their design. Guess what:The formula for heat flow involves a simple (eighth-gradelevel) algebraic equation that specifically requires the kidsto solve multistep equations by combining like terms, usingthe distributive property, or moving variables to one sideof the equation. The formula is q = kA (T i- T o)/s (this is asimplified formula to find conductive heat flow) whereq = heat flow (BTU/hour)k = thermal conductivity (BTU/hour-ft-deg F)A = area of surface through which heat is conducted(Square Feet)s = thickness of insulation material (Feet)T i= Inside Temperature (Degrees F)T o= Outside Temperature (Degrees F)It’s not a difficult problem. It’s simple algebra, but it does agreat job of contextualizing a problem that causes kids a lotof difficulty. Our teachers need to be aware of the problemskids are facing, **and** how to present these problems in anengaging context. We admit that it’s not trivial, but it’scertainly within the capability of our teachers, particularly ifthey team up with a math colleague.Kids also have a lot of difficulty with ratio **and** proportion.We’ve developed an activity where kids design theirown bedroom **and** have to do math related to ratio **and**proportion **and** scale. It’s in context. Kids underst**and** thereason why they have to do the math. The math works in theservice of their design.Is the technology teaching profession capable of raising itslevel of instruction to address the rigor that you suggest isneeded?We believe so, but the key is a change in the undergraduaterequirements. We’ve done a survey of 19 institutionsthat prepare technology teachers at the undergraduatelevel. Most require only one mathematics course of theirfuture technology teachers, **and** sometimes the math is ashop math course without very much rigor. A couple ofschools require two courses (see Table 2). Undergraduaterequirements must change if our teachers are going toaddress any “engineering” content. It destroys our credibilitywhen we claim to be teaching engineering-related materialwhile our teachers have such a poor grounding in math.We can do only so much with in-service professionaldevelopment. It’s treating the wound, not the cause. Our31 • The **Technology** Teacher • **No**vember **2008**