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Louisiana Tech University College of Engineering and Science. Connecting Mathematics with Engineering and the Sciences (Chautauqua workshop). Bernd S. W. Schröder Program of Mathematics and Statistics. College of Engineering and Science.

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College of Engineering and Science

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College of engineering and science

Louisiana Tech University

College of Engineering and Science

Connecting Mathematics with Engineering and the Sciences(Chautauqua workshop)

Bernd S. W. Schröder

Program of Mathematics

and Statistics

College of Engineering and Science


Why connect mathematics with engineering and the sciences

Why connect mathematics with engineering and the sciences?

  • Who are you?

  • Why are you here?

  • (Find people with similar interests.)

College of Engineering and Science


It s the right thing to do

It’s the Right Thing to Do

  • Long standing need for people (including mathematicians/math majors) who can apply mathematics in context.

  • George report

  • Carnegie Initiative papers

  • CUPM recommendations

  • Cognitive research (BSVR)

  • It’s also a lot of fun.

College of Engineering and Science


Most importantly it s why we do mathematics

Most importantly, it’s why we do mathematics.

College of Engineering and Science


Most importantly it s why we do mathematics1

(and back)

but do we start with full generality?

Most importantly, it’s why we do mathematics.

College of Engineering and Science


Best resource your own interests and ideas if they fit

Best resource: Your own interests and ideas, if they fit.

  • The density altitude of air gives the altitude at which dry air (0% humidity) at a temperature of 59F and a standard pressure of 29.92inch-Hg (the International Standard Atmosphere) has the same oxygen content as the air being evaluated. A one degree increase in temperature increases the density altitude of air by 100ft. A 10% change in humidity increases the density altitude of air by 100ft. A 0.01inch-Hg drop in pressure increases the density altitude of air by 100ft.

  • Determine your density altitude if the temperature is 80F with a pressure of 29.90inch Hg and 30\% humidity.

  • Determine your density altitude if the temperature is 100F with a pressure of 29.85inch Hg and 70% humidity.

College of Engineering and Science


Does this problem work for someone

Does this problem work for someone

  • Who is not a drag racer?

  • Who is not a pilot?

  • Who was not “at the race that day”?

  • Who does not live in Louisiana?

  • Does it matter? (It’s virtually impossible to catch everyone.)

  • Would a story around the whole thing help?

College of Engineering and Science


Homework

Homework

  • Think about similar problems/stories/connections that you might be able to easily weave into your class or which you have already used in class.

  • Do you have any right away?

  • We’ll talk about these kinds of examples tomorrow.

College of Engineering and Science


What we must do

What we “must do.”

  • Activity

College of Engineering and Science


What do our students really need

What do our students really need?

  • Content is most effective when considered relevant

  • This can be achieved by providing context

  • Content can be reordered (dependency chart)

  • Technology, not “if?” but “how?”

  • Time is limited

  • Ask hard questions: What is more important: Solid vector analysis or convergence tests for series?

  • Do not sacrifice your identity in the process.

College of Engineering and Science


College of engineering and science

math 240 3

math 241 3

math 2423

Precalc algebra & trig, single

variable differential calculus

Single variable differential

calculus

Integral calculus, intro

differential equations

engr 120 2

engr 121 2

engr 122 2

Problem solving, data

analysis, team skills, statistics

Statics, strengths, report

writing, sketching, design

Circuits, engr economics,

MathCAD, design project

chem 100 2

chem 101 2

phys 201 3

Engineering chemistry

Engineering chemistry

Mechanics

Engineering Fundamentals

Design

Teamwork

Computer Skills

Engineering

Class

Communication Skills

Laboratory Experiences

2 classes/labs (2 hrs each) per week

Big Picture: Integrated Courses

Freshman Year

fall

winter

spring

Plus 1 additional class -- History, English, Art, ...


College of engineering and science

math 243 3

math 244 3

math 2453

Basic statistics, multivariable

integral calculus

Multivariable differential

calculus, vector analysis

Sequences, series, differential

equations

engr 220 3

engr 221 3

engr 222 3

Statics and strengths

EE applications and circuits

Thermodynamics

memt 201 2

physics 202 3

Engineering materials

Electric and magnetic fields,

optics

Engineering Fundamentals

Design

Teamwork

Statistics & Engr Economics

Engineering

Class

Communication Skills

Laboratory Experiences

3 hours lab & 2.5 hours lecture per week

Big Picture: Integrated Courses

Sophomore Year

fall

winter

spring

Plus 1 additional class -- History, English, Art, ...


Statistics qualitative evaluation and anecdotes

Statistics, Qualitative Evaluation and Anecdotes

  • Statistics: Integrated students performed better than non-integrated peers.

  • Focus group: Female students’ performance was positively affected by the availability of peers. “Lagged” students still quite mature.

  • Private conversation: “I slept through the first half of my fields class and still made an A because you got me ready.” (B/C student)

  • Positive feedback from ENGR (FE, grade analysis)

College of Engineering and Science


Challenges

Challenges

  • Facilities

  • Time

  • Materials

  • Diversity of learning styles

  • Interface with other disciplines

  • “This is hard.” (Faculty and students.)

  • “This is not how we used to do things.” (“This is how I would have liked it to be done.”)

  • Plus all the other things we already complain about ;)

College of Engineering and Science


Guide to successful implementation

“Guide” to Successful Implementation

  • Every institution is different.

  • “Change agents’ ” buy-in is necessary.

  • Admin. support is necessary (“small” is o.k.).

  • Money helps, attitude succeeds.

  • Systemic adjustments persist.

  • Side remarks can help (“When … it clicked.”)

  • Student apprehensions (greener grass on the other side), analyze your clientele

  • Challenges make people think.

  • Self-esteem works best when it is earned.

College of Engineering and Science


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