lecture with power (point) teaching math in the 21 st century dr. steve armstrong letourneau...
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Lecture with Power(point)
Teaching Mathin the 21st Century
Dr. Steve ArmstrongLeTourneau University
Longview, TX
www.letu.edu/people/stevearmstrong
Lesson Plans and Lectures
• Written on a scrap of paper
• Ink on your hands• Chalk on your hands
Problems
• "By definition this is an isosceles triangle."
• "Then a miracle occurs"
• "Let's all write this down"
Advantages of Presentation Software
• It looks like an isoscelestriangle
• No more, "What is the second line?"2 2 2
2 2
2 2 21
2 cos
2 cos
cos2
c a b a b C
c a b a b C
or
c a bC
a b
A
B
C
a
b
c
Advantages of Presentation Software
• Animation• Consider the position of an object as a
function of time• The x coordinate is a function of time
x = f(t)• The y coordinate is a function of time
y = g(t)
••time
0
Advantages of Presentation Software
• Animation• Why is the area of the yellow rectangle
at the end =
a bx
( ) ( )x f b f a
Advantages of Presentation Software
• Have slides, will lecture
• "I'm ready for you to teach me what I missed when I was absent yesterday"
NaysayersEdward Tufte, in Wired Article 11/9/2003
• PowerPoint is evil and corrupts communication
• Students who use PowerPoint would do better to learn to write sentences and paragraphs
• Multiple slides stack information in time – results in loss of meaning, perceived relationships
Agree or disagree?
Agree or disagree?
Nay SayersAccording to Tufte this is a
"good" slide.
According to Tufte this is a "good" slide.
"Bad" slides."Bad" slides.
Agree or disagree?
Agree or disagree?
ResponseDoug Johnson, 11/1/2005 Column from Education
World• PowerPoint doesn't bore people:
people bore people.• Choosing the wrong tool for the job is
not the tool's fault.• The same hammer can both break
windows and build cathedrals.
• Good visuals can be exceptionally powerful – many of us are visual learners
Agree or disagree?
Agree or disagree?
Response
• Our purposes are …• Communicate concepts• Attract students' attention, interest• Use text, formulas, graphics, tables
• Our purposes do not include ...• "Memorize these slides by Tuesday"• "Follow along in your book"• "Read together with me"
Length on land
Length underwater Cost on land
Cost underwater Total Cost
0 2353.72 $0.00 $35,305.81 $35,305.81
50 2304.89 $500.00 $34,573.29 $35,073.29
100 2256.10 $1,000.00 $33,841.54 $34,841.54
150 2207.37 $1,500.00 $33,110.61 $34,610.61
200 2158.70 $2,000.00 $32,380.55 $34,380.55
2 4
2
b b ac
a
2 4
2
b b ac
a
Creating a Lesson
• Make the textbookwriters earn theirkeep
• What do theyneed to see andhear?• Story board your lesson
I bet I could use my
notebook of lectures
I bet I could use my
notebook of lectures
Creating a Lesson
• Use a "hook"
I think I see the "rule."
Creating a Lesson
• Let's practice
The Mean Value TheoremLesson 4.2
I wonder how mean this
theorem really is?
Math can be a laughing
matter!
Math can be a laughing
matter!
This is Really Mean
Creating a Lesson
• Gone are the days of hand written formulas
• This one looksisosceles also
2 4
2
b b acx
a
Creating a Lesson
• Where to lay cable for minimum cost • A famous min-max problem in
calculus• Link to Excel spreadsheets for
illustrations
Creating a Lesson
• A great host of information on the web
• Google it!
Accompanying Handout• Student
participation• Not too little• Not too much
• Like Goldilocks, just right
Slopes and Equations of Lines
Lesson 1.1
The Plot Thickens
We plot ordered pairs (x-coord, y-coord)
Where would we plot (4, -2)?
• (2, 1)
•(-1, -3)
• (-5, 1)
Line 'em Up
A line is a collection of points• When the x-coordinate is zero it intercepts the
y-axis
• When the y-coordinate is zero, it intercepts the x-axis
x-intercept
y-intercept
Slope of a Line
Represents the "steepness" of a line• Measured by the change in the y-value divided
by the change in the x-value1 2
1 2
y yy
x x x
•(-3, 2)
(3, 0)
2 0 2 1
3 3 6 3
Equations of a Line
Slope-Intercept Form
Point-Slope Form
y m x b
1 1y y m x x
Horizontal, Vertical Lines
Horizontal linesy = 12
• Note: slope is 0
Vertical linesx = 7
• Note: slope is infinite, or "no slope"
Graphing Lines on the TI Calculator
We wish to graph the equation
Go to the Y= screen – use ♦W or ♦F1
Enter the function on the entry line
It appears in thelist
3 4y x
Graphing Lines on the TI Calculator
Now specify the standard zoom F2 and 6
Function will graph on axes
Parallel and Perpendicular Lines
Parallel lines have the same slope
Perpendicular lines haveslopes that are negativereciprocals
Graph these to verify, use Zoom-Square
27
32
53
y x
y x
32
2y x
Try It Out
Find the equation of a line through (2, -5) and parallel to y = 2x + 4
Find the equation of a line with x-intercept of -2/3 and perpendicular to 2x – 3y = 5
A business has sales of $27,000 in its 2nd year, $63,000 in 5th year. Let y be the sales for the xth year. Assume the data can be approximated by a st. line. Determine an equation for the sales• Use your answer to find out how many hears until
sales surpass $100,000
Assignment
Lesson 1.1
Page 15
Exercises 1 – 59 EOO, 61, 71, 75
Tips
1. Use it as a tool to make math compelling.
2. Keep it simple• Transitions• Object appearances
3. Minimize details in slides. 4. Don't parrot PowerPoint. 5. Don't talk on top of your slides.
Don't parrot PowerPoint
Don't parrot PowerPoint
PowerPoint's lure is the capacity to convey ideas and support a speaker's remarks in a concise manner. That's hard to do through a haze of numbers and statistics. For the most part, most effective PowerPoint displays don't overwhelm viewers with too many figures and numbers. Instead, leave those for a later, more thorough digestion in handouts distributed at presentation's end. If you want to emphasize a statistic in PowerPoint, consider using a graphic or image to convey the point. "For instance, when I once was talking about the prevalence of Alzheimer's patients, I used a photograph of an old woman rather than just throwing up a number on the screen," Kerr says.
PowerPoint's lure is the capacity to convey ideas and support a speaker's remarks in a concise manner. That's hard to do through a haze of numbers and statistics. For the most part, most effective PowerPoint displays don't overwhelm viewers with too many figures and numbers. Instead, leave those for a later, more thorough digestion in handouts distributed at presentation's end. If you want to emphasize a statistic in PowerPoint, consider using a graphic or image to convey the point. "For instance, when I once was talking about the prevalence of Alzheimer's patients, I used a photograph of an old woman rather than just throwing up a number on the screen," Kerr says.
Tips
6. Give it a rest.
Tips
6. Give it a rest. 7. Use vibrant colors. 8. Import other images and graphics. 9. Distribute handouts10. Edit ruthlessly febore presenting
Lecture with Power(point)
Teaching Mathin the 21st Century
Dr. Steve ArmstrongLeTourneau University
Longview, TX
www.letu.edu/people/stevearmstrong
Lecture with Power(point)
Teaching Mathin the 21st Century
Dr. Steve ArmstrongLeTourneau University
Longview, TX
www.letu.edu/people/stevearmstrong