Lecture with Power (point) Teaching Math in the 21 st Century Dr. Steve Armstrong LeTourneau...

Lecture with Power(point)

Teaching Mathin the 21st Century

Dr. Steve ArmstrongLeTourneau University

Longview, TX

www.letu.edu/people/stevearmstrong

SteveArmstrong@letu.edu

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

SteveArmstrong@letu.edu

Lecture with Power(point)

Teaching Mathin the 21st Century

Dr. Steve ArmstrongLeTourneau University

Longview, TX

www.letu.edu/people/stevearmstrong

SteveArmstrong@letu.edu