Keitaro Matsuoka (keitaro@hackinginstructor.com)

Course Design Best Practices

1. Think “Relevant Simple Intricate.” 2. Visualize “mastery blocks.” 3. Generate comprehensive examples. 4. Assessment. 5. End with lead to next topic.

2

Welcome Message Example

Each instructor should post a welcome message and a short bio to the Student Lounge. The

Student Lounge is an area for students to share personal information, discuss issues not related to

the course, share opinions, and just chat. During the first week, the Student Lounge will be a

busy forum. Students are sharing information and welcoming each other to the course.

In addition to a general welcome, explain to the students in your initial post how to use the

Student Lounge. It's an area for them to relax and communicate on a friendly basis one to

another.

Here's an example of the kind of posting that sets the right tone for the class:

or

Welcome to Winter Quarter 2014.

I am Elle O’Keeffe, your Career Services instructor, and together we will

make this a successful quarter.

I hope everyone had/is having/will have a great Holiday Season. My

daughter and I certainly did.

About me:

I have

a BA in English Literature

an MA in Liberal Studies

a graduate certificate in English

an MBA with concentrations in HR and General Management

I am currently working on my PhD in English: Texts and Technology

I have been learning Chinese (Mandarin) since January 2010.

I started learning French a few months ago--so much easier than Chinese.

I read nonstop. Here are a few of my favorites:

Sarah's Key

The Secret Life of Bees

3

Drive

To Kill a Mockingbird

The Lovely Bones

Freakonomics

The list could go on and on...

Zoe is my 74 pound four-legged baby.

I am excited to work with you this quarter. Please watch for announcements and emails from me

which will include info about:

Learning Goals

Concepts

Live Session Opportunities

Technical Tips and Tricks

Due dates

If you have a question or concern, contact me. If you do not know the procedure for something,

contact me. If you need to brainstorm, contact me.

Elle.okeeffe@rasmussen.edu

Skype: Elle_RCO

Best,

Elle O’Keeffe

Notice that this sets me up as a person with plenty of education and varied interests. Also,

note anyone with a dog, anyone who loves languages, anyone who speaks French or

Chinese, anyone who loves to read, now has something in common with me. Finally, note I

have provided multiple ways to reach me. This sends the message that I WANT to be

contacted, and not just in an emergency. Finally, please note that the images break up the

chunks of text.

On the other hand is the example below:

Hello, I am your instructor, Professor Smith, please post

your introduction to this area along with responding to

other learners' post. Thank you.

This example could benefit from a dose of warmth and engagement on the part of the instructor.

To avoid this mistake, ask yourself:

4

· Did I share my degrees and industry background? Is the intro/bio written in my voice? Is there

info in this message that allows students to connect with me, picture me, see commonalities

between them and me?

Best Practice: Make sure you double-back to the Student Lounge the first week or so, specially

looking for new students who've joined the class late.

5

Course Introduction Example

Welcome to Calculus II!

Have you watched Toy Story? It is a series of movies about toys who pretend to be lifeless

when humans are not around, but who come to life when Andy (the little boy who owns

them) leaves his room. The movies focus on Woody, who is a cowboy doll and his comrade

Buzz Lightyear, an astronaut action figure who is named after Apollo 11 astronaut Buzz

Aldrin. Buzz's favorite catchphrase is "To infinity ... and beyond!"

You may be wondering how Toy Story has anything to do with Calculus II. Well, the two

main topics of Calculus II are integration (which is about finding the area under the curve)

and infinite series. You learned about integration in Calculus I. An infinite series is a sum

of numbers that goes on forever. In Calculus II, we extend the integrations further and also

learn about the series that go "to infinity… and beyond!"

This course will also cover some advanced topics and techniques applied by NASA engineers

who build rockets (see, it is actual rocket science!).

You know you can learn calculus. If you are taking this course, you have passed a course in

Calculus I. So congratulations, and let's get ready to take off!

6

Lecture “Block” Examples

Week Title: Module 09 - Inverse, Exponential, and Logarithm Functions Part 2

Page Title: Logarithmic Functions

Logarithmic Functions

The exponential function answers the question, "what is the number if it is raised to a

power?" A logarithmic (or log) function answers the question, "what is the power that the

number was raised to?"

The logarithmic expression, logc x (read "the log base c of x") has a base c and argument

x. See the Illustration below to get an idea of what log functions look like.

Illustration

What is x in the following equations?

𝑙𝑜𝑔381 = 𝑥 3𝑥 = 81, so 𝑥 = 4. 𝑙𝑜𝑔2𝑥 = −5 2−5 = 𝑥, so 𝑥 =

1

32.

Natural and Common Logs

A logarithm's base can be any positive number (not 1). There are two bases that you will

encounter most often. They are Base 10 and Base e.

A log of base 10 is called a common log. Typically, if the base is not specified in a log

expression, it is understood to be 10. For example, log 100 = 2, since 102 = 100.

A log with base e is called the natural log. It is so common that it has its own notation: ln x (natural log of x). So ln 𝑥 = 𝑙𝑜𝑔𝑒𝑥.

Graphs of Logarithms

All log graphs have essentially the same shape with a few important characteristics. Here is a graph of 𝑓(𝑥) = 𝑙𝑜𝑔2𝑥.

Characteristics:

1. There are no negative x values.

2. The y-axis is the vertical asymptote.

3. The graph contains the point (1, 0). Try plotting different log functions to verify this.

2 1 1 2 3

4

3

2

1

1

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Logarithmic Properties

Logarithmic functions possess three major properties. You should be aware of these

properties to help you expand and compact log expressions.

1. Property 1: log 𝑎 + log 𝑏 = log(𝑎 ∙ 𝑏). This means that the log of a product is equal to

the sum of the logs. Example: 𝑙𝑜𝑔 25 + log 2 = 𝑙𝑜𝑔 50 = log 2 ∙ 25

2. Property 2: log 𝑎 − log 𝑏 = log𝑎

𝑏 . This means that the difference of two logs with the

same base is equal to their quotient (division). Example: log 𝑥 − log 𝑦 = 𝑙𝑜𝑔𝑥

𝑦

3. Property 3: log 𝑥𝑎 = 𝑎 log 𝑥. Example: 𝑙𝑜𝑔352 = 2 × 𝑙𝑜𝑔35. The exponent jumps to the

front as a multiplier.

Just remember these logs have nothing to do with the trees!

Week Title: Module 09 - Inverse, Exponential, and Logarithm Functions Part 2

Page Title: Growth and Decay Problems

Exponential Growth and Decay

In reality, it is difficult to truly experience exponential growth, at least over a long period of

time. The reason is that exponential growth typically results in really big, unrealistic

numbers quickly. For this reason, most exponential growth problems are about three major

kinds: continuously compounded interest (seen in the previous module), exponential

growth, and exponential decay. We go over the latter two here.

A common formula for all exponential growth and decay is 𝑃(𝑡) = 𝑁𝑒𝑘𝑡, where P is a function

of time t, and N is the original quantity, and k is the rate of change.

Exponential Growth

If a quantity increases at a rate which is proportional to the size of the quantity itself, it

exhibits exponential growth.

Illustration

A crime scene investigator (CSI) in Miami collects evidence from a corpse. He notes nine

bacterial colonies at 8 a.m. Monday morning. On Tuesday afternoon at 4 p.m., he notices

that the colonies have grown to 113. Assuming that the growth is exponential, how many

colonies will he have on Friday afternoon at 5 p.m. when he needs to present the evidence

to the jury?

8

The time between 8 a.m. Monday to 4 p.m. Tuesday is 32 hours. Plugging in this

information to the growth formula, you get:

9 𝑒𝑘×32 = 113

𝑒32𝑘 =113

9

Take the natural log of both sides:

ln (𝑒32𝑘) = ln (113

9)

32𝑘 = ln (113

9)

𝑘 =ln

1139

32≈ 0.079

Put back the k value into the formula:

9 𝑒0.079×105 = 36034

About 36034 colonies will be present on Friday at 5 p.m.

To do the calculation in Excel, type in:

=9*EXP(0.079*105)

Exponential Decay and Half-Life

Half-Life is the amount of time it takes for a quantity to decay exponentially to become half

of its original quantity.

Illustration

Assume that 800 g of Carbon 14 (also known as radiocarbon, which exists in all living plants

and animals) are initially present. Only 400 g remained after 2.5 years. How much will

remain after 4 years?

Plug in the information into the formula:

800 𝑒𝑘×2.5 = 400

𝑒2.5𝑘 =400

800=

1

2

𝑘 =ln

12

2.5≈ −0.277

Using Excel (=800*EXP(-0.277*4)), you see that about 264 g remain.

9

Calculations Example

xi xi - ( xi - )2

29 39.6 -10.6 112.36

31 39.6 -8.6 73.96

35 39.6 -4.6 21.16

39 39.6 -0.6 0.36

39 39.6 -0.6 0.36

40 39.6 0.4 0.16

43 39.6 3.4 11.56

44 39.6 4.4 19.36

44 39.6 4.4 19.36

52 39.6 12.4 153.76

Sum: 412.4

s2 = 45.8222

Mean 39.6 s = 6.76921

Standard

Deviation 6.769211

Variance 45.82222

To calculate the standard deviation and variance:1) List all the data values .2) Select the cell for the output.3) Use the STDEV or VAR function, as shown below.

To calculate the variance manually:1) List all the data values.2) List the mean of all values.3) Take the difference between the two.4) Square the differences.5) Sum the squares of the differences.6) Divide by (n - 1), which is 9 in this case.7) Take the square root of the variance to get the standard deviation.

You notice that manual calculations and Excel calculations, say for variance, match.

10

Fun and Interactive Discussion Example

Week Title: Module 08 - Inverse, Exponential, and Logarithm Functions Part 1

Page Title: Module 08 Discussion - Cryptography Page Type: Discussion Forum

Assume you are a spy. You need to send an encrypted message to MI6. Your task is to use

a one-to-one function to encode your message using the table below.

A B C D E F G H I J K L M

1 2 3 4 5 6 7 8 9 10 11 12 13

N O P Q R S T U V W X Y Z

14 15 16 17 18 19 20 21 22 23 24 25 26

You decide to use a one-to-one function, 𝑓(𝑥) = 3𝑥 + 1, to encode the message. Agents at

MI6 will use its inverse function to decode the message.

To exchange the message "BE VERY CAREFUL", you will send:

7 16 67 16 55 76 10 4 55 16 19 64 37 because B corresponds to 2 and 𝑓(2) = 7. E corresponds to 5 and 𝑓(5) = 16. Agents at MI6

will use the inverse function 𝑓−1(𝑥) =1

3𝑥 −

1

3 to decode your message. For example, 𝑓−1(7) =

2, which corresponds to B.

Your mission, should you choose to accept it, is to:

1) define your own one-to-one function (initial post), and

2) send an encoded message back to MI6 (initial post), and

3) decode your fellow agent's message to you (response post to another student).

This assignment will self-destruct in 5 seconds!

Please make your initial post by midweek, and respond to at least one other student's post

by the end of the week. Please check the Course Calendar for specific due dates.

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Reflection (dev math) Discussion Example

Reflection Discussion – Week 1 Expectations

For this discussion, please take a few minutes to reflect on your impressions and expectations for this class.

Any feelings/impressions are acceptable (as long as they are honest). Do not feel you need

to be bubbly and positive (there is no expectation that you are excited and thrilled to be

taking a math class). Since this class is partly online, we will rely on the discussion boards

to discuss (and hopefully alleviate) apprehensions, fears, excitement and hopes you may

have with the class. Please use the reply post to encourage and assist your fellow

classmates.