Mathematics Online: A Success Story

Margie Dunn, EdD

Excelsior College

mdunn@excelsior.edu

Excelsior College

Online institution Private, not-for-profit Open-admissions A focus on the adult learner

Average age is 39 Online offers accessibility and flexibility --

especially valuable for the adult learner

Gen Ed requirement : Math

MAT*112 Elementary Algebra

Saw a need to upgrade standards

…. But to what?

Intermediate Algebra?

Adult students: what’s the goal?

MAT*101 Mathematics for Everyday Life

“The vast majority (typically 95%) of non-STEM students will never take another college mathematics course after completing their core requirements. Given this fact, … the focus of [our] approach is less on formal calculation – though some is certainly required – and more on teaching students how to think critically with numerical or mathematical information.”

Bennett, J. & Briggs, W. (2011). Using and Understanding Mathematics: A Quantitative Approach 5th Edition (pp. xi-xii). Pearson Education, Inc.

MAT*101 Mathematics for Everyday Life

Not remedial Unit conversions Financial mathematics (interest, savings,

retirement planning, loans, mortgages) Exponential growth and logarithm scales Mathematics in the arts and nature Statistical reasoning Understanding uncertainty in diagnostic

testing

Four-pronged approach

1) Traditional math homework via MyMathLab

2) Traditional quizzes within MyMathLab

3) Work in groups of 5-6 within Discussion Boards on an extended problem

4) Each student submits their own solution to a problem similar to the Discussion Board extended problem.

Best Practices

Math Education – Extended problems

Requiring struggle Solved in a variety of ways

Group work (communicating/understanding) Computation Critical thinking Element of surprise

Best Practices

Online Education – Group work Community building MyMathLab interactivity Multimedia

Khan Academy Other videos Online computational tools

Instructor facilitation

Best Practices - DB

Instructors Productive facilitation Not the source of the correct answer

Students Responsibility – group finds the answer Community Communication

Best Practices: Rubrics

DB Rubric Sustained participation Meaningful posts

DB and Submission Rubric Accurate solution Justification of reasoning Clear writing

MAT*101 Mathematics for Everyday Life

Handling variability among students: Offer both 15- and 8-week versions “Just in time” remediation (Khan academy)

Comparison … Discussions

MAT*112 Elementary Algebra

Give examples of where you use fractions, decimals and percents in your everyday life. Please include any hints that you may have to make working with fractions, decimals, and percents a little easier.

Comparison … Discussions

MAT*101 Mathematics for Everyday Life

Jill has a swimming pool in her backyard. It is shaped like a rectangle, and measures approximately 16.4 feet wide and 26.25 feet long. It is an average of 5 feet deep. During a few hot weeks during the summer, some water evaporates from the pool, and Jill needs to add 10 inches of water to the depth of the pool, using her garden hose. Although her water pressure varies, the water flows through Jill’s garden hose at an average rate of 10 gallons/minute.

Convert all measurements to metric units (meters, cubic meters, and liters). Reminder: There are 1000 liters in a cubic meter (m3). It is ok to round your answers reasonably.

How much water (how many liters) will Jill need to add to her pool to return the water level to its original depth? How many gallons of water is this? Reminder: Volume = Length x Width x Depth

How long will Jill need to run the hose?

DB interchanges

MAT101:

Student1: When I first looked … I was completely lost … I realized the problem did not require you to know how much total water there was.

Student2: The most helpful part for me … is to identify what is important … I started to look at the water in the pool and it has no influence on our task ..

DB interchanges

MAT101:

Student2 (cont): … from here on out I’ll try to identify the variables that I need ...

Student3: … In the end I was very confident in my answer, but your way was just as efficient and much quicker. Do you think that if we were not working in groups … you would realize how many different ways there might be to solve a problem like this?

One instructor’s experience*

One student starts and gets stuck Another picks up, adds a little more Third student chimes in Problem completed collaboratively. “Nothing earth shattering but I like how the

group dynamics work”

* Comments from Prof. Rob Farinelli

How to encourage participation*

Build success in Week 1: Require early initial posting, announce

requirement in various places Reach out individually to those who do not

post on time Stay positive and supportive Post the DB grading rubric in the group DBs

* Suggestions from Prof. Mark Marino

Rubric provided - enough said?

Examples of math discussion boardresponses are: Solving and posting course mathematical

problems and solutions Sharing with your classmates mathematical

procedures and clarifying understanding of these

To share mathematical websites and material

* Suggestions from Prof. Mark Marino

 

Popular course

YEAR 8-WEEK REGs

15-WEEK REGs

TOTAL REGs

2012 - 2013 852 262 1114

2013 - 2014 1325 139 1464

2014 - 2015 1520 153 1673

How do students do?

Completion rates Over 90% including cancellations Over 95% excluding cancellations

Pass Rate About 96%

Topic: Diagnostic Testing

Consider a particular genetic disease affects 3% of adults in the U.S. population … a genetic test for the gene that causes the disease … is 98% accurate …

Topic: Diagnostic Testing

[Out of 100,000 adults tested]:

1. How many are likely to have the disease?

2. How many who actually have the disease get a positive test result?

3. How many who do not have the disease get a positive test result?

Diagnostic Testing

4. Of the people who get a positive test result, how many of them have the disease? Convert this to a percentage: What percent of people who get a positive result actually have the disease?

5. What does this percentage tell you about the test?

From a student posting ….

Genetic Disease

Summary of Results for Genetic Disease Testing( in which 3000 of the people had the diesase and 97,000 did not)

 Have the Disease Don't have it Total

Test is positive2940

 (true positive)1940

(false postive) 4880

Test is negative60

 (false negative)95060

 (true negative) 95120

Total 3000 97,000 100,000

Refer to handout …

How do we best facilitate? All instructors care and do their best

Carefully placed questions Carefully placed comments Encouraging, but (maybe) too “hands-off” (?)

How can we improve facilitation?

How do you encourage instructors to take the time to develop a deep understanding themselves?

How do you teach good instructors better questioning techniques?

How do you do this at a distance?

Webinars? Pros Cons

Courses where the instructor is the student? Pros Cons

Other ideas?

How can we improve facilitation?

THANK-YOU!

Margie Dunnmdunn@excelsior.edu

Problem Write up assignment

Jose has a fish tank that measures 11.8 inches wide, 19.7 inches long, and 15.7 inches deep. He empties it halfway to clean it. To refill it when he is done, he will fill a one-gallon jug in the sink and carry it to the tank, pour it in, and then return to the sink again.

1. Convert the dimensions of the tank to centimeters. Round all measurements to the nearest whole centimeter.

2. How many liters does Jose need to add to the tank to fill it? (Reminder: 1 liter = 1000 cubic centimeters)

3. How many times will Jose need to carry the jug from the sink to the tank?

MAT101 DB

Suppose you have three student loans …

$10,000 with an APR of 8% for 15 years

$15,000 with and APR of 8.5% for 20 years

$12,500 with an APR of 9% for 10 year

Calculate the monthly payment for each loan individually. How much do you pay total each month?

Calculate the total you will pay over the life of all 3 loans.

You have the opportunity to consolidate these 3 loans into a single loan with an APR of 8.5% and a term of 20 years.

What will be your monthly payment if you consolidate?

How does that payment compare with what you are paying on the three loans individually? Does this result make sense to you.

What will your total payments be over the life of the loan? What are the pros and cons of doing this consolidation?

To get full credit for this write-up, you should:

1. Answer all parts of the problem.

2. Show your justification for every step in your solution. Use clear, mathematically accurate language.

3. Label all numbers with the units they represent (e.g., 0.3048 ft/meter).

4. Clearly state your conclusions using complete English sentences (for example, “Jill needs to add 43 gallons of water to her pool”).

You may use ideas from the discussion board, but you are expected to write your solution using your own words to explain your reasoning. The report should be no more than 3 pages. Ideally, your solution will be typed in MS Word, although you may hand-write mathematical expressions (in dark pen) if need be, and then scan your paper, check that all hand-written portions are legible, and upload it.

“The formal algebraic symbol system evolved to serve the needs of a very elite population of mathematicians/scientists who used it every day over a lifetime. Today we assume that casual students by the millions must learn it for considerably more casual use in their lives.”

Kaput and Roschelle, 1998

Calculus is grounded in algebra