Applied Math

Calling for linear regression application ideas

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In this semester of my PhD education I am taking a course on Project Based Learning (PBL). The major outcome of this class is that I will design a PBL unit. I know that I would like to do this unit on linear regression but I still need help.

I would like to be able to use the project outcomes to help a business, school, or community. The students will be creating a (hopefully) accurate linear regression equation that can be used for prediction. I am looking for ideas of variables that are believed to be associated (e.g. height and weight) that can be researched data can be collected and an analysis can be done.

I have the option of having the students work in groups which means that I could have them each look at a different relationship. The other option would be to have the whole class work on the same relationship and work individually.

No idea is a bad one so please feel free to reply with any brainstorm that may arise.

Thanks ahead of time!

An Idea for a Math Project, “Why Do I Need To Know This?”

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I believe that I have written about this before but I wanted to give a detailed description of the project or “big assignment” that I give in all of my math classes.

The title for everyones project can be “Why Do I Need To Know This?”

As a teacher I have heard my students utter those words so many times that it is a kind of therapy to give them an assignment with that title. I allow them to work in groups or as singles and if there is time in the semester and the class is the right size, I also like to have them give a presentation.

They are to find some real world application for a topic covered in that course and they write a paper about it and give a presentation (whenever possible).

I do this for a couple reasons:

1) I want my students to have a solid answer to the questions “Why do I need math?” or “When will I ever use this?”. If they are forced to study one area where they would use it in their daily lives I believe it will open the door to notice all of the times that they really do use math in their daily lives.

2) Writing a paper is something that students may not like, but they seem to be pretty sure that they can do it. Many of my students come into the classroom thinking that they will do miserably at every aspect of the math class. When they hear that a paper and presentation will be a percentage of their grade it often gives them confidence that they will be able to do at least one part of the class without too much difficulty.

3) Being the person that can give the presentation will often be the thing that will catch a manager’s eye. For this reason I think it is important for students to give as many class presentations as possible. I take the time to get my students to work together on problems in class so that they know as many people in the room as possible. I tell them when we are going over the syllabus that this will be a room full of people who you know and are a little familiar with by the end when you give your presentation, and it is easier to talk to people you are familiar with than those who are strangers (I know that is not the case with singing but I require no singing in these presentations 🙂 ).

What I hope happens through these assignments is that my students are a little more knowledgable about the practical uses of mathematics in their lives, and a little bit more likely to offer to write a paper or give a presentation at work because they have had to do it before.

My students have groaned a little about a paper in a math class, but my response to them is that they want math class to be a little different than all the other ones that they have had in the past and this is different. That usually makes them laugh and stop groaning. Most of my feedback from students has been positive and I have had some really great topics over the semesters. I have listed a couple below:

1. Using Area When Tiling a Floor
2. Parabolas in Missile Projection (the student had grown up in civil war somewhere in Africa)
3. Percentages Used in Figuring Furniture Budgets (the student worked in a furniture store)
4. Probability and Procedures in Craps (the student liked to gamble 🙂 )
5. How Fractions are Used in Music
6. Problem-Solving in a Classroom for Behavior Disorders

These are just a few of the interesting topics my students have come up with. I look forward to seeing what else my students can come up with in future years. If you have any other good ideas I would love to hear about them.

Be Careful How You Use the Pythagorean Theorem

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There are a whole subset of triangles that have one angle that is 90° called right triangles. Often in the “real” world we see these when we are talking about things that meet the ground at this angle and then something that leans up against the thing protruding from the ground. There are many, many applications to these type of problems given the lengths of two sides one can easily find the length of the other using the Pythagorean Theorem.

I often find that my students think that the problems using this theorem are easy to understand and not too bad to compute. The problem with easy is making sure you catch the details.

I was turned onto a really great url in which a professor from the University of Utah describes an embarrassing moment that he had when he quickly tried to do a Pythagorean Theorem in his head and made a big mistake.

I have turned this mistake into a great exam problem ( I use it as an extra credit problem in my Survey of Mathematics class) when dealing with the Pythagorean Theorem.

See if you can easily figure out what the professor did wrong.

http://www.math.utah.edu/%7Epa/math/story.html

I won’t put the answer on here in case my students get lucky and find it, but I will give the hint that another way to think of:

a2 + b2 = c2

is:

(short leg)2 + (long leg)2 = (hypotenuse)2

That should clear it all up!!

Why is Statistics So Scary?

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scared womanI have been completely immersed in the world of statistics for the last three and a half years. I have had the privaledge of teaching for most of that time as well. What I am amazed to see over and over again is that there are hundreds of people out there who are afraid of statistics and don’t know why!

My first question when someone says, “I hate statistics,” is always, “Why?”

The most common answers I get are:

“I am really bad at math.”
“My friend said it was hard, and I have to take it.”
“I hated that class.”

My response to the first one is that statistics uses some basic math but really its the art of understanding information.

To the second I usually say nothing because no one can get through college on what other people do in their classes.

The third is the one that interests me the most because usually a bad instructor was to blame. I don’t ever want to be one of those. Now, you have to know that the reason that I ask why is because as an eductator I want to know things that I can do to improve my students’ experience with statistics.

What I need is the nitty gritty. Why didn’t/don’t you like your statistics class? Is it because the examples didn’t apply to you? Is it because the instructor couldn’t answer your questions? Is it because it was all words and not enough graphics? Is it because you had a bad attitude going into it so the class never stood a chance in your mind? I am looking for people’s specific comments on the question, “Why is statistics so scary?”

What does Human Computer Interaction really mean?

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We have a relatively new “virtual” department at Iowa State University (ISU) called Human Computer Interaction (HCI). What I mean by virtual department is, that in order to get a degree in HCI you must co-major in it and first have a home department. Also, most of the HCI faculty also have home departments somewhere else.

According to Wikipedia, HCI is, “is the study of interaction between people (users) and computers. It is an interdisciplinary subject, relating computer science with many other fields of study and research.”

This is similar to how the field was described to me, with concrete examples of how the fields of psychology and sociology have real issues with trying to make usable software for students in their fields. So, I assumed that this was an accurate description of HCI departments across the board. I had no idea that it so much more complex than that. I was first introduced to it by my advisor in the statistics department who is an HCI faculty member.

I was immediately interested in the field because there is a ton of statistics that goes into determining how successful the programs are, as well as the statistics that are incorporated into research in any field. One of the reason I like statistics so much is that it is applicable to any subject. Having unending interests in many different fields this appealed to me greatly. I soon decided that no matter what I got my PhD in, HCI would be part of it.

That was when I started asking around (I had many friends who were computer science majors). I soon found out that depending on who you asked, ISU either had a great or a horrible HCI department. This confused me because I was under the assumption, as I stated before, that the definition of HCI was the same across the board. After that I did a little asking around and searching on the internet and came up with a little more clarifying information.

At ISU we have a world renowned virtual reality lab (VRAC) and that is the driving force behind our HCI department. A

Below are a few descriptions and bits of information on this field that I was able to find from a couple different institutions, with a little help from Google, of course…

Carnegie Mellon has a Human-Computer Interaction Institute and their mission is:
“To create effective, usable, enjoyable experiences with technology through interdisciplinary research in engineering, design, computer science, and the behavioral and social sciences, and to understand the impact of technology on individuals, groups, and organizations.” ( http://www.hcii.cmu.edu/ ) They also have a video at their site that explains their program.

Stanford University has a neat site with many different publications (.pdf files) about new technologies and techniques in the field. (http://hci.stanford.edu/ ) I read two neat articles about prototyping camera-based interaction through examples, and also one discussing gaze-enhanced scrolling techniques. The first articles describes a new software called Eyepatch, described in the article as a tool that, “allows novice programmers to extract useful data from live video and stream that data to other rapid prototyping tools, such as Adobe Flash, d.tools [14], and Microsoft Visual Basic.” The other article investigates ways to scroll by observing the gaze of the user. I found that information fascinating.

The University of Maryland has a HCI Lab (HCIL) and they describe their work, “The HCIL is an interdisciplinary lab comprised of faculty and students from Information Studies, Computer Science, Education, English, Business, and Psychology. Our current work includes new approaches to information visualization, interfaces for digital libraries, multimedia resources for learning communities, zoomable user interfaces (ZUIs), technology design methods with and for children, mobile and pen-based computing and instruments for evaluating user interface technologies.” (http://www.cs.umd.edu/hcil/about/ )

An Applied Math and Statistics Workshop

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This summer North Carolina State University ran a really neat workshop that involved mathematical and statistics modeling. I am always interested in how people are advancing students in applied math and statistics. The website (see below) for the workshop describes the objective as,

“The objective of the workshop is to expose graduate students in mathematics, engineering, and statistics to challenging and exciting real-world problems arising in industrial and government laboratory research. The students also learn about the team approach to problem solving.”

Real-world problems and a team approach to problem solving are the important things listed in my opinion. There is not enough interest in our fields and I personally believe that is because there aren’t enough people trying to recruit people into the subjects. One way thing that I believe is an integral tool in building interest is showing how the fields of math and statistics apply to the real world. That is one of the main reasons that I fell in love with mathematics as an undergraduate. While some people are born math lovers some of the rest of us have to be converted. My hat’s off to workshops like this one at NC State that highlight the applications of mathematics and statistics in the real world.

The procedure of the workshop was to team up students with the scientists and engineers that deal with the real world problems in their work. The problems that were given to them were to make some advancement in the field in which they worked. There were a couple mentors for each group.

I was also impressed that they didn’t require any experience to apply, just commitment. I like it when programs are open to anyone who may want to try out a little math or stats in the real world.

To read for yourself about the workshop visit the webpage at http://www.ncsu.edu/crsc/imsm/index.php