Robert Chaney, Mathematics

Robert Chaney is a professor of Mathematics at Sinclair Community College, a 2-year public institution. Information for this case study was obtained from an interview conducted on July 25, 2013. This page is part of a collection of profiles about a variety of techniques for integrating Quantitative Reasoning (QR) across the curriculum.


Jump down to Design and Implementation of QR Goals | Key QR Assignment of the Course | Challenges | Advice | Documents

Overview and Context

About the Course

The course is called Technical Mathematics I & II, or Tech Math. I have taught the class for approximately ten years. What makes this course unique is the integrated lab component. The lab activities contextualize math by teaching students to apply algebra to solve specific, real-world problems. One tool I use to contextualize math is SAM, a calculator-controlled robot I co-created with a colleague in the Physics department.

The course is primarily geared towards two-year engineering students, but some of the students who take these courses are going on to a four-year university degree. It is part of the mathematics sequence taken during the first year of a two-year program in engineering. There is some variation on that, depending upon the engineering majors that are taking it. Most of the students are engineering majors, but the majors range from fire safety to computer science. Some of the students have a goal of an associate's degree and some have a 4-year degree goal.

Key QR Assignment Description (links to section in this page)

How Quantitative Reasoning (QR) and Literacy are Approached

Quantitative literacy is having the skills to be able to look at a situation and calculate an answer; or all the things that you would learn in a traditional math class. Quantitative reasoning is taking those skills further so that you can make sense of the real world. You can use what you know in a real setting and look at real problems, quantify them and reason through them to draw a conclusion or solve the problem.

Design and Implementation of QR Goals

Motivation to integrate QR


Originally, I started out trying to answer the questions that you get from students in algebra such as, "What are we going to use this for? "Why am I spending so much time doing this?" and, "I don't see how this connects to anything." I was trying to motivate them to know that their efforts would be worthwhile to them in the long run. Later on I came to realize that using context-based learning not only motivated the students, but more importantly, it helped students learn algebra better.

Personal Statement on Teaching Philosophy and Methods (Acrobat (PDF) 73kB Aug12 13) by Robert Chaney.

QR goals

I want students to transfer what they're learning in the classroom into many different contexts to learn how to apply algebra and how to think of real things algebraically. I also want them to learn the general concepts of algebra and the language so they can still be successful in traditional mathematics and go on to higher-level math courses in engineering, etc.

In Tech Math they use algebra to program an Excel spreadsheet to do calculations that will make the robot do different things. This is how I am getting them connected so that they start to develop a conceptual understanding of variables and how to create functions and graphs and analyze those things to solve real problems.

I never want them to get stuck anywhere where they're just seeing math applied in one context. I want them to understand that the same reasoning--the same procedures and skills--can be applied in a whole lot of varied types of situations. I want them to develop a general understanding of problem solving. So they can look at real situations and start to think of them mathematically, and then be able to use language of mathematics to start to work towards a solution, and so they recognize math in real things. It's not just in the textbook, it's not just for a certain type of problem, it's everywhere. And it can be a valuable tool if they know how to use it.

Pedagogic approaches used

I think contextual learning is very powerful. But I don't see it as replacing traditional education. I developed the idea early on that you don't throw everything else out just because there's a new idea that seems so great. Sometimes I back up on the contextual learning a little and use other methods that are more traditional. But the important thing is to bring these other things in alongside and intermixed with it. It's not just one thing, it's lots of things in a very balanced approach. And that balance can be different from one class to the next.

It takes experience in being able to feel that out. It's hard to write a 'Here's how you do it' book. This is just where I'm at now. Who knows next week, I can change some of these ideas. You can at some level describe what you are doing, but there are so many other things that are important to make it successful that come into play. It's teacher training, it's people to believe in it and who are excited about it. That enthusiasm transfers to students.

Knowing the course is successful

Our efforts have been supported by the National Science Foundation, by Ohio State Grants, the college, and math department at Sinclair.

We have a lot of qualitative data that the students think it's good. The students who like mathematics think it's valuable and they learn more mathematics doing it this way.

In addition, we have quantitative data, including a study done by the math department chair and by the physics department.

Our evidence was compelling enough to convince the mathematics department to allow us to make every section we teach in statistics an activity-based section.

However, we have found that it really takes a full-time effort from somebody to measure improvements in a statistically valid way because it is so complex. Even though we have quantitative evidence, it's not enough to be scientific proof, although the things we are doing align well with the educational literature.

The evidence we have fits with my idea that contextual learning is something that should be done from the beginning, and these skills are developed over time. Over time they become measurable and significant. You can't just take one quarter and think that you've really made such a huge impact on students' reasoning abilities that it's going to be something you can measure.

Key QR Assignment of the Course

This assignment involves using a calculator to program a robot. Throughout the activity algebra is used to automate the robot--to make it be able to think and move. Students build their understanding of algebra through applying what they already know about the context.

The robot's drive motors that have the wheels on them are stepper motors. One of the very simple things I do first is that I have them pick one of the motors up and turn the wheel, and it goes, 'click, click, click, click, click.' As a matter of fact, it will take 480 clicks to make that wheel turn one time. Now everybody has stepper motors at home. They have it in their computers for the disk drives, they have it in their printers. The printer has to go click, click, click, click, click to turn the drum to move the paper forward to get it to a position that it prints on.

I tell students, "We don't want to tell the robot to go 500 clicks forward. What can we do to input something so that you can communicate to the robot in centimeters or inches or feet that you want it to move forward?" We have to find a relationship between the clicks--which is a variable. If you want the robot to go different distances, that's going to be a different number of clicks. If you want it to go 400 clicks, but you tell it to go 800 clicks, it would go twice as far.

But I don't want to talk in clicks, I want to talk to it in centimeters. So the variable of clicks, "X", which would be how many clicks it would take. It's a variable because we don't know how far we want it to go. Tomorrow we may want it to go another distance. So "X" will be a different number tomorrow. It's a variable, it changes from time to time. The path will change, the variable, the distances, the clicks will change.

Challenges

  • You don't always have success. I might do something in the classroom one day and it just doesn't turn out to be a success. The students weren't really excited, or what I was trying to do didn't work. And after all that work, was it really worth going on and doing more? If you really believe in what you're doing, you come back the next day and try it again. Try something different. Learn from failure. Keep going. The goal is good, the end is good, you just keep going.
  • People can say things that make you discouraged. There are different philosophies about how people should be taught in different subjects. There are different teaching styles, and different learning styles. It's hard to prove who's right about lots of things. There were times when people with different teaching philosophies said things that were discouraging.
However, those things that were discouraging to me were good because they helped me think about how to answer them and ultimately, solidify what I had been doing. I could think, "Yes, that's why I'm doing it, and it's right, it's good." So don't get discouraged by what people say. There will be skeptics, but take those things and answer them, learn from them, help them to make your view of it more defined. Help them to help you really know why you're doing what you're doing. Ultimately, looking back on it, it was all good, but was discouraging at times.

Advice

  • Collaboration is important. I worked with Fred Thomas in the physics department right from the beginning who knew more about the electronics and we worked together to build the equipment. He has been a very, very important part. In addition to physics knowledge, he brought a lot of educational philosophy or ideas to the project. Working with people can bring a lot to any project. You can all build something bigger than what you can do by yourself.
  • Learn what others are doing and decide what you want to do. What else is going on? What have other people done and been motivated by and found success in? Then figure out what do you want to do and what you believe in, realizing that there's a lot of room to be creative.
  • Obtain support from the greater educational environment. People need support so that they can motivate themselves because at the beginning because there is a steep learning curve, especially for somebody who has taught traditionally. There is a learning curve on being able to work with students and facilitate their learning in contextual way. You need support in order to develop ideas on how you think about your teaching and how you want to work with those ideas and bring them into the classroom. It's going to be hard at first to figure out how to do that.
  • Don't give up. There were many times early on when I was trying to do some of these things and feeling like, 'I don't think this is working.' There were frustrated days. It took extra work. What brought me back the next time was believing in what I wanted and having enough support to push through the difficult days. But I'd never go back. I can't teach a class without doing something like this. It has a number of rewards and enough good days early on that keep you motivated and keep you going.

Documents

Personal Statement on Teaching Philosophy and Methods (Acrobat (PDF) 73kB Aug12 13) by Robert Chaney.