## Interesting Question

From an earlier project, I had learned of a National Education Association recommendation regarding student to teacher ratio:

NEA recommends an optimum class size of 15 students in regular programs, especially in the early grades, and a proportionately lower number in programs for students with exceptional needs, including children with disabilities and English language learners.

The question I wanted students to investigate is simple: Is there a level that the student to teacher ratio will stabilize to in the long run?

The question is realistic and is generate by a national organization and the data corresponding to this question is completely realistic. Most students enrolled in the class can relate to this question since many of them just graduated from American schools or have children enrolled in American schools.

## Robust Data or Functions

A few years ago I became interested in education statistics. These statistics are readily available at the National Center for Education Statistics. NCES is filled with data regarding every aspect of the American educational system. At this website, you can find statistics about spending, dropouts, numbers of students, number of teachers, students with disabilities and more at the national level down to the county and district level. Using the data tools at NCES, I was able to create an Excel file (and corresponding PDF) containing the number of students and teachers in each state for the years 2000 to 2006.

Student and Teacher Data EXCEL | PDF

## Learning Objectives

For me, the most challenging project to put together is the first one of the semester. At this point, the students are unfamiliar with the entire idea of a project. They do not understand the technology that will be required, the sustained effort, or the technical memo they will complete to demonstrate their understanding of the content.

In addition to teaching all of these topics, there needs to be some mathematical content. My Survey of Calculus class typically begins with a review of nonlinear functions. The students in the class have completed College Algebra and typically have covered the typical subjects of polynomial, rational, exponential and logarithm functions. However, most of them have never had to use these functions in any realistic context. They may have produced some elementary regression models, but nothing that really requires any deep understanding of the nature of these functions.

The learning objectives for the first project are broad:

1. Review elementary nonlinear functions.
2. Apply nonlinear functions in a realistic setting.
3. Apply limits in a realistic setting.
4. Learn how to use the TI calculator and Excel.
• Graph a function
• Graph a scatter plot of data
• Produce a regression model for data
• Format professional looking graphs.
5. Learn how to document a solution strategy.

This may seem like a lot, but I am going to use this project for the first 4 to 5 weeks of class.

## How To

This section is designed to help you nurture a student project from its inception as simply an idea to documents and resources that you can use in your class. This process can have many starting points. In some cases, a project may start out as a learning objective for students. Based on that objective, the project is built by finding appropriate data and then designing a letter to the students and supporting resources. Another option is to steal an idea from a colleague in your department or at a conference. The idea can be molded to suit your learning objectives with supporting resources to guide your students toward successful completion. Most often, my projects start out as interesting data that I have find on websites. Once I find data with a lot of potential, I try to use it in several classes. In this manner, students that take several classes from me (like College Algebra, Finite Math and Survey of Calculus) have a chance to work with data they are familiar with and understand.

Any of these strategies for creating a project needs to have some common elements to be successful:

• Learning objectives for the project;
• Good robust data or functions;
• An interesting question for the students to answer;
• A solution strategy that requires several steps to accomplish;
• Resources to help the students learn the technology skills they will need to solve the problem;
• Resources to help the students learn the mathematics they will need to solve the problem;
• An assessment strategy to evaluate whether the students have met the learning objectives;

In this section, I’ll trace the development of a project I use in Survey of Calculus. This is a course that is taken by business and finance majors during their first two years in college. I teach at a community college and often have high school students from local charter schools enrolled in the class. I designed the project so that it could also be used in four year colleges and universities.

Assessment of the learning objectives are accomplished through a written document I call a technical memo. In this document, students introduce the problem they are solving, explain what their solution strategy is, show their solution, and comment on the validity of their strategy. Since I teach Survey of Calculus in a traditional brick and mortar classroom and online, this document replaces exams in my classes. To ensure students are doing their own work, the projects are specifically designed to engage the students over several weeks. I require check ups regular during these weeks to help guide them and to insure that they are doing their own work. Since students submit several assignments prior to turning in their final technical memo, they are invested in the project and student integrity issues are minimized. The student integrity issues that do arise are easy to detect.

## What Is It?

As you can see from the links below, there are many similar terms that are used to describe very similar student experiences. Some educators describe project based learning, others use a technique called problem based learning. Across the Atlantic, they use enquiry based learning. Project based learning at the primary and secondary level can be different than what is practiced at the college level. Although these individuals might argue that each of these terms is different, I don’t care to engage in this debate. Instead, I’d rather cherry pick what I think is useful in developing meaningful student experiences and assessing student performance. I’ll leave it to you to examine the web sites and develop your own idea of project-problem-inquiry based learning.