Real Math: Eeva Reeder on Projects and Assessment

1. How did you become interested in applied learning, or project-based learning?

I took a few years off from teaching to finish a masters thesis and took a job at a bridge design company and ended up having to apply mathematics. I was hired to be an office manager when they found out I had a math degree, and then they said, "Oh great, we're going to have you do some stress analysis on bridges." And it was just trig-level mathematics, nothing too high. But I was petrified because my work was going to be relied on by some truck driver going over a bridge and no one was double checking my work because I was the subject matter expert, so called, and I realized, here I am, I have a degree in mathematics and I've never had to apply it to a real-world situation and no one's looking over my shoulder to tell me whether it's right or not.

You know, they're not correcting a test. And that fundamentally was the final piece that shifted my thinking to the point where I realized I can't go back to the classroom and do things the same way I always have.

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2. Why did you decide to use project-based learning in your math classes?

The reason I started using project-based learning several years ago was because it became immediately apparent to me as a teacher that talking to kids didn't cause them to really deeply learn concepts.

There was no carryover of concepts -- so I could explain things incredibly clearly, to my mind, and give beautiful examples and counter examples, and they might learn the material, learn it so that they could spit back formulas on a paper-and-pencil test. But there was no carry over a couple weeks later. And the worst part of a lack of carry over was that they weren't able to apply it in a context that was outside of that unit and outside of that worksheet or book page.

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3. What has been the "added value" for your students as they participate in the "design a school" project?

Over the years of doing this project, the students gain in quite a number of different ways. Maybe the least of which is the actual application of math at this point because we've done so many different kinds of applied learning experiences throughout the year. But mathematically, they do gain because they have to pull together the different things that they've learned in class about area and apply it to cost calculations and the aesthetics of geometric shapes and so on.

But a primary interest to me is the fact that they're faced with this really complex problem that has certain constraints and they have to figure out how to make the decisions -- how do you even begin to make the decisions and move the process forward, and how do you do that decision making within a group? And so the communication skills required to work with others, the communications skills required just to get your idea across to the architects to sell your idea and to sell yourselves to the architects ... these are the things that are really maybe the most powerful learnings that come from it: the real-life problem-solving, communication, collaboration skills.

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4. Why do you put so much emphasis on complex collaborative work?

Collaborative work is important because it's real life. You look at how the workplace is changing and has been changing over the last decade, particularly the last handful of years. There are more and more companies of about ten to twelve people, and they're very project-based in the way they approach their work. They go out, make a bid, try to get the work, everybody works together. There's less of a sense of loyalty to a company anymore among the workers than there is a sense of chasing certain projects that interest you. And it's really just model of not only how the workplace works, but how community efforts work. So whether you're involved civically or even your family is a team, very few of us do things completely as an individual endeavor.

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5. Why is performance-based assessment so important?

There are two types of assessment, or two reasons for assessment. One is to give students feedback -- meaningful feedback -- on their work. In other words, feedback about the quality of their work and, more importantly, how they can improve the quality of that work. The other purpose for feedback is to assign a score to student work, give it a grade. And the first kind, giving students meaningful feedback, is much more difficult to do. Particularly if you have, like many high school teachers, five classes, thirty kids in each class, and to really give a kid one-on-one feedback on their work is time-consuming and very challenging.

But in order to assess a student's deep understanding of the subject and their ability to apply a concept, you cannot test those kinds of abilities through a traditional paper-and-pencil, crank-out-the-formulas kind of an assessment. It has to be what we call performance-based assessment. And that's why I do these projects because the project requires the students to create products or performances. And then I have to come up with ways to assess those products and performances -- there is a range of ways that I do this. Typically, with scoring guides that spell out very specifically what it means to "meet standard" -- what it means to exceed standard, what it means to not quite be there and what you have to do to get there.

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6. How are students involved in their own assessment in the design project?

There's one more piece of assessment that the students grade one another on, rather than me, and that is on how they were as teammates. They grade themselves and they're in a much better position to do that than I am since they were the ones that had to work with each other.

They also have a scoring guide that they have to follow and they grade themselves according to the scoring guide. Then they grade each one of their teammates and we create a composite score by adding up self-assessment plus teammates' assessments and dividing by however many team members there were. If there's a great disparity, then we sit down and talk about that, so if you score yourself either way higher or lower than your teammates did, we want to talk about why. But that's very rarely a problem. And kids are amazingly honest.

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7. How do you refine this project from one year to the next?

Would I do things differently next year? Yes. Every year I change this project. Every year I learn something that I can improve on. And that learning comes from observing student work, listening to the feedback I get from architects, and if the quality of student work isn't quite at the level at which I think it could be, then I have to ask myself, what can I change?

For instance, in the beginning, the students had a real difficult time thinking out of the box. Thinking futuristic. And they were designing buildings that were very much like what they had experienced. They weren't going outside of their own experience. So, hallways, lockers, rooms of thirty kids, that kind of thing. And what I really had to do then was examine how I'm presenting the project to the students. The prompt. And that I have refined over the years to the point now where I know that what I'm doing is working because the student work is also -- I'm getting the kind of work that I was expecting to get in the beginning.

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8. How do you balance project-based learning with the pressure to prepare students for high-stakes tests?

My colleagues ask me how do I possibly find time in a curriculum for project-based learning when there are so many concepts to cover, so much curriculum to cover, and pressure to get students ready for high-stakes tests -- these standardized state tests, for example.

My answer to them is that applied learning or project-based learning is the most effective way to deliver information and it's the most effective way for students to understand concepts. So it's the same concepts I'm teaching, it's just more effective and more powerful. And there is a responsibility on me as a teacher to know those tests and to know the concepts that will be on them and then to design the types of products and performances, the types of projects that will require students to use those particular skills. But once they have learned a skill by having to use it, it's theirs. You don't need to cram for it on the test. It's just a way of learning information that works.

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