# Real Math: Eeva Reeder on Projects and Assessment

*Editor's Note: Educational consultant Eeva Reeder passed away in August of 2010 at the age of 53. We are grateful for her many contributions to the field of project-based learning and to *Edutopia*, and she is greatly missed.*

In this 2001 interview, Eeva Reeder, formerly a math teacher at Mountlake Terrace High School in Washington State, elaborates on a geometry project in which her students created designs for a "state-of-the-art" high school.

- How did you become interested in applied learning, or project-based learning?
- Why did you decide to use project-based learning in your math classes?
- What has been the "added value" for your students as they participate in the "design a school" project?
- Why do you put so much emphasis on complex collaborative work?
- Why is performance-based assessment so important?
- How are students involved in their own assessment in the design project?
- How do you refine this project from one year to the next?
- How do you balance project-based learning with the pressure to prepare students for high-stakes tests?

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

## Comments (10) Sign in or register to comment Follow Subscribe to comments via RSS

Great Ideas! I agree, 100%, with everything that is said, including the part where coworkers ask how to balance the projects with the curriculum. As a math teacher myself, I would love to do something like this, but I think my fear is figuring out where and how I would even start. I've been taught in a concrete style. I tend to teach in a concrete style, but that doesn't mean I'm not open to trying something new. I just wish I knew how to start.

I am a retired Engineer. For the last 25 years or so, I have been working as a volunteer in grades 1 thru 6 doing hands on projects with the kids. I use throw away materials, cheap materials, pack rat scrounged materials, etc., to teach important basic concepts in Physics and Math by doing hands on experiments. Working Engineers have a tech support staff. Working teachers do not have any support, let alone tech support. When the Education world wakes up, teachers will have a tech support staff so that they will not need to say "I don't know how to start". This is a cultural problem in the entire Education Establishment from top to bottom. Teachers are being shrtchanged because of lack of support. Children are being short changed because of lack of support. And then kids get to high school and say "I hate Science and Math" and all the wise men rub their hands in dismay and say "How can we stimulate an interest in Science and Math?"

My heart goes out to Amy Johnson and all her peers.

And then Congress distributes a few millions dollars in grants. which have minimal effect because nobody is looking at the basic problem of teaching meaningful hands on construction activities in the low elementary grades. Project design is an Engineering activity!

I work with East Prairie School in Skokie, Illinois. I do a 1/2 hour a week class thru the entire semester. They have a website showing one of my basic water pressure/air pressure activities in action with 18 3rd grade kids.

Threading ones way thru the website is tricky so I cannot include all the instructions here.

I am open to suggestions on sharing some of my concepts and activities.

I am a 5th grade teacher in a regional school district made up of 5 different towns in Massachusetts. I have been asked to develop a curriculum guide with activities and lessons in the area of science and technology for grades 3-5. I would love to hear more about your ideas. Any help or suggestions you can give would be greatly appreciated. Thanks!

Hi, I'm from Malaysia. I have to make a proposal to do my research based on problems that teachers encounter during teaching and learning activities for students aged 13 until 15 years old (secondary school). My question is what is the best method that I can use to do research related to problem solving in Mathematics or to solve direct question in math? Which one do you think better for me to start my research. And what are the other related topics do you think are suitable for me to do a research?

I am a new high school math teacher and I feel very strongly about project based learning as a means to finally answer the eternal question of students, "When am I ever going to need this?" I am working on my Master's degree and I am finding the program to not be geared in the direction that I would like, that is to say that there is not much emphasis on curriculum development. At the moment, I am attempting to develop projects for my own students, such as a more advanced stock market game as well as designing and financing a house. I found your comments to be very insightful and helpful and I will most certainly take them into consideration as move my projects further.

I wonder how you come up with the initial idea for a project. Much like the comment left by Amy Johnson, I have been struggling with that my most critical of first steps and have been unable to find an adequate resource to assist me in this task. Do you have any suggestions as to where I should look?

I am looking for some great project based learning units for 5th grade, specifically 5th grade math. I teach self-contained 5th grade and am wanting something that emphasizes math and is interdisciplinary. I would like to hear from someone who has had success with a particular PBL unit. Thanks!!

Cheryl

Giddings TX

I am wondering what kind of projects this teacher is doing.

Where are you getting your ideas and your information to be successful in the classroom?

I found some great idea in Internet and Math Magazines. Just you need to find some time to search.

Measure your own skin. Math Mgazine.

Pizza Project. Internet

Use the day light and other data from Internet for trig functions.

It will be nice if it would be a place that we could find these w/o wasting to much time.

I do use the projects but that is like 3 projects for course. I would like to know how frequently do you use and if you have examples of these I will mostly appreciate.

I am eager to get started with Project Based Learning in mathematics in my Primary 6 / grade 5 class. I tend to give students projects in Language Arts and Science, however I have never used this approach in mathematics. It makes sense to utilize this technique, so that students understand the relevance of mathematics in "real" situations. Does anyone have any projects that can be used, specifically in mathematics to reinforce: Number Sense, Geometry, 0r Data Handling ? If so I would appreciate hearing about them.

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