Guided-discovery problems can be incorporated into lecture, lab, and field courses. They fit beautifully into the *exploration* phase of the learning cycle approach to teaching (Brown and Abell, 2007). Thus they work best when they are assigned before any lectures or readings on the topic. Because guided-discovery problems are time-consuming and foster deep learning, they are best used to teach course material that is especially important, conceptually difficult, or counterintuitive.

In order to succeed, a guided-discovery problem must be adequately scaffolded (Hogan and Pressley, 1997; Hmelo-Silver and others, 2007) so that students remain within their "zone of proximal development," the zone between what they can do on their own and what they can't do, even with help (Vygotsky, 1978). This scaffolding should be incorporated into:

- the written materials that the students receive,
- the interactions between the instructor and the students, and
- the interactions among the students.

There are a variety of methods for providing the necessary scaffolding, including the 3-step *Learning-for-Use* design framework consisting of motivation, knowledge construction, and knowledge organization (Edelson and others, 2006), and teacher-student conversations in which the teacher does not directly answer student questions but, instead, asks the students a series of questions that steer students in the right direction. These questions may invite students to explain what they already understand, clarify those explanations, provide the evidence and reasoning underlying their assertions, or see the holes in their arguments (Hogan and Pressley, 1997).

*Jump down to read about facilitating Guided Discovery Problems.*

### Creating Guided-Discovery Problems

Gerver and Sgroi (2003) describe eight critical steps necessary in developing successful guided-discovery problems. These steps are...

**Selecting the content:**Choose content that is new but derivable using skills and knowledge that the students already possess. For example, in the Altitude of the Moon and # of Hours it is Up (Acrobat (PDF) 159kB Nov30 08) problem (hereafter referred to simply as the "moon problem"), students draw on their knowledge of Earth's seasons and daily rotation, the phases of the moon, and the altitude of objects in the sky as they figure out why there are variations in the altitude of the moon and the length of time it is up.**Stating the aim:**Clearly state the objectives of the lesson without spoiling the "Aha!" component. In the moon problem, I stated the objectives as a series of questions but they can also be stated as a bulleted list or an introductory paragraph.**Identifying the prerequisites:**Identify the knowledge and skills that students will need in order to successfully complete the problem. Then test to make sure the students have them. In the moon problem, students need to be able to:

- Identify the phase of the moon, given a drawing of the relative positions of the sun, moon and Earth.
- Identify the appropriate solstice or equinox, given a drawing of the relative positions of the sun and Earth and the tilt direction of Earth's axis.
- Use the circle of illumination to determine the proportion of each day that an object in the sky is visible.
- Determine the altitude of an object in the sky, given a drawing of the horizon and the light rays emanating from that object.

**Setting up a graphic organizer:**As you design the lesson, it is very helpful to make a schematic outline that reveals the flow and logic of the lesson. Here, for example is the graphic organizer for the moon problem.

Organizing your thoughts in this way helps you design the lesson in a logical sequence. Structure the activity so that students build an understanding of each underlying concept individually before putting all of the concepts together into a comprehensive model. As possible, include one or more hands-on activities. Analogous models are especially powerful but use them with care - they should really actually show what you want them to show. Design the lesson so that the students must confront common misconceptions as they work. For example, in my activity on seasons, students are confronted with the fact that Earth is closest to the sun in January, directly contradicting the common misconception that seasonal temperature differences are caused by Earth's distance to the sun.**Writing the lesson:**At the beginning of the lesson, trigger students' curiosity by making the problem puzzle-like, a mystery to be solved. A real-life scenario can also heighten engagement by showing students the relevance of the material to be learned. For example, in my Missing Half Dinosaur problem, the students imagine themselves as being in charge of a dinosaur dig and must correctly interpret a fault in order to locate the missing half of the skeleton.

Make the lesson challenging, but not frustrating or anxiety-provoking. Each step should be small enough to feel doable to the student. When incorporating hands-on activities, keep procedures simple and provide clear instructions; the focus should be on understanding what happens, not on doing the experiment "right." Keep the students engaged by keeping busy work, such as repetitive calculations, to a minimum.

The heart of a guided-discovery problem is the leading questions that the students answer along the way. Here is where proper scaffolding is crucial. When well-written, these questions trigger the "Aha!" moments that make guided-discovery problems so exciting and effective. Writing these questions is a delicate balancing act of providing just enough help. If we give too little help, the students feel overwhelmed and give up in frustration. If we give too much help, we rob the students of the thrill of discovery. The students should "gradually see the concepts unfurl" (Gerver and Sgroi, 2003, p. 9). Ask specific questions and make it very clear what you're asking. Avoid asking too much at once; each question should be just a small step toward the final goal. As appropriate, have students complete partial diagrams or tables. Multiple-choice questions can be an effective way to restrict the options available to the students and thus focus their thinking. Frequently ask students to justify their answers, revealing their reasoning. If the remainder of the activity depends upon the correctness of a particular answer, instruct the students request a teacher check before they move on.**Using a naive proofreader:**Before springing a brand-new guided-discovery problem on your students, have a colleague or student work through the activity and uncover any pitfalls such as unclear directions, missing steps, hidden assumptions, or errors.**Writing a follow-up activity to check for accountability:**A guided-discovery problem should be an essential part of the course curriculum, not a fun but irrelevant tangent. Students will not take such lessons seriously unless they know they will be held accountable for the concepts learned. Once, after doing very poorly on an essay question based upon a guided-discovery problem that took the form of a simulation game, a student complained that she had considered it "just a fun game, not something we had to learn." The follow-up activity need not be an exam; it could be another guided-discovery problem that builds on the first, an essay assigned as homework, or a presentation to the class.**Field testing and revising:**Inevitably, your guided-discovery problem will not be perfect the first time, or even the second, third, or fourth. As soon as possible after the lesson, write down what worked, what didn't, and what you would do differently next time. Jot down any ideas for making the lesson more enjoyable or more profound. When I have done so and, especially when I have actually sat down and revised a lesson while it was still fresh in my mind, I have thanked myself profusely the next time I taught that same lesson.

### Facilitating Guided-Discovery Problems

Whether you write your own guided-discovery problem or use one written by somebody else, skillful facilitation is crucial to its success.

**Preparing the Students**

Before the first guided-discovery problem of the course, be especially sure to take some class time to prepare the students for the experience. Students need to know the educational value of everything we ask them to do; they need to buy into guided-discovery problems. If they don't, disaster can result. During my first semester as an assistant professor, I taught a couple of labs for the general education geology course for non-science majors. The required lab book, written by a senior member of my department, featured cookbook-style exercises that focused on developing geology-specific skills such as rock identification and topographic map reading. The students were visibly bored and often off-task. Half way through the semester, I just couldn't take it any more. I wanted to facilitate discovery; I wanted to see "Aha!" moments. And so, one day, I substituted the Geoworld plate tectonics lab for one of the labs in the book. It worked! The students were engaged, they thought long and hard, and they had "Aha!" moments. I was thrilled. After an hour and a half, one student commented, "This is painful!" I smiled, thinking she had understood the "No pain, no gain" truth of deep learning. Another student looked at me, saw my smile, and said, "You're loving this, aren't you?" I admitted that I was. Not until the end of the second lab did I realize that these students had been trying to tell me that they hated the experience. They weren't used to working that hard. They saw no value in this novel challenging guided-discovery experience. They thought I was sadistically torturing them.

After that horrible experience, I began explaining to the students why I was doing what I was doing. I now tell them a little about the research on how people learn science. I point out the beautiful alignment between this research and guided-discovery problems. I do my best to help students see that I give them these problems because I care deeply about their learning, not because I'm lazy or sadistic. Some students still resent being forced out of their comfort zones, but the vast majority enjoy the experience and appreciate the chance to discover concepts for themselves.

**Coaching the Students Through the Problem**

When assigning guided-discovery problems, it is essential to devote some class time for students to work on them. If such time is limited, the early phases of the problem can be assigned as homework. While students are working on the problem in class, skillful scaffolding by the instructor is essential. When students want help, ask them to explain their thinking. Be careful not to evaluate their explanations; instead, note what they reveal about how far the students have gotten in their construction of the concept and exactly where they are stuck. Then give them just enough help (by asking leading questions, providing a piece of information or explaining a concept) to get them unstuck. Once they're on the right track and making progress again, joyfully affirm that progress (Students love this!) and then move on.

These kinds of interactions are some of the most rewarding experiences of my teaching career and I would love to spend such time with each and every student. However, even in small classes, it can be very difficult to get to each student individually. Thus I strongly suggest organizing students into groups and insisting on talking to an entire group at a time.

**Setting Guidelines for Student Interactions**

Guided-discovery problems are ideal for group work. It is best to organize the students into groups of three to five with an even distribution of strong, average and weak students. Instruct them to work together as a team, making sure every member of the team understands the answer to each question before moving on. If strong students resent having to do a lot of explaining, remind them that "the best way to learn something is to teach it" and clue them in on the scaffolding techniques of facilitating student work without giving away the answers.

In introductory level courses and courses for non-science majors, I have found it essential to implement a structure that keeps all of the students in class during the entire class period. If I don't, some students will rush through the problem as quickly as possible in order to get out of class early. These students don't see the problem as an activity with some value for them, but a just another hoop to jump through. That may be their loss, but, by leaving early, they poison the atmosphere for their teammates and for the rest of the class. Within the team, students who don't want to rush will feel pressured to do so anyway. Then, when a team leaves early, others notice and feel inadequate because they haven't yet completed the activity, or they feel like fools for sticking around while others escape. One structure that keeps all of the students in class is to require team presentations during an end-of-class closure session. For example, each team can prepare an overhead transparency and present its answers to a particular subset of the questions. This is also a handy way to ensure that all students have understood all aspects of the problem.