Reprinted from Connect
Vol.8 No.4, March/April, 1995
Focus on: Inquiry Learning
Grade Level: 6-8
Grade Level: K-2
Grade Level: K-8
Grade Level: Professional Development
Grade Level: 3-5

Exploring Inquiry and Problem Solving

by Casey Murrow

Jimmy Karlan strives to create, "Problem solving classrooms where students are as encouraged to find problems as they are to think about how they are going to solve them. [Such a classroom] is also a place where failures are viewed as opportunities and a place to construct one’s own understanding of phenomena."

Karlan is an experienced middle school and upper elementary teacher and teacher educator. He is now completing his work on a doctorate while also working as a researcher on a project called, "Studying Innovations in Math, Science and Technology," for the National Center for Improving Science Education. This project has allowed him to observe in a variety of classrooms where innovative curricula have been implemented, especially Kids Network and The Voyage of the Mimi.

We asked Jimmy Karlan to share his perspectives on problem solving and inquiry with our readers. He suggested that you can think about problem solving as you would a walk through a neighborhood. "If you pick an object or process, you can suggest a problem to explore." He points out that such problems are real-life, local and also,"playful." This word comes up often in his conversation, in the context of playing with an idea, mulling it over and considering how to approach it in the most creative ways. He espouses a formula for problem solving stated as, Problem = Object or Process + Obstacle or Opportunity. Keeping this idea in mind helps to frame the experience for teacher and students. He calculates there are at least a dozen feasible problems that one can investigate with classroom objects like door knobs, erasers, blackboards, water fountains, and windows. "How do erasers and door knobs work? Under what circumstances does the teacher use the eraser? How much fountain water is ‘wasted’ and how do the amounts vary by grades?"

"Teaching K-8 science from a problem-posing context," Karlan says,"challenges teachers to remove themselves from the podium of answers to become partners in discovery. In this new position, success may be proportional to the frequency with which a teacher says, ‘I don’t know. How do you think we can find out?’"

Characteristics of a problem solving classroom

Based on his own teaching and his work with teachers, Jimmy Karlan says he would want to communicate to students that, "I believe you and your classmates have a great deal to learn from one another. I view my role as a facilitator whose purpose is to help you twist, stretch and flip your understanding of various self-selected and teacher selected topics and concepts.... I believe it is important to have opportunities to construct our own knowledge of the world and I hope you leave this class with a greater sense of comfort and excitement with not knowing all the answers."

In our conversation, he noted that, "Choice is a motivator," and he pointed to the value of giving students many choices in planning an inquiry and in carrying it out.

As a researcher, Karlan has seen a great variety of classrooms where teachers and students have opportunities for problem solving. Through that experience, he has developed a list of problem solving dimensions to consider in the development of an activity, including:

• Is the activity bound by rules and prescribed procedures (algorithmic) or is it an open ended hypothesis?
• Does the activity allow the student to pose further problems?
• Is it student or teacher initiated? [Either may be appropriate, given the circumstances.]
• Does it allow for messing about?
• Will the teacher be a facilitator and coach?
• Will the teacher be engaged in continuous assessment?
• Is the subject both relevant and immediate?
• Is it practical or exotic?
• Is there room for engineering, experimenting, researching, thinking and decision making as well as for mathematical applications?
• Is it multi-disciplinary?
• What is the level of dissonance (incongruity, discrepancy) raised by the activity?

Karlan adds a personal note: "I love dissonance. I love being in it. It’s the one time I can really feel my mind thinking, struggling, questioning and exploring. It keeps me focused."

In response to a question about students who press for an answer right away, Jimmy Karlan quotes researcher Catherine Fosnot, "If I told you the answer, those of you still thinking about the problem would probably stop. Those of you who are sure of the answer know it with a "logical necessity’ and don’t need me to confirm it. And those of you who are indeed erroneous in your reasoning, but are convinced you’re right, will simply accept my answer but not change your reasoning."

Working with curricula

Observing curriculum innovations as practised in classrooms, Karlan has seen firsthand the difficulty of implementing curricula that encourage inquiry and demand tremendous flexibility and deviation from traditional teaching roles. Yet, he points out, the teacher’s role remains essential: "In other settings, teachers were primarily sources of knowledge and guides, but now their primary role is to support student-initiated inquiries. The ideal image is that of a fellow investigator searching for answers to unanticipated questions, helping students to evaluate the integrity of their processes, and encouraging them to exchange their various approaches and findings."

Karlan, who has taught in problem solving settings and written curriculum to encourage problem solving (for National Gardening Association, Teachers’ Lab and others), is quick to note that all teachers feel pressures that may not have been addressed by the curriculum author. Time constraints in the classroom are the most commonly noted limitations reported by teachers. In Karlan’s observations and discussions with teachers, he has noted that there may also be conflicts between how the curriculum authors view inquiry learning and how the teacher approaches it. The curriculum may not leave room for student generated problems and other limitations may be present, such as the rigid time limits imposed by telecommunications components of some curricula.

In the broadest sense, Karlan points out, all of us, teachers, curriculum writers and researchers, struggle with the best ways to pose problems and to interact with students to support inquiry.

A problem solving example

We asked Jimmy Karlan to give us an illustration of the difference between an open-ended problem solving approach to an activity and an approach that is hands-on, but does not encourage wide ranging problem solving. Here is his response:

Consider an activity that explores water at its freezing point. The materials would be: plastic container with tight-fitting lid, water, refrigerator with freezer.

The procedure is: (A) Fill the plastic container with so much water that some pours over the top when you put the lid on. (B) Place the container in the freezer and after the water has frozen, note its condition. (C) What happened? How would you explain this?

Another way to approach this same concept (i.e., water expands as it freezes) may be to present the following challenge: Prove at least three things that happen (or don’t happen) to water when it freezes. Be prepared to demonstrate what you have discovered to a skeptic.

Both of these activities provide students with a teacher-selected topic (frozen water). The first, however, offers only one strategy (procedure) that can be used to demonstrate an already given solution (water expands).

The second activity, on the other hand, actually consists of two problems, both of which invite students to develop their own strategies for solving them. First they have to figure out what happens (or doesn’t happen) to water when it freezes. Then they have to figure out how to convince someone else of their discovery. Furthermore, unlike the first activity, this one doesn’t begin by telling students the answer: "Water expands when it freezes."

Both activities are "hands-on." They involve the physical manipulation of everyday objects to gain an understanding of science-related concepts; however, only the second activity involves the manipulation of materials in order to gain an understanding of scientific processes (i.e., controlling variables, making hypotheses, recording data, etc.).

In my view, the first activity is "hands-on," but not "problem-solving;" the second is "hands-on" and "problem-solving." According to Kahney (1986), a person has a problem when she has a goal which cannot be achieved directly. Furthermore, according to Jackson (1983) a Problem = Objective + Obstacle(s). The first activity offers an objective, but it omits any obstacles. Although both activities have clearly stated goals and objectives, only the second does not prescribe a way in which to achieve them; it also includes a varying number and type of obstacles, depending on the student(s). The nature of the second activity more readily invites students to demonstrate and verbalize their conceptions.

Problem-solving science may or may not use everyday objects: Some problem-solving activities may be a purely conceptual experience. Likewise, hands-on science may or may not involve problem-solving.

Gagne (1970) stated that "Problem-solving can be viewed as a process by which the learner discovers the combination of previously learned rules that he can apply to achieve a solution for a novel situation ... but it is also a process that yields new learning." According to this definition, the first activity described above isn’t problem-solving based.

Jimmy Karlan concludes this argument in favor of problem solving approaches by quoting Jerome Bruner’s complex but thoughtful language: "It is only through the exercise of problem solving and the effort of discovery that one learns the working [methods] of discovery. The more one has practice of, the more one is able to generalize what one has learned into a style that serves for any kind of task one may encounter." .

Casey Murrow - Casey Murrow is Co-Director of Synergy Learning and editor of CONNECT.
List all articles by Casey Murrow