The research issue in this study is how to structure collaborative learning so that it improves solving physics problems more than individual learning. Structured collaborative learning has been compared with individual learning environments with Schoenfeld's problem-solving episodes. Students took a pre-test and a post-test and had the opportunity to solve six physics problems. Ninety-nine students from a secondary school in Shanghai participated in the study. Students who learnt to solve problems in collaboration and students who learnt to solve problems individually with hints improved their problem-solving skills compared with those who learnt to solve the problems individually without hints. However, it was hard to discern an extra effect for students working collaboratively with hints-although we observed these students working in a more structured way than those in the other groups. We discuss ways to further investigate effective collaborative processes for solving physics problems. Computer-supported collaborative learning (CSCL) has become a promising tool in science education (Van Boxtel, 2000) . Since collaboration is the process of interaction among peers in order to reach a common goal, it is very important that participants have a clear idea of proper ways to reach the common goal and how to contribute to it as an individual. Successful CSCL structures the collaboration process so that participants' motivation, personalities, prior knowledge, and experiences are combined in a coordinate group effort (Johnson & Johnson, 2000; Koschmann, 1996) . Much research on collaborative problem-solving with computers is about the conditions of collaboration, such as group size, group composition, nature of the *Corresponding author. PO Box 1286, 9701BG Groningen, The Netherlands. E-mail: e.g.harskamp@rug.nl 1670 E. Harskamp and N. Ding task, or communication media and their impact on student learning. Dillenbourg, Baker, Blaye, and O'Malley (1996) expressed in their review of research the need to study the interactive processes in order to delineate which interactive processes may cause student learning. More recently research in CSCL has shown that the frequency of task-related interactions during collaboration is often a good predictor of learning outcomes of individual students. It is assumed that certain types of taskrelated interactions with others lead to the active processing of information by the individual, which can modify the individual's knowledge and skills. This is especially so when peers provide examples of a topic, explain a concept, demonstrate a solution method, or supply specific argumentation. These kinds of verbal interactions are called "elaborations". Elaborations between students are necessary to solve a problem collaboratively in such a way that participants improve their knowledge (Avouris, Dimitracopoulou, & Komis, 2002; Van Boxtel, 2000; Webb & Farivar, 1999) . Yet, it is difficult to trace how structuring of the learning environment effects the stimulation of elaborations between students and how this is related to learning outcomes of individuals. Even in structured CSCL environments students tend to spend much time on superficial aspects of the task rather than on elaborations. This may be due to the fact that students in CSCL do not see all of each other's activities, as in face-to-face collaboration, and feel they have to keep in touch. Hence, in this study we explore students' elaborations in face-to-face collaborative problem-solving and compare these with individual problem-solving. Science education in schools all over the world is increasingly required to produce high-order problem-solvers (UNESCO, 2004) . As problem-solving is about finding a solution to a problem that is relatively new to the learner, it involves the skill to analyze a problem, to apply prior knowledge, to synthesize different bits of knowledge, to make decisions about how to proceed, and to evaluate the steps taken in the solution process (Polya, 1957) . Many researchers have concluded that students may have the necessary prior knowledge for a problem but still cannot solve it (Sfard, Nesher, Streefland, Cobb, & Mason, 1998) . While some students find it difficult to relate the right prior knowledge to the problem, others have difficulty analyzing a problem or carrying out the appropriate calculations. Based on a comprehensive review of research on problem-solving in physics, Maloney (1994) summarized that successful students' problem-solving strategies at least contain conscious qualitative analysis of a problem, making a sketch of the problem, restating the problem in one's own words, and conscious review of equations or theorems that fit the problem. The question for teachers is whether to teach students a step-by-step strategy or to let them construct a strategy on their own. Some researchers demonstrate that students will profit from a step-by-step strategy in solving problems independently (Heller, Keith, & Anderson, 1992) . One example of the possibilities new technology provides is the intelligent tutoring program for solving algebra word problems designed by Conati and Van Lehn (2000). Their program ANDES is showing a computer tutor that is coaching self-explanation when pupils follow the solution of example problems step by step. The program has a rather static view on how to solve problems and teach problem-solving through a procedure of fixed steps. But this procedure is not consistent with genuine problem-solving activity (Sfard & Kieran, 2001; Wilson, Fernandez, & Hadaway, 1993) . In our study a five-episode strategy developed by Schoenfeld in solving mathematical problems was selected because of its suitability for solving problems in physics. According to Schoenfeld (1992 Schoenfeld ( , 1994 one should not dictate strict problem-solving steps but give students room for the development of an individual solving strategy using the following episodes: • Read, analyze the problem (analyze). • Activate relevant knowledge to solve the problem (explore). • Make a plan (plan). • Carry out the plan (implement). • Check the answer (verify). To make students conscious users of the episodes, Schoenfeld asked students procedural questions such as: Can you make a scheme of this problem? What procedure do you know that could help you? Have you made a plan? Did your solution answer the question? By asking these questions students reflect on their use of the episodes and develop self-confidence (Schoenfeld, 1994) . Harskamp and Suhre (in press) developed a computer program for a mathematics course using the episodes of Schoenfeld's approach to help students solve applied mathematics problems. They provided hints in the computer program with each episode. The hints showed students how to act in the different episodes. The program was quite successful. Pol, Harskamp, and Suhre (2005) used the program to supports novices in solving physics problems about forces. The program does not dictate strict problem-solving steps and gives students room to develop an individual solving strategy. Hints are provided for the five episodes and the student may choose hints freely. The research showed that students who had worked with the program with hints could solve physics problems better than their peers who did the program without hints. In both research projects mentioned earlier, students hardly used the hints to verify their answers and on the post-test they had difficulty verifying their answers. So, in these projects, individual problem-solving with hints did not improve students' reflection on problem-solving. This needs special attention in the instructional design (Davis & Linn, 2000) . We want to find out whether collaboration can improve students' reflection on physics problems. About 15 years ago Blaye, Light, Joiner, and Sheldon (1991) showed that children who had previously worked as collaborative pairs on problemsolving in physics were twice as successful on a knowledge test as children who had had the same amount of experience working alone. The researchers conclude that within a small group that works as a team, students tend to spend more time on reflecting and discussing the suggested solution than when students work individually. Nelson (1999) suggests on the basis of her research that if students are frequently engaged in constructive dialog, their knowledge of facts and procedures 1672 E. Harskamp and N. Ding will retain longer and their problem-solving skills in physics will improve more than if they learn individually. However, collaborative learning will be at risk of becoming conversational learning and less effective than traditional learning if a structuring of interactions is absent. Without the presence of tutors, students are inclined to chat and become less oriented at their task. On the basis of their research, Erkens, Kanselaar, Prangsma, and Jaspers (2003), Pena-Shaff and Nicholls (2004) , and Van der Meijden and Veenman (2005) suggest that structuring of the dialogs that students are supposed to have about the problem leads to more frequent higher-level elaboration and makes the process of knowledge construction in the individuals more effective. In structuring the collaboration process it is necessary to overcome impasses and redirect incorrect solution paths, to facilitate problem-solving interaction to keep students engaged, and to suggest how students can take the problem step by step. Students should find the optimal balance of peer interaction and take expert advice. We think that the episodes of Schoenfeld's approach can provide suggestions of how to divide a problem into parts. By providing examples with each episode, students can take expert advice and can redirect themselves if they follow an incorrect solution path. We have evidence that this approach works for individual students (Pol et al., 2005) . In order to make it work for learning in a group we need a script that tells the students how to maintain a balance between peer interaction and expert advice, and how to change between individual activities and peer interaction in solving a problem (Weinberger, Fischer, & Mandl, 2001 ). A script not only improves active participation of students, but can also provide knowledge convergence: finding common knowledge to carry out a task and socially sharing knowledge. Knowledge convergence among peers can be encouraged by shared resources such as hints, examples, and representations (Fischer & Mandl, 2002; Mancini, Hall, Hall, & Stewart, 1998; O'Donnell, 1999 ). Schoenfeld's episodes with hints will show the students examples of high-level information they should provide as a result of their elaboration. The hints should be used after students have discussed their suggestions, prior knowledge, or solution plans. The hints provide feedback on their discussions and show students they are on the right track or provide students with knowledge they could not generate. Under certain conditions collaborative problem-solving will be more effective than individual problem-solving. Students should know what to do and how to work together: some structuring of the process is needed. In previous research with mathematics and physics problems, researchers concluded that episodes with hints to structure the solution process can improve individual problem-solving. But what if students working together on a problem are provided with episodes with hints? Will they improve their problem-solving skills still more? From previous research very little is known about this issue. To explore the effectiveness of variations in structuring of collaborative and individual problem-solving, three research questions and hypotheses are formulated: 1. Does collaborative learning without hints improve students' problem-solving learning compared with individual learning without hints? Hypothesis 1: Collaborative problem-solving with the use of episodes leads to better learning outcome for individuals than individual problem-solving. 2. Does individual learning guided by hints improve students' problem-solving learning compared with learning without hints? Hypothesis 2: Individual problem-solving with the use of episodes and hints leads to better learning outcome for individuals than individual problem-solving with episodes only. 3. Does collaborative learning with hints improve students' problem-solving learning compared with collaborative learning without hints? Hypothesis 3: Collaborative problem-solving with episodes and hints leads to better learning outcome for individuals than collaborative problem-solving with episodes only. Methodology In this research project the episodes of Schoenfeld's (1992) approach serve as stepping stones for problem-solving, and are used to structure students' learning processes. We have designed four conditions: • A condition requiring students to collaborate on problem-solving with the help of hints (CL+H). • A condition requiring students to collaborate on problem-solving without any hints (CL). • A condition requiring students to solve problems individually with the help of hints (I+H). • A condition requiring students to solve problems individually without any hints (I). The study was conducted in a secondary school in Shanghai with a sample of 99 students from two classes of grade 11. The school ranked among the top-five best schools in Shanghai. Students in the study are at the age of 17, coming from families with a wide range of occupations, incomes, and educational levels. Of the sample, 54.5% were female (n = 54) and 45.5% were male (n = 45). The study was a randomized group design with a pre-test and a post-test. Students in each class were assigned randomly to the four conditions. Students in the two collaboration conditions worked in dyads. All students tried to solve the same moderately structured multi-step physics problems. We used new context problems that gave students ample opportunity to read and analyze and would take them some effort to connect with previous physics knowledge. Figure 1 illustrates one of the problems. It is a five-step problem and is used as an example to demonstrate the condition "Collaboration with hints". Students were required to work according to a script on the five episodes. The hints that go with each episode were on cards and numbered sequentially from 1 to 5. The hints consisted of a text that described the main topics in an episode and a diagram that depicted the problem situation. As hints progressed the diagram became more and more detailed. We expected this external representation to help maintain the focus in discussion and we expected the details to help students solve the problems (Jonassen, Peck, & Wilson, 1999) . The hints were put upside down in front of the two students. There are no unbending rules using the hints, but the students first have to think of the answers to fill in on the log sheet and discuss them with each other before using the hints. Problem survey (read, analyze). Students are required to verbalize the problems to identify the known and unknown information of the problem, and determine a general approach that is appropriate to this situation, such as what kind of concepts and principles will be useful in solving this problem. The result of their discussion can be a rough picture showing the objects, their motion, and their direction. Active knowledge (explore). Students are asked to translate their sketch into a scientific description with a diagram. In the diagram they define variables to calculate desired quantities. They write down the formula that may help to solve the problem. The hints may be used only after the discussion. Make a plan (plan). After making a scientific description, students are asked to make a solution plan individually. This plan should involve the steps in the equations and rough estimates of the outcome. Then they are asked to put their plans together to compare. It is not necessary that there must be consent or one must follow the other's plan. Comparison of the solution plan simply makes students aware that more than one solution is possible. They may use the hint to check whether they are on the right track or they may correct their solution plans if necessary. Carrying out the plan (implement). Students are asked to translate their own plan into a series of appropriate mathematical actions by substituting the numerical values into a formula and to solve the final equation. It is necessary for them to check regularly whether they are meeting their targets and revise the plan accordingly.  Based on their answers, students are encouraged discuss their solutions. When they have got the same answers, they are asked to retell their solving process and check whether they have really arrived at the right solution. If their answers are different, they should determine whose is correct or complete. They are also asked to reflect on what they had learnt for future problems and tasks, and what kind of strategies are more efficient and can be adopted later on. At the end, students were given a worked out example as the final judge of their solution. The students wrote their information about the five episodes in a log sheet (see later) and especially elaborate upon the verification of their answers. Both the pre-test and post-test were given in open-question format. Responses on each episode were given from 0 points (no information) to 5 points (correct and detailed information). The students were required to give information about four episodes: analyze, explore, plan, and implement. In total 20 points for each question could be gained. Since students in both pre-test and post-test were asked to solve the problems individually, the final stage-verifying the solution-was not taken into account. Introduction. Prior to the pre-test we used one lesson for an introductory training. First, students of all conditions were shown a videotape. In the videotape, two students solved a physics problem concerning forces while discussing their ideas following the episodes of problem-solving. We showed this video to make sure that all students understood the idea of working with the log sheets. Thereafter, students in condition CL+H were given instruction with a sample problem in how to collaborate in each episode using the hints. The students in condition CL were given instruction with the sample problem in how to collaborate in each episode. In both collaborative conditions students were asked to solve a problem by thinking aloud and following the episodes on their log sheet. The students in I+H were given instruction in how to use the hints with the sample problem. Students in condition I only did the sample problem. All students filled in a log sheet and received the sample answer so that they could verify their solution.
In REF , three groups of students were compared: those who learned collaboratively in groups, those who were provided with hints, and those who learned individually without hints.
Structured Collaboration versus Individual Learning in Solving Physics Problems
International Journal of Science Education
Psychology