Collaboration in Learning and Teaching Statistics

Cary J. Roseth, Joan B. Garfield, and Dani Ben-Zvi
Michigan State University, USA, University of Minnesota, Twin Cities, USA, University of Haifa, Haifa, Israel

Journal of Statistics Education Volume 16, Number 1 (2008), jse.amstat.org/v16n1/roseth.html

Copyright © 2008 by Cary J. Roseth, Joan B. Garfield, and Dani Ben-Zvi all rights reserved. This text may be freely shared among individuals, but it may not be republished in any medium without express written consent from the author and advance notification of the editor.

Key Words: Collaboration; Cooperative learning; Collaborative teaching; Statistics education.

Abstract

This paper provides practical examples of how statistics educators may apply a cooperative framework to classroom teaching and teacher collaboration. Building on the premise that statistics instruction ought to resemble statistical practice, an inherently cooperative enterprise, our purpose is to highlight specific ways in which cooperative methods may translate to statistics education. So doing, we hope to address the concerns of those statistics educators who are reluctant to adopt more student-centered teaching strategies, as well as those educators who have tried these methods but ultimately returned to more traditional, teacher-centered instruction.

1. Collaboration in Learning and Teaching Statistics

Collaboration is not just an end goal of statistics instruction but also a means to help students learn statistics. Indeed, educators, psychologists, and statisticians alike have all called for students to have opportunities to work together as they learn statistics (e.g., Garfield, 1993; Hogg, 1992; Lovett & Greenhouse, 2002). The recently adopted GAISE guidelines (see Franklin & Garfield, 2006) make similar recommendations explicit, stating that, “As a rule, teachers of statistics should rely much less on lecturing, and much more on the alternatives such as projects, lab exercises, and group problem solving and discussion activities” (http://jse.amstat.org/education/gaise/GAISECollege.htm).

While collaboration and student-centered, active learning are relatively simple ideas, implementing such methods is not. Statistics educators may reasonably ask how these teaching methods should be translated to the statistics classroom. As highlighted by the 7^th International Conference on Teaching Statistics (ICOTS), working cooperatively in statistics education involves obvious benefits and challenges, with the latter raising questions about the degree to which cooperative methods actually translate to statistics education (Osvaldo Fabbroni, Chang Lee, Lievesley, Martin-Guzman, Morettin, & Rossman, 2007). This paper addresses this issue by providing specific examples of how statistics educators may apply a cooperative framework to classroom teaching, student assessment, and teacher collaboration. Thus, the purpose of this paper is a practical one, connecting a theoretical framework to guidelines and materials for statistics teachers.

We divide the paper into two sections, the first focusing on cooperative learning in the classroom and the second on collaboration among statistics educators. The argument is made that collaboration among both parties – i.e., among students and among educators – ultimately enhances and sustains the other.

2. Cooperative Learning in the Statistics Classroom

This first section focuses on practical tips and materials for successfully implementing cooperative learning methods in the statistics classroom. We begin, however, by differentiating the terms peer learning, active learning, cooperative learning, and group work. We also introduce social interdependence theory (Deutsch, 1949, 1962; Johnson & Johnson, 1989, 2005), the guiding theoretical framework for much of the research on the effects of cooperation.

2.1 Definition of Terms

How is cooperative work different from group work? To use cooperative learning effectively, statistics teachers must realize that not all groups are cooperative groups. Study groups, lab groups, and discussion groups may be groups, but they are not necessarily cooperative. In fact, while some kinds of groups facilitate student learning and increase the quality of life in the classroom, other types may hinder student learning and create disharmony and dissatisfaction in the classroom (Fiechtner & Davis, 1992).

How is cooperative learning different from active learning? Cooperative learning and active learning are often used interchangeably to describe instructional methods that allow students to solve problems, participate in activities, and discuss content with students. Importantly, cooperative learning is a form of active learning, but active learning is not necessarily cooperative. An important distinction is that cooperative learning methods capitalize on the motivational and epistemic processes occurring between students rather than within any one. This means that cooperative learning methods derive engagement and interest from the way students' individual goals are linked to each other, rather than rely on individual curiosity, work ethic, or the provocative nature of the curriculum, activity, or lesson plan. Put simply: Knowing that your peers’ success depends on your own – that you "sink or swim" together – is a powerful motivator (Kohn, 1986).

An example helps to illustrate the distinction between cooperative learning and active learning. Consider an activity focusing on understanding the standard deviation (for the original lesson plan see http://www.causeweb.org/repository/StarLibrary/activities/delmas2001). Student pairs must decide whether one histogram has a larger standard deviation than another histogram, or if the two histograms have the same standard deviation. This lesson is clearly active in that students are not passive recipients of the teacher’s knowledge. Simply asking students to complete the activity however – even asking students to work together in completing the activity – does not make the activity cooperative. Indeed, it is possible that some students may choose not to engage in the activity, preferring instead to let their partner do all of the work.

Now, consider how the histogram activity may be structured cooperatively. Student pairs are again presented with several pairs of histograms and must decide whether one histogram has a larger standard deviation than another histogram, or if the two histograms have the same standard deviation. Now, however, students are told that after completing the histogram activity, individual students will then form new groups of two and compare their answers. New pairs must reach consensus about their answers and, most importantly, both individuals must be able to explain what characteristics of the graphs support their answer. The instructor will then randomly select one individual from the new pairs to explain their answer for a given problem.

The cooperative structure described above builds on social interdependence theory (Deutsch, 1949, 1962; Johnson & Johnson, 1989, 2005), the basic premise of which is that the way in which interdependence is structured moderates how individuals interact which, in turn, determines outcomes. Cooperative goal structures result in promotive interaction (such as mutual help, sharing resources and information, acting in trustworthy and trusting ways), competitive goal structures result in oppositional interaction (such as obstructing of each other's goal achievement efforts, hiding resources and information from each other, acting in distrustful and distrusting ways), and the absence of goal structures results in the absence of interaction. The basic model proposed by social interdependence theory may be represented as follows:

What is different about the cooperatively structured histogram activity? When individuals perceive that they can reach their goals if and only if the other individuals with whom they are cooperatively linked also reach their goals, social interdependence theory predicts that individuals tend to seek outcomes that are beneficial to all those with whom they are cooperatively linked. Thus, in the histogram activity, individuals know that, after working together, they must individually present their answers to another student. Students also know that, after reaching consensus with their second partner, they may be individually required to justify their answer to the instructor. In short, successful completion of the cooperative histogram activity requires both individual and group efforts. It is in this way that cooperative goal structures tend to result in promotive interaction while competitive and individualistic goal structures result in oppositional or no interaction respectively. Readers interested in the empirical support of social interdependence theory are referred to several meta-analyses (e.g., Johnson & Johnson, 1989; Johnson, Johnson, Maruyama, Nelson, & Skon, 1981; Roseth, Johnson, & Johnson, in press). Readers are also referred to related meta-analyses on cooperative effects, albeit from slightly different theoretical orientations (e.g., Ginsberg-Block, Rohrbeck, & Fantuzzo, 2006; Rohrbeck, Ginsburg-Block, Fantuzzo, & Miller, 2003; Slavin, 1980, 1983, 1995).

From a cooperative learning perspective, any activity may be motivating and interesting if cooperative structures link students’ goals, behavior, and outcomes. In this paper we use cooperative learning as an umbrella term for all forms of peer learning in which students work together to maximize their own and each other’s learning (Johnson, Johnson, & Holubec, 1998). Thus, by cooperative learning we also include collaborative learning, peer tutoring, cross-age tutoring, and other teaching strategies aimed at structuring the way students interact with each other as they learn. For excellent reviews of these methods see O’Donnell (2006), Boud, Cohen, and Sampson (2001), and Falchikov (2001). And, for research focusing on cooperative learning in statistics education, see Chick and Watson (2002), Courtney, Courtney, and Nicholson (1994), Giraud (1997), Keeler and Steinhorst (1995), Magel (1998), Perkins and Saris (2001), and Potthast, (1999).

2.2 Implementing Cooperative Learning

The following sections highlight materials and provide practical tips for effectively using cooperative learning in the statistics classroom. These recommendations are meant to address common concerns about using group work, some of which make instructors reluctant to adopt more student-centered methods or, alternatively, to stop using them after initial difficulties. Our hope is to provide practitioners with the tools and understanding needed to capitalize on the benefits of cooperative learning.

We begin by providing a general introduction to the steps typically involved in a cooperative lesson. We then provide examples of how these methods may be used in the statistics classroom, focusing especially on the use of cooperative learning assessment procedures. We emphasize three statistics activities that are also part of a cooperative learning module available online at the Consortium for the Advancement of Undergraduate Statistics Education, CAUSE (see http://serc.carleton.edu/sp/cause/cooperative/example.html).

Conducting a cooperative lesson typically involves four steps: (a) making pre-instructional decisions about the lesson, (b) explaining the task and cooperative structure to students, (c) monitoring and, if necessary, intervening with each learning group, and after the lesson, (d) processing and evaluating student achievement (Johnson et al., 1998; see also Davis, 1993). While detailed instructions for accomplishing each of these steps is beyond the scope of this paper, we offer a few helpful hints.

Making pre-instructional decisions. Planning a lesson begins with specifying the academic objectives. In cooperative learning, it is also recommend that educators specify the social skill objectives that specify what interpersonal and small group skills are to be emphasized during the lesson. The importance of social skills cannot be overstated as, increasingly, large numbers of children, adolescents, and young adults do not possess the social skills necessary to establish and maintain positive relationships with their peers. Further, research suggests that educators must confront social norms making academic disinterest increasingly acceptable (Steinberg, Brown, & Dornbusch, 1996). Instructors must create the conditions in which students feel safe to say things like, “That’s interesting. Tell me more.” Thus, social skill objectives may enhance student participation in statistics activities.

Explaining the task and cooperative structure to students. The second and arguably most important step in a cooperative lesson is telling your students what to do and how to do it. It is here that instructors must (a) assign students to groups, (b) specify the criteria for successfully completing the activity, and (c) structure the cooperative goals linking individual students.

• Group size. Cooperative learning groups typically range in size from two to five. In general, as the size of the learning group increases, so too do the resources needed to help the group succeed (Johnson & F. Johnson, 2006). Thus, smaller groups are typically more successful than larger groups of students, especially when time is short and/or students lack the skills to work with several peers at once. Larger groups also decrease individual member’s opportunity to contribute; correspondingly, smaller groups make it more difficult for students to hide and not contribute their share of the work. Smaller groups also make it easier to identify any difficulties students may have in working together.
• Individual accountability. Instructors must be clear about the criteria by which student performance will be evaluated. Following Brophy (2004), effective criterion make goals immediate (here and now rather than for the distant future), specific ("answer all questions with no more than one mistake" rather than "do your best"), and challenging (i.e., difficult but reachable). For example, instead of saying "compare the two distributions with your neighbor," it is much more effective to say: "With your neighbor, identify three similarities and three differences between the two distributions. After five minutes I will call on one student at random to share their answers with the class.
• Make positive interdependence explicit. Above all, cooperative goal structures must be made explicit. For example, when using a problem set to review for a quiz, cooperation may be structured by saying: "Each of you has two responsibilities. First, you are each responsible for learning how to solve the problems and, so doing, preparing for the quiz. Second, you are responsible for making sure that every member of your group also knows how to solve the problem. Each member of the group will receive 5 extra points on their individual quiz if all of their group members score above 85%."

Monitoring and intervening during the cooperative activity. Once an activity begins, instructors must monitor and, when necessary, intervene in students’ group work. This is not the time to get a cup of coffee, as cooperative learning requires that teachers observe interaction among group members, and assesses both academic progress and the appropriate use of interpersonal and small group skills. This is also the time when a "window" to student's reasoning and thinking begins to open with student discourse providing a uniquely powerful way for educators to understand how students understand a given concept (Case, 1992).

Group processing. Finally, time should be given for students to process, reflect and evaluate what was helpful and unhelpful in completing the assignment. For example, instructors may ask students to identify at least two behaviors that were helpful to the group and at least two behaviors that would help the group perform even more effectively in the future (Davis, 1993). Not only do these discussions help to clarify whether learning objectives were achieved, they also help to reinforce classroom norms, values and behavioral expectations. Statements like, "Raise your hand if everyone in your group participated in your discussion" makes it clear that, in this classroom everyone’s participation is expected and valued.

Group processing may occur at two levels. Each learning group may discuss what they accomplished or, in whole-class processing, the teacher may give the class feedback with students sharing specific examples from their own groups. For more on group processing, readers are referred to Johnson, Johnson, and Smith (1991a, 1991b), Rau and Heyl (1990), and Walvoord (1986).

2.3 Practical Tips

In this section we suggest some practical tips for statistics instructors willing to try cooperative learning in their classes.

Assigning students to groups. For brief exercises, it should not be a problem for students to work with their friends. For extended cooperative activities however, major problems may emerge from letting students assemble into groups of their own choosing (Fiechtner & Davis, 1992).

Random groups, especially for one-time projects, are easy to assemble. They can be set up before class using a roster or they can be formed spontaneously by having students count off. For example, in a group of 40 students where you want groups of four, ask students to count off from 1 to 10, repeating this four times. Then, ask that all the "1’s" get together in a group, the "2’s" in a second group, etc. This method works well in creating heterogeneous groups as it rearranges students who started the class sitting together.

Using base groups to check in and track preparation for class. In addition to using different, informal learning groups to complete activities during class, students may also be assigned to a consistent base group. At the beginning of class, members of a base group can check in with each other, ask each other questions, compare notes, and discuss their preparation for class. In our own teaching, base group members also give themselves a daily rating on how well prepared for class (e.g., Did they complete the reading, homework problems, etc.?). The base group then calculates the group's average preparation rating and charts it over time. By looking at the group average fluctuate over the semester, students recognize that they are accountable to their peers and gain awareness of their study habits. Students also gain additional experience with interpreting real data.

Getting groups started on an activity. We suggest that students’ first interaction with each other be structured. Never let groups suffer through the awkward silence of "getting started." Social roles inevitably take over in such instances – e.g., the "talkers" always talk, and the "quiet" students always remain quiet. Cooperative groups work best when social roles are trumped by interdependent roles and goal structures. An easy way to structure the way groups get started is to say something like, "You’re probably wondering who will start? The person born closest (or farthest) from this room should begin." Using questions like this provides a quick way for students to interact personally without being too distracting or too "touchy-feely."

Importantly, "structured starts" can also be used post hoc. Anytime instructors hear silence after beginning an activity is an ideal time to say, "You’re probably wondering who will go first…" Structuring the start, even after the fact, helps students begin their work as quickly and as effectively as possible.

Assigning roles to group members. Another practical tip is to assign roles to students that give them a specific task in the group. Assigning roles can help to avoid traditional social roles (e.g., female students serving as the note-taker or male students serving as the group spokesman), and they can also be used to develop thinking and reasoning skills. Following Garfield (1993) and Johnson et al. (1998), examples of such critical-thinking roles include the following:

• Summarizing out loud: A student summarizes out loud what has just been read or discussed as completely as possible and without referring to notes or the original material. Students vocalize their understanding in order to make the implicit reasoning process overt and thus open to correction and discussion.

• Seeking Accuracy: A student seeks accuracy by correcting a member’s summary, adding important information he or she did not include, and pointing out the ideas or facts that were summarized incorrectly (e.g., "I’m not sure if that is right. I thought it was…").
• Seeking Elaboration: A student relates material being learned to earlier learned material and to other things they know (e.g., "This is like what we studied last week…" or, "How does this relate to…?").
• Extending Answers: A student extends other members’ answers or conclusions by adding further information or implications (e.g., "Here is something else to consider…" or, "I also think that…").
• Probing Questions: A student asks questions of the group that lead to deeper understanding of synthesis (e.g., "Would it work in this situation…?", "What else makes you believe…?" or, "Would this also work…?").

Helping students build their teamwork skills. The greater the students’ teamwork skills, the higher will be the quality and quantity of their learning. Operationally, teamwork skills are defined by specifying which behaviors are and are not appropriate within learning groups. It is not enough to tell students what skills you wish to see them use during the lesson. Teachers must also explain exactly what is expected by modeling the skill in front of the class. As an example, consider what it looks and sounds like when students do not pay attention. Not paying attention often looks like slouching, reading the newspaper, completing the Sudoku, checking e-mail, sleeping, etc. Not paying attention often sounds like finger tapping, turning pages, gossiping with a peer, typing, snoring, etc. In our experience, demonstrating such behaviors can offer a moment of levity in the classroom, with humor making it “safe” for students to engage in more productive behaviors that, in other contexts, may not be socially acceptable among their peers. Practical examples of social skills that enhance critical thinking were provided above (see "assigning roles to group members").

Helping a group that is not working well together. Not every group will work well together. Students vary in their preparation, motivation, and preferences for learning. If a group does not seem to be working well together it is important to try to figure out the cause. Is one student unprepared and perhaps not willing to help? Are students sitting silently because they don’t understand where to begin? The teacher can help by going to the group and asking a question or offering a prompt to get them going. If one student seems to be a problem, the teacher can invite that student into the hallway and find out what seems to be going wrong. If a student says that the rest of the group members are not contributing, or that they themselves have not prepared well, the instructor can offer advice to the student or the group, as appropriate.

Here again we emphasize that forming different, random groups for each activity can prevent the problem of some groups working consistently better than others. Simply put, random assignment ensures that individual differences in achievement, interpersonal skills and the like are evenly distributed across learning groups. Over time, these differences are also distributed across all learning groups, ensuring that – again, over time – any effects of between-group differences are minimized. Importantly, randomization of student groups also helps students to get to know as many of their classmates as possible, a key step in turning a classroom into a caring, supportive learning community. Consider the following student’s comment on the introductory statistics course evaluation:

"I have never had a professor or instructor that was this effective … I always felt valued, always … we would work in groups frequently which always helped … Big picture: he provided a unique learning environment that will help a variety of learning styles … Working in groups has made a big impact. Having built rapport with the other students quickly in the semester helped. Having a base group and assigned seating really helped not feel so lost. Having to report to what level we did our homework to our base groups, made each of us accountable and probably made each of us come to class more and do homework more. Overall, I can’t compare his style to any other professor or instructor I have ever had here…"