The following is an incomplete list of resources. If you have suggestions (we are smarter together after all!), please use the comment feature at the bottom of this page. Please include the APA citation and a brief description.
RESOURCES ABOUT COMPLEX INSTRUCTION
Cohen, E. G. (1994). Designing groupwork: Strategies for the heterogeneous classroom, (2nd ed.). New York: Teachers College Press.
This book is the foundation for work on Complex Instruction. We highly recommend it as the first book (or second book if you want to read our Smarter Together book first) people read about CI. The book includes an appendix of “group skill-building” exercises that are really useful for teaching students new norms and roles of working in groups.
Featherstone, H. F., Crespo, S., Jilk, L. M., Oslund, J., Parks, A., & Wood, M. B. (2011). Smarter together! Collaboration and equity in the elementary math classroom. Reston, VA: National Council of Teachers of Mathematics.
This book describes our work with Complex Instruction and elementary classrooms. It offers information on the philosophy and pedagogy of CI and descriptions of instructional strategies along with mathematics tasks. While the book focuses on elementary classrooms, we have heard from teachers of secondary and college students who have found the book useful. Here’s a link to the book at NCTM: http://www.nctm.org/catalog/product.aspx?id=13785. And here’s a link to our facebook page: https://www.facebook.com/SmarterTogetherCollaborationandEquity
Watanabe, M. (2011). “Heterogenius” Classrooms: Detracking Math and Science–A Look at Groupwork in Action [with DVD]. New York: Teachers College Press.
This book provides examples of CI in action in secondary mathematics and science classrooms. We recommend it as an excellent guide for what detracking and using groupwork could look like in secondary classrooms.
Horn, I. S. (2011). Strength in numbers: Collaborative learning in secondary mathematics. Reston, VA: National Council of Teachers of Mathematics.
This book describes how secondary mathematics teachers can implement CI in their classrooms to support all students in learning rigorous mathematical content.
Stanford Complex Instruction Webpage: http://cgi.stanford.edu/group/pci/cgi-bin/site.cgi
This is the birthplace of CI! This webpage has classroom video and an annotated bibliography of reference articles (most of which are not included below).
BOOKS WITH GROUPWORTHY TASKS:
Erickson, T. (1989). Get it together: Math problems for groups grades 4-12. Berkeley: EQUALS.
This book has many problems for cooperative problem solving groups in grades 4 and up.
Erickson, T. (1997). United we solve: 116 math problems for groups grades 5-10. Oakland, CA: eeps media.
This book is a follow up to Get it Together and continues Get it Together’s pattern of math problems designed especially for groups. Some materials from the book are also available online: http://www.eeps.com/products/uws_stuff/unitedwesolve.html
Goodman, J. M. (1992). Group solutions: Cooperative logic activities for grades K-4. Berkeley: Lawrence Hall of Science.
This book has tasks appropriate for younger students. The tasks have many features that make them excellent starting places for groupwork with elementary students. While the tasks primarily focus on mathematics and science, teachers will find that other content areas (such as social studies) are included, making this an excellent resource for elementary teachers.
Goodman, J. M. (1997). Group solutions, too!: More cooperative logic activities for grades K-4. Berkeley: Lawrence Hall of Science.
A sequel to Group Solutions, this book has more terrific activities for grades K-4.
Fisher and Frey (webpage: http://www.fisherandfrey.com/) Nancy Frey and Douglas Fisher
These folks have a fabulous webpage and many terrific group work resources. We highly recommend their article, The First 20 Days: Establishing Productive Group Work in the Classroom (http://fisherandfrey.com/_admin/_filemanager/File/First_20_Days.pdf)
BOOKS WITH MATHEMATICAL TASKS
Burns, M. (2007). About teaching mathematics: A K-8 resource. Sausalito, CA: Math Solutions Publications.
This classic text for mathematics professional development and pre-service teacher preparation includes many classroom-tested activities that teach a variety of mathematical content. Not all of the tasks are groupworthy, but many are.
Lampert, M. (2001). Teaching problems and the problems in teaching. New Haven, CT: Yale University Press.
This book describes a year of teaching mathematics in a fifth grade classroom. Lampert describes, in great detail, her pedagogical decisions and teaching moves and she also includes many math tasks she used in her classrooms along with the work her students produced. Lampert’s tasks could easily be adapted for groupwork.
Schwartz, J. L. & Kenney, J. M. (2008). Tasks and rubrics for Balanced Mathematics Assessment in primary and elementary grades. Thousand Oaks, CA: Corwin Press.
This book contains several math tasks can be adapted for group work. There are several other books written by the Balanced Assessment in Mathematics team as well as tasks, rubrics, and sample work available at http://balancedassessment.concord.org/
Stenmark, J. K., Thompson, V., & Cossey, R. (1985). Family math. Berkely: Lawrence Hall of Science.
This book contains many rich tasks designed for engaging families in mathematics together. Many of the tasks can be adapted for group work.
Van de Walle, J. A., Karp, K. S., Bay-Williams, J. M. (2010). Elementary and middle school mathematics: Teaching developmentally, 7th Ed. New York: Allyn & Bacon.
This is just one of many textbooks written by John Van de Walle and his colleagues. All of these textbooks provide many excellent mathematical tasks that can be adapted for groupwork. We all use this textbook in our own work with preservice elementary teachers and we highly recommend it.
SOME RESEARCH PUBLICATIONS RELATED TO COMPLEX INSTRUCTION
Boaler, J. (2006). How a detracked mathematics approach promoted respect, responsibility, and high achievement. Theory into Practice, 45 (1), 40-46.
This article describes the ways in which the mathematics department of an urban, ethnically diverse school brought about high and equitable mathematics achievement. The teachers employed heterogeneous grouping and complex instruction, an approach designed to counter status differences in classrooms. As part of this approach teachers encouraged multidimensional classrooms, valued the perspectives of different students, and encouraged students to be responsible for each other. The work of students and teachers at Railside School was equitable partly because students achieved more equitable outcomes on tests, but also because students learned to act in more equitable ways in their classrooms. Students learned to appreciate the contributions of students from different cultural groups, genders, and attainment levels, a behavior termed relational equity. This article describes the teaching practices that enabled the department to bring about such important achievements.
Boaler, J. (2006). Urban success: A multidimensional mathematics approach with equitable outcomes. The Phi Delta Kappan, 87 (5), 364-369
By revamping their school’s entire mathematics program, the teachers at an urban high school were able to help their disadvantaged students attain high levels of mathematical understanding. Just as important, Ms. Boaler notes, the students learned to appreciate the contributions of all their peers, regardless of gender, ethnicity, or social class.
Boaler, J. (2008). Promoting “relational equity” and high mathematics achievement through an innovative mixed ability approach. British Educational Research Journal, 34(2), 167-194.
Equity is a concept that is often measured in terms of test scores, with educators looking for equal test scores among students of different cultural groups, social classes or sexes. In this article the term ‘relational equity’ is proposed to describe equitable relations in classrooms; relations that include students treating each other with respect and responsibility. This concept will be illustrated through the results of a four-year study of different mathematics teaching approaches, conducted in three Californian high schools. In one of the schools—a diverse, urban high school—students achieved at higher levels, learned good behaviour, and learned to respect students from different cultural groups, social classes, ability levels and sexes. In addition, differences in attainment between different cultural groups were eliminated in some cases and reduced in all others. Importantly, the goals of high achievement and equity were achieved in tandem through a mixed- ability mathematics approach that is not used or well known in the UK.
Boaler, J., & Staples, M. E. (2008). Creating mathematical futures through an equitable teaching approach: The case of Railside School. Teachers College Record, 110 (3), 608-645.
One of the findings of the study was the success of Railside school, where the mathematics department taught heterogeneous classes using a reform-oriented approach. Compared with the other two schools in the study, Railside students learned more, enjoyed mathematics more and progressed to higher mathematics levels. This paper presents large scale evidence of these important achievements and provides detailed analyses of the ways that the Railside teachers brought them about, with a focus on the teaching and learning interactions within the classrooms.
Cohen, E. G., Brody, C. M., & Sapon-Shevin, M. (Eds.). (2004). Teaching cooperative learning: The challenge for teacher education. SUNY Press.
Teacher educators from ten institutions and programs in the United States, Canada, and Germany describe the ways in which they have changed teacher preparation to more fully incorporate cooperative learning concepts. Analytical commentaries on the programs highlight the learning experience of these programs as well as underlying issues of needed reforms in teacher education. Included among best practices in education, cooperative learning may require a shift in program philosophy and disciplinary areas to meet the challenge of complex organizations and diverse student populations. As the essays in the volume demonstrate, a new alignment of field experiences to provide support for novices to implement cooperative strategies, and to receive timely and effective supervision for these attempts, may also be required.
Cohen, E. G., & Lotan, R. A. (1997). Working for Equity in Heterogeneous Classrooms: Sociological Theory in Practice. Sociology of Education Series. New York, NY: Teachers College Press
Sociological theory and method have been used to develop a theory of complex instruction (CI). CI enables teachers to teach at a high intellectual level while reaching a wide range of students. Teachers work to create equal-status interaction within small groups as students use each other as resources to complete challenging group tasks. The following selections in this collection explore the use of CI in classes with diverse students: (1) “Equity in Heterogeneous Classrooms: A Challenge for Teachers and Sociologists” (Elizabeth G. Cohen); (2) “Complex Instruction: An Overview” (Rachel A. Lotan); (3) “Organizing the Classroom for Learning” (Elizabeth G. Cohen, Rachel A. Lotan, and Nicole C. Holthuis); (4) “The Power in Playing the Part” (Dey E. Ehrlich and Marcia B. Zack); (5)”Understanding Status Problems: Sources and Consequences” (Elizabeth G. Cohen); (6) “Raising Expectations for Competence: The Effectiveness of Status Interventions” (Elizabeth G. Cohen and Rachel A. Lotan); (7) “The Effect of Gender on Interaction, Friendship, and Leadership in Elementary School Classrooms” (Anita Leal-Idrogo); (8) “Principles of a Principled Curriculum” (Rachel A. Lotan); (9) “Effects of the Multiple-Ability Curriculum in Secondary Social Studies Classrooms” (Bert Bower); (10) “What Did Students Learn?: 1982-1994” (Elizabeth G. Cohen and others); (11) “Sociologists in the Land of Testing” (Elizabeth G. Cohen); (12) “The Relationship of Talk and Status to Second Language Acquisition of Young Children” (H. Andrea Neves); (13) “Complex Instruction and Cognitive Development” (Rachel Ben-Ari); (14) “Teachers as Learners: Feedback, Conceptual Understanding, and Implementation” (Nancy E. Ellis and Rachel A. Lotan); (15) “Principals, Colleagues, and Staff Developers: The Case for Organizational Support” (Rachel A. Lotan, Elizabeth G. Cohen, and Christopher C. Morphew); (16) “Linking Sociological Theory to Practice: An Intervention in Preservice Teaching” (Patricia E. Swanson); (17) “Organizational Factors and the Continuation of a Complex Instructional Technology” (Rene F. Dahl); and (18) “A Viewpoint on Dissemination: (Nikola N. Filby). Three appendixes contain class, student, and teacher evaluation instruments. (Contains 43 tables, 14 figures, and 198 references.)
Cohen, E. G., Lotan, R., Scarloss, B., E.Schultz, S., & Abram, P. (2002). Can groups learn? Teachers College Record, 104(6), 1045-1068.
This is a study of assessment of the work of creative problem-solving groups in sixth-grade social studies. We test the proposition that providing students with specific guidelines as to what makes an exemplary group product (evaluation criteria) will improve the character of the discussion as well as the quality of the group product. To assess the group’s potential for successful instruction, we examine the character of the group conversation as well as the quality of the group product. We present a statistical model of the process of instruction that connects the use of evaluation criteria, group discussion, creation of the group product, and average performance on the final written assessment.
Cohen, E.G., Lotan, R., Scarloss, B., Arellano, A.R. (1999) Complex Instruction: Equity in cooperative learning classrooms. Theory into Practice, 38, 80-86.
Many educators view cooperative learning as an alternative to tracking and ability grouping and as an appropriate and promising strategy for academically and linguistically heterogeneous classrooms. When students work in small groups, they talk and work together and serve as resources for one another. However, cooperative learning also poses a serious instructional dilemma when it creates situations in which students who are academically low achieving or who are social isolates are excluded from the interactions. Thus, rather than increasing equity, cooperative learning also has the potential to reinforce a severe educational and social problem. In this paper, we focus on two dimensions of equity when considering student learning in small groups: access and equitable relations. First we ask: Do students who do not read at grade level or who are not proficient in the language of instruction have opportunities to use the instructional materials and complete the group activities? Do other group members prevent them from examining, or manipulating these materials? Second, we ask: How can the teacher ensure that all group members are active and influential participants and that their opinions matter to their fellow-students?
Crespo, S. & Featherstone, H.F. (2013). Counteracting the language of math ability: Preservice teachers explore the role of status in elementary classrooms. In L.J. Jacobson, J. Mistele & B. Sriraman (Eds.) Mathematics Teacher Education in the Public Interest. Charlotte, N.C.: Information Age Publishing.
Elofson, S. (2015). The relationship between assigning competence and students’ perceptions of their mathematical abilities (Master’s thesis). Retrieved from http://archives.evergreen.edu/masterstheses/Accession89-10MIT/Elofson_S_MIT2015.pdf. Link here.
This masters thesis describes an action research project done by Sonja Elofson in her classroom. It describes assigning competence and offers examples the author assigning competence to her students. The thesis also describes how students responded to this teacher move. This thesis is a terrific resource for anyone seeking more information about assigning competence.
Esmonde, I. (2009). Ideas and identities: Supporting equity in cooperative mathematics learning. Review of Educational Research, 79 (2), 1008-1043.
This review considers research related to mathematics education and cooperative learning, and it discusses how teachers might assist students in cooperative groups to provide equitable opportunities to learn. In this context, equity is defined as the fair distribution of opportunities to learn, and the argument is that identity-related processes are just as central to mathematical development as content learning. The link is thus considered between classroom social ecologies, the interactions and positional identities that these social ecologies make available, and student learning. The article closes by considering unresolved questions in the field and proposing directions for future research.
Horn, I. S. (2005). Learning on the job: A situated account of teacher learning in high school mathematics departments. Cognition and Instruction, 23(2), 207-236.
To investigate teachers’ everyday on-the-job learning, I used a comparative case study design and examined the work of mathematics teachers in 2 high schools. Analysis of interviews, classroom observations, and teachers’ conversations highlighted 3 key resources for learning: (a) reform artifacts oriented the teachers’ attention to key concepts of a reform, whereas the interactions surrounding them established local meanings; (b) conversation-based classification systems communicated pedagogical assumptions; and (c) the rendering of classroom interactions in conversations shaped opportunities for teachers to consult with and learn from colleagues. Taken together, these learning resources provide a conceptual infrastructure for teachers to make sense of their practice. This research highlights the social and situated nature of teachers’ pedagogical reasoning and specifies the role of teacher community in teacher learning.
Horn, I. S. (2008). Turnaround students in high school mathematics: Constructing identities of competence through mathematical worlds. Mathematical Thinking and Learning, 10(3), 201-239.
This analysis joins together two lines of work: research on students’ mathematical identities and on curricular organization that supports equitable academic outcomes. This article conceptualizes students’ sense of mathematical competence as emerging through the interaction between their extant identities and the mathematical worlds they encounter in the school. Using data from a five-year mixed methods longitudinal study comparing students’ mathematical experiences in two high schools (Boaler, 2006), I focus on seven students who showed initial and unexpected success in mathematics. One department provided more resources for students to develop identities of mathematical competence, while the second department naturalized differential outcomes for students. An examination of two student trajectories, one from each school, illustrates how mathematical identities were constructed across, as well as within, classrooms. I argue that students’ mathematical identities emerge beyond a single classroom, and to achieve equitable outcomes, we must look not only at the work of individual teachers but also at teacher collectives who support mathematical achievement.
Horn, I.S. (2010). Teaching replays, teaching rehearsals, and re-visions of practice: Learning from colleagues in a mathematics teacher community. Teachers College Record, 112(1), 225-259.
Theoretically, this article illustrates a process of learning as recontextualization, as the teachers work between general teaching principles and specific occurrences in their classrooms. Practically, by highlighting the work that teachers do to make sense of innovative practices, this analysis provides a description of how collegial conversations can support teachers’ informal learning, supporting the development of professional communities.
Horn, I.S. & Little, J.W. (2010). Attending to problems of practice: Routines and resources for professional learning in teachers’ workplace interactions. American Educational Research Journal, 47(1), 181-217.
The authors investigate how conversational routines, or the practices by which groups structure work-related talk, function in teacher professional communities to forge, sustain, and support learning and improvement. Audiotaped and videotaped records of teachers’ work group interactions, supplemented by interviews and material artifacts, were collected as part of a 2-year project centered on teacher learning and collegiality at two urban high schools. This analysis focuses on two teacher work groups within the same school. While both groups were committed to improvement and shared a common organizational context, their characteristic conversational routines provided different resources for them to access, conceptualize, and learn from problems of practice. More specifically, the groups differed in the extent to which conversational routines supported the linking of frameworks for teaching to specific instances of practice. An analysis of the broader data set points to significant contextual factors that help account for the differences in the practices of the two groups. The study has implications for fostering workplace learning through more systematic support of professional community.
Jilk, L.M. (in press).“Everybody can be Somebody.” Expanding and Valorizing Secondary School Mathematics Practices to Support Engagement and Success. In N.S. Nasir, C. Cabana, B. Shreve, E. Woodbury, and N. Louie (Eds). Those kids, our kids: Teaching mathematics for equity. NY: Teachers College Press.
Jilk, L.M. & O’Connell, K. (in press). Reculturing high school mathematics departments for educational excellence and equity. In N.S. Nasir, C. Cabana, B. Shreve, E. Woodbury, and N. Louie (Eds). Those kids, our kids: Teaching mathematics for equity. NY: Teachers College Press.
Jilk, L. M. (2010). Becoming a “liberal” math learner: Expanding secondary school mathematics to support cultural connections, multiple mathematical identities and engagement. Kitchen, R.S. & Civil, M. (Eds).Transnational and Borderland Studies in Mathematics Education. Routledge Press.
Staples, M. (2007). Supporting whole-class collaborative inquiry in a secondary mathematics classroom. Cognition and Instruction, 25(2-3), 161-217.
Recent mathematics education reform efforts call for the instantiation of mathematics classroom environments where students have opportunities to reason and construct their understandings as part of a community of learners. Despite some successes, traditional models of instruction still dominate the educational landscape. This limited success can be attributed, in part, to an underdeveloped understanding of the roles teachers must enact to successfully organize and participate in collaborative classroom practices. Towards this end, an in-depth longitudinal case study of a collaborative high school mathematics classroom was undertaken guided by the following two questions: What roles do these collaborative practices require of teacher and students? How does the community’s capacity to engage in collaborative practices develop over time? The analyses produced two conceptual models: one of the teacher’s role, along with specific instructional strategies the teacher used to organize a collaborative learning environment, and the second of the process by which the class’s capacity to participate in collaborative inquiry practices developed over time.
DISSERTATIONS INVOLVING COMPLEX INSTRUCTION AND MATHEMATICS
Jilk, L. M. (2007). Translated mathematics: Immigrant women’s use of salient identities as cultural tools for interpretation and learning. (Order No. 3298057, Michigan State University). ProQuest Dissertations and Theses, 209. Retrieved from http://ezproxy.library.arizona.edu/login?url=http://search.proquest.com/docview/304848309?accountid=8360. (304848309).
Oslund, J. A. (2009). Stories of change: Narrative perspectives on elementary teachers’ identifying and implementation of new mathematics teaching practices. (Order No. 3364731, Michigan State University). ProQuest Dissertations and Theses, 229-n/a. Retrieved from http://ezproxy.library.arizona.edu/login?url=http://search.proquest.com/docview/304950898?accountid=8360. (304950898).
