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Complex Instruction: High-Quality Mathematics for All Learners

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Over the past several posts, I have been exploring how to make the mathematics curriculum more equitable. Another important aspect of equity is making sure that all learners have access to the mathematics being taught. Complex Instruction (CI) is one way of doing this.

CI looks at student engagement as an issue of status. Some students are assigned high status by their peers and teacher, whereas other students are assigned low status (through praise, listening to their ideas, body language, etc.). Low-status students rarely have their ideas taken seriously and are often excluded from group work, thus causing them to disengage with mathematics. CI teaching involves group-worthy tasks and pedagogical moves to support all learners.

Group-Worthy Tasks 

Group-worthy tasks draw on a variety of mathematical smartnesses. Most group-worthy tasks draw on several of the Standards for Mathematical Practice, and many teachers list the multiple smartnesses needed before beginning and then explicitly call attention to them throughout the task and during the wrap up.

Group-worthy tasks also make it difficult for one student to take over. In one task I created, each group member had his or her own set of shapes to sort however he or she wanted. As each person shared the sort, the other group members had to place a new shape in the appropriate place in their sort, which forced them to listen to one another’s ideas.

Pedagogical Moves 

One of my favorite pedagogical moves in CI is requiring all questions to be group questions. If someone calls the teacher over, the teacher can ask anyone in the group what the question is; if that person doesn’t know, the teacher can leave, saying, “It sounds like you need to discuss this as a group before calling me over again.” Another favorite is group quizzes in which teachers randomly choose a student who must explain a final solution/product after working on a task. This process holds all students accountable for learning the content, and it forces the students to support one another’s learning. If a student struggles, the teacher can leave, giving him or her a few minutes to consult with group members before the teacher returns.

Perhaps one of the most important pedagogical moves is assigning competence. The teacher watches for learners who are making mathematical contributions and then points them out publicly. Although this should be done for all students, it is of particular importance for low- status students because it will help them and their classmates see that this individual has something valuable to contribute. Assigning competence is made easier when tasks draw on multiple smartnesses—this makes it possible for more learners to contribute and it makes it less likely that any one student will excel at all aspects of the task.

Resources 

Smarter Together! Collaboration and Equity in the Elementary Math Classroom provides a wonderful introduction to CI.

• The NRICH website has a section explaining CI.

• I and several of the Smarter Together! authors are working to develop CI resources and lessons.

What do you do to reach all learners? Do you have experience with CI?

 


Mathew FeltonMathew Felton is an assistant professor of mathematics education in the department of mathematics at the University of Arizona and will be starting in the department of teacher education at Ohio University this fall. He is a coauthor of Connecting the NCTM Process Standards and the CCSSM Practices. His research focuses on supporting current and future teachers in connecting mathematics to real-world contexts and on teachers’ views of issues of equity, diversity, and social justice in mathematics education.


Can I add to your wonderful list of resources? Readers interested in CI might also consider:

Designing Groupwork, Cohen and Lotan, Teachers College Press
The original work, now in its third edition. It explains the underlying theory in clear language, and is not math-specific.

Strength in Numbers, Horn, NCTM
Math-specific, comprehensive secondary CI resource.

Mathematics for Equity, Nasir, Cabana, Shreve, Woodbury and Louie, Teachers College Press
A comprehensive compilation of research at Railside High, which used CI as the basis for its entire math program, with additional chapters on specific strategies and structures developed by teachers to create a complete CI-based math program.

“Heterogenius” Classrooms, Watanabe, Teachers College Press
A collection of articles and videos on math teaching strategies, including a chapter on Laura Evans, a terrific CI teacher.

Groupwork in Diverse Classrooms, Shulman, Lotan and Whitcomb, Teachers College Press
A thoughtful collection of short case studies designed to help teachers discuss CI principles and strategies in realistic contexts. A Facilitator’s Guide is sold separately by the same publisher.

Working for Equity in Heterogeneous Classrooms, Cohen and Lotan, Teachers College Press
The original theory and research on which Designing Groupwork was based.
Posted by: CarlosC_58870 at 8/8/2014 7:30 PM


How about adding College Prepatory Math - Common Core Algebra, Common Core Geometry, Common Core Algebra II, middle school (Common Core Courses 1-3), plus several other options - to your references. They totally support what you have said above with Pedagogical Moves and Group Worthy Tasks! They even have group norms and roles embedded into their program!
TheresaR
Posted by: TheresaR_58778 at 8/10/2014 6:03 PM


All great resources; thanks you two!
Posted by: MathewF_09852 at 8/19/2014 2:30 PM


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