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 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
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.
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.
Smarter Together! Collaboration and Equity in the Elementary
Math Classroom provides a wonderful introduction to CI.
The NRICH website has a section
I and several of the Smarter Together!
authors are working to develop CI resources and
What do you do to reach all learners? Do you have experience with CI?
Mathew 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.