Modeling mathematics begins with problems to solve. Students should
experience lessons and tasks that connect mathematical ideas to relevant
everyday life. These lessons should be challenging and allow for
Representations provide a way of communicating students’ mathematics thinking but are also powerfully tools for thinking.
They make mathematical ideas more concrete and available for reflection.
They help students remember their thinking as they record steps. They
provide a record of students’ efforts to understand and make their
understanding available to others for interpretation.
Students must be able to explain the mathematical meaning of each part
of their representation. When teachers keep track of student thinking,
strategies, or representations, that can be a public record. Recorded on
chart paper, these records can be available for later reference. Public
records could show different strategies for the same problem or
different representations on the same concept. They can also record
students’ developing ideas that could lead to mathematical