Mathematically Significant Instructional Learning Experiences

Hands-on, minds-on, and authentic learning tasks have the following features:

• The tasks meaningfully involve the big ideas of mathematics and connect powerfully to other areas of inquiry.

• The tasks often relate to problems that students encounter in their lives or communities.

• Students have an active role in formulating, designing, and managing the tasks.

• The tasks build on mathematically interesting questions or problems that students themselves have raised.

• The tasks involve nonroutine problems - that is, there is no way to specify in advance how to solve the problems and there are many ways in which the problems may be solved.

• The issues and problems involved in the tasks can be viewed from multiple perspectives, so that they require nuance judgment and decisionmaking.

• The tasks contain concepts or themes that are rich enough to be explored over a substantial period of time, from a week to an entire school year or beyond.

• The tasks connect meaningfully to each other to bring about significant mathematical development over the course of the school year and, ultimately, throughout the pre-K-12 experience.

• The tasks generate new knowledge and products and often have spinoffs into other projects.

• The tasks often require the strategic use of technology and the thoughtful design of a methodology to conduct the inquiry.