This article focuses on the Thinking Through a Lesson Protocol (TTLP) that is intended to facilitate the design of lessons based on cognitively challenging mathematics tasks. Included is a discussion of the key features of the TTLP, suggestions on ways in which the protocol can be used as a tool for collaborative lesson planning, and a discussion of the potential benefits of using the TTLP. Teachers are encouraged to reflect upon their practice and consider teaching practices over time.

An activity done by eighth grade students using data that was gathered from sun-shadow observations.

Mathematics teachers need to provide explicit language instruction for students learning English. By differentiating instruction in mathematics, teachers can plan and provide instruction in mathematics with the goal of providing access to all students. Constructing knowledge leads to greater understanding and principles of language acquisition provide a framework to support differentiating the mathematics classroom.

Students doing mathematics through the lens of (artistic) performance. Students are encouraged to discuss and reflect upon their mathematical experiences much like they would a favorite book or movie. Students are encouraged to explore complex mathematical relationships that offer the potential for them to experience significant mathematical surprise and insight.

Focus on the issues of coaching and assessing. A preservice middle school teacher's unique solution to the Pizza Problem was not what the professor expected. The student's solution strategy, based on sequences and a reinvention of Pascal’s triangle, is explained in detail. Both the teacher and student are involved in a meaningful dialogue to uncover the mathematics "behind a mess."