Students thrive when presented with tasks that are approachable, challenging, and interesting. Remembering to challenge all students is essential, not just those who excel in mathematics; teachers need to open the door to meaningful mathematics for every learner. In this exploration into subtraction patterns, teachers will see how curious young…

The impulse to investigate the natural world is deeply rooted in our earliest childhood experiences. This notion has long guided researchers to uncover the cognitive mechanisms underlying the development of scientific reasoning in children. Until recently, however, research in cognitive development and education followed largely independent…

"Principles and Standards for School Mathematics" (NCTM 2000) proposes that mathematics instruction provide opportunities for students to engage in mathematical inquiry and in meaning-making through discourse. Mathematics teachers are encouraged to build on student discoveries in designing subsequent instruction. In this article, the author…

Describes an activity for introducing elementary school students to the surprising Mobius band. Incorporates elements of experimentation and exposes the deceptively simple Mobius band as a rich resource for discovery. Provides an opportunity for young learners to participate in the process of scientific inquiry within a mathematical framework.…

Presented are four mathematical discoveries made by students on an arithmetical function using the Fibonacci sequence. Discussed is the nature of the role of the teacher in directing the students' discovery activities. (KR)