Since the 1950s, the understanding of how the base 10 system works has been encouraged through alternative base systems (Price 1995; Woodward 2004). If high school students are given opportunities to learn other base systems and analyze what they denote, we believe that they will better understand the structure of base 10 and its operations…

Shapedoku is a new type of puzzle that combines logic and spatial reasoning with understanding of basic geometric concepts such as slope, parallelism, perpendicularity, and properties of shapes. Shapedoku can be solved by individuals and, as demonstrated here, can form the basis of a review for geometry students as they create their own. In this…

Problem solving is a necessary component of developing a strong mathematics curriculum that will help all students achieve their life goals, regardless of their specific academic plans. What day-to-day instructional decisions do teachers need to make if they believe that problem solving is a vehicle for learning mathematical content? In this…

"Reasoning and sense making should occur in every classroom every day," states "Focus in High School Mathematics: Reasoning and Sense Making" (NCTM 2009, p. 5). As this book suggests, reasoning can take many forms, including explorations and conjectures as well as explanations and justifications of student thinking. Sense making, on the other…

This article describes an engaging, data-gathering activity that allows students to explore relationships between latitude and average monthly temperatures of cities in the Western Hemisphere. This data-gathering activity covered interesting and important mathematical ground and engaged students from the start. While students searched for their…