In this reflection of teaching, we describe a series of activities that introduce the Taylor series through dynamic visual representations with explicit connections to students' prior learning. Over the past several decades, educators have noted that curricular materials tend to present the Taylor series in a way that students often interpret as…

Reading comprehension is key to knowledge acquisition and to reinforcing memory for previous information. While reading, a mental representation is constructed in the reader's mind. The mental model comprises the words in the text, the relations between the words, and inferences linking to concepts in prior knowledge. The automated model of…

Kinematics is a topic students are unknowingly aware of well before entering the physics classroom. Students observe motion on a daily basis. They are constantly interpreting and making sense of their observations, unintentionally building their own understanding of kinematics before receiving any formal instruction. Unfortunately, when students…

As teachers working with students in entry-level algebra classes, authors Amy Nebesniak and A. Aaron Burgoa realized that their instruction was a major factor in how their students viewed mathematics. They often presented students with abstract formulas that seemed to appear out of thin air. One instance occurred while they were teaching students…

With the growing emphasis on the development of scientific inquiry skills, the display and interpretation of data are becoming increasingly important. Graph interpretation competence is, in fact, essential to understanding today's world and to be scientifically literate. However, graph interpretation is a complex and challenging activity. Graph…

This article describes an activity through which students collect data and explore ways to display them through graphs and charts. It also motivates various summary measures for location, spread and shape. Finally, it gives an introduction to concepts of validity, reliability and unbiasedness.

Hierarchical graphs represent relationships between objects (like computer file systems, family trees etc.). Graph nodes represent the objects and interconnecting lines represent the relationships. In two experiments we investigated what concepts are necessary for understanding hierarchical graphs, what misconceptions evolve when some of the…