Teaching and Learning the Derivative in Senior High School

Contrasting the Educational Traditions of Taiwan and Germany to Explore the Connection between Prior Knowledge, Learning Opportunities and Superficial vs. In-depth Knowledge about the Concept of Derivative

Understanding the concept of derivative is crucial in upper secondary education, but is challenging for many students. Previous research from different countries indicates that knowledge acquired by students is often limited to simple differentiation rules but knowledge about the derivative concept is scarce.

Using Sfard’s process-object framework, we examine students' knowledge about the concept of derivative distinguishing between operational, structural and pseudostructural knowledge. These different levels of knowledge are related to students' prior knowledge before learning the derivative in mathematics class and to the typical learning opportunities as manifested in textbooks. Contrasting the different educational traditions on the topic of differentiation in Taiwan and Germany allows a nuanced view of the role of the various influencing factors. This will be used to identify opportunities to improve the teaching of in-depth knowledge about the concept of derivative.

Kristin Litteck, Aiso Heinze (IPN Kiel, Germany)

Pin-Chen Guo, Kai-Lin Yang (National Taiwan Normal University Taipei, Taiwan)