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…

College calculus plays an important role in STEM students' degree and career aspirations. One of the key factors considered in assessing a student's ability to be successful in calculus is their proficiency in topics from prior mathematics courses such as algebra and precalculus. This study set out to examine the impact of students' precalculus…

Precalculus and single-variable calculus courses are a critical early juncture for the success of science, technology, engineering, and mathematics (STEM) students in the United States (US). The default course structure is often a required three-term sequence of precalculus, differential calculus, and integral calculus. In this paper we analyse…

We present an embodied theory of transfer as applied to mathematical ideas. Project-based learning (PBL) offers important sites for investigating transfer because students and teachers must track mathematical invariant relations that are embedded in complex settings where knowledge and information is distributed and extended across various…

Active learning involves students engaging with course content beyond lecture: through writing, applets, simulations, games, and more (Prince, 2004). As mathematics is often viewed as a subject area that is taught using more traditional methods (Goldsmith & Mark, 1999), there are actually many simple ways to make undergraduate mathematics…

The Harry Potter series furnishes many instances of both good and bad teaching. From them, we can learn more about three principles outlined in "How People Learn" (National Research Council 2000a). (1) Teachers should question students about their prior knowledge, as Professor Lupin does before his lessons; (2) we should encourage students to…

Children who come to school without numerical game-playing experience have trouble with math relationships in direct-instruction situations. This article explores the varied roles of active thinking, social interaction, previous knowledge, and child-initiated choice in children's development of math concepts. Self-esteem cannot be built by doing…

The 12th iteration of the International Conference on Educational Data Mining (EDM 2019) is organized under the auspices of the International Educational Data Mining Society in Montreal, Canada. The theme of this year's conference is EDM in Open-Ended Domains. As EDM has matured it has increasingly been applied to open-ended and ill-defined tasks…

In this article, the author presents findings of a project that focused on identifying elements in the learning environment that promote numeracy outcomes. The project--"Numeracy Research and Development Initiative"--was undertaken in eight schools across a range of settings within the three schooling systems in Queensland and was…