Part I: Preface

Abstract

Learning and teaching mathematics and statistics lives within the wide cultural context of mathematical and statistical practices in many areas of work and of play across our cultures. We notice that mathematics and statistics are not homogeneous, even as practiced by pure and applied mathematicians and statisticians. The formal logical face (echoed as the Platonist description in Aikenhead) is not what most mathematicians and statisticians live as researchers (Burton 2004), nor is it what is typically found in our upper level post-secondary mathematics and statistics classrooms. The chapters here better match the observations that the cognitive bases of mathematical learning, even of proofs, are much more diverse and engaging (Tall et al. 2012). More broadly, the insights of books such as The way we think (Fouconnier and Turner 2002), connect working with multiple representations and simulations across multiple disciplines, including mathematics, with how cognitive blending connects among multiple representations.