Commentary on Problem Solving Heuristics, Affect, and Discrete Mathematics: A Representational Discussion

Abstract

Advances in Mathematics Education is a new and innovative book series published by Springer that builds on the success and the rich history of ZDM—The International Journal on Mathematics Education (formerly known as Zentralblatt für Didaktik der Mathematik). One characteristic of ZDM since its inception in 1969 has been the publication of themed issues that aim to bring the state-of-the-art on central sub-domains within mathematics education. The published issues include a rich variety of topics and contributions that continue to be of relevance today. The newly established monograph series aims to integrate, synthesize and extend papers from previously published themed issues of importance today, by orienting these issues towards the future state of the art. The main idea is to move the field forward with a book series that looks to the future by building on the past by carefully choosing viable ideas that can fruitfully mutate and inspire the next generations. Taking inspiration from Henri Poincaré (1854–1912), who said “To create consists precisely in not making useless combinations and in making those which are useful and which are only a small minority. Invention is discernment, choice”, this is our attempt to create something new for the field by making useful combinations of existing ideas with those that are considered to be at the frontiers of the field of mathematics education research today, to carefully select from the past and cross-fertilize ideas across generations with the hope of producing something relevant, forward oriented, synthetic and innovative. The series is supported by an editorial board of internationally well-known scholars, who bring in their long experience in the field as well as their expertise to this series. The members of the editorial board are: Ubiratan D’Ambrosio (Brazil), Miriam Amit (Israel), Jinfa Cai (USA), Helen Forgasz (Australia), and Jeremy Kilpatrick (USA).