Umeå Mathematics Education Research Centre (UMERC)

UMERC is an interdisciplinary network of researchers, research students and teachers from school and university, who are engaged in research and research education in connection to the UMERC research themes.

Latest publications from UMERC

Development of Mathematics Teaching: Design, Scale, Effects. Proceedings from Madif9: The Ninth Swedish Mathematics Education Research Seminar, Umeå, February 4-5, 2014


The grammar and conceptualisation of motion in Iwaidja


Different languages have different ways of using spatiallanguage, grammatically and conceptually. Thispaper reports on aspects of the language of motion inIwaidja, an indigenous Australian language. The waythat Iwaidja groups and separates spatial concepts suchas direction, height and movement in relation to anotherobject are briefly described using examples from aroute description task. The implications are discussedin terms of how understanding these grammatical featurescan help teachers of Indigenous students, as wellas providing keys to cross-linguistic investigations ofmathematical ...

Impact of differing grammatical structures in mathematics teaching and learning


This book examines multiple facets of language diversity and mathematics education. It features renowned authors from around the world and explores the learning and teaching of mathematics in contexts that include multilingual classrooms, indigenous education, teacher education, blind and deaf learners, new media and tertiary education. Each chapter draws on research from two or more countries to illustrate important research findings, theoretical developments and practical strategies. (From book cover)

Examining social situation of development, with two students of mathematics at grade four, in different national contexts


This paper discusses the Vygotskian construct of social situation of development in relation to two students we call Nelly and Brian, as they learn mathematics in respective grade four classrooms in Sweden and USA. Nested within larger action research projects, both students are found to exhibit developmental crisis, as they transit from familiar environments in primary grades and meet newer demands at middle school. The construct of social situation of development, treated herein as an exploratory framework, is understood in terms of instructional environments of students, their emotion...

A Beautiful Proof by Induction


The purpose of this note is to present an example of a proof by induction that in the opinion of the present author has great aesthetic value. The proof in question is Thomassen’s proof that planar graphs are 5-choosable. I give a self-contained presentation of this result and its proof, and a personal account of why I think this proof is beautiful.

A secondary purpose is to more widely publicize this gem, and hopefully make it part of a standard set of examples for examining characteristics of proofs by induction.

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