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Encountering Algebra

Cecilia Kilhamn and Roger Säljö, eds.
Publication Date: 
Number of Pages: 
[Reviewed by
Erica R. Miller
, on
In Encountering Algebra: A Comparative Case Study of Classrooms in Finland, Norway, Sweden, and the USA, the authors provide a glimpse of how algebra is first introduced to students around the world. The research monograph is built upon case studies of classrooms in each country and highlights differences in instruction. The case studies were drawn from the VIDEOMAT project, which focused on studying the national curricular documents in the four countries previously mentioned. Since algebra is not well defined in the field and approached differently in different curriculum materials, the researchers asked the teachers to identify themselves where in the school curriculum algebra was first introduced to the students. As a result, the researchers observed students in different grade levels (ranging from 6 – 8). Initially, the researchers observed and recorded the first four consecutive days of instruction and then asked each teacher to implement a lesson developed by the research team involving a matchstick task. This approach allowed the researchers to observe differences in how algebra is introduced and to examine how students across all four countries engaged with a common task.
To focus the content of the first four empirical chapters, which provide case studies of the first four teacher-planned lessons given by teachers in each country, the research team translated all curriculum materials and transcripts into English and coded them. As a result of this analysis, researchers from each country chose to highlight different themes while also emphasizing cultural elements of instruction that were prevalent in each country. The Swedish team focused on mathematization and participation in classroom discourse, the Norwegian team focused on the design and use of instructional examples, the Finnish team focused on solving equations and the principle of equality, and the USA team focused on teachers’ beliefs about algebra. In the final empirical chapter, the authors conduct a discourse analysis of the fifth researcher-planned lesson and provide descriptions of how students approached the matchstick task, analyze student argumentation in four target student groups (one from each country), and compare and contrast similarities and differences in students’ discourses.
This book is a valuable resource for those who are interested in studying either the teaching and learning of algebra or similarities and differences in mathematics instruction around the world. Detailed descriptions of the observed classrooms are provided and include transcripts of teacher and student dialogue, examples of curriculum materials and tasks, and descriptions of physical manipulatives and symbolic representations. While the study is grounded in theory, each theory used is explained thoroughly and it is not assumed that the reader has prior knowledge of these subjects. However, the technical language and methods used do make less suited for an undergraduate audience. In summary, the book provides an interesting and enlightening glimpse into how algebra is introduced to students around the world.


Dr. Erica R. Miller is an Assistant Professor of Mathematics at Virginia Commonwealth University. Her research interests lie in the area of undergraduate mathematics education, primarily in the professional development of undergraduate mathematics instructors.