Mathematics teaching has its own imperatives: mathematical practice and the work of mathematics instruction
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ORIGINAL ARTICLE
Mathematics teaching has its own imperatives: mathematical practice and the work of mathematics instruction Patricio Herbst1 · Daniel Chazan2 Accepted: 6 April 2020 © FIZ Karlsruhe 2020
Abstract How should we expect growing understandings of the nature of mathematical practice to inform classroom mathematical practice? We address this question from a perspective that takes seriously the notion that mathematics education, as a societal enterprise, is accountable to multiple sets of stakeholders, with the discipline of mathematics being only one of them. As they lead instruction, teachers can benefit from the influence of understandings of mathematical practice but they also need to recognize obligations to other stakeholders. We locate how mathematics instruction may actively respond to the influence of the discipline of mathematics and we exemplify how obligations to other stakeholders may participate in the practical rationality of mathematics teaching as those influences are incorporated into instruction. Keywords Mathematical practice · Instruction · Curriculum · Instructional exchanges · Professional obligations · Practical rationality · Didactical contract · Didactical transposition · Professional community · Mathematicians
1 Introduction There has been a history of influences from the discipline of mathematics on the mathematics curriculum. For example, as high schools started to emerge in the U.S., artifacts from the discipline, such as Newton’s Principia, English translations of Legendre’s Elements de geometrie, or English versions of Euclid’s Elements (e.g., Playfair, 1860) were identified as sources of the knowledge students were expected to acquire (Grabiner, 1977; Herbst, 2002). Likewise, in the mid twentieth century, the Bourbaki effort in the foundations of mathematics spawned the controversial “new math” movement that pushed for a reorganization of the curriculum according to the ideas and concepts that were then central to the contemporary organization of the discipline (e.g., sets; Dieudonné, 1973, Thom, 1971).
* Patricio Herbst [email protected] Daniel Chazan [email protected] 1
School of Education, University of Michigan, Ann Arbor, USA
College of Education, University of Maryland, College Park, USA
2
Moreover, through the twentieth century, mathematicians have participated in processes of policy making related to the school mathematics curriculum. Mathematicians have been included in blue ribbon committees that opined on the curriculum needed in schools. For example, late in the twentieth century, the National Research Council’s (NRC) report Everybody Counts (NRC, 1989), which included pure and applied mathematicians among its writers, highlighted the importance of applications of mathematics in the workplace to promote that the curriculum would include the study of mathematical models of real world and scientific phenomena. Also, professional efforts to improve the mathematics curriculum in the United States, such as the NCTM (1989, 2000) Standards have included
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