Mathematics-for-Teaching: an Ongoing Investigation of the Mathematics that Teachers (Need to) Know

Abstract

In this article we offer a theoretical discussion of teachers' mathematicsfor-teaching, using complexity science as a framework for interpretation. We illustrate the discussion with some teachers' interactions around mathematics that arose in the context of an in-service session. We use the events from that session to illustrate four intertwining aspects of teachers' mathematics-for-teaching. We label these aspects "mathematical objects," "curriculum structures," "classroom collectivity," and "subjective understanding". Drawing on complexity science, we argue that these phenomena are nested in one another and that they obey similar dynamics, albeit on very different time scales. We conjecture (1) that a particular fluency with these four aspects is important for mathematics teaching and (2) that these aspects might serve as appropriate emphases for courses in mathematics intended for teachers.

Sınıf Öğretmenliği Programı Öğrencilerinin Matematiksel Alan Bilgilerinin İncelenmesi

“…Baş, Çakmak, Işık ve Bekdemir'in de (2015) matematik öğretmeni adaylarıyla yürüttükleri çalışmada da, öğretmen adaylarının düşüncelerini matematiksel semboller kullanarak ifade edemedikleri görülmektedir. Oysaki matematiksel gösterimleri kullanabilmek, önemli matematiksel kaynaklara ihtiyaç duyulan öğretimin genel görevlerinden biri olarak görülmekte (Ball, Thames, & Phelps, 2008); ayrıca kavramları bir sembolik sitemden diğerine dönüştürme matematik öğretenler için anahtar bir yeterlilik sayılmaktadır (Davis & Simmt, 2006). Çünkü sembollerin doğru anlamlandırılması, kişiyi doğru kavramsallaştırmaya götürebilecektir (Yeşildere, 2007).…”

Mathematics for teaching and deep subject knowledge: voices of Mathematics Enhancement Course students in England

“…The research we report is part of a larger project (project name) and its study of what and how mathematical knowledge for teaching, or more simply 'mathematics for teaching' (cf Davis & Simmt, 2006), is taking shape in and across ranging contexts of mathematics teacher education.…”

“…Davis & Simmt, 2006;Krauss, Baumert, & Blum, 2008;Ma, 1999). In this paper we investigate and describe how students of a mathematics course for prospective secondary mathematics teachers in England, where 'understanding mathematics in depth' was an explicit goal, talk about this notion.…”

Mathematics Teachers’ Didactic Strategies: Examining the Comparative Potential of Low Inference Generic Descriptors

“…The role of questioning within explanation also seems ambiguous. Brent Davis and Elaine Simmt (2006), in discussing the role of explanation as a means by which distributed prior knowledge can be made collective, tacitly incorporate not only discussion but questioning as elements of explanation. Borko (2004, 8), however, discusses questions and explanations as "specific instructional features," implying a distinction.…”