Teacher feedback on procedural skills, conceptual understanding, and mathematical practices: A video study in lower secondary mathematics classrooms

This chapter discusses how the use of Dynamic Geometry Software (DGS) can be used to support students' engagement with the Standards for Mathematical Practice as outlined in Common Core State Standards for Mathematics (CCSS-M). In particular, the aim of this chapter is to (1) describe what students' strategic use of appropriate tools might entail in a DGS environment, and (2) argue that for students to engage in these practices in a DGS environment, they must construct meaning for and with these tools in the process of instrumental genesis. Illustrative examples are provided from three secondary mathematics classrooms, and the chapter concludes with recommendations for future research and teacher education in this area.

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Concreteness Fading Strategy: A Promising and Sustainable Instructional Model in Mathematics Classrooms

Sustainability ◽

10.3390/su12062211 ◽

2020 ◽

Vol 12 (6) ◽

pp. 2211 ◽

Cited By ~ 1

Author(s):

Hee-jeong Kim

Keyword(s):

Instructional Strategies ◽

Conceptual Understanding ◽

National Curriculum ◽

Instructional Model ◽

Abstract Concepts ◽

Mathematics Classrooms ◽

Study Support ◽

Principles And Standards ◽

Concreteness Fading

Conceptual understanding has been emphasized in the national curriculum and principles and standards across nations as it is the key in mathematical learning. However, mathematics instruction in classrooms often relies on rote memorization of mathematical rules and formulae without conceptual connections. This study considers the concreteness fading instruction strategy—starting with physical activities with manipulatives and gradually fading concreteness to access abstract concepts and representations—as a promising and sustainable instructional model for supporting students in accessing conceptual understanding in mathematics classrooms. The results from the case study support the validity of the concreteness fading framework in providing specific instructional strategies in each phase of concept development. This study implies the development of sustainable teacher education and professional development by providing specific instructional strategies for conceptual understanding.

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Teachers' Interpretations of Effective Whole-class Interactive Teaching in Secondary Mathematics Classrooms

Educational Studies ◽

10.1080/0305569022000003717 ◽

2002 ◽

Vol 28 (3) ◽

pp. 265-274 ◽

Cited By ~ 27

Author(s):

Sonia Jones ◽

Howard Tanner

Keyword(s):

Secondary Mathematics ◽

Interactive Teaching ◽

Mathematics Classrooms ◽

Whole Class

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An exploration of teacher and student perceptions of blended learning in four secondary mathematics classrooms

Mathematics Education Research Journal ◽

10.1007/s13394-020-00359-2 ◽

2020 ◽

Author(s):

Catherine Attard ◽

Kathryn Holmes

Keyword(s):

Blended Learning ◽

Student Perceptions ◽

Technology Use ◽

Online Teaching ◽

Mathematics Learning ◽

Secondary Mathematics ◽

Pedagogical Practices ◽

Alternative Methods ◽

Learning Approaches ◽

Mathematics Classrooms

Abstract The COVID-19 pandemic forced many teachers around the world to make a sudden switch from face-to-face to online teaching. This shift in practice has provided an opportunity to reconsider how technology use in mathematics education can be utilised to improve student engagement. In this study, we explore four case studies of Australian secondary mathematics classrooms conducted prior to the COVID-19 pandemic to examine how teachers are using blended learning approaches and how their students perceive these pedagogical practices. Findings across all four sites indicate that technology use expands student opportunities to engage with mathematics learning through the provision of multiple pathways and methods of access. Specifically, we find evidence supporting the use of blended classroom teaching strategies to provide differentiation and personalised learning approaches; visualisation and dynamic manipulation of mathematics concepts; and alternative methods for teacher-student feedback and communication. We argue that the student learning experience in mathematics can be enhanced through a variety of blended learning approaches by allowing for diverse points of access to learning opportunities which are more closely aligned to individual learning needs and free from the temporal constraints of the classroom.

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Power in Numbers: Student Participation in Mathematical Discussions in Heterogeneous Spaces

Journal for Research in Mathematics Education ◽

10.5951/jresematheduc.44.1.0288 ◽

2013 ◽

Vol 44 (1) ◽

pp. 288-315 ◽

Cited By ~ 52

Author(s):

Indigo Esmonde ◽

Jennifer M. Langer-Osuna

Keyword(s):

African American ◽

High School Students ◽

Mathematics Learning ◽

Figured Worlds ◽

African American Student ◽

American Student ◽

School Students ◽

Mathematical Practices ◽

Mathematics Classrooms ◽

Mathematical Discussions

In this article, mathematics classrooms are conceptualized as heterogeneous spaces in which multiple figured worlds come into contact. The study explores how a group of high school students drew upon several figured worlds as they navigated mathematical discussions. Results highlight 3 major points. First, the students drew on 2 primary figured worlds: a mathematics learning figured world and a figured world of friendship and romance. Both of these figured worlds were racialized and gendered, and were actively constructed and contested by the students. Second, these figured worlds offered resources for 1 African American student, Dawn, to position herself powerfully within classroom hierarchies. Third, these acts of positioning allowed Dawn to engage in mathematical practices such as conjecturing, clarifying ideas, and providing evidence.

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