scholarly journals Do cultural norms influence how teacher noticing is studied in different cultural contexts? A focus on expert norms of responding to students’ mathematical thinking

ZDM ◽  
2020 ◽  
Author(s):  
Anika Dreher ◽  
Anke Lindmeier ◽  
Paul Feltes ◽  
Ting-Ying Wang ◽  
Feng-Jui Hsieh
Keyword(s):  
Mathematics Education ◽  
Mathematical Thinking ◽  
Instructional Quality ◽  
Specific Aspect ◽  
Teacher Noticing ◽  
Concurrent Process ◽  
Cultural Contexts ◽  
Mathematics Classrooms ◽  
Parallel Text ◽  
Open Question

Abstract As an important component of teaching expertise, teacher noticing is gaining growing attention in our intercultural mathematics education community. However, it is likely that in many cases the researchers’ perspectives on what characterizes high instructional quality in mathematics classrooms shape what they expect teachers to notice. In particular, it is an open question how potentially different norms of instructional quality influence how teacher noticing is operationalized in East Asian and Western cultures. Consequently, in a first step, this bicultural research project on teacher noticing in Taiwan and Germany focuses on exploring the researchers’ frames of reference for investigating teacher noticing. In this paper, we thus propose a concurrent process for developing vignettes and eliciting corresponding expert norms as a prerequisite to investigating teacher noticing in a way that is sensitive to different cultural contexts. In this process, the research teams in both countries developed in parallel, text vignettes in which, from their perspective, a breach of a norm regarding a specific aspect of instructional quality was integrated. In an online expert survey, these vignettes were then presented to German and Taiwanese researchers in mathematics education (19 from each country) to investigate whether these experts recognize the integrated breach of a norm. This approach allows researchers to identify potentially different norms of instructional quality in mathematics classrooms. In particular, by means of a specific representation of practice, it became visible how expert norms of responding to students’ mathematical thinking can be different from a Taiwanese compared to a German perspective.

scholarly journals Enhancing Pre-service Teachers’ Noticing: A Learning Environment about Fraction Concept

2021 ◽  
Vol 4 (1) ◽  
pp. 1
Author(s):  
Pedro Ivars
Keyword(s):  
Mathematics Education ◽  
Learning Environment ◽  
Training Programs ◽  
Mathematical Thinking ◽  
Learning Trajectory ◽  
Teacher Noticing ◽  
School Teachers ◽  
Primary School Teachers ◽  
Teacher Training Programs ◽  
Pre Service Teacher

Professional noticing allows teachers to recognise important events in a classroom and give effective responses using their knowledge. Hence developing this competence in teacher training programs is an issue in the Mathematics Education field. In this study, we present the design of a learning environment about the part-whole meaning of fraction to develop pre-service primary school teachers’ noticing of students’ mathematical thinking. The learning environment is designed around three tasks (vignettes) that pre-service teachers have to analyse using knowledge from research on mathematics education provided as a students’ hypothetical learning trajectory. Eighty-five pre-service teachers participated in this learning environment. Results allows us to characterise the enhancement of pre-service teacher noticing through looking at the changes in the discourse generated in the three tasks.

Using Photographs and Learning Trajectories to Enhance Teacher Noticing to Support Formative Assessment

2020 ◽  
pp. 134-149
Author(s):  
Katherine Ariemma Marin ◽  
Sarah A. Roller ◽  
Elizabeth Petit Cunningham
Keyword(s):  
Data Analysis ◽  
Formative Assessment ◽  
Mathematical Thinking ◽  
Student Thinking ◽  
Learning Trajectories ◽  
Early Childhood Mathematics ◽  
Teacher Noticing ◽  
Mathematics Classrooms ◽  
New Framework

In this chapter, the authors propose a re-imagined framework for formative assessment that weaves professional teacher noticing with the use of learning trajectories and photographs. Photographs can be used to capture “disappearing data” in early childhood mathematics classrooms as a way of documenting children's mathematical thinking and used in data analysis for formative assessment. A case study, including a series of photographs of a single child's work on a one more/one less task is used to demonstrate the ways in which this new framework can be used as part of a coaching cycle aimed at improving formative assessment. The coach supports the teacher in using photographs to document student thinking; employing professional noticing coupled with learning trajectories to identify where the student's work is along the Base 10 progression of counting; and synthesizing noticings and trajectories to plan instructional next steps. Implications for both teaching and research are identified and explored.

Towards Flipped Learning in Upper Secondary Mathematics Education

2020 ◽  
Vol 5 (1) ◽  
pp. 1-15
Author(s):  
Robert Weinhandl ◽  
Zsolt Lavicza ◽  
Stefanie Schallert
Keyword(s):  
Secondary Education ◽  
Mathematics Education ◽  
Mathematics Learning ◽  
Flipped Learning ◽  
Educational Innovations ◽  
Design Based Research ◽  
Secondary Mathematics Education ◽  
Upper Secondary Education ◽  
Mathematics Classrooms ◽  
Upper Secondary

Challenges for students in the 21st century, such as acquiring technology, problem-solving and cooperation skills, also necessitates changes in mathematics education to be able to respond to changing educational needs. One way to respond to these challenges is utilising recent educational innovations in schools, for instance, among others are flipped learning (FL) approaches. In this paper, we outline our explorative educational experiment that aims to investigate key elements of mathematics learning in FL approaches in upper secondary education. We describe the methodologies and findings of our qualitative study based on design-based research to discover key elements of FL approaches in upper secondary education. Analysing the data collected over ten months suggested categories (a) confidence when learning; (b) learning by working; and (c) flexibility when learning could be essential to understand FL approaches practices in mathematics classrooms.

scholarly journals Inclusion as Ethics, Equity and/or Human Rights? Spotlighting School Mathematics Practices in Scotland and Globally

2017 ◽  
Vol 5 (3) ◽  
pp. 172-182
Author(s):  
Dalene M. Swanson ◽  
Hong-Lin Yu ◽  
Stella Mouroutsou
Keyword(s):  
Human Rights ◽  
Mathematics Education ◽  
School Mathematics ◽  
Mathematics Classrooms ◽  
Socially Constructed ◽  
Mathematics Practices ◽  
Hierarchical Nature ◽  
The Government ◽  
Additional Support ◽  
Educational Inclusion

Mathematics education has been notoriously slow at interpreting inclusion in ways that are not divisive. Dominant views of educational inclusion in school mathematics classrooms have been shaped by social constructions of ability. These particularly indelible constructions derive from the perceived hierarchical nature of mathematics and the naturalised assumption that mathematisation is purely an intellectual exercise. Constructions of ability, therefore, emanate from the epistemic structures of mathematics education as predominantly practiced worldwide, and the prevalence of proceduralism and exclusion in those practices. Assumptions about ‘ability’ have become a truth to mathematical aptitude held by mathematics teachers in schools. This includes schools across Scotland. In Scotland, the government owes the ‘included pupil’ a legal obligation to provide additional support for learning under section 1(1) of the Education (Additional Support for Learning) (Scotland) Act 2004. However, classroom practices deployed around socially-constructed notions of ability have seen schools moving away from an emphasis on ‘additional’ to an expansive interpretation of ‘different from’ in the language of section 1(3)(a) of the Act 2004. This shift, therefore, reinstalls exclusionary effects to school mathematics practices by creating the conditions for some pupils, constructed in terms of disabilities or low ability, to be afforded a more inferior education than others. While philosophical conversations around whether these practices are ethical, egalitarian or democratic might ensue, there is also the human rights angle, which asks whether such practices are even lawful.

Teachers' Perspectives Using the Instructional Quality Assessment as a Professional Development Tool

2019 ◽  
pp. 41-58
Author(s):  
Amber Grace Candela
Keyword(s):  
Professional Development ◽  
Quality Assessment ◽  
Instructional Practices ◽  
Mathematics Teachers ◽  
Instructional Quality ◽  
Mathematics Classrooms ◽  
Development Tool ◽  
Teachers Perspectives ◽  
Cognitively Demanding Tasks

This chapter will provide readers with an overview of professional development created and enacted to support teachers' selection and implementation of cognitively demanding tasks using the Instructional Quality Assessment as the professional development tool. This case study seeks to give voice to mathematics teachers in third through eighth grades who participated in the professional development as they share their perspectives on using the instructional quality assessment rubrics and structure of professional development. The goal of this chapter is to provide an overview of the structure of the professional development, and share the aspects of the professional development the teachers identified as supportive or a hindrance when planning and implementing tasks in their mathematics classrooms. With this information, the article concludes by discussing ideas for future professional development aimed at providing teachers with instructional practices to incorporate into classrooms.

English Learners in K–12 Mathematics Education: A Review of the Literature

2018 ◽  
Vol 88 (6) ◽  
pp. 879-919 ◽  
Author(s):  
Zandra de Araujo ◽  
Sarah A. Roberts ◽  
Craig Willey ◽  
William Zahner
Keyword(s):  
Mathematics Education ◽  
English Learners ◽  
Teaching And Learning ◽  
Empirical Studies ◽  
Future Research ◽  
Sociocultural Perspective ◽  
Mathematics Classrooms ◽  
Persistent Pattern ◽  
Mathematics Teaching And Learning ◽  
K 12

Alongside the increased presence of students classified as English learners (ELs) in mathematics classrooms exists a persistent pattern of the marginalization of ELs. Educators have sought research to identify how to provide ELs with high-quality mathematics education. Over the past two decades, education researchers have responded with increased attention to issues related to the teaching and learning of mathematics with ELs. In this review we analyzed literature published between 2000 and 2015 on mathematics teaching and learning with K–12 ELs. We identified 75 peer-reviewed, empirical studies related to the teaching and learning of mathematics with ELs in Grades K–12 and categorized the studies by focus (Learning, Teaching, and Teacher Education). We synthesize the results of these studies through the lens of a sociocultural perspective on language in mathematics. We then discuss avenues for future research and calls to action based on the extant body of literature.

Mathematics Education and Language Diversity: A Dialogue Across Settings

2013 ◽  
Vol 44 (1) ◽  
pp. 119-128 ◽  
Author(s):  
Mamokgethi Setati Phakeng ◽  
Judit N. Moschkovich
Keyword(s):  
South Africa ◽  
Mathematics Education ◽  
Language Diversity ◽  
Mathematics Classrooms ◽  
Multilingual Classrooms ◽  
Research Findings ◽  
Diversity Issues ◽  
Similarities And Differences ◽  
Research In Mathematics Education

This article shares the authors' views on language-diversity issues in research in mathematics education. Described are tensions, questions, and myths that they have regularly faced as researchers. They use similarities and differences in two settings (multilingual classrooms in South Africa and U.S. mathematics classrooms with Latino/a students) to illustrate the complexity of this work and illuminate research findings.

scholarly journals Mathematics education and the dignity of being

Pythagoras ◽  
2012 ◽  
Vol 33 (2) ◽  
Author(s):  
Paola Valero ◽  
Gloria García ◽  
Francisco Camelo ◽  
Gabriel Mancera ◽  
Julio Romero
Keyword(s):  
Mathematics Education ◽  
Secondary School ◽  
Latin American ◽  
Teacher Educators ◽  
Mathematics Curriculum ◽  
School Mathematics ◽  
Critical Geography ◽  
Mathematics Classrooms ◽  
The Enlightenment ◽  
Political Approach

On the grounds of our work as researchers, teacher educators and teachers engaging with a socio-political approach in mathematics education in Colombia, we propose to understand democracy in terms of the possibility of constructing a social subjectivity for the dignity of being. We address the dilemma of how the historical insertion of school mathematics in relation to the Colonial project of assimilation of Latin American indigenous peoples into the episteme of the Enlightenment and Modernity is in conflict with the possibility of the promotion of a social subjectivity in mathematics classrooms. We illustrate a pedagogical possibility to move towards a mathematics education for social subjectivity with our work in reassembling the notion of geometrical space in the Colombian secondary school mathematics curriculum with notions of space from critical geography and the problem of territorialisation, and Latin American epistemology with the notion of intimate space as an important element of social subjectivity.

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