Investigating Secondary Preservice Teacher Noticing of Students’ Mathematical Thinking

2017 ◽  
pp. 49-72 ◽  
Author(s):  
Erin E. Krupa ◽  
Maryann Huey ◽  
Kristin Lesseig ◽  
Stephanie Casey ◽  
Debra Monson
Keyword(s):  
Preservice Teacher ◽  
Mathematical Thinking ◽  
Teacher Noticing

Noticing Student Mathematical Thinking Within the Context of Lesson Study

2019 ◽  
Vol 71 (5) ◽  
pp. 568-583 ◽  
Author(s):  
Pınar Guner ◽  
Didem Akyuz
Keyword(s):  
Teacher Education ◽  
Preservice Teacher ◽  
Lesson Study ◽  
Teacher Education Program ◽  
Mathematical Thinking ◽  
Middle School Mathematics ◽  
Teacher Noticing ◽  
Teaching Practicum ◽  
Group Members ◽  
Study Process

The purpose of this study is to investigate a preservice middle school mathematics teacher’s noticing of student mathematical thinking within the context of lesson study as a component of a teaching practicum course in a teacher education program. This study also examines how preservice teacher education experiences in the context of lesson study influence the noticing skill of the participant preservice teacher, Lisa. Results indicated that the lesson study process supported teacher noticing of student mathematical thinking as the preservice teacher engaged in planning, teaching, and reflecting on the lessons. It was found that the collaborative and reflective structure of lesson study based on the anticipation of students’ thinking and interactions between group members significantly increased the level of noticing. The study also revealed that reading about mathematics subjects and the classroom teacher’s feedback proved helpful to develop Lisa’s noticing.

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.

Teacher Noticing of Mathematical Thinking in Young Children’s Representations of Counting

2020 ◽  
Vol 51 (3) ◽  
pp. 268-300
Author(s):  
Madhuvanti Anantharajan
Keyword(s):  
Mathematical Thinking ◽  
Kindergarten Teachers ◽  
Teacher Noticing ◽  
Early Mathematics ◽  
Transitional Kindergarten ◽  
Mathematical Ideas ◽  
Class Time ◽  
Different Levels

Counting is fundamental to early mathematics. Most studies of teaching counting focus on teachers observing children count. The present study compares mathematical ideas that 12 PK, transitional kindergarten (TK), and kindergarten teachers noticed from observing their own students count during a classroom session of Counting Collections with ideas that they noticed outside class time in the same students’ representations of counting on paper. Inviting teacher noticing in representations (a) drew attention to distinct conceptions that children required to represent counting; (b) increased the number of mathematical ideas that participants perceived in students’ thinking; and (c) helped participants perceive different levels in, and their own uncertainties about, students’ understanding. This study suggests that teacher noticing in children’s representations of counting can deepen teachers’ understanding of students’ mathematical thinking.

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.

Review of Mathematical Thinking and Problem Solving.

1996 ◽  
Vol 41 (1) ◽  
pp. 80-80
Author(s):  
Daniel Stalder ◽  
Shubhangi Stalder
Keyword(s):  
Problem Solving ◽  
Mathematical Thinking

Thinking About Mathematical Thinking

PsycCRITIQUES ◽  
2010 ◽  
Vol 55 (23) ◽  
Author(s):  
Gordon Pitz
Keyword(s):  
Mathematical Thinking
Sign in / Sign up

Export Citation Format

Share Document