Mathematics Teacher Noticing Research Articles

Mathematics Teacher Noticing: A Case of Students' Cognition of a Course Content

It is essential for Course Lecturers and Course Tutors to be aware of their students' cognition. It is noteworthy in the context of teaching and learning. Teacher recognition is critical to improving classroom teaching and learning and has been the core mandate of every educational institution worldwide. And it has become critical that various approaches and shifts be learned and incorporated into the educational system. This study used a purely qualitative approach and a Single Case Design. It also determined the cognition level of topics facilitated by a Course Lecturer or Course Tutor and topics learned in groups by students. It was carried out to ascertain the cognition of some university students enrolled in a semester course. The Teacher Noticing framework was used for this. A diagnostic test was used in the study to assess the cognitive level of the topics covered in the fifteen (15) undergraduate participants' courses. The "ACS Model" conceptual framework was contextualized or framed to notice students' understanding and cognition in three levels: "A" for accuracy, "C" for creativity, and "S" for stumbling. Within the time frame, eight related topics were covered. About 85% of the topics were taught with the help of the lecturer, and 15% were taught by the students in groups. The course lecturer also reiterated the few topics covered in groups. The findings indicated that university students (N=8) performed better than non-university students (N=8), with a percentage increase of 75.54% for topics covered by the course lecturer compared to 24.46% for topics covered by group projects. When comparing the topics covered with the instructor acting as the facilitator, topics 2 and 4 have higher means and lower standard deviations (mean = 2.8000, SD =.56061, and mean = 2.0667, SD =.88372, respectively). It is advised that the course lecturer and mathematics instructors use diagnostic tests and quizzes to monitor students' understanding of the subjects covered. In order to support teacher professional development and student assessment, it is advised that Teacher Noticing be incorporated into classroom discussions.

Teachers’ noticing to promote students’ mathematical dialogue in group work

How can teachers refine their strategies for purposefully engaging students in mathematical discussions when students are working in groups and the teacher enters an ongoing group conversation? In three educational design research cycles, four teachers collaborated with a researcher for one year to analyse, design and evaluate strategies for engaging students in small-group mathematical discussions. The idea of noticing (Mason in Researching your own practice: the discipline of noticing, RoutledgeFalmer, London, 2002; Sherin et al. in Mathematics teacher noticing: seeing through teachers’ eyes, Taylor & Francis, New York, 2011) was used to organize the findings—by paying attention to aspects in the mathematical discussions and interpreting the interactions, teachers could together refine their own actions/responses to better support students’ work. The Inquiry Co-operation Model of Alrø and Skovsmose (Dialogue and learning in mathematics education: intention, reflection, critique, Kluwer Academic Publishers, Dordrecht, 2004) was used as a theoretical base for understanding qualities in mathematical discussions. Ehrenfeld and Horn’s (Educ Stud Math 103(7):251–272, 2020) model of initiation-entry-focus-exit and participation was for interpreting and organizing the findings on teachers’ actions. The results show that teachers became more aware of the importance of explicit instructions and their own role as facilitators of mathematical questions to students, by directing specific mathematical questions to all students within the groups. In this article, by going back and forth between what happened in the teachers’ professional development group and in the classrooms, it was possible to simultaneously follow the teachers’ development processes and what changed in students’ mathematical discussions.

Investigation of the Rate and Ratio’s Teaching Process in the Context of a Mathematics Teacher's Noticing

Öğretmenlerin sınıflarında neyin dikkate değer olduğuna karar vermesi, yaşanan özel durumları analiz edip anlamlandırabilmesi ve öğretimlerini buna göre düzenlemesi fark etme (noticing) olarak tanımlanmaktadır. Bu araştırmanın amacı bir ortaokul matematik öğretmeninin kendi öğretim sürecini fark etme becerisi çerçevesinde analiz etmesinin matematiği öğretme bilgisi ve mesleki gelişimine olan katkısını incelemektir. Çalışma eylem araştırması deseninde yürütülmüştür. Katılımcılar bir ortaokul matematik öğretmeni ile yedinci sınıfta öğrenim gören 17 öğrencidir. Öğretmen, oran-orantı konusunun öğretimi sırasında derslerini video kayıt altına almıştır. Bu kayıtları izleyerek ders analiz günlüklerini oluşturmuş ve bu günlükleri içerik analizi yöntemiyle analiz etmiştir. Öğretmen video kayıtlarını analiz etme yoluyla öğrenci düşünmelerine daha fazla dikkat etmeye başlamış ve bunlar üzerinde ayrıntılı düşünme fırsatı bulmuştur. Yaptığı analizlerde ders içerisinde yeterince dikkat etmediği veya gözden kaçırdığı noktaları yakalayarak öğretimini buna göre düzenlemiştir. Araştırma oran-orantı konusu özelinde yürütüldüğünden öğretmen bu konuya ait öğrenci güçlüklerini belirlemiş ve çözüm önerileri geliştirmiştir. Ayrıca dersin planı ve akışıyla ilgili olumlu ve olumsuz noktaları tespit eden öğretmen ilerleyen zamanlarda yapacağı öğretim için fikir sahibi olmuştur.

Study on Factors of Prompting Mathematics Teacher Noticing and Functions of Teacher Training A Case Study of a Teacher Training for Elementary School Teachers based on Lesson Study

Study on Factors of Prompting Mathematics Teacher Noticing and Functions of Teacher Training A Case Study of a Teacher Training for Elementary School Teachers based on Lesson Study

Examining aspects of teachers’ posing of problems in response to children’s mathematical thinking

The mathematics education field recognizes the importance of noticing children’s mathematical thinking as a means for supporting children in learning mathematics (Sherin et al. Mathematics teacher noticing. Routledge, New York, 2010). Using the existing literature base around teachers’ knowledge of children’s mathematical thinking and participants’ problem posing in response to children’s mathematical thinking, we developed the Responding Rubric, which measures four elements of responding to children’s mathematical thinking (group or individual responses, consideration of children’s existing strategies, anticipation of children’s future strategies, and a responsive problem). Using the Responding Rubric, we were able to illustrate elements of teachers’ responding skills. Following our presentation of findings, we discuss how our results further our understanding around teachers’ noticing skills and provide directions for future research.

Book Review: Multiple Perspectives of Teacher Noticing: An Emerging Area of Research

“Noticing matters” (p. 223). Through these words in the concluding chapter, Alan Schoenfeld succinctly captures the theme of this seminal book, Mathematics Teacher Noticing: Seeing Through Teachers' Eyes. The book received the American Education Research Association 2013 Exemplary Research in Teaching and Teacher Education Award. It addresses a variety of meanings and interpretations of teacher noticing from Dewey's earlier work of inner and outer attention to more specific variations such as that of professional noticing, as defined by Jacobs, Lamb, and Philipp. Chapter contributors have provided the foundation and framing of teacher noticing as a construct for studying and improving teaching.