Further Investigation into the Quality of Teachers’ Noticing Expertise: A Proposed Framework for Evaluating Teachers’ Models of Students’ Mathematical Thinking

Abstract

Because teachers cannot directly access the processes by which students construct their mathematical knowledge, Teacher Noticing, an activity that involves observing students' work, interpreting students' mathematical thinking about a task based on their remarks or actions, and responding to their thinking, is important to grasp students' mathematical understanding. A possible way for teachers to develop noticing expertise is to engage in a situation focused on student thinking such as clinical interviews. However, noticing students' thinking productively through clinical interviews remains a challenge, especially for pre-service teachers, not only because it requires a broad range of knowledge but also because of the absence of a framework to inform and evaluate the process. This paper addresses the development of such a framework for evaluating the quality of pre-service teachers' noticing expertise in a context where students' thinking is emphasized by removing normal classroom interruptions. It then demonstrates how the framework can be used for this purpose through three empirical examples of pre-service teachers who engaged in an intervention that involved conducting clinical interviews and analyzing students' mathematical thinking by watching video-recordings of their clinical interviews.

The role of tutors in mathematical noticing in an undergraduate quantitative literacy course: Conceptualising the time value of money

“…however, there is a general consensus that it influences the quality of mathematics instruction (Jacobs et al 2010;Lee 2018). Part of the findings of the study have shown that tutors accurately identified mathematical concepts that were challenging to the students -the assumption here is that the tutor noticing that did take place is evidence-driven.…”

Didactic Potential of Using Mobile Technologies in the Development of Mathematical Thinking

“…The development of mathematical thinking presupposes a problematic approach to education, which determines the importance of the teacher's work in overcoming fear among students for mathematical research activities (Fouze & Amit, 2018;Lee' 2018;Ramdani, Syamsuddin, & Sirajuddin, 2019;Tambunan, 7 / 20 2019). The authors also believe that it is necessary to take into account students' previous experience in the study of new methods of solution.…”

Prospective Mathematics Teachers as Learners in University and School Contexts

“…Understanding teacher learning as "change in discourse over time" (Wilson, Sztajn, Edgington, Webb, & Myers, 2017;p. 570), in particular changes in prospective teachers' discourse on mathematics teaching, can be interpreted as an indicator of enhanced noticing (Ivars, Fernández, Llinares & Choy, 2018). For example, showed that the use of a hypothetical learning trajectory of the part-whole meaning of fractions as a framework to interpret students' mathematical thinking helped prospective teachers improve their mathematical discourse in two ways: firstly, progressing from elaborating a less detailed discourse (in which they did not give evidence or they added unnecessary information from students' answers) to entering a more detailed discourse; and secondly, considering students' answers as examples of more general categories.…”