Opportunities to Notice: Chinese Prospective Teachers Noticing Students’ Ideas in a Distance Formula Lesson

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Published: 
April 2016

Source: Journal of Mathematics Teacher Education, 19(4): 325–347 (2016)

(Reviewed by the Portal Team)

This article examines the noticing of six Chinese mathematics prospective teachers (PSTs) when looking at a procedural error and responding to three specific tasks related to that error.

Methods
The participants were six Chinese prospective teachers, who were enrolled in a 4-year mathematics-major undergraduate program designed to prepare future mathematics teachers.
The authors showed the participants a video clip during interviews in order to elicit prospective teachers’ noticing of students’ mathematical ideas. The clip showed that one student’s procedural error consisting of exchanging the order of coordinates when applying the distance formula.

The authors were interested to examine how the six prospective teachers applied their pedagogical content knowledge (PCK) as they noticed this error.
The authors examined the six prospective teachers’ responses to the following three related tasks. Task A: If you were the teacher, how would you respond to this student?
Task B: How would you teach students the distance formula using an ‘‘inverse’’ right-angled triangle? Task C: How would you plan a lesson for teaching the distance formula?
Data were collected through video-stimulated interviews focused on the distance formula.


Discussion 
The results demonstrate that all six PSTs attended to the order exchange issue. The participants were able to attend to, interpret, and respond to the order exchange issue from various perspectives. The authors argue that this variety of perspectives suggests a variety of access to PCK and prior experiences as students of mathematics. 

In addition, the participants who embraced more than one interpretation of the order exchange also crafted more advanced approaches in their responses to the three tasks.
The authors also argue that an important finding demonstrate that the six PST’s prior orientations and resources informed what they noticed. The findings reveal that not only what they attended but also how they interpreted what they attended and how they responded has important PCK and cultural dimensions.

This study has some implications for teacher educators.
First, PSTs’ professional noticing ability is most effectively developed in conjunction with other relevant teaching knowledge.
Second, the teacher educator plays a very important role in editing and selecting appropriate video clip content and topics to elicit PSTs’ attention, interpretation, and responses to students’ mathematical thinking.
Finally, the findings provide a good example of the sorts of tasks teacher educators can use to help prospective teachers connect diverse mathematical understanding with teaching.

The authors conclude that PSTs’ prior learning resources and beliefs, pedagogical content knowledge, and the selection of tasks are all tied to their professional noticing of students’ mathematical thinking at the early stage of their teacher education. 

Updated: Feb. 11, 2018
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