Preparing Beginning Teachers to Elicit and Interpret Students’ Mathematical Thinking

Published: 
Jul. 01, 2013

Source: Teaching and Teacher Education, Volume 28, Issue 7, p. 1038-1048, July 2013.
(Reviewed by the Portal Team)

In this study, the authors examined their efforts to teach beginning teachers’ formative assessment practices, specifically to elicit and interpret students’ mathematical thinking.
The authors addressed to the following research question:
How can teacher education assignments be designed to support interns in learning to do the work of teaching?

Method
The context for the study is an assignment in an elementary mathematics methods course. The assignment-to interview a student to learn about his or her thinking-is a typical teacher education activity that we use to provide beginners an opportunity to learn to elicit, probe, and interpret student thinking.


In this version (the “Student Thinking Interview”), prospective teachers select mathematics tasks from a given “task pool,” plan for and audio record an interview with an individual student, and then use the data to craft evidence-based claims about the student’s mathematical understanding or skill.
Data were collected through the students' work on major course assignments and assessments, including written work, audio and video records of practice, and instructor feedback.
The authors analyzed data from seven interns selected from our larger data set.

Conclusion: implications for the design of scaffolds

This study surfaced a number of important ideas about scaffolding students’ learning of practice in the context of a commonly used teacher education assignment.
While each scaffold examined in this paper appeared to support and shape student performance, it was routinely the case that some aspects of students’ practice were being scaffolded while others were left under scaffolded.
These scaffolds consistently focused on procedure, helping students to engage in the doing of teaching.

This seems consistent with the authors' increased focus on the doing of teaching; however they noted multiple cases where additional conceptual and metacognitive scaffolding could have enhanced students’ practice and supported their understanding of the components of and rationales for the practice.
Fixed scaffolds designed in advance (hard scaffolds) and scaffolds crafted in the moment based on the unfolding circumstances (soft scaffolds) were both useful in supporting and shaping student practice.

This analysis also suggests that it is important to consider the function of scaffolds that are distributed across an assignment, particularly when a scaffolded practice is contingent on another practice, as in the Student Thinking Interview.
It is difficult to effectively support a nuanced assertion about student thinking if the task pool does not support interns in securing the type or depth of information necessary to construct such an assertion.
When practices have a contingent relationship in an assignment, it makes sense that the scaffolds distributed across the assignment would also have a contingent relationship.

The authors conclude that given the complex nature of teaching work, exploring ways of maximizing the productivity of practice-based assignments in teacher education is crucial. Understanding the design and function of scaffolds can support work to that end.
Attention to how scaffolds shape beginners’ practice positions the field to improve supports for early teaching experiences and to consider how scaffolds can be phased out over time.
Attention to the challenges and sustainability of the work of teacher educators with respect to scaffolds positions the field to improve how scaffolds are focused, distributed, and improved.

Updated: Sep. 30, 2014
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