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Learning to Elicit Student Thinking in

An Early Field Experience

Kristen Bieda¹, Brady Tyburski¹, Fran Arbaugh², Michelle Cirillo³

¹Michigan State University, ²The Pennsylvania State University

³University of Delaware

UTE

MPT

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Other Team Members

Kevin Voogt�Grace College

Maria Isabel Perez�Michigan State University

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Session Overview

Situating the Problem

Context of Our Work

The Eliciting Cycle Framework

Data analysis activity

Results: PST Challenges with Eliciting

Discussion and Implications

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Situating the Problem

Well-prepared beginning teachers of

mathematics are developing as reflective practitioners who elicit and use evidence of student

learning and engagement to analyze their teaching (Standards for Preparing Teachers of Mathematics, Indicator C.2.4, AMTE, 2017)

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Situating the Problem

Eliciting student thinking is a formative assessment practice (Black & Wiliam, 2009) that can result in enhancing students’ conceptual understanding (Franke, Turrou & Webb, 2011).
“Caring about what students think is foundational to teaching” (Shaughnessy & Boerst, 2018, p. 42)
Research on sites for learning to elicit student thinking: In-person versus simulations (Shaughnessy, Boerst & Farmer, 2019; Lee et al. 2021)

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Context of Our Work

Undergraduate Teaching Experience for Mathematics Pre-Service Teachers (UTEMPT)

NSF-funded, four-year collaborative project between Michigan State University, Penn State University, and University of Delaware

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Context of Our Work

Mathematics Teaching Methods Course

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Context of Our Work

Mathematics Teaching Methods Seminar

University Teaching Experience

MTEs mentor during planning, teaching and debrief

Mentor teachers or MTEs model instruction for first few weeks

Lower-level undergraduate course (prior to Calculus)

Plan and Co-teach ~ 2 Lessons

Debrief after each session

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Situating the Problem

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Situating the Problem

Representations of (Proficient)Practice (Grossman et al., 2009)

(Proficient)Decomposition

(Proficient)Representation

(Proficient)Approximation

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Situating the Problem

Representations of (Beginning) Practice (Grossman et al., 2009)

(Beginning)Decomposition

(Beginning) Representation

(Beginning) Approximation

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Research Foci

Refine decompositions (Grossman et al., 2009) of eliciting student thinking to develop a framework that reflects aspects of eliciting students’ thinking that is being attempted by novices

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The Eliciting Cycle Framework

Cyclic Visual for Eliciting & Interpreting Student Thinking �(TeachingWorks, 2019)

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The Eliciting Cycle Framework

Initial �Elicitation

Cycle �End

Continued �Eliciting

Response

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The Eliciting Cycle Framework

Initial �Elicitation

Cycle �End

Response

No Response

Continued �Eliciting

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An Example of Eliciting Student Thinking

Two questions:

What elements do you notice about how the PST elicited student thinking?
What moment(s) felt like the end of an eliciting cycle? Why?

Lead up to clip: https://www.youtube.com/watch?v=KZ56AVqfcM8 (UD_231801_2, 29:30 - 33:52)��To help process this model and its potential utility in analyzing PSTs’ attempts at EST, we’re going to share a clip with you. As you watch this clip, consider these two questions. *Read Questions* ��The overarching question being discussed here is: �Q: “What is the maximum area of a dog pen that can be made with 60 ft of fencing and what are the dimensions of such a pen?”��Before this clip, the PST provided two visual examples of fences to show how side lengths impact area followed by asking students “which one they would prefer to have their dog in.” With those examples in tow, the eliciting cycle begins…�

—�Facilitate any discussion RE: what participants notice about PST eliciting practices.

-Nature of elicitation Q

-Does the teacher justify the Q?

-Restating/rephrasing the Q?

-Relational aspects with students (affirmation, praise, lack of participation, etc.)

-Prior knowledge

-Building on student work (revoicing, etc.)��Two extreme options for cycle ends:

-When the entire Q is done. This is one whole eliciting cycle. �-When PST attempt to eliciting a new mathematical aspect (e.g., the A&P formulas, the process for re-arranging the formulas, the process for solving one formula in terms of the other, etc.)�

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Macro/Micro Eliciting Cycles

Cycle 1

Cycle 2

Cycle 3

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Macro/Micro Eliciting Cycles

Initial Elicitation

Response

No Response

Continued �Eliciting

Cycle �End

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Practices for Eliciting Student Thinking

Franke et al. (2009) & Shaughnessy et al. (2019)

Ask specific questions focused on student thinking�
Elicit the steps of a students’ process AND the understanding of the steps�
Attend to student ideas (Revoicing, follow-up Qs)�
Avoid non-ideal practices (e.g., leading questions, re-directing students to a different process, evaluating)�

Past research suggests PST behaviors consistent with centering/eliciting student thinking. S&B have especially active in pushing thinking on the decomposition on EST, especially in teaching simulations. Collectively, past reseach suggets the need to…*read list*��As Kristen said, one of our main goals with this work is to decompose the practice of eliciting student thinking for novices in an authentic classroom setting. Past studies attempting to decompse this practice either concern the work of in-service teachers (Franke et al.) or they have built many of their finding from teaching simulations. Past research also tends to focus on the same lesson/problem (a single simulation) or a single mathematical topic (e.g., one algebra unit). The data set we used consisted of PSTs teaching a number of topics in an authentic classroom setting, which required us to grapple with what was common across different contexts

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Attending to PSTs Eliciting Student Thinking

Our Framework

3 Key elicitation questions

What content does the PST attempt to elicit?

Single answer? Process? Explanation?�

Is the elicitation specific or general?�
Is the elicitation based on student thinking?

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Attending to PSTs Eliciting Student Thinking

Our Framework

Other types of practices we attend to�

Follow-up practices (Repeating/rephrasing Q, providing clarification on Q)�
Attending to student ideas (Revoicing, extending student thinking)�
Non-ideal elicitation practices (funnel to answer, multiple choice, directs students to use a specific procedure)

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Attending to PSTs Eliciting Student Thinking

Our Framework

Other types of practices we attend to�

Involving other students (elicits additional responses)�
Moves that communicate/share thinking publicly (Creates and/or uses visual aid, asks students to present)�
Facilitating mathematical conversation (Connects to prior knowledge, inserts terminology)�
Affirmation, evaluation, & feedback on student thinking

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Research Foci

(2) Explore challenges PSTs face when attempting to elicit student thinking during initial attempts when teaching in an early field experience

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Data Sources

Videorecorded data from UTE classes at all three institutions during the 2018-2019 academic year
For this talk, we focus on data from a representative sample of video across all three sites that involved moments where MTEs flagged instructional dilemmas PSTs experienced during whole-class discussion episodes. (N=36; n=15)
PSTs were interviewed about these moments, and described these dilemmas as surfacing:

Unexpected student response

Unexpected (lack of) student response

Breakdown in PST-student communication

Managing student contributions

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Results - Across Dilemmas

Generally, PSTs initial elicitation move was to create or share a visual aid to ground discussion

PST: Just a re-draw of what the diagram says.

{drawing}

PST: Now we’re trying to find the length of the shadow cast by the building. That’s going to be that bottom leg of our triangle. So we’ll label that x.

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Results - Managing Student Contributions

each time we wrap our radius around it is 1 radian.

Student: We got 2.

PST: Is it 2? How did you get that?...

PST: Alright, let’s bring it back together. Um…can Table 1, please tell me, what you got for A.

Student: I don’t know this one.

PST: You don’t know? Well, Ok, let’s work through this. We know that our radius is 5, right? And looking at what we just learned we know that,

Prior to dilemmas involving managing student contributions, PSTs’ initial elicitations typically involve seeking an answer.

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Results - PST-Student Communication Breakdown

PST: Alright, so we’re going to bring it back together so we can talk about each of the graphs. [To student] Can you talk about B&C?

[Student]: Inaudible

[Class talking]

MTE: {to student} Go ahead. {to class} Up here please. Up here please.

Student: So basically I was torn between B and C because of these two (gestures to elmo). These people were just going back in time on the ferris wheel.

MTE: Show us where it goes back in time.

These episodes rarely involve initial elicitations seeking an answer.

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Discussion and Implications

Framework (still in development!) allows for decomposition of novice eliciting practice

Results afford insights to support MTE noticing of PSTs’ eliciting practice

Breaking down eliciting into phases can potentially offer insights into the evolution of dilemmas

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Thank you!

Contact Information

Kristen Bieda (kbieda@msu.edu)
Brady Tyburski (tybursk2@msu.edu)

Find us online at https://bit.ly/utempt

Materials for this presentation were developed through funding from the National Science Foundation (DRLs 1725910, 1725920, 1726364; Bieda, Arbaugh, Cirillo PIs). Any opinions, conclusions, or recommendations contained herein are those of the presenters and do not necessarily reflect the views of NSF.

UTE

MPT