The Development of Preservice Teachers’ Visions of Mathematics Instruction

Temple A. Walkowiak Carrie W. Lee

Ashley N. Whitehead

NCTM Research ConferenceBoston, MA

April 15, 2015

Purposes

Context

Significance

Research Questions

Methods

Findings

Implications

Next Steps

Contact Info & Acknowledgements• Temple Walkowiak, Principal Investigator

temple_walkowiak@ncsu.edu• Carrie Lee, Graduate Research Assistant

cwlee5@ncsu.edu• Ashley Whitehead, Graduate Research Assistant

anwhiteh@ncsu.edu• Co-PIs: Ellen McIntyre, Sarah Carrier, Steve Porter,

Jayne Fleener, Margareta Pop Thomson• Senior Researchers: Michael Maher, James Minogue,

Andrew McEachin• GRAs: Daniell DiFrancesca, Beth Greive• Project Manager: Rebecca Lowe

This work is funded by the National Science Foundation under Award #1118894. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of NSF.

Purposes

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Purposes• Describe the larger context and significance of

the work

• Share findings about the development of our preservice teachers’ visions of mathematics instruction over the course of their teacher preparation program

• Outline implications and next steps

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Methods

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Context • STEM-Focused Elementary Teacher

Preparation Program

• Project ATOMS: Accomplished Elementary Teachers Of Mathematics and Science

5-year grant project funded by

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Context

Knowledge:Content Knowledge; Pedagogical Content

Knowledge

Beliefs: Efficacy;

Epistemological

Elementary Teacher of STEM Content

Teaching Practices: Standards-Based

Student Outcomes

Project ATOMS

Knowledge:Content Knowledge; Pedagogical Content

Knowledge

Beliefs: Efficacy;

Epistemological

Elementary Teacher of STEM Content

Teaching Practices: Standards-Based

Student Outcomes

Project ATOMS

Theoretical Perspective• Teachers’ Vision (Hammerness, 2001)

• “A set of images of ideal classroom practice for which teachers strive” (p. 143)

• Visions of high-quality mathematics instruction (Munter, 2014)

• Appropriation of Pedagogical Tools (Grossman, Smagorinksy, & Valencia, 1999)

• “The process through which a person adopts pedagogical tools available for use in particular social environments” (e.g., preservice programs) (p. 15)

Beliefs: Efficacy;

Epistemological

Teaching Practices: Standards-Based

Visions

Purposes

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Significance

Research Questions

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Significance• Call for longitudinal studies of teacher preparation

programs (AACTE; Cochran-Smith & Zeichner, 2010)

• Teachers must first be able to articulate their vision before enacting it (e.g., Hammerness, 2006)

• Past work in mathematics has focused on visions of practicing teachers over time (Munter, 2014)

• Work with preservice teachers has been focused on science (Windschitl, Thompson, & Braaten, 2008)

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Research Questions• How do elementary preservice teachers’ visions of

the teacher’s role in mathematics instruction evolve over the course of their teacher preparation program? • What are the changes in visions, if any, from the

beginning to the midpoint of the teacher preparation program?

• What are the changes in visions, if any, from the midpoint to the end of the teacher preparation program?

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Methods: Participants• n = 18

• “traditional” undergraduate students approximately 20-22 years old

• 17 female, 1 male

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Methods: Data CollectionTimeline Data Collection* or

Program FeatureStart of Junior Year *Beginning-of-Program (BOP) Interview

Fall of Junior Year K-2 Mathematics Methods CourseK-2 Field Placement (86 contact hours)

Spring of Junior Year 3-5 Mathematics Methods Course3-5 Field Placement (86 contact hours)

End of Junior Year *Midpoint-of-Program (MOP) Interview

Fall of Senior Year Student Teaching Placement (121 contact hrs)

Spring of Senior Year Full-time Student Teaching (525 contact hours)

End of Senior Year *End-of-Program (EOP) Interview

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Methods: Data Collection• Interview Questions:

1. Consider your own experiences learning mathematics at any time in your life. Describe a learning experience in mathematics that was particularly effective for you. What made it effective? (BOP only)

2. Describe a math lesson in an elementary school classroom that you would consider to be effective and explain why you consider it to be effective.

3. What the teacher does and what the students are doing during mathematics instruction are really important. Describe what you think the teacher should be doing most of the time, and describe what you think the students should be doing most of the time.

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Methods: Analysis• VHQMI Framework (Munter, 2014)

1. Teacher as Motivator

2. Teacher as Deliverer of Knowledge

3. Teacher as Monitor

4. Teacher as Facilitator

5. Teacher as More Knowledgeable Other

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Findings

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Findings

BOP MOP EOP0

1

2

3

4

Four Illustrative Cases

Gretchen Tori Gabriella Shelly

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12 participants progressed from BOP to EOP.

13 participants progressed from BOP to MOP.

6 participants decreased from MOP to EOP (and 7 stayed the same).

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GretchenTeacher as Deliverer of Knowledge (1)

Teacher as Facilitator (3)

Teacher as Monitor (2)

Probably the teacher’s job should be more as explaining the lesson, seeing if the student is following…Giving them a chance to come up and do examples to keep them engaged…also maybe after he or she has done the lesson giving them practice by themselves.

The most effective part was allowing them to manipulate those cubes and discover for themselves…that’s the most effective process where you just don’t tell students but you allow them to learn for themselves and discover things on their own. After we let them manipulate the cubes, we talked about it and we talked about, you know, how volume was calculated with those cubes.

Then I am letting them do some practice… practice problems and so once they're doing practice problems, they might be able to collaborate with each other, and I am walking around taking more anecdotal records to see what else do I need to teach them.

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Tori is similar to Gretchen:

13 participants progressed from BOP to MOP.

6 participants decreased from MOP to EOP (and 7 stayed the same).

BUT

2 participants decreased from BOP to EOP.

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ToriTeacher as Monitor (2)

Teacher as Facilitator (3)

Teacher as Deliverer of Knowledge (1)

By group discussions...maybe they can work together on it and use their thinking processes and critical thinking to come together and all come to a conclusion or maybe they have to work it out themselves….For the most part, I think the teacher should be making sure that they’re...doing it accurately, and helping them to explain if not why, why’s that not right.

I think that during math time, it’s more effective if students are working together...They really work together...and they’re able to really help each other and guide each other.

I tried to make this list of steps. I gave them all a sheet and then made them study it. I made a poster in front of the classroom that went along with the lesson….I feel that it was also effective because I was able to break it down into different levels and give them steps one by one.

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4 participants stayed the same from BOP to EOP.

3 of those participants remained at level 2 (monitor) at BOP, MOP, and EOP.

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GabriellaTeacher as Monitor (2)

Teacher as Monitor (2)

Teacher as Monitor (2)

Teachers should be giving examples [and] walking around…the kids will be able to help each other.

It wasn’t just me talking the whole time, they got to talk to their classmates… and work in partner groups. it’s so hard for kids to be silent all the time. And so, just like giving them that extra 2 to 3 minutes to talk, even if it’s about math, they’re just like so much happier.

Kids need to talk about math. They need to figure out not just like what I’m saying, but they need to figure out with their partners….I was pulling kids up to the front of the room… that way I know everybody’s paying attention.

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12 participants progressed from BOP to EOP.

4 of those participants steadily progressed from BOP to MOP to EOP.

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ShellyTeacher Deliverer of Knowledge (1)

Teacher as Monitor (2)

Teacher as Facilitator (3)

I feel like the teacher should be giving examples of what she is doing like writing out examples....as you do the lesson you explain what you are doing and so that they know what the process is and how they are supposed to do it.

The teacher would first off let the students kind of explore an idea…like have them explore what they think they should do maybe and then allow them time to do that and then pull them in and like guide them towards the best way to go about finding the answer or doing the problem.

[The teacher] allows the students to talk to each other together to try to figure things out…. I feel like the teacher is more like a facilitator so she's there to help the students...talk to each other so like she would ask a question like, ‘Talk me through this answer’.

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Implications• Methods courses

– Continue focus on standards-based instruction in methods courses.

– Give explicit attention to PSTs’ instructional visions in methods courses, and require PSTs to analyze field placement experiences in light of their visions. (Hammerness, 2003)

• Student teaching placements– Investigate the role of the student teaching. – Examine alignment between methods courses

and field placements at a finer-grain level.• What is the role of the realities of schools (e.g.,

accountability/testing pressures; pacing/curriculum guides)?

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Next Steps in Our Work• Follow 16 case studies in 1st year of teaching.

– Data collection includes interviews, classroom observations

• Investigate relationship between instructional vision trajectories and entry characteristics (e.g., childhood experiences in school mathematics).

• Examine relationship between visions and other constructs of interest (e.g., mathematical knowledge for teaching; efficacy beliefs).

Purposes

Context

Significance

Research Questions

Methods

Findings

Implications

Next Steps

Contact Info & Acknowledgements• Temple Walkowiak, Principal Investigator

temple_walkowiak@ncsu.edu• Carrie Lee, Graduate Research Assistant

cwlee5@ncsu.edu• Ashley Whitehead, Graduate Research Assistant

anwhiteh@ncsu.edu• Co-PIs: Ellen McIntyre, Sarah Carrier, Steve Porter,

Jayne Fleener, Margareta Pop Thomson• Senior Researchers: Michael Maher, James Minogue,

Andrew McEachin• GRAs: Daniell DiFrancesca, Beth Greive• Project Manager: Rebecca Lowe

This work is funded by the National Science Foundation under Award #1118894. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of NSF.