the development of preservice teachers’ visions of mathematics instruction temple a. walkowiak...
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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
Context
Significance
Research Questions
Methods
Findings
Implications
Next Steps
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
Purposes
Context
Significance
Research Questions
Methods
Findings
Implications
Next Steps
Context • STEM-Focused Elementary Teacher
Preparation Program
• Project ATOMS: Accomplished Elementary Teachers Of Mathematics and Science
5-year grant project funded by
Purposes
Context
Significance
Research Questions
Methods
Findings
Implications
Next Steps
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
Context
Significance
Research Questions
Methods
Findings
Implications
Next Steps
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)
Purposes
Context
Significance
Research Questions
Methods
Findings
Implications
Next Steps
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?
Purposes
Context
Significance
Research Questions
Methods
Findings
Implications
Next Steps
Methods: Participants• n = 18
• “traditional” undergraduate students approximately 20-22 years old
• 17 female, 1 male
Purposes
Context
Significance
Research Questions
Methods
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Implications
Next Steps
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
Purposes
Context
Significance
Research Questions
Methods
Findings
Implications
Next Steps
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.
Purposes
Context
Significance
Research Questions
Methods
Findings
Implications
Next Steps
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
Purposes
Context
Significance
Research Questions
Methods
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Implications
Next Steps
Findings
Purposes
Context
Significance
Research Questions
Methods
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Implications
Next Steps
Purposes
Context
Significance
Research Questions
Methods
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Implications
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Findings
BOP MOP EOP0
1
2
3
4
Four Illustrative Cases
Gretchen Tori Gabriella Shelly
Purposes
Context
Significance
Research Questions
Methods
Findings
Implications
Next Steps
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).
Purposes
Context
Significance
Research Questions
Methods
Findings
Implications
Next Steps
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.
Purposes
Context
Significance
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Methods
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Implications
Next Steps
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.
Purposes
Context
Significance
Research Questions
Methods
Findings
Implications
Next Steps
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.
Purposes
Context
Significance
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Methods
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Implications
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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.
Purposes
Context
Significance
Research Questions
Methods
Findings
Implications
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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.
Purposes
Context
Significance
Research Questions
Methods
Findings
Implications
Next Steps
12 participants progressed from BOP to EOP.
4 of those participants steadily progressed from BOP to MOP to EOP.
Purposes
Context
Significance
Research Questions
Methods
Findings
Implications
Next Steps
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’.
Purposes
Context
Significance
Research Questions
Methods
Findings
Implications
Next Steps
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)?
Purposes
Context
Significance
Research Questions
Methods
Findings
Implications
Next Steps
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.
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