Using field-based assignments in math methods courses can help address the disconnect teacher candidates often experience between their prior math learning, developing understanding of learning theories, and clinical experiences. The document discusses how assignments like observations, interviews, and teaching help unify these experiences when supported by coursework. However, research shows methods courses may not be long enough to affect lasting change. Therefore, it is important to understand how field-based assignments specifically support teacher candidate learning and practice. The presentation aims to provide a rationale for these assignments, examples used, and their impact on developing teacher candidates' visions and skills in teaching mathematics.

1. Using Field-Based
Assignments to
Develop Visions and
Skills with Best
Practices in Teaching
Mathematics
Nicole Rigelman, Portland State University
Gina Post, Wittenberg University
Association of Mathematics Teacher Educators Annual Conference
February 10, 2012

2. SessionOverview
 Provide you with
 a rationale for using field-based assignments in
math methods courses,
 a framework for gradual increase of student
interaction,
 data regarding the impacting such assignments
have on teacher candidates vision and skills with
research-based practices, and
 an opportunity to discuss ideas for implementation
with colleagues.

3. The Problem
 Teacher candidates often wrestle with the disconnect
between their personal prior mathematics learning
experiences, their developing understanding of
learning theories, and their clinical experience.
- Zeichner, 2010; Allsopp, DeMarie, Alvarez-McHatton, and Doone, 2006

4. A Response
 To unify these experiences many teacher
educators incorporate guided
observation, interview, and teaching assignments
that are supported by course-based
reading, discussion, and reflection.

5. However…
 research suggests that methods courses are of too
short duration to affect any lasting change in
teacher candidate attitudes and beliefs about
teaching.
- Ball, 1996; Borko& Putnam, 1996

6. Therefore,
 it is imperative that teacher educators determine
in what ways and to what extent field-based
assignments support teacher candidate learning
and practice.

7. So…
 What are some of examples of field-based
assignments you currently use in your setting?
 Why?

8. Research Question
 In what ways and to what extent do field-based
assignments support teacher candidate learning
and practice?
 Common Field-Based Assignments
 Inquiring to Understand
 Math Mini-Lessons/Routines
 Problem-Based Lesson

9. “Classroom discussion based on students’ own
ideas and solutions to problems is absolutely
‘foundational to children’s learning’” (p. 21). I
believe that students need to be guided, but also
need to have time to explore concepts on their own.
This allows for independent learning and can result
in more confident students. When students are
given opportunities to work out problems on their
own, they are more likely to remember.
[I] noticed that as I am teaching I like to
guide students to the correct answer,
which is a bad trait. I need to help students
justify their answer, so that they become
confident in their mathematical skills.

10. I love letting the students share their thoughts with
a partner, not only so I can ensure everyone has a
chance to speak, but also so I can hear the
mathematical discourse that can occur between
peers. I find it so interesting when students who are
seemingly best friends can argue about which
number is a divisor and which is a quotient, fight
over who is right, and then go back to being best
friends after class. I also enjoy when I hear a student
talking about math after class is over, I then know
math has permeated their thinking and the lesson
must have intrigued at least that student.

11. In the video, I noticed myself helping too
much. It’s so hard not to! I realized that I
have to back off and give the student
some space to see what they are doing.
Some things may take a while to sink in, I
can’t keep pushing. I also tried to
encourage her too much.
Overall I learned a lot from [the Inquiring to
Understand] project and also learned that I have a lot
more to learn about this teaching technique. I saw a
lot of connections from our readings and classroom
discussions to this project. I would like to get to learn
more about how to introduce and “teach” a new
operation or skill using this technique because I’m still
really confused about how that would work.

12. After reviewing all of my results from the student and peer
interviews, I realized that I really enjoyed using this protocol...
I believe that I now have a better sense of the way that I can
impact student’s mathematical thinking on a daily basis in the
classroom. By using the inquiring questions I found out a great
deal about students strengths, difficulties, and misconceptions
about the math that they were doing. By using this protocol
formally or informally in the classroom I think that I could get
students to really think about math rather than simply “doing”
math. I believe that the understanding of mathematical
concepts gets even deeper when students are asked to justify
and contemplate their reasoning behind doing math the ways
in which they do.

13. I realize today was my first day attempting this method, so I
think tomorrow can only be better. I need to remember for
tomorrow to pay closer attention while the students are
exploring and utilize some “talk moves” during this time as well
and not just during the explaining time...
Today, I found it a little easier to keep track of the students and
the strategies they used along with posing individual questions
to understand their thinking during the explore period. This
helped me better sequence the students for the explaining
period...To be honest, I do not know if I ordered in a
meaningful way, and I do not know how to tell...I chose
strategies that were suitable to the word problem. I would have
liked students to catch on that they could have added by
counting by 10, but that strategy was never presented.

14. We have been learning about an inquiry-based
curriculum and how to really allow students to
own their thinking. Through completing
assignments such as Inquiring to Understand and
the PBL, I have been able to incorporate some of
this in the classroom. This not only has shown me
what an inquiry-based classroom might look
like, but has given me the chance to understand
how my students think in math, which will only
help in future instruction…. These Connecting to
the Field Assignments really taught me that the
more you know about your students, the more
effective you will be when teaching lessons

15. What influence have your field-based
assignments had on teacher
candidates’ visions of and skills with
mathematics teaching?
How do you know?

16. References
Allsopp, D. H., DeMarie, D., Alvarez-McHatten, P., & Doone, E. (2006).
Bridging the gap between theory and practice: Connecting courses
with field experiences. Teacher Education Quarterly, 33(1), 9-35.
Ball, D. L., (1996). Teacher learning and the mathematics reforms:
What we think we know and what we need to learn. Phi Delta
Kappan, 77(7), 500-508.
Borko, H., & Putnam, R. T. (1996). Learning to teach. In D. C. Berliner
& R. C. Calfee (Eds.), Handbook of educational psychology (pp. 673708).New York: Macmillan.
Zeichner, K. (2010). Rethinking the connections between campus
courses and field experiences in college and university-based
teacher education. Journal of Teacher Education, 61(1-2), 89-99.