Hyejin Park
Nick Gomez
1
Rationale for the teacher education course we designed
In order to cultivate more competent teachers, what does a teacher education
program need to consider further? Many studies (Bruower, 1989; Goodlad, 1991;
Grossman, Hammerness, & McDonald, 2009) pointed out that the lack of connection
between theory and practice is still one problem teacher preparation programs have. In
doing so, the studies showed that most novice teachers are struggling with how to
transform the knowledge/theory they learned from teacher education programs into
practice in the school context. That is, the integration of theory and practice, as well as the
need for more teaching experience aligned with the current vision of mathematics teaching,
is essential in teacher education. Such a course can provide preservice teachers
opportunities to experience how to put theory into practice and to reflect on their
preparation for teaching before starting as full-time teachers. However, many teacher
education programs still have limitations to provide such integration programs. Thus, this
course as an integration program is intended to decrease the gap between theory and
practice. Also, it is designed to show how to effectively train preservice teacher’s teaching
of mathematics by using the content knowledge and pedagogical content knowledge they
already acquired before taking this course. Therefore, preservice teachers will be required
to take this course after completing all the content and method courses they should take
and before their student teaching assignment.
In this course, to develop the relationships between theory and practice, we will use
a revised version of Micro-teaching Lesson Study (MLS), which Fernández (2005, 2010)
implemented in her method course in a teacher education program. It was developed by
combining micro-teaching with Japanese study. Fernández (2005, 2008) showed that,
through MLS, preservice teachers can explore how to put theory into practice and develop
their content knowledge and their pedagogical content knowledge. Thus, MLS will meet our
goals of the course. MLS consists of four repeated cycles (processes): co-planning, teaching,
co-analysis and co-revision of one lesson which preservice teachers will teach to their
student-peers (or to secondary students) during the course. Unlike micro-teaching, which
generally lasts 5-20 minutes is intended to develop teaching skills, MLS will last 20-30
minutes and will focus more on collaborative work and on student learning. Also, unlike
lesson study, which is implemented in a typical size class, MLS is applied to a reduced class
size (e.g. 5-10 student-peers). So, we’ll limit the number of students enrolled in the course
to about 12-15. A class size that is a multiple of three is preferred but plans can be adapted
if necessary for larger groups.
At the beginning of the course, prospective teachers will be required to choose two
lessons with which they are unfamiliar or which they lack understanding; one should be a
middle school lesson and the other should be a high school lesson. The options will be
based on communication between instructor(s) and the classroom teacher. The instructor
will also advise the students on which lessons are appropriate to prepare for their field
experience. The goal of each lesson should be to develop students’ learning of mathematics
by improving students’ reasoning skills and to develop their understanding of
mathematical concepts in ways that align with the reform vision of learning of
mathematics. Also, based on the prospective teachers’ mathematical abilities, and, ideally,
on their different images of teaching (attained through a beliefs questionnaire), the
instructor will form small heterogeneous groups to promote effective course work. Each
group will include 3 or more members with different levels of mathematical abilities. The
mathematical abilities of the prospective teachers will be assessed through a pre-test that
is distributed on the first day of class. The test will include student work to be analyzed,
hypothetical situations, questions about student misconceptions, and problem solving
situations. Then, group members will start co-planning the lesson. One lesson study will
take 4 weeks. The instructor will give them guidance on how MLS works and will discuss
reform-oriented teaching and learning of mathematics by analyzing several case studies of
in-service teachers’ classroom practice.
During the co-planning of the lesson, preservice teachers will be given some time to
think about the lesson by asking questions such as “ What dilemmas or difficulties is your
group facing with regard to this lesson and its implementation? What lesson-related goals
does you group have for the students? What student responses, comments, or questions
will your group look for as evidence of understanding and achieving lesson goals and
objectives? (Molina, 2012, appendix B)” After designing the lesson plan, they will be
required to submit a First Lesson Plan Draft with all the supporting materials they will use
in teaching. The instructor will provide feedback and commentary on drafts. Then, one of
the group members will teach the lesson to their student-peers for 20-30 minutes based on
their lesson plan. The other group members (2 members) will observe the lesson,
especially focusing on the student-peers’ learning activities or behaviors in class. All
groups’ teaching will be videotaped. Outside of class, group members will watch a
videotaped recording of one of the group members’ lessons and analyze it. (That is,
preservice teachers will analyze only the lesson taught by their own 3-person group.)
During the analysis of videotapes, the instructor will give some advice or feedback about
their teaching.
After completing and revising their analysis, they will be required to hand in a
summary of observations and revisions about the first lesson they taught, which is the
Second Lesson Plan Draft, especially focusing on what the strengths and weaknesses of the
first lesson were and what parts of the lesson should be changed or explained further
(Molina, 2012). Again, one of the group members, who did not teach before, will teach the
lesson based on the revised lesson plan and the other group members will observe the
student-peers’ actions in class. Then, again, they will analyze the second lesson taught,
which will also be videotaped. The preservice teachers will repeat the same process one
more time. That is, they’ll teach the lesson three times during the MLS. Then, preservice
teachers will have to hand in the Final Revision Lesson plan, and they’ll go out and teach it
in a school. Their teaching in a real math classroom will also be videotaped and, again,
preservice teachers will analyze their teaching and prepare a presentation for peers about
what they learned from the school context and what parts of their lesson plan need to be
altered by considering the school context.
During this course, preservice teachers will be given two practicums. Both will take
place in professional development schools (PDS). According to the National Council for
Accreditation of Teacher Education professional development schools “are innovative
institutions formed through partnerships between professional education programs and P12 schools” (NCATE.org, n.d). Consequently, this partnership allows this class to be held at
the middle and high school in which pre-service teachers will be preparing lessons for. This
also allows for the prospective teachers to observe the classroom that they will be teaching
in. This also allows for more open communication between the instructor(s) and the
Hyejin Park
Nick Gomez
3
classroom teacher to guarantee the prepared lessons are appropriate for students. Time in
class will be given for students to observe and work with individuals in the classes they will
teach in. Through the MLS and field experience, we expect preservice teachers will learn
how to put theory into practice and to check their preparation for teaching.
However, along with using MLS, this course will focus on pre-service teachers’
change in beliefs toward the current vision of mathematics teaching. Throughout their
teacher education programs, prospective teachers face conflicts between their past
experiences and who they want to be. One perspective on this discord is discussed by
Britzman (2009):
Newcomers learning to teach enter teacher education looking backward on
their years of school experience and project these memories and wishes into
the present that they then identify with as somehow indication of what should
happen or never happen again (p. 28–29).
Thus, as teacher educators, we must aid students in the compromises made between past,
present and future. The clash between “where I’ve been,” “who I am” and “who I want to
be” affects the way in which an individual’s beliefs, values, and conceptions form during
this time. Therefore, to better prepare teachers for reform oriented mathematics teaching
(NCTM, 1989), an exploration of the student’s relationship with mathematics is necessary
(Drake, Spillane, & Hufferd-Ackles, 2001). Thus, the students will complete a mathematics
autobiography assignment, which will allow them to delve into their past. In this
assignment the students write about the relationship they have had with mathematics and
learning mathematics. This aids students in opening up and “lifting the veil” on the ways
that these experiences affect the lens through which they view mathematics education.
Students will explore critical events that have shaped who they are as mathematics
teachers as well as important “scenes” at various times in their lives as prospective
teachers. For this assignment, we modify Drake et al.’s (2001) mathematics life-story to
focus the students on plumbing into their past.
Additionally, the way the students envision themselves as professionals influences
the classroom practices they find important to convey (Hammerness, 2006). Therefore, the
students’ images of their futures are explored through a vision statement that is modified
throughout the semester. Hammerness (2001) defines teacher vision as consisting of
“images of what teachers hope could be or might be in their classrooms, their schools, their
community and, in some cases, even society” (p. 145, emphasis in original). By writing a
vision statement (Hammerness, 2006), the students will be able to do two things: (a)
deeply explore the focus, range, and distance of their vision (Hammerness, 2001) and (b)
be given a tool to look into their beliefs about teaching mathematics (Hammerness, 2003).
By having students dig into their beliefs through reflections, case studies, and the
analysis of peer work with MLS, we hope to make students more aware of their beliefs and
how these beliefs influence their practice as well as revealing to them a way to build a
bridge between theory and practice.
Course Title
EMAT 5001 – Bridging Practice and Theory: Explorations of Self as Teacher
Course Catalog Description
Through micro-teaching, reflections, and explorations of self, the prospective teachers
consider their part in constructing the bridge between theory and practice.
Instructor Information
Maestra D. Clase
105 Aderhold Hall
Maestra@uga.edu
Course Description and Goals
This course is designed to give you an opportunity to dissect your mathematics
teaching and practice as well as your beliefs about the current vision of mathematics
teaching. Through the deconstruction and analysis of your own teaching, practices and
beliefs, one is able to create for themselves a vision of learning and teaching of
mathematics that meets the goals of reform-oriented mathematics. In addition, through
Micro-teaching Lesson Study (MLS), this class gives you the chance to analyze and discuss
your own practice with student-peers in order to develop your teaching skills, content
knowledge and pedagogical knowledge, and to change your image of teaching mathematics.
During the course, you will participate in collaborative work such as planning,
implementing, analyzing and revising lessons. This opens up more possibilities for
discussions on what it means to teach and learn mathematics, especially focusing on the
current vision of teaching and learning mathematics. You will be working in groups of three
and participating in MLS enactments. Additionally, this course is designed to give you an
opportunity to demonstrate what you have learned in your undergraduate studies—
content and pedagogical knowledge—and to check your preparation for teaching before
becoming a full-time teacher. Also, in terms of beliefs, students will be delving into their
past, present, and future images of self to explore what defines their image of “self as
teacher.” Their past will be explored through their relationship with mathematics, their
future through a vision statement, and the present with a series of reflections and
questionnaires.
The main goal of this course is to explore the space between theory and practice. It
is the goal of the instructor(s) to aid the prospective teacher to close this gap. Through the
process of MLS, you can experience how your content knowledge should be altered in
Hyejin Park
Nick Gomez
5
practice in order to develop students’ mathematics reasoning and their mathematics
abilities. Also, you will be able to identify what content or pedagogical knowledge you lack
and find out how such knowledge can be developed. Finally, the explicit opportunity is
given to you to delve into your images of “self as teacher.”
By the end of this course, students will:
1) know how to use their content and pedagogical knowledge in practice in
ways that meets the vision of the reform-oriented learning and teaching of
mathematics
2) have explored their vision of self
3) be able to articulate what they have learned in this course
4) be proficient in designing lessons
5) investigate the extent of their preparation for teaching in the school context
6) develop understanding of students’ learning of mathematics
7) develop their content and pedagogical knowledge of mathematics
8) appreciate the importance of collaborative planning
Materials
All readings will be provided for you.
Course Requirements
The prerequisite for this course is completion of all content and methodology courses.
Active participation is essential. Therefore, your attendance throughout the semester and
communication with your group will be necessary not only for you to be successful but also
for others in the class. The ability to read critically and analyze the choices, results, and
your own interpretations of text will be essential to your success in the class.
Professional behavior is expected at all times. When presenting and sharing an idea the
way one communicates is key. Additionally, the manner in which one responds is just as
important. We must be open to critique and allow others the opportunity to explore the
fine threads that hold our ideas together.
Academic Honesty
As a University of Georgia student, you have agreed to abide by the University’s academic
honesty policy, “A Culture of Honesty,” and the Student Honor Code. All academic work
must meet the standards described in “A Culture of Honesty” found at
www.uga.edu/honesty. Lack of knowledge of the academic honesty policy is not a
reasonable explanation for a violation. Questions related to course assignments and the
academic honesty policy should be directed to the instructor.
Accommodations
Reasonable accommodations will be made for students with verifiable disabilities. In order
to take advantage of available accommodations, students must register with the Disability
Resource Center at 114 Clark Howell Hall. For more information about UGA’s policy on
working with students with disabilities, please see
http://drc.uga.edu/procedures/TableOfContents.php
Grading procedures
Your final grade will be based on the following:
Mathematics Autobiography/Vision Statement
Final draft of lesson (x2)
Presentation (x2)
Final Portfolio (x2)
Weekly Reflections (multiple)
15%
25%
25%
25%
10%
Assignments
- Vision Statement:
In this paper you will be describing how you envision your practices in your future
classroom. This will be refined and modified throughout the semester. See assignment
sheet for further details.
- Mathematical Autobiography:
In this paper you will be investigating and reflecting on your relationship with
mathematics in your life. See assignment sheet for further details.
- Micro-teaching Lesson Study (MLS) Plans:
The construction of well thought out and worthwhile lesson plans takes time. It also
requires the collaboration of others with varying perspectives. These lesson plans are
to demonstrate the results of four weeks’ worth of contemplation, revisions,
modifications, dry runs, and improvements. Rough drafts will be submitted at the end of
every week. Final drafts will be tested during your field experience week. See rubric for
more information.
- Weekly Summary and Reflections:
You will write a weekly reflection that will focus on two aspects of the class. The first is
the Micro-teaching Lesson Study (MLS) that occurs and the other on the weekly reading
assignments. When reflecting on the MLS aspect you are to focus on the progress and
process of the overall lesson, the discussion that ensued, and the conclusion about the
lessons goals, achievements, and results. When reflecting on the readings you are
expected to go “beyond the author” (Gadamer, 1975) and make connections to your
experiences as students or with previous field experiences. The reflection should also
include how the reading changed your perspective on this experience that you had.
- Presentation of Experience:
At the end of the four week of MLS and class taught during the field experience, each
group will be responsible for presenting a case study of the lesson. Groups are to give a
detailed description of the lesson, the actions of the students (this includes bringing in
student work), the moves the groups made, the analysis of the observers, and the
modifications that should be done if the lesson is done again. See rubric for more
information.
Hyejin Park
Nick Gomez
7
- Final Portfolio
With the final portfolio you will demonstrate the progress you believe you have made
throughout the semester. All claims will be backed up with evidence from the class. See
rubric for more information.
Tentative course schedule
Date
Topics
Week1
Introduction and
Survey
What is MicroTeaching Lesson Study
(MLS)?
Week2
Week3
Week4
MLS #1 (Middle School
Standard)
MLS #1
Week5
MLS #1
Week6
Week7
Week8
MLS #1
Field Experience
Presentations
Week9
Week10
Week11
Week12
MLS #2 (Secondary
Standard)
MLS #2
MLS #2
MLS #2
Week13
Out in Field
Week14
Week15
Presentations
Work on Final
Portfolio (NO CLASS)
Submission of
Portfolio
Week16
Reading to be
discussed
N/A
Assignments
McMahon & Hines
(2008)
Fernández (2010)
Mergler & Tangen
(2010)
Bartell, Meyer, Knott
and Evitts (2008)
Smith, Hughes, Engle,
and Stein (2009)
Vision Statement
Reading Reflection
(RR) #1
Vennebush, Margquez,
and Larson (2005)
Taber (2009)
Fiore (1999)
Jones, Hopper, Franz,
Knott and Evitts
(2008)
Barnes (2009)
Allen (2012)
McCoy (2008)
Weiss and MooreRusso (2012)
Gilbert and Gilbert
(2002)
Johanning (2010)
RR #2
Mathematics
Autobiography
RR#3
RR #4
RR #5
RR #6
RR #7
RR #8
RR #9
RR #10
RR #11
RR #12
RR #13
Reading Reference List
Allen, K. C. (2012). Keys to successful group work: Culture, structure, nurture. The
Mathematics Teacher, 106(4), 308–312.
Barnes, P. A. (2009). Empowering students through data. The Mathematics Teacher, 102(8),
614–620.
Bartell, T. G., Meyer, M. R., Knott, L. & Evitts, T. A. (2008). Addressing the equity principle in
the mathematics classroom. The Mathematics Teacher, 101(8), 604–608.
Fernández, M. L. (2010). Investigating how and what prospective teachers learn through
microteaching lesson study. Teaching and Teacher Education, 26(2), 351–562.
Fiore, G. (1999). Math-Abused students: Are we prepared to teach them? The Mathematics
Teacher, 92(5), 404–406.
Gilbert, M. C. & Gilbert, L. A. (2002). Challenges in implementing strategies for genderaware teaching. Mathematics Teaching in the Middle School, 7(9), 522–527.
Johanning, D. I. (2010). Informing practice: Helping students develop capacity for transfer.
Mathematics Teaching in the Middle School, 16(5), 260–264.
Jones, B. R., Hopper, P. F., Franz, D. P., Knott, L. & Evitts, T. A. (2008). Mathematics: A second
language. The Mathematics Teacher, 102(4), 307–312.
McCoy, L. P. (2008). Poverty: Teaching mathematics and social justice. The Mathematics
Teacher, 101(6), 456–461.
McMahon, M.T. & Hines, E. (2008). Lesson study with preservice teachers. The Mathematics
Teacher, 102(3), 186–191.
Mergler, A. G., & Tangen, D. D. (2010). Using Microteaching to Enhance Teacher Efficacy in
Pre-Service Teachers. Teaching Education, 21(2), 199–210.
Smith, M. S., Hughes, E. K., Engle, R. A., & Stein, M. K. (2009). Orchestrating discussions.
Mathematics Teaching in Middle School, 14(9), 548–556.
Taber, S. B. (2009). Capitalizing on the unexpected. Mathematics Teaching in the Middle
School, 15(3), 148–155.
Weiss, M. K. & Moore-Russo, D. (2012). Thinking like a mathematician. The Mathematics
Teacher, 106(4), 269–273.
Vennebush, G. P., Marques, E., & Larsen, J. (2005). Embedding algebraic thinking
throughout the mathematics curriculum. Mathematics Teaching in the Middle School,
11(2), 86–93.
Suggested/Optional readings
Reading from other content areas or general education research is important to broaden
our perspectives of the field in which we live and work in. Below are some suggested
readings to expand your horizons.
Ayers, W. (2010). To teach: The journey of a teacher. New York, NY: Teachers College Press.
Block, A. A. (2000). I’m only bleeding: Education as the practice of social violence against
children. New York, NY: Peter Lang Publishing.
Britzman, D. (2003). Practice makes practice: A critical study of learning to teach. Albany,
NY: SUNY Press.
Freire, P. (2000). Pedagogy of the oppressed. New York, NY: Bloomsbury Academic.
Goodlad, J. I. (1984). A place called school. New York, NY: McGraw Hill.
Hyejin Park
Nick Gomez
9
hooks, b. (1994). Teaching to transgress: Education as the practice of freedom. New York,
NY: Routledge.
Kohl, H. (1995). I won’t learn from you: And other thoughts on creative maladjustment. New
York, NY: New Press.
Ladson-Billings, G. (2009). The dreamkeepers: Successful teachers of African American
children. San Francisco, CA: Jossey-Bass.
Silin, J. G. (1995). Sex, death, and the education of children: Our passion for ignorance in the
age of AIDS. New York, NY: Teachers College press.
References
Britzman, D.P. (2009). The very thought of education: Psychoanalysis and the impossible
profession. Albany, NY: SUNY Press.
Brouwer, C. N. (1989). Geïntegreerde lerarenopleiding, principes en effecten [Integrative
teacher education, principles and effects]. Amsterdam: Brouwer.
Carter, G., & Norwood, K. S. (1997). The relationship between teacher and students’ beliefs
about mathematics. School Science and Mathematics, 97(2), 62–67.
Drake, C., Spillane, J. P., & Hufferd-Ackles, K. (2001). Storied identities: Teacher learning
and subject-matter context. Journal of curriculum studies, 33(1), 1–23.
Fernández, M. L. (2005). Learning through microteaching lesson study in teacher
preparation. Action in Teacher Education, 26(4), 36–48.
Fernández, M. L. (2008). Developing knowledge of teaching mathematics through
cooperation and inquiry. Mathematics Teacher, 101(7), 534–538.
Fernández, M. L. (2010). Investigating how and what prospective teachers learn through
microteaching lesson study. Teaching and Teacher Education, 26(2), 351–562.
Gadamer, H.G. (1975). Truth and Method. New York, NY: Continuum Publishing.
Goodlad, J. I. (1991). Why we need a complete redesign of teacher education. Educational
Leadership, 49(3), 4–10.
Grossman, P., Hammerness, K., & McDonald, M. (2009). Redefining teaching re-imagining
teacher education. Teachers and Teaching: Theory and Practice, 15(2), 273–289.
Hammerness, K. (2001). Teachers’ visions: The role of personal ideals in school reform.
Journal of Educational Change, 2, 143–163.
Hammerness, K. (2003). Learning to Hope, or hoping to learn?: The role of vision in the
early professional lives of teachers. Journal of Teacher Education, 54(1), 43–56.
Hammerness, K. (2006). Seeing through teachers’ eyes: Professional ideals and classroom
practices. Williston, VT: Teachers College Press.
National Council for Accreditation of Teacher Education (NCATE) (2010). Professional
development schools. Retrieved from
http://www.ncate.org/Accreditation/AllAccreditationResources/ProfessionalDevel
opmentSchools/tabid/497/Default.aspx
National Council of Teachers of Mathematics (NCTM) (1989). Curriculum and evaluation
standards for school mathematics. Reston, VA: National Council of Teachers of
Mathematics.
Roxanne V Molina, "Microteaching Lesson Study: Mentor interaction structure and its
relation to elementary preservice mathematics teacher knowledge development"
(January 1, 2012). ProQuest ETD Collection for FIU. Paper AAI3517029.
http://digitalcommons.fiu.edu/dissertations/AAI3517029