1. Overview
This proposal seeks to develop facilities that support curricular changes and supports the
establishment of outreach opportunities focused on improving mathematics education,
particularly in an urban setting. The primary goal is to restructure the secondary mathematics
education curriculum through collaboration with an urban school district. This will be made
possible by creating a “model” secondary classroom and providing funding to allow secondary
students from the city of Erie school district to participate directly in the training of preservice
mathematics teachers. This collaboration involves redesigning the mathematics methods courses
to include preparing and teaching conceptually-based, technology-rich lessons to urban students.
The secondary goal of this project is to build a cohort of secondary mathematics teachers from
local public schools interested in promoting effective implementation of technology for the
purpose of improving mathematics education. Professional development experiences aimed at
preparing teachers to use technology to advance mathematics education will empower this cohort
of teachers to effectively implement technology in their own classes.
A detailed description of the proposed model classroom, curricular changes, and outreach
program are provided in section 2. The anticipated contributions of the proposal, including
advancements related to three key challenges facing mathematics education are described in
section 3. Section 4 describes methods for assessing the impact of the proposed curriculum
changes and professional development workshops, including plans for disseminating findings
and sharing pedagogical products. Finally, section 5 describes secondary benefits likely to result
from the development of a model classroom and collaborative curriculum.
2. Description of Project
2.1 Description of Model Classroom.
The proposed model classroom will provide an authentic learning environment for
students in the mathematics education program by establishing a learning environment for
preservice teachers that more closely mimics the secondary school mathematics classrooms in
which they'll teach. The typical college classroom of forty or more desks crowded in tight rows
and a teacher's podium perched prominently in the front of the room is not consistent with the
layout in most secondary classrooms. The model classroom will provide a learning space more
adaptable for collaboration and small group work, with room for the teacher to move among
groups and facilitate discussions. Other features of secondary classrooms, such as bulletin
boards, a teacher's work station, and storage for manipulatives and supplies will also be
incorporated into the model classroom.
In addition to changes in layout, the model classroom will be equipped with technology
and manipulatives suitable for secondary instruction. Technology provided in the model
classroom will include a smart board, document camera, laptops with installed mathematics
software, a classroom set of graphing calculators with wireless connection capabilities for
automatic feedback and data sharing, a motion detector, and a calculator lab station. In addition,
the room will be equipped with video equipment for taping lessons, providing students with
opportunities to watch and reflect on their own instructional practices. The room will also be
equipped with manipulatives that promote hands-on exploration of mathematical concepts.
2.2 Description of Curricular Changes.
The current curriculum includes three mathematics methods courses, MTHED 411,
MTHED 427, and MTHED 412. Students typically enroll in MTHED 411 and 427 concurrently
in the spring semester of their sophomore year. MTHED 411 is an introductory course in
methods for teaching secondary mathematics and MTHED 427 focuses on technological tools
and pedagogical strategies for effective implementation into classroom activities. While enrolled
in these courses, students have no first-hand experiences teaching secondary students. The only
field experience taken prior to enrolling in these courses consists of relatively low-involvement
observations of secondary mathematics teachers. MTHED 412 is an advanced mathematics
methods course and is typically taken in the fall semester of the junior year, concurrent with
enrollment in the junior field experience. This field experience involves active participation in
secondary classrooms two half-days each week, including teaching lessons under the supervision
of a mentor teacher.
The proposed curricular changes involve refocusing all class readings, discussions, and
activities in MTHED 411, MTHED 427, and MTHED 412 to prepare students to design and
teach lessons to visiting secondary students from the Erie School District. At the beginning of
the semester, students enrolled in MTHED 411 and MTHED 427 will participate in professional
development focused on teaching engaging lessons to inner-city students. Experienced teachers
from the Erie School District will provide information regarding strategies and special
considerations for working with a diverse population. Throughout the semester, the topics
traditionally taught in MTHED 411 (i.e., lesson planning and general pedagogical approaches,
questioning and levels of cognitive demand, and implementation of high level tasks) and
MTHED 427 (i.e., competency with educational technologies, and promoting exploration and
conjecturing with technology) will be taught with the overarching goal of using these ideas to
plan and teach lessons to visiting secondary students. In this way, both courses will be divided
into approximately four or five units, with each unit culminating in a lesson taught in the model
classroom to secondary students from the Erie School District. The planning of each lesson will
be a collaborative process, with students working together to design and teach conceptually-rich,
technology-based lessons. The curriculum will also include time for students to reflect on their
lessons and make modifications and adaptations for future lessons.
The focus of MTHED 412, the following fall semester, will continue this emphasis on
using the course content to design and teach lessons to visiting city-school students. However,
since students will already have one semester of teaching experience and will be gaining
additional experience in their field placements, students will take on increased responsibility for
planning and teaching the lessons. Rather than a whole group effort, students will work in pairs
or triads to design and teach their lessons. The focus of the lesson reflections and adaptations
will be more specialized, focusing on course goals such as adapting instruction to learners' needs
and promoting discourse in the classroom.
2.3 Description of Technology Outreach.
Local school districts will be invited to choose one or two teachers to become members
of a focus group committed to improving the use of technology in mathematics education.
Selected teachers will receive a small stipend for participating in approximately six one-day
workshops over the course of a year. The focus of the workshops will be on implementing
technology in ways that encourage students to think mathematically, including exploring and
making mathematical conjectures. The technological focus of the workshops will be adjusted
based on the technologies available to teachers in the participating schools. In addition to these
workshops, the focus group will participate in sharing best practices and will be encouraged to
serve as mentors for teachers in their own districts. The group will focus on producing and
disseminating information on technology activities and best practices. The following year, a new
cohort of mathematics teachers will be invited to participate in the workshops. The first year
participants will take an active role in leading the workshops, including modeling lessons
designed and taught in their own classes, and serving as mentors to the first-year members.
3. Anticipated Contributions
There are many challenges that face mathematics education, in general, and university
secondary mathematics education programs, in particular. While not an exhaustive list, three
particular challenges are addressed here. These challenges include (1) preparing quality teachers
who are prepared and willing to teach in urban schools, (2) closing the gap between theory and
practice in mathematics methods courses, and (3) effectively teaching with technology in ways
that promote conceptual understanding.
3.1 Quality Teachers in Urban Schools.
The National Council of Teachers of Mathematics' (NCTM) equity principle supports a high
quality mathematics education for all students, regardless of race, gender, or socioeconomic
status (NCTM, 2000). Yet the challenge of recruiting and retaining quality teachers in urban
school districts threatens the equity of instruction for these inner-city school students.
3.1.1 Description of the Problem
Research has shown disparities in the quality of teachers employed at urban versus
suburban and rural school districts. Highly qualified teachers in urban districts are more likely
than their less qualified peers to be hired in schools they find more desirable. This leads to
highly qualified teachers leaving urban settings, and results in lesser qualified teachers at the
schools most in need of highly qualified educators (Lankford, Loeb, & Wyckoff, 2002).
Additionally, salary increases and other incentives aimed at attracting and maintaining highly
qualified teachers in urban schools have not been successful in closing the gap in teacher
qualifications. As a result, it is important to consider the reasons for teachers' unwillingness to
teach in urban settings, including the quantity and quality of their experiences teaching diverse
populations. Stoddart (1993) recognized the "reluctance of the graduates of traditional teacher
education programs to work in urban schools" (p. 29) as one factor in the disparity in teacher
quality between urban and suburban schools. While it is important that preservice teachers gain
experience with diverse populations, it is a delicate balance between much-needed exposure and
overwhelming preservice teachers with difficult teaching environments. According to Stoddart
(1993), education programs may discourage students from working in urban schools by either (1)
avoiding preservice teacher interaction with diverse learners altogether or (2) overwhelming
students with teaching placements in diverse settings without adequate support or preparation.
3.1.2 Contribution of Proposed Project
Like many preservice teachers, the majority of mathematics education students at Penn
State Erie attended suburban high schools and have little experience with diverse populations.
Without high-quality, well-structured opportunities to teach inner-city students, these preservice
teachers may be unwilling to accept teaching positions in urban districts upon graduation.
However, Stoddart's (1993) findings suggest that if preservice teachers' first experiences with
urban students occur as part of student teaching, the result might be to overwhelm and deter
future employment in an urban district. This project will ensure preservice teachers are prepared
for their introductory experiences with urban students by providing professional development
experiences taught by experienced teachers. Additionally, inviting inner-city students to
participate in lessons planned and taught collaboratively, under the supervision of the
mathematics education faculty member will provide a less threatening environment for
preservice teachers to gain comfort in teaching a diverse group of students. Students will build
confidence over time, leading into their second semester when they will collaborate to co-prepare
and co-teach a lesson to a diverse group of inner-city students. This gradual introduction and
adequate preparation of preservice teachers to urban school students will provide the necessary
experience without overwhelming the future teachers. As a result, the preservice teachers are
more likely to have positive experiences, which may lead to an increased willingness to teach in
an urban setting upon graduation.
3.2 Theory Versus Practice
Mathematics methods courses teach theory and provide pedagogical techniques with the goal of
preparing preservice teachers to use research-based instructional strategies. However, preservice
teachers' personal educational experiences and mentor teachers' philosophies may be stronger
forces in shaping future educational practices.
3.2.1 Description of the Problem
A current area of concern with teacher education programs is the disconnect between
mathematics methods courses and field placement experiences. In particular, methods courses
are generally taught in a university setting, by a faculty member who never observes the
preservice teacher in a secondary classroom. This traditional separation between methods
courses and field experiences raises many concerns. Without a link between coursework and
field experiences, the theory presented in a methods course is not practiced and refined. One of
the most important skills for a teacher is the ability to reflect and adapt lessons based on
classroom outcomes (NCTM, 2000). Reflection is even more critical for preservice teachers as
they reflect not only on particular tasks or lesson features, but on general approaches and theories
regarding effective instruction. If theory is taught independent of field experiences, preservice
teachers do not have an opportunity to reflect on and refine their own theories of teaching and
learning (Britzman, 1991).
Additionally, traditional field experiences away from the university setting have been
scrutinized for de-emphasizing or even contradicting the theory taught in methods courses.
Mathematics education is often criticized for emphasizing procedures without meaning, while
reforms in mathematics education stress conceptual understanding based on reasoning and sense
making (NCTM, 2000, 2009) to prepare students for the mathematics they'll experience in the
workplace. Despite methods courses that emphasize research-based teaching practices,
preservice teachers often retain their traditional notions about mathematics (Civil, 1993). This
resistance to change may be caused by students' own experiences in secondary mathematics
education (Ball, 1988, 1990) or as a result of field placements which act as a "conservative
force" (Ebby, 2000, p.70 ). In order to minimize the risk of a field experience serving to
counteract the theory taught in methods courses, placements should be chosen at schools with
teachers whose philosophies are in line with these teachings (Curcio, Artzt, & Porter, 2005).
While field placements can be carefully selected to involve mentor teachers believed to value
conceptual understanding and standards-based instruction, once the student is in a placement the
university has very little control over the quality of the student teaching experience.
3.2.2 Contributions of Proposed Project
The proposed curricular changes integrate students' first teaching experiences into the
theoretical framework of the methods courses. Students will be provided with opportunities to
test the theory and pedagogical strategies learned in the methods courses while teaching real
secondary students. Currently, students' only opportunities to teach lessons while learning about
the theory in MTHED 411 and MTHED 427 occur during peer teaching assignments. It is not
until later, during field and student teaching placements, that students teach real secondary
students. Although peer teaching can be valuable, teaching a lesson to a group of future
mathematics teachers is much different from teaching to a group of secondary students. With
this project, preservice teachers will be able to combine the timeliness of applying theoretical
ideas and pedagogical strategies as they are introduced in methods courses, with the authenticity
of teaching real secondary students in a nurturing environment. The lessons learned from these
early experiences linking theory and practice will provide a foundation for future teaching
practices.
3.3 Effectively Implementing Technology (**Note: Add data collected from local school
districts regarding available technology)
Although technology is now widely available, it is not widely used by all teachers. Furthermore,
simply incorporating technology into a preexisting mathematics lesson does not guarantee
improved instruction. While technology has great potential in promoting students' mathematical
thinking and awareness, a great deal of knowledge is required for teachers to incorporate
technology into the classroom effectively.
3.3.1 Description of the Problem
Access to technology has become a reality in most secondary schools. According to data
from the National Center of Educational Statistics (NCES), ninety-seven percent of all public
school teachers reported having computers in the classroom every day, with a ratio of one
computer for every 5.3 students (Gary & Lewis, 2010). Teachers in urban districts, or districts
with large percentages of students on free and reduced lunch reported access very similar to
teachers in rural or suburban districts, as well as districts with fewer students on free and reduced
lunch (Gary & Lewis, 2010). Unfortunately, availability does not guarantee instructional use;
and instructional use does not guarantee effective implementation.
Mishra and Koehler's (2006) study of teachers’ development of rich technology use in the
K-12 classroom, led them to explore the relationship between technology, pedagogy, and content
in planning and implementing effective lessons. Technological Pedagogical Content Knowledge
(TPCK) is the intersection of all three of these domains, and is described by Mishra and Koehler
(2006) as being “…different from the knowledge of a disciplinary or technology expert and also
from the general pedagogical knowledge shared by teachers across disciplines” (p. 1028-1029).
Just as knowledge of mathematics does not qualify an individual to teach mathematics,
knowledge of how to use technology does not guarantee it will be successfully integrated into an
educational setting. In fact, teachers need a great deal of specialized knowledge about
technology. Teachers must know how the technology supports the content they are teaching and
incorporate pedagogical techniques for using the technology effectively. Traditional methods of
professional development that simply provide tutorials on how to use technology are not
effective.
When used effectively, technology should not be an afterthought, simply added to
preexisting lessons. However, this is how many teachers use technology in their classrooms
(Cuban, Kirkpatrick, & Peck, 2001). In particular, technology is often used to promote drill and
skill rather than conceptual understanding or problem solving. This emphasis on technology to
promote low-level skills is particularly prevalent among high poverty districts compared with
low poverty districts. According to Gray & Thomas (2010), 61% of low poverty teachers and
83% of high poverty teachers reported using technology for this purpose. NCTM's (2000)
technology principle promotes using technology in a way that allows students to make and test
conjectures, fostering student engagement at a higher level of abstraction and generalization than
accessible without technology. Promoting use of technology for conceptually-rich discovery of
mathematical ideas requires providing professional development experiences that help teachers
to recognize technology as a valuable tool for exploring mathematical relationships, while
providing opportunities for the teachers to reflect on their own discoveries and their development
of technology-rich lesson plans (Bowers & Stephens, 2011).
3.3.2 Contributions of Proposed Project
This project seeks to improve the quality of technology implementation by providing
professional development experiences for preservice and in-service teachers. As previously
mentioned, an entire course (MTHED 427) is already designed with the goal of linking the
mathematical content, pedagogical practices, and technological considerations involved in
teaching with technology. However, this project will improve the ability of this course to meet
that goal by (1) providing access to more technology, including technology prevalent among
local schools, and (2) incorporating preparation and implementation of technology-rich lessons
to secondary students as a key component of the course. This reiterates the contributions to
closing the theory versus practice gap, providing students with authentic experiences
incorporating technology into lessons and reflecting on their successes and failures in doing so.
The proposed focus-group of in-service secondary teachers will broaden the
technological impact of the project. In particular, the professional development experiences will
better prepare the participating teachers to meaningfully incorporate technology into their own
teaching practices. Another goal of this group will be to develop and share resources and best
practices. In addition to sharing these ideas with one another, participants will be encouraged to
take these resources and pedagogical approaches back to their schools to share with other
mathematics teachers. The result will be to broaden the use of technology in local school
districts, while focusing this use on activities that promote conceptual understanding of
mathematical ideas.
4. Evaluation & Dissemination of Findings
In order to measure the program's effectiveness, data will be collected to evaluate progress
toward each of the anticipated contributions.
4.1 Measuring Outcome of Experiences with Urban Students
The major goal of collaborating with an urban district is to provide preservice teachers
with positive experiences teaching inner-city students. In order to measure the impact of these
experiences, a pre/post survey will be administered to gauge the preservice teachers' attitudes and
beliefs about teaching diverse learners. Comparing pre and post-results will indicate the
program's effectiveness in providing opportunities that improve preservice teachers' attitudes and
confidence regarding teaching inner-city students. Since most students from the program are
placed in an urban setting for either their junior field or student teaching experiences, data can
also be collected from the mentor teachers regarding the preservice teachers' preparation for
working in an urban environment. In addition to the mentor teacher's evaluation, a common
evaluator from the Erie School District will also observe the preservice teachers in their urban
placements to evaluate their overall preparedness and confidence. Since the true measure of the
success will be students' attitudes when applying for jobs, students will be surveyed again upon
graduation to measure their willingness to accept a position in an urban school district. Postgraduation employment information will also be tracked to look for patterns in terms of actual
job placement for the participating students.
4.2 Measuring Outcome of Merging Theory and Practice
If the program is successful in merging theory and practice, the curricular goals of the
mathematics methods courses should appear in the planning and implementation of the lessons
taught by the students. In order to measure this, an outside reviewer from the Erie School
District will be asked to assess the lessons presented to the Erie School District students. These
evaluations will focus on the presence and extent of use of the main ideas from the mathematics
education curriculum, including theoretical underpinnings and pedagogical approaches. Use
should increase throughout the semester while students progress from MTHED 411 and 427 to
MTHED 412. Additionally, to measure long-term effectiveness, the university supervisor and
mentor teachers will be asked to rate their student teachers' implementation of the ideas
fundamental to these courses. This is an important component in light of previous research that
suggests field placements can negate the teachings of methods courses (Curcio, Arzt, & Porter,
2005; Ebby, 2000).
4.3 Measuring Outcome of Technology Implementation Outreach
The impact of the project on the effective use of technology should be measured for both
preservice teachers and in-service teachers taking part in the technology workshops. The impact
on student use of technology can be measured by an outside evaluator's critique of the quality
and effectiveness of the technology implementation in the lessons taught to the Erie School
District students. The longer-term results can be tracked, once again, by following-up with
students to assess the frequency and quality of technology implementation in field and student
teaching placements. Additionally, surveys will be administered to students before and after
enrolling in MTHED 427 to measure changes in students' beliefs about the role of technology in
the mathematics classroom and pedagogical considerations for using technology most
effectively.
The impact of the workshops and sharing of best practices among members of the
technology cohort will be measured through a pre and post-survey. This survey will include
questions designed to reflect the teachers' attitudes towards technology implementation,
frequency and nature of technology use in their classes, and considerations for quality
implementation of technology. Additionally, since the goal of this workshop is to extend the use
of quality technological activities beyond the members of the cohort, the other mathematics
faculty at the schools of the participating teachers can be surveyed at the beginning and end of
the school years to assess whether the impact has extended beyond the cohort itself. Any
resources that the cohort develops, such as a website of shared resources and best practices, can
also be evaluated by an outside source.
4.4 Dissemination of Findings
This project has the potential to inform the literature on mathematics education in several
ways. The principal investigator will be engaged in analyzing the outcomes of the curricular
changes and technology workshops as they pertain to current mathematics education research. It
is expected that several journal articles and conference presentations will result. These results
hold potential implications for mathematics education programs and professional development
programs. The findings may also have broader implications for teacher preparation programs in
other content areas, since the impact of this program on preservice teachers' attitudes toward
employment in urban districts is not tightly linked to mathematics.
In addition to contributions to the body of theoretical research in education, the lesson
plans designed and taught by the preservice teachers and in-service technology participants will
be shared in pedagogical journals and at mathematics education conferences. Financial support
for preservice and in-service teachers to attend such conferences will aid in this dissemination of
pedagogical materials. The lessons, best practices, and technological considerations developed
by the technology focus group will be disseminated to local school districts to encourage others
to adapt and use the lessons and techniques in their classrooms.
5. Additional Contributions
In addition to the primary goals described previously, the establishment of a model
classroom is likely to have additional benefits. With these facilities, the mathematics education
students will have an opportunity to present mathematically-rich lessons to students enrolled in a
mathematics freshman seminar, as well as to provide technology and teaching workshops for
faculty. The many outreach events that are held on campus could benefit from these facilities,
and with appropriate space, additional outreach events can be pursued. In addition, the
mathematics department offers a course for elementary education majors, Math 200, that
provides an advanced look at elementary mathematics and prepares future elementary teachers
for explaining the mathematical concepts and procedures. This class focuses heavily on using
manipulatives to explain elementary mathematical principles, and would benefit from the
authentic learning environment and access to technology and manipulatives. This will lead to
enriching the educational experience and knowledge of teaching mathematics among another
group of future teachers.
Another contribution that cannot be overstated is the possible impact on the students of
the Erie School District who will participate in the lessons taught by the preservice teachers.
These students will benefit mathematically from engaging, technology-rich mathematics lessons
that focus on building conceptual understanding. However, the secondary students will also get
valuable experience from visiting a college campus and interacting with college students. Since
many of these students may not have other opportunities to visit a college campus, their
participation in this project could provide critical experiences that encourage them to consider
furthering their education after graduation from high school.
References
Ball, D. L. (1988). Unlearning to teach mathematics. For the learning of mathematics, 8(1), 4048.
Ball, D. L. (1990). Breaking with the experience in learning to teach mathematics: The role of a
preservice methods course. For the learning of mathematics, 10(2), 10-16.
Bowers, J. S., & Stephens, B. (2011). Using technology to explore mathematical relationships:
A framework for orienting mathematics courses for prospective teachers. Journal of
Mathematics Teacher Education. Advanced online publication. doi: 10.1007/s10857-0119168-x
Britzman, D. P. (1991). Practice makes practice: A critical study of learning to teach. New
York: State University of New York Press.
Civil, M. (1993). Prospective elementary teachers' thinking about teaching mathematics. Journal
of Mathematical Behavior, 12, 79-109.
Cuban, L., Kirkpatrick, H., & Peck, C. (2001). High access and low use of technologies in high
school classrooms: Explaining an apparent paradox. American Educational Research Journal,
38, 813-834.
Curcio, F. R., Artzt, A. F., & Porter, M. (2005). Providing meaningful fieldwork for preservice
mathematics teachers: A college-school collaboration. Mathematics Teacher, 98, 604-609.
Ebby, C. B. (2000). Learning to teach mathematics differently: The interaction between
coursework and fieldwork for preservice teachers. Journal of Mathematics Teacher
Education, 3, 69-97.
Gray, L., Thomas, N., and Lewis, L. (2010). Teachers’ Use of Educational Technology in U.S.
Public Schools: 2009 (NCES 2010-040). National Center for Education Statistics, Institute of
Education Sciences, U.S. Department of Education. Washington, DC.
Lankford, H., Loeb, S., & Wyckoff, J. (2002). Teacher sorting and the plight of urban schools:
A descriptive analysis. Educational Evaluation and Policy Analysis, 24, 37-62.
Mishra, P., & Koehler, M. J. (2006). Technological pedagogical content knowledge: A
framework for teacher knowledge. Teachers College Record, 6, 1017-1054.
National Council of Teachers of Mathematics (NCTM). Focus in high school mathematics:
Reasoning and sense making. Reston, VA: NCTM, 2009.
National Council of Teachers of Mathematics (NCTM). Principles and standards for school
mathematics. Reston, VA: NCTM, 2000.