Introduction:
When I first started to think about this project, I thought that I would like to work on an implementation, which dealt with my subject area of mathematics.  An idea came to mind after reading some literature as well as speaking with some of my colleagues.  I chose my topic for this implementation project to be one of a specialized mathematics instruction in the elementary school.  Many students come into the middle schools dreading their math courses.  Not only do they have these very negative attitudes about mathematics in general, but also many have not yet learned the basics.  These basics are necessary for continuing on in mathematics in the middle and high schools and many have been passed on to the middle schools without knowledge of the basic structures of mathematics.  Part of this problem lies in then instruction of math in the primary grades.
Many elementary teachers themselves do not like math.  They probably had about as much trepidation about doing math when they were in school.  This negative attitude is then passed on to the students and affects their method of instruction.  But this isn’t the only problem, to compound, many of these teachers do not have a sound knowledge of the subject matter and therefore are not able to teach the structures of math in such a way as to foster a more conceptual understanding from their students.  Elementary teachers are expected to be able to teach all of the disciplines to their students with only minimal knowledge, many only learn enough math just to be able to teach it.  No one person can be expected to have concrete knowledge of all subject matter.   It is not a feasible expectation.  But for some reason our elementary schools are designed in just that way- one teacher to teach all subjects to youngsters for the very first time.  Students who are in the elementary schools are just beginning their academic careers and it is here where they are supposed to learn the structures of each subject area so that they can further their pursuit of knowledge in the middle and high schools.
But how can we as educators think that it is possible for one teacher to do all of this, with limited knowledge and very often very negative attitudes?
In my implementation of a specialized mathematics curriculum in the elementary schools, I would attempt to address these issues.  My program would set up a type of partnership team with middle school math teachers and the elementary teachers.  In the pilot portion of this implementation the math teachers would be teaching the kindergarten grades.  The purpose of this implementation would be to place the responsibility of teaching mathematics on the mathematics teachers from the middle school.
By utilizing this type of partnership between secondary and elementary teachers, we would be building a sense of community within the school district.  So often there is such a separation between the elementary and secondary curriculum as well as a separation of their environments. There is very seldom any thought given to how one school might help the other.  After all, shouldn’t we all be after the same goal for all of our students, that being a high value placed on the best learning and instruction possible?
While fostering a sense of community with in the school district is very important, the main purpose of this change, however, is to improve and foster greater mathematics learning of the students right from the very beginnings of their learning.
My ultimate and ideal outcome from this implementation would be to have specialized mathematics instruction for all of the grades in elementary school.  I really feel that a teacher needs to have a very deep knowledge of a subject matter to be able to teach it effectively and in a way that promotes conceptual understanding.  From this specialized instruction would come forth a greater understanding and knowledge of the structure of mathematics and of the interconnectedness of all of the concepts.
This area of mathematics curriculum and instruction change is important to me for many reasons.  The first being because I am studying to be a mathematics teacher and I would like to see math taught to students in the most effective way possible.  I enjoy math, it has always interested me and I did well in it.  But I do know that math is not for everyone and that it can be difficult as well as frustrating for many.  Another reason why this area is important to me is because I have two young children who are just beginning to explore their knowledge of their world.  My son is five and my daughter is three and a half and they both are just so excited when they learn something new and they are so eager to learn.  I want for them to always feel this way when it comes to school and learning.  Their excitement as well as all young children’s, should be kept alive and not dampened by any means.  I feel that many times in elementary school this is where children form their opinions and attitudes about school and about subject matter.  I feel that certain subject areas, such as math and science, really need to be taught by someone who has deep knowledge of the subject matter and who really enjoys it. This is by no means any reflection on the teaching abilities of the elementary teachers, but they cannot possibly have mastery of all subjects.  I think that our young children deserve to be taught by teachers who do have mastery, especially at such a young age where they can learn so much!

Review of Literature:
When reviewing the NCTM standards for K-4, it is very apparent that there is indeed a need for the curriculum to be conceptually oriented (NCTM, 1989).  This type of approach enables children to acquire clear concepts by constructing their own meaning and being able to see connections in various situations.  “A conceptually oriented curriculum can result in programs that are better balanced, more dynamic, and more appropriate to the intellectual needs and abilities of children” (NCTM, 1989, p. 17).  This type of curriculum also results in the attainment of skills necessary to move on in mathematics instruction in the middle school.  So what they NCTM standards are saying is that the mathematics curriculum in the elementary grades had to be changed from the instruction of facts and formulas and rules to concepts and how these concepts all relate to one another. Elementary mathematics education should reinforce a child’s natural curiosity about math (National Research Council, 1989).  So if this in indeed what the standards are trying to do, then what type of teacher is capable of teaching these concepts and does not need to rely on the memorization of facts?
When I started to research this topic I found that there were definite factors which influenced how a student learns math.  These included teachers’ attitudes towards math in general and teachers’ actual content knowledge.  How a teacher views math itself to me is a big factor.  Not only can a teacher’s conceptions of mathematics be learned by the students, but also a teacher’s attitudes, such as excitement or anxiety towards math can be picked up by the students as well (Brown & Baird, 1993).  According to Thompson (1992), a number of studies in mathematics education have indicated that teachers’ beliefs about math and its teaching play an important role in shaping the teachers’ pattern of instruction.   A teacher’s enthusiasm will be passed on to students in the way in which the material is presented, in the activities which are utilized and just by the overall learning environment in the classroom.  On the other hand, if a teacher doesn’t care for math or has anxiety every time the word “math” is mentioned this too will be sensed by the students and will tend to have a negative effect on the learning of this subject for the students.
Now about this anxiety that many elementary teachers have about math and about teaching it, where does it come from?  Often a lack of deep understanding of mathematics can cause anxiety or negative attitudes towards math in general (Brown & Baird, 1993).  Many elementary teachers, a few of whom I spoke with, do not have the deep knowledge of mathematics and this causes their anxiety.  This anxiety not only causes anxiety in the students, but it also affects they ways in which these teachers teach math.  According to Foss & Kleinsasser ( 1993), this feeling of anxiety reinforces the belief that computational skill and memorization should drive math curriculum and that teaching mathematics is rule bound and about “telling.”
Many elementary teachers tend to see math as just bits of procedural knowledge, which is not connected.  Thus teaching math becomes just computation after computation with little or no application.
While a teacher’s beliefs and conceptions of mathematics do indeed have an immense influence on their instruction, so too does their knowledge of math.  Teachers with greater mathematical knowledge tend to be more conceptual in their teaching, while teachers with lower levels of knowledge tend to be more rule based (Brown & Baird, 1993).  Also those teachers with limited knowledge see only one way of solving a problem and that is the textbook’s way.  They are not open to different ways of solving a problem if it is not the way in which they taught it.  However, a teacher with more in-depth knowledge of math will have better ways of representing the subject matter to make I more interesting and comprehensible to the students.
It is also true that if a teacher has a deep understanding of mathematics, it is because he or she has chosen to pursue this knowledge.  While on the other hand, those with limited knowledge, mainly elementary teachers, many only took the very few required courses which will enable them to teach, they did not take these courses because they wanted to.  Can you see how this greatly affects each teacher’s attitudes about math and how he or she will transfer this attitude on to their students?
According to the National Research Council (1989), they too feel that it is time that we specialize our mathematics instruction in elementary school.  It is felt that the United States is one of the few countries in the world, which expects that elementary school teachers are able to teach all subjects equally well.  This could be done by other implementations such as team teaching where one teacher would teach math and science while the other would teach English and history.  Or possibly a certified specialist who could lead in the curricular development and assist regular teachers (National Research Council, 1989).
While I was not able to find any literature, which cited specific examples of my implementation, it was apparent to me that many feel that there is indeed a need to look into mathematics instruction in the elementary grades and to how it is being taught.

Goals:
A good outcome from this implementation would be that there would be a specialized mathematics instruction in the elementary school.  A sort of partnership team between middle school mathematics teachers and the elementary school teachers would be developed. This would ultimately bring the students to a mastery level of the structures of mathematics and of the concepts so that they can then move on to middle school to further their education in mathematics.
I think that for the time being, the process itself of implementing this change would be the primary focus.  This change would be sort of a structural change in how the elementary school curriculum is set up from one teacher teaching all subjects to specialized teaching.  If this process is successful, then maybe we can proceed to change the entire format of the elementary curriculum to have specialized teaching of all subject matter.
I would want the schools, both the middle and elementary, to grow in a way of realizing that there needs to be community between the two.  There needs to be the realization that all schools in a district should be working towards to good of all students.
Needs Assessment:
To determine if there is actually a need for establishing a partnership between middle school mathematics teachers and elementary school teachers, I would first conduct a survey amongst the teachers.  This survey would pose such questions as: What are your feelings about mathematics in general?  How do you feel about teaching mathematics?  How would you summarize your knowledge of the subject matter?  These questions would try and get at the teachers’ true feelings about mathematics, about learning and teaching of mathematics.  I would also talk to the middle school mathematics teachers individually to survey their feelings as how the students are coming to them.  What is their level of knowledge in mathematics, do they have the basics which are necessary to continue and what are their attitudes regarding math?
I would then gather more quantitative data such as records to show grades, test scores, any data, which would reflect any numbers as to how students are a actually doing in mathematics.
I would then take all of the data gathered from the surveys, the grades etc, and see if they support my idea.  According to my research and from talking with both sets of teachers, the data would indeed support the need for this implementation.
I would go on to then put together a focus group consisting of middle school mathematics teachers and elementary school teachers from the district.  The group would also involve any administrative personnel.  In this focus group I would discuss my findings to prove to them that there is a need for this change in instruction at the elementary level.  As a group, we would all need to discuss our thoughts and feelings on the subject, and we would need to listen to one another.  I would attempt to provide them with a sense that this change would benefit all.
This implementation would benefit the students because they would be receiving a much more conceptualized instruction instead of mere rote memorization.  The teachers would also benefit by lessening the “load” of the elementary teacher.  As stated earlier, no one teacher can have mastery of all the disciplines.  Many elementary teachers feel so bogged down with all that they are expected to teach to their students.  Many also do not feel comfortable or capable of teaching mathematics and this implementation would free up some of their time and lessen their anxiety.
However, what will ultimately need to change for this implementation to be successful is for the teachers of both schools to see that they need to work together.  There needs to be a feeling of community within the district itself, and amongst the schools.  Their needs to be a shared vision by all involved that learning is of the utmost importance for our children.  Everyone needs to work together to see that the children are receiving the best possible education possible.
Implementation Plan:
For this change to come about I will first need to make sure that those people involved get a clear picture of the focus of the change.  Basically this would involve defining the student outcomes, building a shared vision of this implementation, one in which everyone has ownership.  Everyone needs to be involved and feel as though they have say in it.  Also for this change to succeed one cannot proceed too fast or some of the problems, which may develop may be overlooked.   The change cannot be too slow or you may run into many becoming disinterested.  I feel that you need to proceed at a steady pace, however always willing to stop and possibly see why a problem has occurred and adapt accordingly.
The implementation itself requires the use of many resources, one of the first being that of human resources.  The human resources which would be involved are the teachers.  These would include the middle school math teachers as well as the kindergarten teachers of the pilot school.  Another human resource would be that of the administration of the district, mainly of the schools which are involved.  The parents of the incoming kindergarten students would also be a resource in this implementation.
Another resource, which we would need to obtain, is that of time.  Time would have to be set aside before the start of the school year for the partnership team to get together to discuss their strategy.  Time would also have to be allotted for the middle school math teachers so that they would be able to come to elementary school for three hours each day.  Time would also need to be allotted for the partnership team to meet during the day, as often as needed, to assess the progress.
Perhaps one of the most important resources for this change is that of commitment.  Before this implementation can actually begin, there has to be commitment on the part of all of those involved- those in the partnership team as well as the administration and parents.  Once these resources are in place, the steps of the implementation itself can then be formulated.

Stage 1 (April/May):
? After the needs assessment data has been collected and compiled, I will formulate a focus group consisting of all elementary teachers and middle school mathematics teachers in the district.  This focus group would also include administration such as the principals of the schools and the superintendent.  In this group the needs assessment data will be discussed and I will attempt to prove to the group that there is indeed a need for specialization of mathematics in the elementary schools.
? At this point I will explain my implementation plan to them. “ A partnership will be developed between two middle school mathematics teachers and the kindergarten teachers from the pilot school.  The middle school math teachers will come to the elementary school each day to teach mathematics to the kindergarten students.  The two sets of teachers would work together on the instruction, each handling his or her expertise.  The middle school math teacher would actually handle the mathematics instruction, while the kindergarten teacher would be there for support in teaching elementary age children.
[For the initial implementation of this plan we would concentrate only on the kindergarten classes.  The reason being is that it makes sense to start at the very beginning to try and change instruction practices and to get the students accustomed to conceptual mathematics teaching right from the start.]

Stage 2 (End of June after School Closes):
? At this point the pilot elementary school would be chosen.  This would depend mainly on which teachers were most committed to this change and vision, and who were most positive about it.

Stage 3 (July/August):
? Once the pilot school has been chosen, the middle school math teachers and the kindergarten teachers would get together to form the partnership team.
? The team would then discuss what their vision would be and hopefully it would be a shared vision.  The vision would hopefully be one of valuing learning, interdependence and teamwork.  At this point we might also find it necessary to work on team skills.  As there also might still be some skepticism at this point we would make sure to keep the lines of communication open.
? The team would then discuss the curriculum and instruction and formalize each team member’s responsibility.
? The middle school math teachers would be responsible for the mathematics instruction as well as the assessment.  This instruction would consist of teaching the basic structures of math through making connections and not just via memorization.  The curriculum would continue to follow the standards.
? The kindergarten teachers would be responsible for guiding the math teachers in teaching of elementary age children in comparison to the middle school age students.  They will be available to help the math teachers get to know their students.
? In addition to teaching mathematics to the kindergarten students, the middle school math teachers would be responsible for setting up a math lab.  The purpose of this lab will be to help any teacher in the elementary school who may be having difficulties with the instruction of math.  The lab will also be for any student in the school who may be having difficulties with math.

Stage 4 (Mid-End August):
? The partnership team will meet with the parents of the incoming kindergarten students for the up coming year.  This meeting will inform the parents of the specifics of the new specialized mathematics instruction.  This will also give the parents, as well as the students, an opportunity to meet with the math teachers.

Stage 5 (September): The beginning off the new school year!
? Math will be taught at the same time each day.  The middle school math teachers will come to the elementary school to teach the kindergarten classes.  They will come to the school each day for about 3 hours (the exact time will have been decided in Stage 3).  About 1 hour will be for
the actual instruction and the remaining 2 hours will be set aside for lab.
Stage 5 will continue to proceed through out the year with regular revisits by the team to Stage 3.  Ideally what I would like to see happen is the this specialized instruction would continue with each incoming kindergarten class and also remain and follow with these first group of students as they progress through elementary school.
While the actual stages of this implementation seem pretty cut and dry written down on paper, there will always be problems and complications, which may arise.  When this does happen we will need to step back and adapt as necessary, but we must continually assess the progress so that we will be observant when these problems occur.
Some of the problems, which I foresee with my change, are as follows:
? Reluctance on the part of the elementary teachers to hand over a part of their teaching responsibilities to another teacher.
? Feeling on the part of the elementary teachers that they are being told that they are not doing a good enough job – that their teaching abilities are being questioned.
In reference to these first two examples it is important to note that this change is in no way a reflection on the elementary teachers’ teaching abilities.  No one person can be expected to have mastery of all subject matter, when their education only prepares them for enough knowledge of each subject matter to teach it.  The main point of this implementation is to improve the mathematics education of the younger students- to foster more positive attitudes about math and to not put so much pressure on the elementary teachers.  This belief will be reiterated at the beginning of the process as well as throughout to make sure that no one feels as though his or her teaching abilities are being under attack.
? Problems in scheduling for the middle school teachers might arise.
? As this change would involve a restructuring, so to speak, of the traditional elementary school, one may run into opposition by some faculty and community who are of the “old school” of thought.  They would believe that one teacher should teach all subjects to each class.  Another augment for this might also be that young students need to have stability with one teacher and by having another teacher come in to teach math might cause some anxiety.  My feeling is that young children are very resilient when it comes to change.  They tend to handle change much better than adults do so I really do not foresee this being a problem.
At this point in time, I am not really sure that I feel comfortable giving a definite timetable as to how long this change would take.  I think that we would really need to assess each year to see how we are progressing.

Assessment:
Assessment of this change will be ongoing.  The students will continually be assessed to make sure that they are reaching the learning objectives and that they are gaining knowledge.  Looking at students’ journals and portfolios we should see a remarkable improvement in student understanding of math (and maybe it won’t).  On a day to day basis, the students will be required to write in their journals at the end of each math class to basically summarize what they have learned for that day’s lesson.  In their entries we should be able to see structural and concrete understanding of the concepts as they will be explaining in their own words, their understanding of it.
The math teachers will also be assessed to make sure that they are meeting the objectives and to make sure that their relationships with the students is a positive one.
As far as assessing to see if the change has been a success, as I said before it will not be possible in the first year.  We will be able to look at the grades at the end of the year and compare to previous years.  The students in the first year will be assessed via tests and possible performance tasks as well as journals to see if they have indeed learned some basic structures and understanding of the concepts.
Also by surveying the kindergarten teachers you might be able to sense if they are a little less stressed by not having to teach math.  You might also survey any of the other elementary teachers to get their feeling on the math lab.
However, concrete assessment of this change would take place a few years down the road, perhaps in six years when these kindergarten students are in the sixth grade.  At this point we would be able to see whether these students have the knowledge of the basic structures and concepts of mathematics which they will need to proceed on to middle school.  Testing as well as assessment of journals and portfolios and perhaps even surveying the students might be ways of assessment.  You would be able to ask the students their feeling about the specialized math as well as about math in general.
To promote the on-going life of this project we would really need to have some impressive results.  There would be a need to see concrete evidence that the students are indeed gaining structural knowledge of math and well as obtaining positive attitudes.  Assessment would need to be ongoing so that we could check and recheck to make sure that things are running smoothly. If necessary, there would have to flexibility in the change so as to allow for any future problems or concerns.  But most of all, we would need to keep the strong commitment from the teachers and administration and even the parents.

REFERENCES
Brown, C. A., & Baird, J. (1993). Inside the teacher: Knowledge, beliefs, and attitudes. P. S. Wilson (Ed.), Research ideas for the classroom: High school mathematics (pp. 245-259). New York, NY: Macmillan.
Edwards, A., & Ogden, L. (1998). Constructing curriculum subject knowledge in primary school teacher training. Teaching & Teacher Education, 14 (7), 735-744.
Foss, D. H. & Kleinsasser, R. C. (1996). Preservice elementary teachers’ views of pedagogical and mathematical content knowledge. Teaching & Teacher Education, 12 (4), 429-442.
Lubinski, C. A. (1994). The influence of teachers’ beliefs and knowledge on learning environments. Arithmetic-Teacher, 41 (8), 476-479.
National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: The National Council of Teachers of Mathematics, Inc.
National Research Council. (1989). Everybody counts: A report to the nation on the future of mathematics education. Washington, DC: National Academy Press.
Thompson,A. G. (1992). Teachers’ beliefs and conceptions: a synthesis of the research. In D. A. Grouws (ed.), Handbook of research on mathematics teaching and learning (pp. 127-146). New York: Macmillan.