THE NEW MATH…TEACHER!

Paul Gosse
Faculty of Education

Abstract

The implications of the shifting demographics of the mathematics teacher population in Newfoundland on leadership, professional development and employment opportunities have been noticeable for some time. The painting of this landscape now is the product of a broad base of personal experience gathered through living on the coattails of a sweeping generational demographic–the baby boomers–and a concern that a body of committed professionals has been set adrift during recent educational reform, curricular and systemic, in Newfoundland. Tensions of the rapid generational transition we are going through will be expanded upon as will some concerns about collegial casualties that may occur during the next three to five years (i.e. 2000- 2003/5).

Foreword

This paper is an attempt to paint one current view of the landscape that is the teaching force in Newfoundland as we enter the third millennium, with a particular focus on mathematics teachers. This view is framed against a time-line tracing most of the baby boomer generation through eras of influence socially and professionally, with emphasis on mathematics as a subject context.

The W.W.II baby boom is typically associated with births occurring between 1946 and 1965. Those born in 1946 would typically have entered the teaching force in Newfoundland in their early twenties and would likely now have retired from teaching [Early Boomers]. Those born in 1955 would typically have entered the teaching force in NF in their early twenties (i.e. in the late 1970s) and would likely be eligible to retire between 2005 and 2010. These teachers with about 25 years of experience make up a large portion of the Newfoundland teaching force [Mid- Boomers].  Those born in 1965 would typically have entered the teaching force in Newfoundland in their early twenties (i.e. in the late 1980s) and would likely be eligible to retire between 2015 and 2020. These teachers with about 10-15 years of experience make up a significant portion of the teaching force [Late-Boomers].  The remainder of the working teachers are not baby boomers and represent those born between 1965 and 1979 [Generation X'ers]. High school in Newfoundland was extended as grade twelve was introduced in the early 1980s. Together with programming changes over time, this typically translated into teachers entering the workforce at 25 years of age or older. These teachers with about 1-10 years of experience currently make up a small portion of the teaching force.

NeXters are not yet in the teaching force…those born after 1980 would likely be completing pre-requisites for entrance to teacher training programs. They will be pre service teachers enjoying observation days and internships over the next five years. These teachers will have experienced current methods engaging changing curriculum usually with a technologically literate base. They may also be a critical pool of personnel, and one that should be attended to if concern about attractiveness of the workplace in the face of numerous retirement vacancies is deemed to be a potential problem.

Some tensions surrounding the sociological phenomenon of baby boomers include generational tensions in terms of employment opportunity–when positions become available for generationally trailing teachers. Other tensions occur when employers attempt to appropriately fill numbers of rapidly opening positions. There is the interesting challenge then of perhaps having the least experienced teachers as the most qualified in the candidate pool for current educational leadership positions.

We live in a time of exploding technologies and an emphasis on co-operative learning and other group strategies intended to improve team-building and communication skills, of alternative assessment strategies, of interdisciplinary coherence in curriculum documents and of increased public awareness and accountability. Educationally, these are very dynamic and changing times. Few professionals, young or old, in any field have any baseline experience with which this pace of change -- and its effect on the workplace -- is comparable. The current pace of educational change, placed in the context of a rapidly changing teacher demographic, presents many personal and management challenges for teachers of all ages and for the administrators that hire them.

The Context

Reform

Reform takes many forms. For many teachers, reform maybe associated with the shift in the nature of materials and methods as a constructivist-style reform framework and more cross- subject coherence engage curricula. The breadth of this shift, and the momentum curricular reform now seems to possess, can cause stress. Another reform in Newfoundland education involves tailoring curriculum content toward special student needs. This has occurred virtually simultaneously with shifting mathematics curriculum, creating a dual shift for Newfoundland mathematics teachers–a shift in content and methods (really a dual shift on its own) and a shift to a stratified curriculum delivery model known as Pathways. Technology is also reforming teaching. Whether it be school intranets for attendance and record keeping, web based course delivery, teaching with/through technology, or simply guiding teachers toward forms and information that now only appears online, teachers rapidly are coming to grips with a very different classroom reality than existed even ten years ago.

Recent Decades and The Shift

In this brief overview of historical context, it is necessary to step in and out of a local Newfoundland context. Generally, the larger perspective is presented with relevant Newfoundland circumstances noted as well.

Late 1960 to early 1970s

The late 1960s through the early 1970s was a time of societal questioning, of rebellion, and of the establishment attempting to maintain itself. Societal tensions were abundant. Youth sought freedom of expression without establishment trappings. At the same time, the post-war boom was fading and attention was returning to education as a means of securing prosperity. This was also an era which witnessed Vietnam and the space race. There was a perceived need to maintain technological advantages to act as a deterrent to a Third World War. This lent authority to a Back-to-Basics movement in schooling during the days of flower power. The subject of mathematics was a cornerstone in this Back-to-Basics curriculum.

Late 1970s through the 1980s

The late 1970s through the early 1980s saw a questioning of educational product. Was the focus on basics producing results? How were we, and North America as a whole, faring against other countries andcultures in education -- in mathematics in particular? Computing power was showing signs of changing much of the manner in which the world did business and communicated. Would we be ready? Was our curriculum up-to-date?  Back-to-Basics curriculum was growing old.

Furthermore, cognitive theory (what we know about how we learn) was making strides forward (thanks in part to a century of warfare and a culture affected by the now much more common medium of television).  It was becoming much more chic, not to mention pedagogically reasonable, to ground curricular change in sound learning theory. For example, many educational documents of that era reflect the language of behavioral psychology, using descriptions such as… "The student should be able to…sketch the graph of y = x2."

Professional organizations of mathematics teachers began to react to societal angst regarding the nature of mathematics curriculum and the delivery of mathematics in schools. Pressure to reveal the real benefits of mathematics instruction, including questioning the manner and methods used to deliver it, were increasing. Yet, mathematics seemed mired in a traditional style of instruction that increasingly contributed to teachers of the subject appearing as traditionalist icons and not dynamic educators actively searching for the most modern methods of instruction to engage and enable children.

The National Council of Teachers of Mathematics (NCTM) researched and proposed a curriculum framework and delivery model for mathematics built upon a popular cognitive theory, constructivism. This framework first took the form of the Curriculum and Evaluation Standards for School Mathematics commonly referred to as The Standards. High on the list of inaction in this framework is a technology friendly common core curriculum differentiated by the depth and breadth of treatment and the nature of the applications. In the slipstream of this first reforming document came Professional Standards for Teaching Mathematics (1991) and Assessment Standards for School Mathematics (1995).

The Shift

NCTM suggested a re-thinking of delivery of mathematics curriculum to include more use of concrete manipulatives, alternative sources of assessment data, incorporation of technology including use of graphing calculators, and even writing for formative and summative purposes in mathematics!  This occurred at a time when many experienced teachers had born witness to what could be termed educational fads…initiatives which waxed brilliantly and may have failed to deliver the results desired under the conditions in place. In their waning they effectively create a backwash view that perhaps the status quo would have been better and moneys better spent enhancing other aspects of schooling rather than pursuing the exercise that apparently ended up near where it started. The position could be taken, for example, that NCTM's platform would end up like so many others as just another fad.  A particular mental model seemed entrenched and unchallenged.

Mathematics is often be perceived as a bastion of the traditional. Incorporating alternative assessment methods such as portfolios and journals formally into mathematics assessment would certainly be viewed as a departure from methods that many would claim were "tried and true".  Reduced emphasis on "drill and practice", while not necessarily viewed as a bad thing, did not appear to be embraced by teacher practice at this time. A focus on group work and engaging in problem solving through cooperative learning, using activities where students actively generate authentic data, may certainly have seemed non-traditional enough to provoke nervous commentary among any teacher whose methods might generally be considered traditionalist. The departure toward the more student empowering approach of constructivism may have made visualization of how such a classroom might look and function difficult for many. This may have been made more tenuous by the fact that few teachers could be held up as models of such an approach. Clearly, healthy skepticism toward the approaches put forward by NCTM should not have been unforeseen.

The College Board's Advanced Placement (AP) Calculus courses were willing to challenge their own perceptions of traditional calculus content and delivery. How calculus was taught under AP dramatically changed during the 1990s. This was largely a result of the power and ease of use of graphing calculators to enhance instruction. The status of strands of content and specific sub- topics were, and are, consistently scrutinized as to their relevance, given current tools such as graphing calculators.

NCTM proposed a tack not dissimilar to The College Board's…that traditional strands be questioned, that their role be re-evaluated, and that their treatment be examined in light of the use, purpose and tools of the day. As one example, Statistics and Data Management as a content strand is to receive increased emphasis under an NCTM framework and would embrace technology in its treatment. Congruent triangle proofs from Euclidean Geometry will receive less emphasis.

While duly noted by many teachers as a possible change force, NCTM's thrusts did not seem broadly embraced by all but the strongest of its own advocates. This is perhaps due in part to the reliability of the fad experience. That is, past experiences which seemed to support the notion that "This too shall pass" and implied a return to a state similar to present conditions, may have made teachers generally reticent to invest significant effort up front. Another consideration, also, was the problem such a radical shift in emphases generates in terms of the redevelopment of teacher generated resources. Resources tailored to the language and approach of older curriculum documents and styles would have to be revised.  Clearly this would increase the workload for practicing teachers in the updating of personal materials…no small task given the fundamental shift NCTM was proposing. In addition, it may well have been virtually impossible for practicing teachers to envision many of the directions of NCTM in any kind of a concrete fashion since it may not have formed a part of their individual pre service or in-service experience. This is no criticism of any teacher. Rather is speaks to the magnitude of the departure suggested by NCTM at the time.

It is worth noting that, in the 1980s, education did not generally fare well in the fiscal scheme of things. Many Newfoundland schools were asked to do more with less and serious questions were raised about right sizing of educational resourcing. Professional development funding underwent similar scrutiny. Apparently, the bell tolling shifting educational sands and a clear need for professional support did not appear to be in sync with fiscal Newfoundland.

The 1990s

The 1990s in Canada brought the School Achievement Indicators Program. This effort of the Council of Ministers of Education, Canada (CMEC), contributes to increased awareness of provincial performance on a national assessment criteria. The late 1980s through 1990s also brought about several provincial blocs of curriculum development and purchasing power such as the Pan Canadian Curriculum, the Western Canadian Protocol, and the Atlantic Provinces Education Foundation. These blocs were expressions of a desire to have the most modern and effective curriculum possible and were intended also to improve standards and reduce overall costs, thereby not taxing further what was now the fiscal reality.

The 1990s in Newfoundland saw program consultants at the Department of Education reduced in number. Similar actions followed at school boards as the boards themselves were collapsed in 1997 from 26 to 10, with commensurate personnel adjustments. Provincial in-service models were re-thought. Provincial personnel who formerly conducted in-service sessions for teachers were now program development specialists only; responsibility for implementation shifted largely to board personnel. Effectively, real take-up rates, and some would argue opportunities, for professional development seemed seriously affected.

A teachers' strike in 1994 publicized issues such as class size, workload and job stress as immediate concerns. The Newfoundland education system seemed to be feeling the stress of accomplishing more with less.  It was also a time when finding specialist teachers in some core areas was becoming more difficult and boards would begin to face the struggle of attracting quality candidates to their more demanding positions. At the same time, teacher demand elsewhere in Canada seemed to be increasing and active recruitment of Newfoundland pre service teachers continued.  As technology exploded and educational structures began to show their age, the reality of the burdens on Newfoundland educators become more obvious.

The 1990s, however, was also the era that saw The College Board's AP programs first creep into Newfoundland schools and with them examinations that were credible, valuable and in growing demand. The calculus courses under this program required calculator treatment in a form not seen before. In fact, by 1995, the AP Calculus AB mathematics examination was graphing calculator active; the exam was designed to take full advantage of graphing calculators. This was a change force that provoked a re-thinking of calculus education, not just in high schools but in post secondary institutions. It also fostered in AP teachers an awareness of standards in feeder courses and of access to and flexibility with technology. In the 1990s, the AP Calculus curriculum had evolved from non-calculator-active (i.e. classic style calculus delivery) to scientific calculator- active (available for portions of the exams only), and eventually to graphing calculator-active where the machine is necessary, assumed present in instruction, and needed in many examination problems. This AP evolution occurred simultaneously with the emergence of mathematics reform as a powerful force in curriculum.

Beyond 2000

NCTM has continued its efforts in an updating of its Standards document framework embodied as Principles and Standards for School Mathematics scheduled for publication in April 2000. As one indicator of influence, some testing programs are actively meshing existing provincial curricula against the draft of such framework documents in establishing and/or revising mathematics testing criteria.

Teacher Training and Early Experience

Born 1955

Teachers born in 1955 have about 25 years of experiencei n the year 2000 making up the largest portion of the teaching force [Mid-Boomers].  Those teachers were initially trained in the mid to late 1970s in the midst of the Back-to-Basics movement in education. During the mid 1970s to late 1980s, these teachers would witness some curriculum changes that were essentially incremental changes or were based on initiatives that would wax and wane as did many fads of the 1960s and 1970s.

Born 1965

Teachers born in 1965 with about 12-15 years of experience make up a significant portion of the teaching workforce [Late-Boomers].  These teachers were trained in the late 1980s…  The Standards were on the horizon. During pre service education, these teachers would witness a shift to more behavioral language in curriculum documents and the growing question about how best to engage technology in the classroom.  In the late 1980s, teachers generally were beginning to hear about issues like alternative assessment, manipulatives and graphing calculators.

Born 1975

The remainder of teachers are not baby boomers…they are teachers with less than 10 years of experience and make up a small portion of the teaching force. Pre-service teaching methods for many of these teachers would begin to serve more of the sorts of initiatives proposed by The Standards. Traditional views of mathematics methods would likely be challenged in- training. Teaching with technology, whether manipulative or electronic, would become much more of a reality.

Summary

The phenomenon that has become mathematics reform is unique many ways. The impact on assessment strategies, the perspective on technology incorporation and the apparent durability of the platform seem to have become realities. Different generations of teachers have different perspectives and experiences but they commonly face the challenge of significantly adapting their practice. How well have professional development opportunities and levels of resource allocation in Newfoundland prepared and supported teachers for engaging the practices that current curriculum and policies seem to be embracing?

Generation X'ers in particular are at an interesting career juncture. While possessing the least voice demographically, the least  seniority, and  little or no administrative authority, they may possess in advance the very skill sets necessary to adapt well to a reform driven curriculum.  How might this play out during the hiring rounds that will accompany the retirement of the mid- boomers?

Discussion

The available technological tools and pedagogical shifts associated with reform driven curriculum affect all teachers. Few teachers overtly claim to be well prepared in managing such change. One parallel that strikes the author as having a few similar characteristics, and therefore possibly a few practical lessons, was the introduction of the ordinary scientific calculator and the effect it has had on practice. Calculators have been available for some time. In the mid to late 1970s, tables of logarithms and trigonometric values became redundant with the availability of the scientific calculator. Through the 1980s, calculators became more commonplace in the hands of students. There was some question raised about the impact such a device might have on students' numeracy? Would students become calculator dependent or were they simply becoming technologically literate in the tool of the day?

This tool placed mathematics teachers in an interesting and tenuous position. There seemed to be little or no initial (and apparently no subsequent) broad-based training in appropriate incorporation of scientific calculators into instruction no matter what the grade level. Sparse research offerings at the time most likely made the development of wise strategies for employment of that resource difficult. Yet, the presence of calculators in the classroom became a reality and something teachers began to deal with on a daily basis.

An interesting dichotomy results when the possibility of a calculator dependent generation of learners is contrasted with the background of their teachers (who themselves were in all likelihood not as calculator literate in the 1980s as they would be today). One might think that teachers raised on mental math and pencil and paper would rail against unguarded calculator use in a classroom! As many teachers may have found, however, attempts at controlling the use of a calculator may have been perceived as disempowering the student or as removing the opportunity for the child to become literate in a blossoming technology. This duality may have caused some teachers to struggle with what exactly might best serve students in terms of calculator application. Certainly, as professionals, teachers would exercise their best judgment and do whatever they felt was in students' best interests.

It would be reasonable, then, to expect some clarifying information and direction for teachers, students and the public regarding the treatment such technology should receive. Such parameters would normally be established through definitive guidelines in curriculum documents or through working guidelines set by teachers themselves within a school system or board. They would be supported through professional development if necessary and would consider any available research.

General statements about calculator use crept into curriculum documents through the 1990s. For the most part, however, teachers themselves seemed charged with defining the role scientific calculators would play in learning. While teachers are perfectly capable of making judgements about pedagogical matters, a lack of external clarity surrounding definitive use and place of calculators, to say nothing of establishing conventions for use and providing a baseline calculator literacy in-service, certainly are factors in any calculator related issues discussed today.

Similar concerns might be expressed regarding graphing calculator use today or the general expectation that technology be smoothly integrated into curriculum. Such concerns might also be expressed regarding a broadening of assessment strategies and cross curricular coherence in mathematics teaching. Effectively, teachers may feel they are in the same position with respect to reform initiatives, that a lot of the implementation is being left to the best efforts of teachers as professionals. While teachers are certainly professionals in their fields, they do not publish the curricular rules which govern them. Responsible implementation, in a manner consistent with curricular intent, demands at the very least concurrent field support through professional development. Otherwise, we may look back in ten more years wondering why another factor that could have been controlled has emerged as an issue in the teaching of mathematics.

Implementation of the stratified student support in the form of a Pathways model appears to have increased teacher accountability and workload. Teachers are now explicitly involved with modification and enrichment of individual course elements and managing the natural increase in record keeping.

At a time when accountability, testing programs and public interest in educational matters have increased generally, early retirement may be more attractive than ever for mid-boomer teachers. In Newfoundland,there is certainly evidence of such a phenomenon. It is also evident on a national scale. For example, in a recent media piece on the CBC National News, educators point to a shortage of up to 20 000 teachers by the year 2001 as increases in graduates from teacher training programs lag behind the dramatic increases in retirement upon eligibility.

Conversations the author has held with many recent retirees immediately prior to their retirement indicated that there was certainly a reticence about leaving a career they enjoyed so much. For many of those teachers, the retirement decision seemed out of tune with much of their careers. Political concerns surrounding collective bargaining may have contributed to the decision to retire, for some measure of control seemed lost. For a generation that over several decades possessed much of societal purchasing power and may actually have dampened the pace of change through sheer demographic breadth, retirement under such perceived conditions seems less than appropriate and perhaps somewhat unfortunate.

Owing to the pace of change in general, and in mathematics education in particular, this may well be a difficult time to attract credible candidates to leadership positions within education, positions which many mid-boomers currently hold (For example, 1999-2000 data from the Newfoundland Department of Education database -- generated for the author on March 24,2000 -- indicate that, of active full-time teaching units, the vast majority of Department Head positions in schools are held by teachers aged 45 years and older. The same is true of Program Specialist positions at the school board level and of administrators). Newfoundland school boards are progressing through the pains of wholesale re-organization. They are now poised to lose the tail end of the mid boomers to retirement, effectively releasing decades of experiences in leadership at all levels of schooling. Attracting candidates to leadership positions during times of such change may prove challenging. With the present age stratification of the teaching force in Newfoundland, as in many other locations, new hiring are likely to involve younger, perhaps much younger, personnel with the potential to occupy positions of leadership for some time. Can we speak of an "echo"?

One question arising through this transition in leadership is: "Are positions being filled with candidates who would do the best job in the same or better circumstances, or are conditions such that some candidates are choosing not to apply?" They may not be the same thing. For example, many leadership roles today are perceived as very stressful. Many late-boomers may         be at points further along in their career and personal lives when faced with decisions about upward mobility than their senior colleagues were. What might normally be perceived as a rite of ascendancy may not hold attraction for late-boomers. However, difficulty attracting first-rate candidates to positions would rarely be obvious to the public since positions within hierarchies become filled as a matter of course and the system rumbles on.

At a time when mathematics in particular is changing so much, and there is the potential for this turnover of leadership to influence mathematics delivery for 10-15 years, a clear view of the characteristics, background, and abilities of the candidates measured against the needs of each school has never been more important. Depending on circumstances in individual boards and schools, it may be the teachers with less than 10 years of experience who now find themselves qualified, informed and occasionally alone in their willingness to apply for positions of leadership.

Concluding Concerns

There is a generational shift occurring that has not been witnessed in Newfoundland education on this scale before, and there are-- and will continue to be -- casualties. All teachers are now faced with dramatic changes in methods and technologies which many claim have not been supported by professional development. All teachers deserve accessible growth opportunities that enhance ability to create and deliver educational experiences under the terms set out by the province and its boards.

Given the magnitude of change and the historical context of recent educational change, adequate information and enabling opportunities seems the minimum degree of reasonable support for those who find themselves within three to five years of retirement. I feel sure that, if given a choice, teachers would say their last years should in many ways be their best years. Neglect in terms of support for those teachers may compromise what is possibly our richest educational resource in a generational window that is rapidly closing.

For the many reasons discussed earlier, teachers at mid-career may also feel unsupported professionally through this time of significant curricular change. They may be viewed, however, as providing the next generation of leaders. Many such teachers may struggle with gauging their own state of preparedness for the demands of such change. Many cannot be presumed to be hungry for the pressures of leadership. Like their more experienced colleagues, these teachers may not have anticipated or been explicitly prepared for the changes they are facing. Factors contributing to any continuation of such tendencies risk disenfranchising teachers who may be struggling through these changes and who might potentially influence students for 10-15 years.

There are those early in their careers who may also be looked to for leadership at a time when education is at the very least a hectic and stressful existence. Candidates may seek opportunities, but we must be sure to ask what they are offering.

If not through the 1990s, now is the time to reexamine what it is that teachers are expected to do and how the employer supports them in doing it. Now is the time to re-focus on reasonable expectations that an employee knows will be accompanied by re-training and material support as the world changes. To do less may risk disenfranchising more senior and mid career teachers and risk exacerbating the teacher shortages already predicted, while further compromising the leadership pool in the process.

A re-socialization of mathematics teachers in this province has begun and, at least in light of mid-boomer retirement and consequent hirings, will last at least three to five years. How will the new culture look? What will its defining characteristics be? We finally seem to have arrived at a more realistic embodiment of "new math". For that, of course, we will need The New Math…Teacher!


References

Canadian Broadcasting Corporation (2000). Number of teachers in decline. National News Transcripts. Available online:
http://www.tv.cbc.ca/national/trans/T000321.html

Government of Newfoundland and Labrador (2000). Data from active teacher database generated for author March 24,2000.


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