Archived Information

Secretary's Mathematics and Science Initiative

Teacher Knowledge Working Group Report

# Introduction

The primary goal of the Teacher Knowledge Action Plan is to ensure that
all components of mathematics teacher education link together to create
a seamless set of career experiences for teachers. We envision a system
that produces and sustains teachers who understand both mathematics and
children's learning. The system incorporates policy support at all
levels so that preservice education, credentialing procedures,
induction, professional development programs, and opportunities for
teacher leadership are connected.

We do not currently have a continuous system of training and
professional development for teachers that includes early coursework,
clinical experiences, induction, and career pathways supported through
ongoing development [^1].[^2] The Teacher Knowledge Action Plan seeks to
create partnerships of professional organizations, foundations,
businesses, publishers, school systems, colleges and universities,
states, and federal agencies that result in a more coherent and
effective system of support for teachers.

We want the teaching of mathematics to be viewed as a true profession.
Therefore, all teachers must have a sound knowledge of mathematics and a
desire to develop the habits of mind required for a rigorous
understanding of the subject. Professional teachers must be aware of and
versed in an array of sound pedagogical methods and continually study,
practice, examine, and compare new and old ideas about teaching.
Professional teachers are informed by research on student learning and
continuously experiment with incorporating research-based practices into
their classrooms. Those who enter the profession from other mathematics
or science careers need opportunities to link their professional
knowledge and experience to the knowledge base in teaching and learning
and the realities of working in classrooms.

The five-year Action Plan focuses on the career experiences of teachers
in grades K-8 because of the urgency we feel for increasing their
content knowledge and teaching skills in mathematics. Many elementary
teachers have had few courses in mathematics as a part of their
undergraduate preparation, and 65.2% of middle school students are
taught by teachers without a major or certification in mathematics. [^3]

The research base for mathematical teaching and learning is
under-developed and incomplete, and one of the major goals of the
overall Secretarial initiative for mathematics is to support more
research in this area. Based on what we know, however, we have
confidence that increasing teachers' content knowledge and related
teaching skills can contribute to better teaching and student learning.
The *Background Paper* for the Mathematics Initiative summarizes the
research base on which the Action Plan is based.

The Action Plan follows a similar sequence that recognizes the different
needs teachers have at various stages in their career. These stages are:
preservice, induction, inservice, alternative route and mid career, and
teacher leader. Within each of these stages, the Action Plan recommends
activities to: (1) identify the most promising practices and research
available; (2) promote implementation of practices based on the
promising practices and research; (3) develop networks and communication
venues to support individuals and groups engaged in the work; and (4)
conduct evaluation and research on the work carried out as a part of the
Action Plan in order to further develop the knowledge base on improving
teacher quality.

## **Primary Goal**

## All elementary and middle school teachers will have strong mathematics content knowledge and teaching skills to meet States' requirements that all teachers be highly qualified by the NCLB target date of 2005-2006. Veteran teachers will have opportunities to develop high levels of expertise as they move through their careers.

## 

## **Overview**

The Action Plan addresses two of the most significant issues in
mathematics education -- the need for greater content knowledge and
related teaching skills, and the need for improved training and
professional development to develop this knowledge. While much more
research is needed in these areas, there is some evidence that provides
guidance to this document:

-   Teacher quality characteristics such as a degree in the field to be
    taught are significantly and positively correlated with student
    outcomes. [^4]

```{=html}
<!-- -->
```
-   Many elementary and middle schoolteachers report that they do not
    feel they have sufficient background in the mathematics they
    teach.[^5]

-   According to NCES data, in 1999-2000 the majority (65.2%) of middle
    school students are taught mathematics by teachers that have neither
    an undergraduate major or certification in mathematics. Teachers
    with elementary certification most often have very little academic
    preparation in mathematics.[^6]

-   For elementary and middle grade students to become proficient in
    mathematics, it is critical that their teachers have a solid
    understanding of the mathematical concepts they teach and are
    skilled in content-based instructional practices. [^7]

-   Professional development for elementary and middle school teachers
    who need more content knowledge in mathematics requires intensive
    instruction in mathematics. This is best accomplished through
    sustained professional development organized around key content and
    that takes place over time.[^8]

-   Veteran teachers with strong content knowledge and teaching skills
    benefit from opportunities to provide leadership within the schools
    to develop further their knowledge and skills, and expand their
    career options. More advanced opportunities can entice them to stay
    in the teaching profession and allow them to contribute in a
    significant way to the overall improvement of schools.[^9]

#  

# 

# 

# Career Experiences of Teachers: PRESERVICE EDUCATION

**Pre-Service Goal:** Arts and Science faculty in collaboration with
Education faculty of Institutions of Higher Education (IHEs) will offer
teacher preparation programs that include significant preparation in
appropriate mathematics content, and related teaching skills.

## 

## **Background** 

There are over 1,300 teacher preparation institutions with a wide range
of program designs. The programs usually contain components that include
subject matter coursework, pedagogical preparation, and clinical
training. Sound research on teacher preparation programs is sparse and
more is needed.[^10]

The nature and quantity of the subject matter preparation needed by
prospective teachers is a ripe area for more research. [^11]^0^ However,
enough evidence has accumulated to provide a starting point for the
Action Plan. Although the appropriate kind or amount of subject matter
preparation has not been determined conclusively by research, there is a
positive correlation between teachers' subject matter preparation and
their effectiveness in the classroom. [^12]

Greater involvement by arts and science faculty in partnership with
colleges of education and school and local school districts is a
promising strategy for improving teacher-education programs.[^13]^1^
This involvement allows for increased attention to content knowledge
with courses taught by content experts who are actively engaged in their
fields. In many cases, the mathematics disciplinary faculty have not
been actively involved in preparing preservice teachers, but it makes
sense that mathematics departments should have a responsibility for
increasing prospective teachers' knowledge in the discipline.

## 

## **Action Strategies**

(1) Develop frameworks for undergraduate courses and course sequences
    that identify the mathematical knowledge required by elementary and
    middle school teachers. Mathematicians must be centrally involved in
    this work in collaboration with mathematics educators and teachers.
    The frameworks serve as a basis for developing and field-testing
    undergraduate mathematics courses offered to teachers.

> *Responsible***:** Mathematicians, mathematics educators, national
> professional associations, university leaders.
>
> *Outcome:* Frameworks for pre-service teacher preparation programs
> that provide thorough preparation in mathematics.

(2) Encourage the development and evaluation of courses and course
    sequences in undergraduate preparation programs that embody the
    frameworks recommended in Strategy 1. Analyze existing materials,
    textbooks, and courses to determine their match to the frameworks'
    recommendations. These efforts should involve collaborations between
    schools of arts and sciences (A&S) and schools of education (ED),
    and should be supported by the president or chancellor to ensure
    visibility and on-going support of the work.

> *Responsible:* Institutions of Higher Education, Local School
> Districts, Foundations, Business community.
>
> *Outcome:* Preservice preparation programs that improve the
> mathematics content of prospective teachers and improve collaboration
> between A&S and ED departments at IHEs.

(3) Improve the accountability systems available to assess K-8
    preservice teachers' content knowledge. The assessment systems
    should take account of both the frameworks developed in Strategy 1
    regarding the mathematical content teachers need to know, and the
    requirements of NCLB.

> *Responsible:* States, National Testing Companies, IHEs.
>
> *Outcome:* Assessments of K-8 pre-service teachers' content knowledge
> that embody the frameworks developed in Strategy 1.

(4) Review and modify certification requirements based on assessments of
    teachers' mathematical content knowledge developed in Strategy 3 and
    on the frameworks developed in Strategy 1.

> *Responsibility:* States, Institutions of Higher Education
>
> *Outcome*: State certification requirements for K-8 teachers that
> embody the frameworks developed in Strategy 1 and use assessments
> developed in Strategy 3 to measure the mathematical content knowledge
> of prospective K-8 teachers.

(5) Create networks to communicate information on and provide support
    for improving preservice mathematics learning and the assessment of
    that learning. Examples of useful networks could include
    mathematicians responsible for teaching preservice teachers, IHE
    department heads and deans, and state policy makers overseeing
    teacher assessment and certification.

> *Responsible:* Professional Associations, Foundations, IHEs, State
> Agencies.
>
> *Outcome:* Support and information for individuals and groups revising
> the mathematics courses and assessments offered to K-8 preservice
> teachers.

(6) Conduct research and evaluation studies on the effectiveness of
    undergraduate mathematics courses offered to K-8 preservice
    teachers. Collect existing research and evaluation studies. Evaluate
    programs developed under Strategy 2.

> *Responsible:* Professional Organizations, Federal Agencies, States,
> IHEs.
>
> *Outcome:* An analysis of the research and evaluation data on efforts
> to improve the content knowledge in K-8 preservice teachers, and
> identification of successful programs. A compendium of successful
> inservice programs, with evidence on why the programs worked and the
> results that were achieved will be developed.

# Career Experiences of Teachers: INDUCTION

**Induction Goal**: States and districts will establish comprehensive
induction programs to support novice K-8 teachers of mathematics.

**Background**

A significant number of teachers (up to 50% in some areas) leave
teaching within five years, and research on their reasons for leaving
found that many cited lack of support and difficult working conditions
as the greatest problems \[citation\]. While many places offer some kind
of support for beginning teachers, many of these programs are
superficial, involving little more than assigning a mentor teacher to
provide limited support.[^14]^3^ Relatively few programs provide support
over time, and even fewer offer systematic help with content knowledge
and related teaching skills.

## 

##  **Action Strategies**

(1) Develop a set of promising practices for high-quality and extensive
    induction programs. These might include: mentoring programs;
    sustained relationships between IHEs and districts to continue the
    development of teachers' content knowledge; assignment policies that
    do not burden new mathematics teachers with the most challenging
    students and overwhelming schedules; and, on-going assessment of
    teachers' skills and content knowledge. Promising practices will be
    identified based on their potential to improve retention rates of
    new teachers and support development of pedagogical skills and
    knowledge that are linked to mathematics content.

*Responsible:* Federal Agencies, Professional Societies, Local School
Districts.

> *Outcome:* A set of promising practices for induction programs are
> developed and disseminated.

(2) Develop and evaluate model induction programs and policies that are
    based on the promising practices developed in Strategy 1. Encourage
    support for novice teachers that includes mathematical content
    knowledge and teaching skills. Advocate for stronger induction
    programs.

> *Responsible:* School Districts, IHEs, States, Professional
> Associations.
>
> *Outcome:* Examples of induction programs that improve the skills and
> retention rates for new teachers, and that have evaluation data on the
> strategies that were successful..

(3) Establish an interactive, online network for such groups as novice
    elementary and middle school mathematics teachers, veteran teachers
    and administrators with responsibility for the orientation of new
    teachers. The networks should provide support for new teachers as
    well as provide a forum for exchange of ideas about successful
    approaches to induction.

> *Responsible:* Local Districts, Federal Agencies, Professional
> Societies, and Business Groups.
>
> *Outcome:* Networks that support new teachers and the veteran teachers
> and administrators who work with them. The networks permits online
> discussion groups, information sharing such as research, evaluation,
> proven teaching practices, and ways to understand and teach complex
> content.

(4) Conduct research and evaluation studies on induction programs and
    policies to determine which programs are the most successful and why
    they are successful. Evaluate programs developed under Strategy 2.
    Providers of induction programs should document their evaluation
    results and submit them for review and dissemination.

> *Responsible:* Federal Agencies, State Agencies, IHEs, and
> Foundations.
>
> *Outcome:* Successful, research-based practices on induction programs
> are identified and disseminated. A compendium of successful
> professional development programs, with evidence on why the programs
> worked and the results that were achieved.

# Career Experiences of Teachers: INSERVICE PROFESSIONAL

#  DEVELOPMENT

## 

**Inservice Goal:** State and local education agencies will provide
substantial professional development opportunities that increase
teachers' mathematical content knowledge and teaching skills, leading to
improvement in student learning.

## 

## **Background**

Research has indicated that teacher quality is an important factor in
increasing student achievement, and that on-going professional
development should be viewed as a prerequisite for retaining a
well-qualified teaching force[^15] [^16]^5^ [^17]^6^. Fifty-two percent
of middle grade mathematics teachers do not have a major or minor in
mathematics [^18], indicating a lack of content knowledge as they enter
the profession. The 1999 evaluation of the Eisenhower Professional
Development Program suggests that successful professional development
focuses on strengthening teachers' content knowledge and on how students
learn particular content, but that these areas are not the norm for most
professional development that is offered.

The Third International Mathematics and Science Study (TIMSS), as well
as other studies, have challenged the nation to make the school
mathematics program more ambitious. To implement more challenging
curricula, a substantial investment in teacher professional development
is needed. Many teachers will need to learn more complex content than
their original training provided.[^19]^4^

## 

## **Action Strategies**

(1) Develop a set of promising practices for high quality professional
    development opportunities in mathematics for inservice teachers. The
    promising practices should include as attention to: the content
    knowledge required to teach effectively at various grade levels;
    effective teaching strategies; how much professional development is
    needed to effect changes in teacher behavior (duration); effective
    formats for delivering professional development; how content,
    format, and duration should match the purpose of professional
    development and the current skill levels of the teachers; and,
    examples of high quality professional development. As part of
    identifying promising approaches to professional development, state
    NCLB plans for highly qualified teachers of elementary and middle
    school mathematics should be analyzed.

> *Responsible:* Federal agencies, Professional Associations, States and
> local school districts, IHEs.
>
> *Outcome:* A set of promising practices that provide guidance on
> effective professional development is developed and widely
> disseminated.

(2) Conduct analysis of existing professional development programs to
    determine the degree to which they align to the promising practices
    identified in Strategy 1. Based on this analysis, professional
    development programs are redesigned, implemented, and evaluated to
    determine their effectiveness.

> *Responsible:* States, Local School Districts, Universities, and
> Professional Organizations.
>
> *Outcome:* High quality professional development opportunities are
> developed, implemented, and evaluated.

(3) Assess the quality and effectiveness of professional development
    opportunities and curriculum materials offered by professional
    organizations and other non-school based groups o determine how they
    align to the promising practices identified in Strategy 1. These
    groups should determine how their work supports the important
    curricular goals established by states or districts.

*Responsible:* Professional Organizations, Informal Education
Organizations, Scientific Societies, IHEs, Foundations, Business Groups.

*Outcome:* Stronger implementation of specialized curricula and
professional development and better evaluation results on these efforts.

(4) Establish on-line networks of groups providing professional
    development to teachers within specialized areas, with the purpose
    of supporting their efforts and sharing information.

*Responsible:* Professional Organizations, Professional Development
Providers, Federal Agencies, Universities, States, Local School
Districts.

*Outcome:* Enhanced communication and support among professional
development providers.

(5) Research and evaluate professional development efforts that align
    with the promising practices identified in Strategy 1. Professional
    development providers should document their evaluation results and
    submit them for review and dissemination.

*Responsible:* Federal Agencies, Professional Development Providers.

*Outcome:* A compendium of successful professional development programs,
with evidence on why the programs worked and the results that were
achieved.

Career Experiences of Teachers: ALTERNATIVE CERTIFICATION

> PRACTICES AND CAREER CHANGERS

## 

**Alternative Certification Goal:** States and districts will design
alternative certification programs that facilitate and support promising
candidates entering the mathematics teaching profession.

## **Background** 

The shortage of highly qualified teachers is more acute in the area of
mathematics than in most content areas[^20]^7^. Many of the traditional
teacher training and state licensure systems are under-producing highly
qualified mathematics teachers. [^21][^8^]{.mark} If schools are not
able to attract talented people and keep them in the classroom, student
academic performance will suffer.[^22]^9^ The difficulty of adequately
staffing classrooms with qualified teachers is more severe in schools
serving low-income, high minority enrollment, urban or extremely rural
communities. [^23]^0^

#### Alternative route programs have been successful in recruiting a more diverse pool of teachers, and all but nine states have approved an alternative route to certification [^24]***^7^***. Alternative routes that require high standards for admission, substantial pedagogical training, mentoring, and evaluation tend to be more successful in producing highly qualified teachers. [^25]***^1^***

#### 

#### Action Strategies

(1) Develop a set of promising practices for mathematics teachers
    entering the profession from alternative routes, including those
    entering at mid-career. These should include: a diagnostic system to
    identify capabilities of prospective elementary or middle school
    mathematics teachers in mathematical content knowledge; systems of
    high-quality professional development geared specifically to the
    wide-ranging interests and needs of individuals entering the
    professions from alternative routes; examples of effective
    administrative support for these individuals; examples of effective
    assignment policies that do not burden new mathematics teachers with
    the most challenging students and overbearing schedules.

The promising practices should include individuals entering the
profession through alternative routes, and individuals who change from
other careers into teaching, focusing on their preparation in
mathematics content knowledge and teaching skills.

> *Responsible:* National and State Entities Providing Alternative
> Routes to Teaching, Mathematics Groups, Federal Agencies.

## Outcome: A set of promising practices for alternative routes and mid career programs for mathematics teachers.

(2) Review and revise alternative certification requirements based on
    the promising practices identified in Strategy 1. Develop and
    evaluate programs and other mechanisms to ensure that teachers
    entering through these routes are encouraged, and receive strong
    preparation and support in mathematics.

> *Responsible:* State Education Agencies, Local School Districts,
> Institutions of Higher Education.
>
> *Outcome:* Stronger and more varied alternative routes for bringing
> talented individuals into teaching mathematics.

(3) Establish networks of programs and individuals involved with
    alternative routes to certification in order to share information,
    expertise, and advice.

> *Responsible:* Professional Organizations, Federal Agencies, IHEs,
> States, Local School Districts.
>
> *Outcome:* Enhanced communication and information sharing among groups
> and individuals involved with alternative routes to certification.

\(4\) Conduct research and evaluation to identify and develop successful
alternative

> route programs. Focus especially on programs developed under Strategy
> 2.

*Responsible:* Federal Agencies, States, Foundations, Professional
Organizations.

> *Outcome:* Dissemination of successful sound evaluation results on
> effective alternative route programs.

# Career Experiences of Teachers: TEACHER LEADERSHIP

## 

**Teacher Leadership Goal:** States and districts will establish
programs to identify, support, and deploy a cadre of teacher leaders in
mathematics to work as mentors, resource teachers, demonstration
teachers, peer coaches, and professional development providers.

## **Background**

> Accomplished and veteran teachers are critical to the success of
> schools. Their experience and wisdom are important resources, but are
> often not called upon as often as they could be in efforts to improve
> schools. Often, veteran teachers feel they have to move out of the
> classroom in order to have a broader impact and more varied
> professional opportunities.
>
> The TIMSS study has identified key practices in high performing
> countries that draw on the knowledge of experienced teachers. For
> example, in Japan teacher leaders collaborate to develop lessons that
> are taught in the school through a process of development, testing,
> and revision. In addition, teacher leaders are responsible for
> training new teachers, and work with them over several years before
> the new teachers are allowed to assume a full teaching load. These
> sorts of leadership opportunities diversify the work responsibilities
> of veteran teachers, which is important in retaining them in the
> profession.

## 

## **Action Strategies**

(1) Develop a set of promising practices on effective professional
    development opportunities in mathematics for veteran teachers, and
    on ways that teacher leaders can contribute to improving mathematics
    instruction in the schools. These should include such opportunities
    as: learning specialized, advanced mathematics; leadership training;
    understanding student learning and cognition; and, understanding how
    to work with adults as a mentor. In addition, effective ways that
    teacher leaders can work within schools should be identified.

*Responsible:* National Organizations, Federal Agencies.

*Outcome:* A set of promising practices that can be widely disseminated.

(2) Offer professional development programs and leadership opportunities
    for teacher leaders that are aligned with the promising practices
    identified in Strategy 1. These opportunities should be carefully
    evaluated to determine what practices best contribute to teacher
    learning at an advanced level and help to keep exemplary teachers in
    the classroom.

*Responsible***:** School Districts, Institutions of Higher Education,
Professional Organizations.

*Outcome:* Expanded opportunities for veteran teachers.

(3) Develop opportunities at the school, district, state and national
    level for teacher leaders to participate in activities, including:
    mentoring novice teachers, developing curricula and analyzing
    existing materials, participating in 'teacher in residence'
    programs, providing professional development, among others. These
    opportunities should be based on promising practices developed in
    Strategy 1 and aimed at keeping exemplary veteran teachers involved
    in work that is directly relevant to teaching and learning.

> *Responsible:* Schools, Local School Districts, States, Professional
> Organizations, Professional Development Providers.
>
> *Outcome:* A diverse array of professional opportunities for teacher
> leaders that keep them engaged in work directly relevant to
> instruction is available.

(4) Establish networks to support teacher leaders and those developing
    strategies for supporting the development of teacher leaders.

*Responsible:* States, Local School Districts, Institutions of Higher
Education, and Professional Organizations.

> *Outcome:* Greater collegiality and support for teacher leaders and
> others working with them.

(5) Conduct research and development studies on how best to support the
    development of teacher leaders. Evaluate programs developed under
    Strategy 2 and Strategy 3.

> *Responsible:* Federal Agencies, Institutions of Higher Education,
> Local School Districts.
>
> *Outcome:* A stronger research and evaluation base on effective ways
> to work with veteran teachers is available. A compendium of successful
> approaches to working with veteran teachers, with evidence on why the
> approaches worked and the results that were achieved.

[^1]: ^1^ National Research Council. *Educating Teachers of Science,
    Mathematics and Technology: New Practices for the New Millenium.*
    Washington, DC: National Academy Press,  2001

[^2]: ^2^ Bransford, J.D., Brown, A.L. and Cocking, R.R. (EDs.) *How
    People Learn: Brain, mind, experience, and school.* Washington, DC:
    National Academy Press, 1999.

[^3]: ^3^ Seastrom,M.M., Gruber,K.J., Henke,R.R., McGrath, D.J., and
    Cohen,B.A. (2002). Qualifications of the Public School Teacher
    Workforce: Prevalence of Out-of-Field Teaching 1987-88 to 1999-2000
    (NCES 2002-603),tables B-8 and B-9. Data from the U.S. Department of
    Education, NCES, Schools and Staffing Survey (SASS), "Public Teacher
    Questionnaire," 1999-2000 and "Charter Teacher Questionnaire,"
    1999-2000.

[^4]: ^343^ Sanders,W., & Rivers, J. (1996). Cumulative and residual
    effects of teachers on future student academic achievement.
    Knoxville,TN: University of Tennessee Value-Added Research and
    Assessment Center

[^5]: ^?4^ Weiss, I., Pasley, J., Smith, P.S., Banilower, E.R., & Heck,
    D. J. (2003). "Looking inside the classroom".

[^6]: ^5^ U.S. Department of Education, National Center for Education
    Statistics. 2002. Qualifications of the Public School Teacher
    Workforce: Prevalence of Out-of-Field Teaching 1987-88 to 1999-2000.
    Washington, DC: GPO, Tables B-11 and B-12.

[^7]: ^6^ David Cohen and Heather Hill. *Learning Policy: When State
    Education Reform Works.* New Haven and London. Yale University
    Press. 2001.

[^8]: ^6^

[^9]: ^7^ <http://www.cpre.org/Publications/rb31.pdf> (page 7)

[^10]: ^8^ U.S. Department of Education. "A Talented, Dedicated and
    Well-Prepared Teacher in Every Classroom".
    http://www.ed.gov/PDFDocs/speakerskit.pdf.

[^11]: ^10^ Meeting the Highly Qualified Teachers Challenge. The
    Secretary's Second Annual Report on Teacher Quality. See page 48.

[^12]: ^9^ Meeting the Highly Qualified Teachers Challenge. The
    Secretary's Second Annual Report on Teacher Quality. See pages
    44-51.

[^13]: ^11^ No Child Left Behind -- Title II

[^14]: ^13^ Britton, E., Paine, L., Pimm, D., & Raizen, S. (2003).
    Comprehensive teacher induction: Systems for early career learning.
    Dordrecht/Boston/London: Kluwer Academic Publishers.

[^15]: ^3^

[^16]: ^15^ Ronald Ferguson. Paying for Public Education: New Evidence
    on How and Why Money Matters. Harvard Journal of Legislation, Vol.
    28 (Summer 1991), 465-498.

[^17]: ^16^ Greenwald, R., Hedges, L.V., Laine, R.D., The effect of
    school resources on student achievement. Review of Educational
    Research, Vol. 66 (Fall 1996), 361-396.

[^18]: ^5^

[^19]: ^14^ William H. Schmidt, et al. *Why Schools Matter: A
    Cross-National Comparison of Curriculum and Learning.* Published by
    Jossey Bass in San Francisco, 2001

[^20]: ^17^ National Association of State Boards of Education. October
    2002. "State incentive programs for recruiting teachers: Are they
    effective in reducing shortages. Issues in Brief. Alexandria, VA:
    NASBE.

[^21]: ^18^ U.S. Department of Education, Office of Postsecondary
    Education. 2002. Meeting the Highly Qualified Teachers Challenge.
    Washington, DC.

[^22]: ^19^ Prince, C.D. (2002). Higher pay in hard-to-staff schools:
    The case for financial incentives. Arlington, VA: American
    Association of School Administrators.

[^23]: ^20^ The Education Trust. All Talk, No Action.
    http:..www2.edtrust.org/NR/rdonlyres/8DE64524-592E-4C83-A13A-6B1DF1CF8D3E/0/AllTalk.pdf.

[^24]: ^17^

[^25]: ^21^ <http://www.abell.org/pubsitems/ed_cert_1101.pdf>;
    <http://epaa.asu.edu/epaa/v10n36.html>;
    http://www.abell.org/pubsitems/ed_cert_rejoinder_1101.pdf.