**Response to the Request of the National Mathematics Advisory Panel**

**for Public Comment**

**from the**

**American Association of Colleges for Teacher Education (AACTE)**

September 6, 2007

Presented on behalf of AACTE by

William F. Tate IV

Edward Mallinckrodt Distinguished University

Professor in Arts & Sciences and Chair, Department of Education

Washington University in St. Louis

AACTE, representing 800 schools, colleges, and departments of education
across the nation, is pleased to have this opportunity to testify before
the National Mathematics Advisory Panel. We recognize the nation's
critical need to increase the quantity and quality of scientific
personnel to compete in the global economy and to bolster the technical
skills of our workforce to enhance creativity and innovation. Obviously,
the teaching and learning of mathematics is critical to addressing that
need.

Our comments are focused on elementary and middle school (K-8)
mathematics education, according to the Panel's charge, and, as
requested, we cite our sources of research evidence. In cases where
definitive findings do not exist, we reference the best judgment of the
profession. Our remarks address item (e) in the Executive Order creating
the panel---*"the training, selection, placement, and professional
development of teachers of mathematics in order to enhance students
learning mathematics."*

AACTE offers eight policy recommendations to the Panel that we believe
would significantly improve the quality of mathematics teaching and
teacher preparation programs. Briefly, the recommendations are

1.  Support syntheses and wide dissemination of the best research
    available

2.  Support research on critical mathematics teacher/teaching issues

3.  Encourage consensus-building efforts to develop high-level student
    mathematics standards

4.  Support the development of student data systems with links to
    teacher preparation programs

5.  Support teacher preparation reform at both state and federal levels

6.  Eliminate out-of-field teaching

7.  Encourage investments in mathematics teacher recruitment and
    retention efforts

8.  Correct the inequitable distribution of high-quality teachers

These recommendations are embedded in the following discussion of
several key issue areas.

**1. Teaching knowledge, skills, practices, and tools**

The Panel is unquestionably aware of the paucity of rigorous research on
what is considered the core question of education: What is it about
teaching that influences students' learning?---a deficit acknowledged in
the recent update to the *Handbook of Research on Mathematics Teaching
and Learning.*[^1] It is critical that such knowledge be continually
sought and made known to collegiate education faculty members across the
country. Their often-underestimated impact on tens of thousands of new
teacher hires, as well as on the professional development of employed
teachers in schools and districts nationwide each year, is unparalleled.
Yet the value of comprehensive reviews and syntheses of the most
rigorous research on what mathematics teachers should know and how they
should teach it, seems not to be apparent. Examples of such findings
include the following:

-   The National Research Council in 2001 urged that, beginning in
    preschool, educators should help students extend their rudimentary
    comprehension of numbers, and that in later years the curriculum
    should link calculation to everyday situations to help students make
    such connections. Further, educators should teach important concepts
    in depth rather than covering many topics superficially. Carpenter
    et al. determined that teachers should know how to help students
    connect new knowledge to what they already know, create a structure
    for the new knowledge, engage students in inquiry and
    problem-solving, and take responsibility for validating their ideas
    and procedures. Thus mathematics teachers should have a coherent
    vision of (a) the structure of the ideas and practices they are
    teaching, (b) students' conceptions, misconceptions, and
    problem-solving strategies, (c) students' typical learning
    trajectories, (d) the tasks, tools, and scaffolding to support
    student sense-making, and (e) the class norms and activity
    structures that support learning. Teachers thus need flexible
    knowledge they can adapt to their students and the demands of
    situations as they arise in classes.[^2]

-   The positive effect on student learning of elementary mathematics
    teachers' mathematical knowledge for teaching---an effect with as
    big an impact on mathematics learning as student poverty or
    race---is surely well known to National Mathematics Advisory Panel,
    f or the concept *mathematical knowledge for teaching* was conceived
    by Task Group Chair Deborah Ball and her colleagues.[^3] They have
    made significant contributions to describing and developing methods
    for assessing Shulman's "pedagogical content knowledge"[^4] that
    mathematics teachers need to know (i.e., teachers' skills, such as
    pinpointing sources of errors, illustrating key concepts on the fly
    as needed in the classroom, and explaining multiple routes to the
    same end). Their national study of 700 elementary teachers in
    low-income schools found that the students of those with the higher
    scores on a "mathematical knowledge for teaching" test had the
    highest math learning gains.

-   Regarding effective instructional programs, one particularly
    exceptional, experimental study was conducted by Carpenter et al.
    (2003)[^5] on *Cognitively Guided Instruction* (CGI). Title I
    students in Milwaukee whose teachers used CGI showed stunning gains
    over those whose teachers did not. The results were subsequently
    replicated in schools in several other states. A second
    instructional program, *Active Mathematics Teaching*,[^6] derived
    from direct instruction, has also been evaluated through a true
    experimental design and its positive results replicated in a variety
    of settings.

> The research reviews and synthesis efforts, such as those mentioned
> above, are typically inaccessible to teachers and teacher educators.
> Publications whose sponsors do not have large promotional budgets may
> receive their brief "media moment" in the sun and then fade away with
> the next day's news. But more likely, they simply appear once in a
> subscription-based research journal that can easily be missed by busy
> practitioners. Ironically, the most significant research findings of
> all are synthesized in an expensive volume[^7] which--- even if a copy
> is available in a library ---is not easily accessible to faculty and
> teachers.
>
> The Education Department's What Works Clearinghouse (WWC)---an
> important effort to determine, using highly rigorous research
> standards, which instructional programs are effective in increasing
> student achievement, and to make that information available free and
> accessible to all via the web---has unfortunately, reported
> inconclusive, and thus not useful findings. For example, WWC's reviews
> of the *Connected Mathematics Project*---a problem-centered curriculum
> designed for all students in grades 6-8--- and of *Transition
> Mathematics*---a one-year curriculum that aims to increase 7th through
> 12th grade students\' skills in applied arithmetic, pre-algebra, and
> pre-geometry---found both programs to have "mixed effects" on
> mathematics achievement. UCSMP Algebra, a one-year course, appropriate
> for grades 7-10, designed to increase students\' skills in algebra,
> was found by WWC to have "potentially positive" effects on mathematics
> achievement.

**RECOMMENDATION #1:** **The National Mathematics Advisory Panel should
request major government support for syntheses and wide dissemination of
the best research available on the teaching and learning of K-8
mathematics.** This should be an on-going service provided without
charge to the public.

2.  **Teacher preparation**

High-quality preparation is, of course, essential to enabling
candidates' development of the knowledge, skills, and professional
dispositions they need to teach. Research shows that well-prepared
teachers are more likely to remain in the teaching profession[^8] and to
produce higher levels of achievement among students.[^9] Preparation
programs also help solve key policy issues, including the shortage of
teachers in particular content areas; the inequitable distribution of
teachers on the basis of race/ethnicity and socioeconomic status; and
the paucity of minority representation within the educator workforce.

Despite their recognized importance, these programs are frequently
criticized---often in terms of their length, admission and graduation
standards (either too high or two low), or their level of practicality
(overly theoretical or too methods-based). Thus several key questions
arise, listed below as A, B, and C.

A.  *[What constitutes a high-quality preparation program?]{.underline}*
    In 2001, the NRC described the features that mathematics, science,
    and technology teacher education programs should exhibit.[^10] These
    include the following:

-   Be collaborative endeavors developed and conducted by
    mathematicians[^11], education faculty, and practicing K-12 teachers
    with assistance from members of professional organizations and
    mathematics-rich businesses and industries....

-   Help prospective teacher to know well, understand deeply, and use
    effectively and creatively the fundamental content and concepts of
    the disciplines that they will teach...

-   Unify, coordinate, and connect content courses in mathematics with
    methods courses and field experiences....

-   Teach content in ways that allow students to appreciate the
    applications of mathematics....

-   Provide learning experiences in which mathematics is related to and
    integrated with students' interests, community concerns, and
    societal issues....

-   Integrate education theory with actual teaching practice, and
    knowledge from mathematics teaching experience with research on how
    people learn mathematics

-   Provide opportunities for prospective teachers to learn about and
    practice teaching in a variety of school contexts and with diverse
    groups of children

-   Encourage reflective inquiry into teaching through individual and
    collaborative study, discussion, assessment, analysis, \[and\]
    classroom-based research and practice; and

-   Welcome students into the professional community of educators and
    promote a professional vision of teaching. (pp. 69-71)

> However, incorporation of each and every feature, to constitute the
> ideal preparation program, is rarely possible, and the level of
> mastery of mathematics content and related pedagogical skills by
> teacher graduates of preparation programs is frequently
> challenged.[^12] Further, research on the effect of mathematics
> teachers' preparation, as measured by coursework, on their students'
> achievement, is ambiguous. Monk found that secondary teachers'
> postsecondary coursework predicted eventual student achievement, but
> that mathematics teachers who took more than three mathematics courses
> fared worse than those who took fewer; student gains were more clearly
> tied to teachers' *education* courses.[^13] Steiner makes an important
> point as well---that while we know a lot about desired program
> characteristics, we can't know for sure the effects of specific
> programs. This is because studies don't control for the differences in
> who enters them and because hard data on the effects of teacher
> practices on their students' achievement are not yet available. If
> education schools simply reflect the ability of their entering
> students, he notes, then the programs don't have much to show for
> their effort.[^14]

B.  *[What do we know about the quality of existing preparation
    programs?]{.underline}* U.S. teacher preparation is highly variable
    in structure, and probably in content. Some programs begin with
    college freshmen, others take midlife career changers; some last 1
    year, some 2, some 4, some 5; some programs for elementary teachers
    include only a mathematics course or two, and others include
    several. Although some course titles may appear in every program
    (e.g., methods of teaching elementary school mathematics), the
    written descriptions of those courses vary widely; and the enacted
    curriculum also varies. Programs' content and structure might
    appropriately change, depending on who was admitted, and on
    characteristics of graduates.[^15]

> Little is known about the content or methods courses offered by
> teacher preparation programs in the United States. Experts acknowledge
> that no national, summary information exists as to the content of the
> mathematics and mathematics education courses being provided to
> teacher candidates,[^16] perhaps due partially to higher education's
> history of autonomy and diversity.[^17]

C.  *[What can be done to ensure that programs attain and maintain the
    necessary level of quality?]{.underline}* A plethora of differing
    standards**,** frameworks, benchmarks, and course-content guidelines
    as to what mathematics students should learn and teachers should
    teach, have evolved, which may help explain the variation in teacher
    education programs. These include state student learning standards
    and curriculum requirements/frameworks; NAEP's mathematics
    standards; the American Diploma Project and AP courses; the
    international standards of TIMSS and PISA; the Conference Board of
    the Mathematical Sciences' "MET," teaching standards of state
    education boards; preparation program approval requirements of state
    agencies; the frameworks of testing companies (e.g., Praxis exams),
    the Professional Standards for Teaching Mathematics and Focal Points
    of the National Council of Teachers of Mathematics, the preparation
    program unit standards of the National Council for Accreditation of
    Teacher Education, and the content standards for accomplished
    teachers of the National Board for Professional Teaching Standards.

> Typically, soon after their release, standards are subjected to a
> long-term updating process.[^18] Since 2002, 38 states have developed
> or revised their mathematics curriculum standards for students;[^19]
> and state boards and agencies regularly reconsider course requirements
> for preparation programs and the content and passing scores of their
> teacher licensing tests.[^20] Mathematics learning expectations vary
> across the states along several dimensions, including level of
> specificity, language used to convey learning goals, and grade
> placement of specific learning expectations. Taken as a national
> collection, they highlight the lack of national consensus as to common
> learning expectations in mathematics at particular grade levels---a
> situation that can lead to confusion.[^21]

**RECOMMENDATION #2: The National Mathematics Advisory Panel should urge
support for research on critical mathematics teacher/teaching issues.**
This research should include, at a minimum, a description of the current
status of mathematics preparation on the part of K-8 teachers; the
essential content for high-quality mathematics teacher preparation; the
optimal length of coursework and clinical experiences and combinations
thereof; and research on the ideal structure, nature, and sequences of
courses.

Regarding ensuring the necessary level of program quality, we make the
following recommendations:

**RECOMMENDATION #3: The National Mathematics Advisory Panel should
encourage consensus-building efforts to develop high-level student
mathematics standards.** Several efforts are now proposed or under way
to develop student mathematics (and science) standards---either through
collaborations of states or national voluntary standards efforts---that
are pegged at high levels. These include the 29-state America Diploma
Project under Achieve, Inc.,[^22] as well as the national efforts
outlined in several pieces of congressional legislation[^23] and in the
National Science Board's draft national action plan to improve the
nation's STEM education system.[^24] Efforts such as these, to update
existing standards and clearly articulate, according to international
benchmarks, what students at various levels should know and be able to
do regarding P-12 mathematics, would provide critical information to
upgrade teacher preparation programs.

**RECOMMENDATION #4: The National Mathematics Advisory Panel should
support the development of student data systems with links to teacher
preparation programs.** Better information is needed on the actual
performance of teachers in classrooms, particularly on their ability to
increase student learning. Although several states are developing and
piloting data systems that follow the achievement of K-12 students,
links are needed to data on the characteristics of their teachers'
preparation programs. If such data were available, preparation programs
could be modified accordingly, increasing their effectiveness to the
benefit of the institutions, the candidates, the schools and, ultimately
the achievement of students. We urge the Panel to recommend the
appropriation of funds sufficient for all states to develop and
implement longitudinal data systems with the capacity to track the
performance of individual students from year to year, link those
students with their teachers, determine the impact of teachers over
several years, link those teachers to their preparation programs, and
ultimately identify the program characteristics associated with the
greatest levels of student achievement.

**RECOMMENDATION #5: The National Mathematics Advisory Panel should urge
support for teacher preparation reform at both state and federal levels.
*At the state level,*** factors beyond the control of preparation
institutions affect their ability to create their own programs as they
might wish. These include decisions by state boards, agencies, and
legislatures as to student standards, student curricula, teaching
standards, specialist designations and requirements, teacher licensing
exams, and their passing scores as well as appropriations for
preparation program improvement, induction, and professional
development.[^25]

A key factor in reform is inclusion of teacher preparation within the
state's alignment ladder, as proposed by the Business-Higher Education
Forum (BHEF). Program admission requirements, specialized content
courses, and graduation standards for teacher candidates should be
aligned with the state's P-12 content standards. Both content and
teaching methods courses should be redesigned to help future teachers
make insightful connections between the mathematics they are learning
and the mathematics they will teach. We agree with BHEF that each state
must provide colleges and universities with incentives for evaluating
and modifying teacher education programs. [^26]

***At the federal level,*** we urge the Panel to support the following
research-based proposals:

-   **Mandated extensive, supervised clinical experience.** Considerable
    variation exists in the extent and rigor of the teacher candidates'
    clinical experience required by states. About three quarters of the
    states require some clinical experience, which may range from 5 to
    20 weeks.[^27] Research suggests that sustained, high-quality
    clinical experience is related to teacher retention. Candidates who
    have had student teaching are twice as likely to stay past the first
    year of teaching as those who have not. Prospective teachers should
    exhibit consistent success through a substantial preservice clinical
    experience involving a variety of challenging situations and
    supervised by both university- and school-based faculty. AACTE
    recommends at least 15 weeks at 30 hours per week, or a total of 450
    hours for clinical experience.

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-   **Required assessment of teaching performance.** A major omission in
    the nation's system of determining the quality of entry-level
    teachers is an assessment of their ability to teach. Innumerable,
    and frequently inadequate, tests of content knowledge, professional
    knowledge, and in some cases subject-specific pedagogy, are
    available and used by states in licensing teachers. However, the
    ability of teachers to actually teach is, with few exceptions, not
    part of the licensing process. A growing body of research indicates
    that performance assessments that include evidence from actual
    teaching practice can better evaluate instructional practice and can
    serve as powerful professional learning experiences. Reports of the
    National Research Council[^28] and the National Academy of
    Education[^29] call for such assessments.

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-   **A major investment in school/university partnerships.** This is
    the major legislative vehicle for teacher preparation reform, as it
    brings together the mathematics program within arts and sciences,
    one or more K-12 districts, and the teacher education program to
    support fledgling mathematics teachers with effective strategies,
    understandings, and techniques. Appropriation levels for such
    partnerships have been minimal at both state and federal levels.

**3. Out-of-field teaching**

The problem of out-of-field teaching---in which teachers are assigned to
teach subjects that do not match their training or education---is a
crucial issue for the teaching and learning of mathematics. Highly
qualified teachers may actually become "unqualified" if assigned to
teach subjects for which they are not prepared. Ingersoll describes this
as "a chronic and widespread problem," as his data show that about one
third of all mathematics classes in grades 7-12 are taught by teachers
who have neither a major nor a minor in mathematics or a related
discipline.[^30] Data show that virtually all U.S. teachers have
completed a bachelor's degree, and over 90% hold regular teaching
certificates. Yet 65% of middle school mathematics teachers did not have
an undergraduate or graduate major in mathematics, according to
1999-2000 SASS.

This is *not necessarily due to inadequate preparation*; it could be due
to the lack of fit between teachers' fields of preparation and their
teaching assignments. Assuming that the decades-old practice of
out-of-field assignment continues due to its efficiency and cost-savings
aspects, then its elimination will not be easily accomplished simply by
legislative fiat.[^31] Interestingly, only 21 states have a ban or cap
on the number of out-of-field teachers.[^32] Nations with high-scoring
students, such as Korea and Japan and Singapore, *tend to have very
little out-of-field teaching.*[^33]

**RECOMMENDATION #6: The National Mathematics Advisory Panel should call
for the elimination of out-of-field teaching.** With 18% of middle
school mathematics teachers assigned "out of field," it is important to
take a stand to discourage this practice. The Panel should recommend
that all states phase out the practice of out-of-field teaching by
setting a disappearing cap on the number of out-of-field placements
permitted by each district each year until ultimately, the cap becomes a
ban.

**4. Mathematics teacher supply and distribution issues**

-   **The Mathematics Teacher Shortage**. The first recommendation of
    the National Academies' *Rising Above the Gathering Storm* is to
    increase America's talent pool by vastly improving K-12 mathematics
    and science education. In 1999-2000, the latest year for which
    figures were available, of the total number of public K-12 teachers,
    160,000 taught mathematics.[^34] About two thirds of the nation's
    K-12 teachers are expected to retire or leave the profession over
    the coming decade, and by 2015, the shortage of highly qualified
    mathematics and science teachers is expected to reach 283,000. [^35]

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-   **Recruitment and retention of mathematics teachers.** We know that
    one third of teachers (in general) leave within 3 years and half
    within 5 years. Mathematics (as well as science) teachers are
    significantly more likely to move from, or to eave their teaching
    jobs because of job dissatisfaction than are other teachers (40% of
    mathematics and science teachers compared with 29% of all teachers);
    and nationally, mathematics teachers have the highest annual teacher
    turnover rate (16.4%) among various fields.[^36]

-   **Lack of diversity of mathematics teachers.** A substantial
    imbalance exists in the racial and ethnic makeup of the nation's
    teaching workforce compared to students in the classroom. Although
    the student population is becoming more and more diverse, the face
    of the teaching profession is not keeping pace. Fully 42% of all
    students in our public schools are members of minority groups. In
    urban areas, minority students constitute clear enrollment
    majorities, with Hispanic students now the largest minority group in
    the nation. Yet teaching continues to be dominated by European
    Americans.

**RECOMMENDATION #7. The National Mathematics Advisory Panel should
encourage investments in mathematics teaching recruitment and retention
efforts.** Given the shortage, the high rates of turnover and
out-of-field teaching, and the lopsided diversity among mathematics
teachers, it is necessary to launch a concerted recruitment/retention
effort. Research shows that strong induction programs with trained
mentors make a positive difference in the retention of novice teachers
and in improving teaching practice within the school.[^37] Further,
growing interest exists in enabling school districts to offer STEM
teachers compensation that is more closely aligned with that available
in other economic sectors.[^38] Nothing less than a federal "Marshall
Plan" is needed to greatly enhance the recruitment and retention of
excellent mathematics teachers, particularly for high-need schools.
Substantial funds should be authorized for a variety of promising
purposes:

-   Joint collegiate/school urban teaching academies

-   Noyce Scholarships, which provide funds that higher education
    institutions may use to encourage STEM majors to become K-12
    mathematics teachers

-   Service scholarships and forgivable loans for the training of
    outstanding candidates who agree to teach in high-need schools

-   Matching grants to state and districts for high-quality induction
    programs and support structures for new teachers in high-need
    schools

-   Teaching assignments for new teachers that support their induction
    into the field

-   Significant bonuses, in the range of \$10,000 to \$15,000 a year,
    for National Board-certified teachers who agree to teach in poor
    urban or rural schools

-   The ultimate development of a national database and analytic agenda
    for monitoring and ameliorating teacher supply and demand across the
    country such that all high-need schools have high-quality teachers

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-   **Inequities in the distribution of mathematics teachers.** Poor
    students and students of color are most likely to be taught by
    inexperienced and underqualified teachers. Recent data indicate that
    children in the highest-poverty schools are assigned to novice
    teachers almost twice as often as children in low-poverty schools.
    Similarly, students in high-minority schools are assigned to novice
    teachers at twice the rate as students in schools without many
    minority students. A recent study by the American Institutes of
    Research that directly addresses middle school mathematics students
    found that only 70% of economically disadvantaged eighth-grade
    students had teachers with a major or minor in mathematics, compared
    to 83% of eighth-grade students who were not so classified.
    Economically disadvantaged students were also less likely to have a
    certified mathematics teacher (89%) than those who were not (94%).
    Further, students in high-ability mathematics classes were more
    likely (86%) to have teachers with a major or minor in
    mathematics/mathematics education than those in mixed- or
    low-ability mathematics classes (66%). Students in low-ability
    classes were also less likely to have a teacher with more than 5
    years' experience in mathematics instruction (58%) than students in
    high-ability classes (74%).[^39]

**RECOMMENDATION #8: Correct the inequitable distribution of
high-quality teachers.** The Panel's report should clearly articulate
this educational travesty and insist on enforcement of existing
reporting requirements, on the prohibition of district maldistribution
practices, and on the appropriation of funds to carry out the
recruitment/retention recommendations noted above.

On behalf of teacher preparation programs across the nation, we thank
the Panel members for your attention and for the good work you are doing
to help improve mathematics teaching and learning.

------------------------------------------------------------------

Attachment: *Preparing STEM Teachers: The Key to Global
Competitiveness*. AACTE. June 2007

[^1]: The enabling condition of "opportunity to learn," and teaching
    that promotes conceptual development, as well as teaching that
    facilitates efficiency in executing skills, are the teaching
    features that the latest review of research links consistently with
    student achievement. See: James Hiebert and Douglas A. Grouws, "The
    effects of classroom mathematics teaching on students' learning," in
    *Second handbook of research on mathematics teaching and learning*,
    Frank K. Lester, Jr. (Ed.), A project of the National Council of
    Teachers of Mathematics (Charlotte, NC: Information Age Publishing,
    2007), 371-404.

[^2]: National Research Council. *Adding it up: Helping children learn
    mathematics*. J. Kilpatrick, J. Swafford, and B. Findell (Eds.).
    Mathematics Learning Study Committee, Center for Education, Division
    of Behavioral and Social Sciences and Education. Washington, DC:
    National Academy Press, 2001.

[^3]: See: Heather C. Hill, Brian Rowan, and Deborah Loewenberg Ball,
    "Effects of teachers' mathematical knowledge for teaching on student
    achievement," *American Educational Research Journal*, 42(2) (2005),
    371-406; Deborah Loewenberg Ball & Hyman Bass, "Interweaving content
    and pedagogy in teaching and learning to teach: Knowing and using
    mathematics. In J. Boaler (Ed.), "Multiple perspectives on the
    teaching and learning of mathematics" (pp. 83-104). Westport, CT:
    Ablex, 2000; Deborah Loewenberg Ball, Heather C. Hill, & Hyman Bass,
    "Knowing mathematics for teaching: Who knows mathematics well enough
    to teach third grade, and how can we decode?," *American Educator*,
    Fall 2005; Heather C. Hill & Deborah Loewenberg Ball, "Learning
    mathematics for teaching: Results from California's mathematics
    professional development institutes, *Journal for Research in
    Mathematics Education*, 35(5) (2004), 330-351.

[^4]: Lee. S. Shulman, "Merging content knowledge and pedagogy: An
    interview with Lee Shulman." *Journal of Staff Development,* 13(1)
    (Winter 1992), 14-17.

[^5]: Carpenter, T., Blanton, M.L., Cobb, P., Franke, M.L., Kaput, J., &
    McClain, K. (2004). Scaling up innovative practices in mathematics
    and science. *Research Report*. Madison, WI: National Center for
    Improving Student Learning and Achievement in Mathematics and
    Science.

[^6]: Good, T. L., Grouws, D.A., and Ebmeier, H. *Active mathematics
    teaching*. New York: Longman, 1983.

[^7]: For example, the cost of the recent (2007) *Second handbook of
    research on mathematics teaching and learning*, Frank K. Lester, Jr.
    (Ed.), just mentioned, is \$400.

[^8]: Richard M. Ingersoll, University of Pennsylvania, Analysis for
    NCTAF of the2000-01 Teacher Follow up Survey. See National
    Commission for Teaching and America's Future, *No Dream Denied: A
    Pledge to America's Children, Summary Report* (Washington, D.C.:
    NCTAF, 2003), 84-85.

[^9]: Suzanne M. Wilson, Robert E. Floden, and Joan Ferrini-Mundy,
    *Teacher Preparation Research: Current Knowledge, Gaps, and
    Recommendations: A Research Report Prepared for the U.S. Department
    of Education* (Seattle: Center for the Study of Teaching and Policy,
    2001).

[^10]: See: Judith T. Sowder, "The mathematical education and
    development of teachers," in *Second handbook of research on
    mathematics teaching and learning*, Frank K. Lester, Jr. (ed.), A
    project of the National Council of Teachers of Mathematics
    (Charlotte, NC: Information Age Publishing, 2007), p. 199-200.

[^11]: "Science and technology" were included in the original document
    but omitted in this chapter of the *Second Handbook*.

[^12]: See, for example: Liping Ma, *Knowing and teaching elementary
    mathematics*. Mahwah, NJ: Lawrence Erlbaum Associates, 1999;
    National Research Council, Committee on Science and Mathematics
    Teacher Preparation, *Educating teachers of science, mathematics,
    and technology*: New practices for the new millennium. Washington,
    DC: National Academy Press, 2001; Susan Goya, "The critical need for
    skilled math teachers," *Phi Delta Kappan* (87) 5 (January 2006),
    pp. 370-371.

[^13]: David H. Monk, "Subject area preparation of secondary mathematics
    and science teachers and student achievement," *Economics of
    Education Review* (13), 125-145.

[^14]: Remarks of David Steiner, Dean of the School of Education at
    SUNY/Hunter College, at a National Council on Teacher Quality panel
    discussion on July 27, 2007 in Washington, DC.

[^15]: Report of working group 7 -- Teacher preparation, *Proceedings of
    the NCTM Research Catalyst Conference*: September 11--13, 2003, p.
    173; Telephone conversation with Dr. Kathryn Chval, Assistant
    Professor, University of Missouri/Columbia, January 4, 2007;

[^16]: Report of working group 7 -- Teacher preparation, *Proceedings of
    the NCTM Research Catalyst Conference*: September 11--13, 2003*;*
    See also: Sandra Stotsky, "How state boards of education can upgrade
    math teaching in the elementary school," EdNews.org, March 19, 2007.

[^17]: Comments made at the June 4-5, 2007 Michigan State University
    policy forum, "Preparing Mathematics Teachers to Make a Difference:
    Why Teacher Education Matters."

[^18]: For example, James Lewis, University of Nebraska at Lincoln, at
    Michigan State University's June 4-5 2007 Policy Forum on "Preparing
    Mathematics Teachers to Make a Difference: Why Teacher Education
    Matters," recommended revising the MET standards to include further
    study of fractions, integers, rationals, and real numbers, by
    elementary teachers, as well as the study of statistics, functions
    and an introduction to algebra. He also suggested possible
    additional courses for middle grade teachers: Number Theory and
    Cryptology, Discrete Mathematics, Using Mathematics to Understand
    our World, and Concepts of Calculus. Other presenters made further
    suggestions.

[^19]: Barbara Reys and Glenda Lappan, "Consensus or confusion? The
    intended mathematics curriculum in state-level standards," *Phi
    Delta Kappan* (88) 9, 676-680.

[^20]: Massachusetts is an example: its Board of Education has recently
    voted on additional course requirements and a more demanding
    mathematics test for elementary and special education teachers.
    *\[Penny: check its status.\]*

[^21]: Reys and Lappan, "Consensus or confusion," *Phi Delta Kappan*.

[^22]: See: <http://www.achieve.org/node/604>

[^23]: For example, the Dodd-Ehlers bill, also known as the SPEAK Act
    (Standards to Provide Educational Attainment for all Kids), S 224
    and HR 325, and Senator Kennedy's SUCCESS Act (States Using
    Collaboration and Coordination to Enhance Standards for Students), S
    164.

[^24]: National Science Board, *A National Action Plan for Addressing
    the Critical Needs of the U.S. Science, Technology, Engineering, and
    Mathematics Education System*.---Draft for Public Com*ment.*
    NSB/HER-07-9, Revised August 9, 2007.

[^25]: See: Business-Higher Education Forum, *A commitment to America's
    future: Responding to the crisis in mathematics & science
    education*, Washington, DC, January 2005.
    [www.bhef.com](http://www.bhef.com/).

[^26]: *Ibid*, pg. 20.

[^27]: Melissa McCabe, "State of the states,' in *Quality counts: A
    decade of standards-based education. 2006.* *Education Week*, Vol.
    25, No. 17, January 5, 2006. pp. 72-89.

[^28]: National Research Council. 2001 *Testing teacher candidates: The
    role of licensure tests in improving teacher quality.* Committee on
    Assessment and Teacher Quality, Mitchell, K.J., Robinson, D.Z.,
    Plake, B.S., and Knowles, K.T., editors. Board on Testing and
    Assessment, Center for Education, Division of Behavioral and Social
    Sciences and Education, Washington, DC: National Academy Press, p.
    172.

[^29]: Linda Darling-Hammond and Joan Baratz-Snowden (Eds.), *A good
    teacher in every classroom: Preparing the highly qualified teachers
    our children deserve* (San Francisco: Jossey-Bass, 2005, pp. 62-63.

[^30]: Richard M. Ingersoll, "Four myths about America's teacher quality
    problem," Chapter 1 in Developing the teacher workforce---103^rd^
    Yearbook of the National Society for the Study of Education, (Eds.
    M. Smylie and D. Miretzky. University of Chicago Press, 2004.

[^31]: Ingersoll, *Ibid.*

[^32]: Melissa McCabe, "State of the states," in *Quality counts: A
    decade of standards-based education.* 2006. *Education Week*, Vol.
    25, No. 17, January 5, 2006, p.89.

[^33]: Richard M. Ingersoll, "Comparative Study of Teacher Preparation
    and Qualifications in Six Nations," *CPRE Policy Briefs*, RB-47,
    February 2007.

[^34]: The National Academies, *Rising above the gathering
    storm---Energizing and employing America for a brighter economic
    future.* Report of the Committee on Prospering in the Global Economy
    of the 21^st^ Century: An Agenda for American Science and
    Technology. Committee on Science, Engineering, and Public Policy.
    (Washington, DC: The National Academies Press, 2006.)

[^35]: National Center for Education Statistics, *Projection of
    education statistics to 2014* (Boston, MA: National Center for
    Education Statistics, 2005).

[^36]: Richard M. Ingersoll, "Is there a shortage among mathematics and
    science teachers?," *Science Educator*, 12,1 (Spring 2003).

[^37]: Thomas M. Smith and Richard M. Ingersoll, "What are the effects
    of induction and mentoring on beginning teacher turnover?" *American
    Educational Research Journal* 41, no. 2 (2004).

[^38]: National Science Board, *A National Action Plan for Addressing
    the Critical Needs of the U.S. Science, Technology, Engineering, and
    Mathematics Education System*.---Draft for Public Com*ment.*
    NSB/HER-07-9, Revised August 9, 2007.

[^39]: Elizabeth Greenberg, David Rhodes, Xiaolan Ye, and Fran
    Stancavage, "Prepared to teach: Teacher preparation and student
    achievement in eighth-grade mathematics." Paper presented at AERA
    Annual Meeting in San Diego, April 12-16, 2004 based on work
    performed by American Institutes for Research under a cooperative
    agreement with IES, p. 19.