Mathematics: Arizona

Delivering Well Prepared Teachers Policy

Arizona requires all elementary teacher candidates to pass the NES Elementary Education content test, which consists of two separately scored subtests. Mathematics counts for 50 percent of subtest two and is combined with other subject areas, specifically, science and the arts, health and fitness. Because the test does not report a specific math score, a teacher candidate could answer many math questions incorrectly and still pass the test.

The framework for Arizona's test covers numbers and operations, data analysis, and basic concepts of geometry and algebra. However, the standards are not specifically geared to meet the needs of elementary teachers.

**Require all teacher candidates who teach elementary grades to pass a rigorous mathematics assessment.**

Although Arizona is on the right track in requiring an elementary assessment with subtests, the state's efforts fall short by combining math with other subjects and not reporting a specific subscore for math. Arizona should strengthen its policy by testing mathematics content with a rigorous assessment tool, such as the test required in Massachusetts that evaluates mathematics knowledge beyond an elementary school level and challenges candidates' understanding of underlying mathematics concepts. Such a test could also be used to allow candidates to test out of coursework requirements. Teacher candidates who lack minimum mathematics knowledge should not be eligible for licensure.

**Require teacher preparation programs to provide mathematics content specifically geared to the needs of elementary teachers.**

Arizona must ensure that new teachers are prepared to
teach the mathematics content required by the state's college- and career-readiness standards. Although Arizona's subject-matter test requires some knowledge in key areas of
mathematics, the state should require teacher preparation programs to provide
mathematics content specifically geared to the needs of elementary teachers.
This includes specific coursework in foundations, algebra and geometry, with
some statistics coursework.

Arizona stated that rules governing the approval of educator preparation programs require “…that candidates demonstrate competencies as
articulated in the Board approved professional teaching standards or
professional administrative standards, relevant Board
approved academic standards, and relevant national standards.” The state
noted that there is now a process in the review of educator preparation
programs that requires evidence that program completers have been
prepared to teach both Arizona Board approved academic standards and
relevant national standards.

- Admission into Teacher Preparation
- Elementary Teacher Preparation
- Elementary Teacher Preparation in Reading Instruction
- Elementary Teacher Preparation in Mathematics
- Early Childhood
- Middle School Teacher Preparation
- Secondary Teacher Preparation
- Secondary Teacher Preparation in Science and Social Studies
- Special Education Teacher Preparation
- Special Education Preparation in Reading
- Assessing Professional Knowledge
- Student Teaching
- Teacher Preparation Program Accountability

- State Data Systems
- Evaluation of Effectiveness
- Frequency of Evaluations
- Tenure
- Licensure Advancement
- Equitable Distribution

**Required math
coursework should be tailored in both design and delivery to the unique needs
of the elementary teacher.**

Aspiring elementary teachers must acquire a deep
conceptual knowledge of the mathematics that they will teach, moving well
beyond mere procedural understanding. Their training should focus on the
critical areas of numbers and operations; algebra; geometry and, to a lesser
degree, data analysis and probability.

To ensure that elementary teachers are well trained to teach
the essential subject of mathematics, states must require teacher preparation
programs to cover these four areas in coursework that it specially designed for
prospective elementary teachers. Leading mathematicians and math educators have
found that elementary teachers are not well served by courses designed for a
general audience and that methods courses also do not provide sufficient
preparation. According to Dr. Roger Howe, a mathematician at Yale University:
"Future teachers do not need so much to learn more mathematics, as to
reshape what they already know."

Most states' policies do not require preparation in
mathematics of appropriate breadth and depth and specific to the needs of the
elementary teacher. NCTQ's reports on teacher preparation, beginning with *No Common Denominator: The Preparation of
Elementary Teachers in Mathematics by America's Education Schools* in 2008
and continuing through the *Teacher Prep
Review *in 2013 and 2014 have consistently found few teacher preparation programs across
the country providing high-quality preparation in mathematics. Whether through
standards or coursework requirements, states must ensure that their preparation
programs graduate only teacher candidates who are well prepared to teach
mathematics.

**Many state tests
offer no assurance that teachers are prepared to teach mathematics.**

An increasing number of states require passage of a
mathematics subtest as a condition of licensure., but many states still rely on
subject-matter tests that include some items (or even a whole section) on
mathematics instruction. However, since subject-specific passing scores are not
required, one need not know much mathematics in order to pass. In fact, in some cases one
could answer every mathematics question incorrectly and still pass. States need
to ensure that it is not possible to pass a licensure test that purportedly
covers mathematics without knowing the critical material.

The content of these tests poses another issue: these tests
should properly test elementary content but not at an
elementary level.
Instead, problems should challenge the teacher candidate's understanding
of underlying concepts and apply knowledge in nonroutine, multistep
procedures. The test required by
Massachusetts and now by North Carolina as well remains the standard bearer for a high quality, rigorous
assessment for elementary teachers entirely and solely focused on mathematics.**Elementary Teacher Preparation in Mathematics: Supporting Research**

For
evidence that new teachers are not appropriately prepared to teach mathematics,
see NCTQ,* No Common Denominator: The Preparation of Elementary Teachers
in Mathematics by America's Education Schools* (2008) at: http://www.nctq.org/p/publications/docs/nctq_ttmath_fullreport_20090603062928.pdf.

For
information on the mathematics content elementary teachers need to know, see
National Council of Teachers of Mathematics, "Highly Qualified Teachers: A Position of the National Council of Teachers of Mathematics," (July 2005).
See also Conference Board of the Mathematical
Sciences, The Mathematical Education of Teachers, Issues in Mathematics, Vol. 11,
(American Mathematical Society in cooperation with the Mathematical Association
of America, 2001), p. 8.

For
evidence on the benefits of math content knowledge on student achievement, see S. Kukla-Acevedo "Do Teacher Characteristics Matter? New Results on the Effects of Teacher Preparation on Student Achievement." *Economics of Education Review*, Volume 28, 2009, pp. 49-57; H. Hill, B. Rowan
and D. Ball "Effects of Teachers' Mathematical Knowledge for Teaching on Student Achievement," *American
Educational Research Journal, *Volume 42, No. 2, Summer 2005, pp. 371-406.

For
information on where states set passing scores on elementary level content
tests for teacher licensing across the U.S., see chart on p. 13 of NCTQ "Recommendations for the Reauthorization of the Elementary and Secondary Education Act, Removing the Roadblocks: How Federal Policy Can Cultivate Effective Teachers," (2011).