Teaching Mathematics: Arizona
Elementary Teacher Preparation Policy
Analysis of Arizona's policies
Mathematics Test Requirements: Arizona requires all elementary teacher candidates to pass the National Evaluation Series (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.
Additionally, in lieu of passing the state's required content test, Arizona also allows candidates to demonstrate subject-matter
knowledge using one of the following methods:
- National Board Certification,
- "Verification of experience teaching courses relevant to a content matter or subject area for the past two consecutive years, and a total of three years at one or more accredited postsecondary institutions."
- Minimum of five years of work experience "relevant to a subject area of certification,"
- Three years of full time teaching experience "in any state, including Arizona in a self-contained K-8 classroom," or
- A bachelor's degree or higher in a "relevant subject area."
Mathematics Preparation Standards: Arizona does not have articulated teaching standards that its approved teacher preparation programs must use to frame instruction in elementary mathematics content such as; mathematics foundations and areas such as algebra, geometry and statistics.
Provisional and Emergency Licensure: Because provisional and emergency licensure requirements are scored in Provisional and Emergency Licensure, only the test requirements for the state's initial license are considered as part of this goal.
Recommendations for Arizona
Require all teacher candidates who teach elementary grades to pass a rigorous mathematics assessment.
Arizona should assess 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.
Ensure that teacher preparation programs require mathematics content geared towards the needs of elementary teachers.
Arizona should require teacher preparation programs to train candidates in key areas of mathematics, including specific coursework in foundations, algebra and geometry, with some statistics coursework. Doing so helps ensure that all teachers are well prepared in mathematics instruction before entering the classroom. Additionally, articulated math preparation standards help ensure that any subsequent test adoptions are aligned with Arizona's expectations for what candidates should know and be able to do.
State response to our analysis
Arizona was helpful in providing NCTQ with facts that enhanced this analysis.
Updated: February 2020
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Teacher Preparation
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How we graded
2B: Teaching Elementary Mathematics
- Content Knowledge: The state should require:
- All elementary teacher candidates to pass a rigorous elementary math content exam in order to attain licensure.
- Teacher preparation programs to deliver elementary math content coursework of the appropriate breadth and depth to all elementary teacher candidates. This coursework should build a strong conceptual foundation in elementary math topics and should align with recommendations of professional associations such as the Conference Board of the Mathematical Sciences and the National Council of Teachers of Mathematics.
The entire goal score may be earned based on the following:
- Full Credit: The state will earn full credit if it requires new elementary teachers to pass a math content test or separately scored math subtest prior to obtaining licensure.
- Three-quarters credit: The state will earn three-quarters of a point if it requires elementary teachers to pass a math content test or separately scored math subtest prior to obtaining licensure. but also allows exceptions, or delays passage of tests for any reason.
- One-half credit: The state will earn one-half of a point if it requires elementary teachers to pass a math content test or separately scored math subtest prior to obtaining licensure, but also offers multiple elementary licenses with differing requirements.
- One-quarter credit: If the state does not require a math content test, but adequate math teacher preparation standards exist, it is eligible for one-quarter of a point.
Research rationale
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.[1] 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 is specially designed for prospective elementary teachers.[2] 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.[3] 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."
States' policies should require preparation in mathematics of appropriate breadth and depth and specific to the needs of the elementary teacher. Reports by NCTQ on teacher preparation, beginning with No Common Denominator: The Preparation of Elementary Teachers in Mathematics by America's Education Schools (2008) and continuing through the Teacher Prep Review, have consistently found few elementary teacher preparation programs across the country providing high-quality preparation in mathematics.[4] 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.[5] 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.[6] The MTEL test required by both Massachusetts and North Carolina remains the standard bearer for a high quality, rigorous assessment for elementary teachers entirely and solely focused on mathematics.
[1] For evidence on the benefits of math content knowledge on student achievement, see: Kukla-Acevedo, S. (2009). Do teacher characteristics matter? New results on the effects of teacher preparation on student achievement. Economics of Education Review, 28(1), 49-57.; Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers' mathematical knowledge for teaching on student achievement. American educational research journal, 42(2), 371-406.
[2] For information on the mathematics content elementary teachers need to know, see: National Council of Teachers of Mathematics. (2005, July). Highly qualified teachers: A position of the National Council of Teachers of Mathematics.; See also: Conference Board of the Mathematical Sciences. (2001). The mathematical education of teachers (Vol. 11). American Mathematical Society.
[3] For evidence that new teachers are not appropriately prepared to teach mathematics, see: Greenberg, J., & Walsh, K. (2008, June). No common denominator: The preparation of elementary teachers in mathematics by America's education schools. National Council on Teacher Quality. Retrieved from http://www.nctq.org/dmsView/No_Common_Denominator_NCTQ_Report
[4] National Council on Teacher Quality. (2016, December). Landscapes in teacher prep: Undergraduate elementary. National Council on Teacher Quality's Teacher Prep Review. Retrieved from http://www.nctq.org/dmsView/UE_2016_Landscape_653385_656245
[5] 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: National Council on Teacher Quality. (2011). Recommendations for the reauthorization of the Elementary and Secondary Education Act. Retrieved from http://www.nctq.org/p/publications/docs/nctq_eseaReauthorization.pdf
[6] National Council of Teachers of Mathematics (2005, July). Highly qualified teachers: A position of the National Council of Teachers of Mathematics.