Mathematics: Arizona

2011 Delivering Well Prepared Teachers Policy

Arizona relies on its standards for teacher preparation programs and its subject-matter testing framework as the basis for articulating its requirements for the mathematics content knowledge of elementary teacher candidates.

The state does not specify any coursework requirements regarding mathematics content. However, the state has articulated teaching standards that its approved teacher preparation programs must use to frame instruction in elementary mathematics content. According to these standards, candidates must "demonstrate knowledge" of mathematics. Unfortunately, these standards lack the specificity needed to ensure that teacher preparation programs deliver mathematics content of appropriate breadth and depth to elementary teacher candidates.

Arizona requires that all new elementary teachers pass its general subject-matter test, the Arizona Educator Proficiency Assessment. The test's standards address content in mathematics foundations, but although they outline such areas as algebra, geometry and data analysis, the standards are not specifically geared to meet the needs of elementary teachers. The test also lacks a specific passing score for mathematics, so one can likely fail the mathematics portion and still pass the test. Further, the results of a NCTQ study on the preparation of elementary teachers in mathematics questions the rigor of Arizona's test, finding that its items representing elementary school content assess understanding at too superficial a level.

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

Although Arizona standards and subject-matter testing framework require 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.

**Require teacher candidates 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.

Arizona acknowledged that NCTQ's analysis is correct but added that it is incomplete. The state noted that teachers who teach grades 7-12 whose primary assignment is in an academic subject must demonstrate proficiency by passing the appropriate portion of the Arizona Teacher Proficiency Assessment, with the subject areas of demonstrated proficiency specified on the certificate. If an assessment is not offered in a subject area, then the candidate must complete a minimum of 24 semester hours of courses in the subject. Further, elementary teachers teaching a core academic subject in grades 7-8 must pass either the AEPA Middle School Mathematics or the AEPA 7-12 Mathematics exam.

This goal is focused on elementary math teachers. For NCTQ's analysis regarding Arizona's middle grades policies, see Goal 1-E. For NCTQ's analysis regarding the state's secondary teachers policies, see Goal 1-F.

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

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

Aspiring elementary teachers must begin to 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 report No Common Denominator: The Preparation of Elementary Teachers in Mathematics by America's Education Schools found that only 13 percent of teacher preparation programs in a national sample were 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.

###### Research rationale

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

Only Massachusetts has developed a rigorous assessment for elementary teachers entirely and solely focused on mathematics. Other states 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, 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 and middle school content but not at an elementary or middle school level. Instead, problems should challenge the teacher candidate's understanding of underlying concepts and apply knowledge in nonroutine, multistep procedures. Unfortunately, this is not the case in the tests currently in use in most states.

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 Kukla-Acevedo "Do Teacher Characteristics Matter? New Results on the Effects of Teacher Preparation on Student Achievement." Economics of Education Review, 28 (2009): 49-57; H. Hill, B. Rowan and D. Ball "Effects of Teachers' Mathematical Knowledge for Teaching on Student Achievement," American Educational Research Journal (2005).

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's "Recommendations for the Reauthorization of the Elementary and Secondary Education Act, Removing the Roadblocks: How Federal Policy Can Cultivate Effective Teachers?" (2011).