Teaching Mathematics: Arizona

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.

Content Knowledge
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. 
• 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. 

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.