Elementary Teacher Preparation in
Mathematics: California

2011 Delivering Well Prepared Teachers Policy

Goal

The state should ensure that new elementary teachers have sufficient knowledge of the mathematics content taught in elementary grades.

Meets in part
Suggested Citation:
National Council on Teacher Quality. (2011). Elementary Teacher Preparation in Mathematics: California results. State Teacher Policy Database. [Data set].
Retrieved from: https://www.nctq.org/yearbook/state/CA-Elementary-Teacher-Preparation-in-Mathematics-6

Analysis of California's policies

California relies on its subject-matter testing requirements 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, but it does require that all new elementary teachers pass the California Subject Examination for Teachers (CSET), a multiple subjects test. 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 CSET's mathematics content is more rigorous than the Praxis II test most states use, but the CSET still does not ensure that candidates have appropriate mathematics knowledge. The CSET requires passing subscores on all three subtests that comprise the overall test, but the mathematics and science scores are combined, so one can likely answer many mathematics questions incorrectly and still pass the test.

Citation

Recommendations for California

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

Require teacher candidates to pass a rigorous mathematics assessment.
California should require a passing score specifically in math for its content assessments to ensure that teacher candidates have adequate mathematics knowledge and understanding of underlying mathematics concepts. Such a score could be used to allow candidates to test out of coursework requirements. Teacher candidates who lack minimum mathematics knowledge should not be eligible for licensure.

State response to our analysis

California recognized the factual accuracy of this analysis. However, the state added that NCTQ's comment that "one can likely answer many mathematics questions incorrectly and still pass the test" is incorrect. It asserted that the scoring rubric is designed to prevent this very scenario. 

Last word

It is important that California has designed its scoring rubric to ensure that candidates have knowledge in each area of its combined subtests. It would be even more helpful to candidates and preparation programs if the state established separate passing scores.  

How we graded

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

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.

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. 

Research rationale

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).