Mathematics: California

Delivering Well Prepared Teachers Policy

California requires all elementary teacher candidates to pass the California Subject Examination for Teachers (CSET), a multiple subjects test. Although the CSET's mathematics content is more rigorous than the Praxis II test that most states use, 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 it may be possible to answer many mathematics questions incorrectly and still pass the test.

Further, California's testing standards address content in mathematics foundations, but although they outline areas such as algebra, geometry and data analysis, the standards are not specifically geared to meet the needs of elementary teachers.

**Require teacher candidates to pass a rigorous mathematics assessment.**

Although California 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. California 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.

California asserted that NCTQ overlooks the fact that California’s teacher preparation programs are at the graduate level. Candidates complete all of their content coursework at the undergraduate level prior to beginning teacher preparation, not during graduate level teacher preparation. The CSET examinations confirm that the candidate possesses the requisite content knowledge prior to entry into the program or prior to being allowed to student teach.

The mathematical content knowledge required of California’s elementary teachers goes beyond “minimum mathematics knowledge at an elementary school level,” as NCTQ inaccurately states. The CSET examinations have been revised and updated to fully address the California Common Core State Standards relevant to multiple subject as well as single subject teachers, and the multiple subject program coursework that prepares teacher candidates to take the CSET has also been updated to include these standards. It is not possible, as NCTQ states, for a candidate to “answer many mathematics questions incorrectly and still pass the test.” The CSET examination is not statistically a compensatory scoring model manner precisely to prevent such a situation from occurring. Candidates must have strong knowledge of both mathematics and science in order to pass the CSET subtest covering these two content areas.

- 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).