The state should ensure that new elementary teachers have sufficient knowledge of the mathematics content taught in elementary grades.
Colorado requires that all new elementary teachers pass either the state's PLACE (Program for Licensing Assessments for Colorado's Educators) elementary assessment or the Praxis II Elementary Education: Content Knowledge (5018) test. Neither test provides a specific mathematics subscore, so it may be possible to fail the mathematics portion and still pass the test. Further, while these tests cover important elementary school-level content, they barely evaluate candidates' knowledge beyond an elementary school level, do not challenge their understanding of underlying concepts and do not require candidates to apply knowledge in nonroutine, multistep procedures.
In its program approval standards, Colorado requires teacher candidates to demonstrate the ability to "develop in students an understanding and use of number systems and number sense, geometry, measurement, statistics and probability, and function and use of variables." 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.
Require all teacher candidates who teach elementary grades to pass a rigorous mathematics assessment.
Colorado 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.
Require teacher preparation programs to provide mathematics content specifically geared to the needs of elementary teachers.
Colorado recognized the factual accuracy of this analysis. The state also indicated that Colorado's Educator Licensing Act is being updated and aligned with the state standards and initiatives. According to the state, this includes aligning the elementary education endorsement rules with the Colorado Academic Standards across content areas, including mathematics. The alignment work will include adoption of assessments for teachers that match the standards adopted in rule.
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).